Element Cards Number Operations Fractions
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=Teaching Fractions= | =Teaching Fractions= | ||
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==Websites== | ==Websites== | ||
[http://www.teachingideas.co.uk/maths/contents_fractions.htm http://www.teachingideas.co.uk/maths/contents_fractions.htm] | [http://www.teachingideas.co.uk/maths/contents_fractions.htm http://www.teachingideas.co.uk/maths/contents_fractions.htm] | ||
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[http://www.mathsisfun.com/converting-decimals-fractions.html http://www.mathsisfun.com/converting-decimals-fractions.html] | [http://www.mathsisfun.com/converting-decimals-fractions.html http://www.mathsisfun.com/converting-decimals-fractions.html] | ||
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[http://www.mathplayground.com/ http://www.mathplayground.com/] | [http://www.mathplayground.com/ http://www.mathplayground.com/] | ||
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[https://www.khanacademy.org/ https://www.khanacademy.org/] | [https://www.khanacademy.org/ https://www.khanacademy.org/] | ||
− | [http://www.mathhelp.com/ http://www.mathhelp.com/] | + | |
+ | [http://www.mathhelp.com/ http://www.mathhelp.com/] | ||
==Other Resources== | ==Other Resources== | ||
[http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf] | [http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf] | ||
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+ | [http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | ||
− | =CCC Mathematics | + | =CCC Mathematics: Number Operations (Fractions)= |
{|border=1 | {|border=1 | ||
− | || | + | |colspan=3|'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. |
|- | |- | ||
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||'''Strand:''' Number Operations (Fractions, Ratios, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ratios, Proportions) | ||
− | ||'''Family:''' Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family:''' Representing |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' |
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|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Folding a sentence strip into 2, 4, and 8 equal pieces | * Folding a sentence strip into 2, 4, and 8 equal pieces | ||
* Folding a sentence strip into 3 and 6 equal pieces | * Folding a sentence strip into 3 and 6 equal pieces | ||
− | * Model-Lead-Test | + | * Model-Lead-Test<nowiki>*</nowiki> |
* Partitioning: Breaking an object or set of objects into pieces | * Partitioning: Breaking an object or set of objects into pieces | ||
* Pizza Fractions: Using cutout of pizza/pizza circle with fractions written on them that can be placed on a fraction template | * Pizza Fractions: Using cutout of pizza/pizza circle with fractions written on them that can be placed on a fraction template | ||
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|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Visual models with pre-marked and pre-divided regions | * Visual models with pre-marked and pre-divided regions | ||
* Graph paper | * Graph paper | ||
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|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | + | | colspan=3|'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. |
|- | |- | ||
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||'''Strand:''' Number Operations (Fractions, Ratios, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ratios, Proportions) | ||
− | ||'''Family:''' Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family:''' Representing |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' |
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|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Folding a sentence strip into 2, 4, and 8 equal pieces | * Folding a sentence strip into 2, 4, and 8 equal pieces | ||
* Folding a sentence strip into 3 and 6 equal pieces | * Folding a sentence strip into 3 and 6 equal pieces | ||
− | * Model-Lead-Test | + | * Model-Lead-Test<nowiki>*</nowiki> |
* Partitioning: Breaking an object or set of objects into pieces | * Partitioning: Breaking an object or set of objects into pieces | ||
* Pizza Fractions: Using cutout of pizza/pizza circle with fractions written on them that can be placed on a fraction template | * Pizza Fractions: Using cutout of pizza/pizza circle with fractions written on them that can be placed on a fraction template | ||
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|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Visual models with pre-marked and pre-divided regions | * Visual models with pre-marked and pre-divided regions | ||
* Graph paper | * Graph paper | ||
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|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | + | | colspan=3|'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. |
|- | |- | ||
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||'''Strand''': Number Operations (Fractions/Ratios/Proportions) | ||'''Strand''': Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family''': Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family''': Representing |
|- | |- | ||
− | ||'''Progress Indicator:''' ''E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' | + | | colspan=3|'''Progress Indicator:''' ''E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' |
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− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Before introducing fraction, use fraction bars: | * Before introducing fraction, use fraction bars: | ||
** Describe a fraction bar in multiple ways (e.g., present a fraction bar with four parts and two parts shaded red and describe the representation as the color and the number of parts shaded (a red bar with two parts shaded); four parts and two parts shaded (without using color); or two out of four parts are shaded). | ** Describe a fraction bar in multiple ways (e.g., present a fraction bar with four parts and two parts shaded red and describe the representation as the color and the number of parts shaded (a red bar with two parts shaded); four parts and two parts shaded (without using color); or two out of four parts are shaded). | ||
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|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Geoboards | * Geoboards | ||
* Dot-paper | * Dot-paper | ||
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* iPad applications | * iPad applications | ||
* Objects (e.g., apples) shared equally and matched with a fraction card | * Objects (e.g., apples) shared equally and matched with a fraction card | ||
+ | |} | ||
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{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.2a and 2b Understand a fraction as a number on the number line; represent fractions on a number line diagram. | + | | colspan=3|'''CCSS:''' 3.NF.2a and 2b Understand a fraction as a number on the number line; represent fractions on a number line diagram. |
− | + | <ol type=lower-alpha><li> Represent a fraction 1/b on a number line diagram by defined the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.</li> | |
− | + | <li> Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.</li></ol> | |
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||'''Strand''': Number Operations (Fractions, Ratios, Proportions) | ||'''Strand''': Number Operations (Fractions, Ratios, Proportions) | ||
− | ||'''Family:''' Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family:''' Representing |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' |
|- | |- | ||
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− | ||'''Suggested Instructional Strategies''': | + | | colspan=3|'''Suggested Instructional Strategies''': |
− | * Use multiple exemplar or time delay to teach parts of a whole | + | * Use multiple exemplar or time delay to teach parts of a whole<nowiki>*</nowiki> |
* Have students show a subset of a set (1 of the 6 objects are red/square/rough) | * Have students show a subset of a set (1 of the 6 objects are red/square/rough) | ||
− | * Use Model-Lead-Test to demonstrate and teach students to fold sentence strips | + | * Use Model-Lead-Test to demonstrate and teach students to fold sentence strips<nowiki>*</nowiki> |
− | * Use Model-Lead-Test to demonstrate and teach students draw regions and partition on graph paper | + | * Use Model-Lead-Test to demonstrate and teach students draw regions and partition on graph paper<nowiki>*</nowiki> |
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* Color tiles | * Color tiles | ||
* Pattern blocks or sets of objects | * Pattern blocks or sets of objects | ||
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* Objects (e.g., apples) shared equally and matched with a fraction card | * Objects (e.g., apples) shared equally and matched with a fraction card | ||
− | |||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | + | | colspan=3|'''CCSS:''' 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. |
|- | |- | ||
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||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family: '''Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family: '''Representing |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1n Comparing and modeling fractions, including with different denominators'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1n Comparing and modeling fractions, including with different denominators'' |
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− | ||'''Instructional Strategies:''' | + | |colspan=3|'''Instructional Strategies:''' |
* Teach numerator = part, and denominator = whole using a model. Types of models may include area or region models (e.g., pattern blocks, pie pieces, and grid or dot paper), length models (e.g., number lines, Cuisenaire rods, fraction rods, line segment drawings, etc.), and set models (e.g., drawings using X's and O's, two-color counters in loops on paper). | * Teach numerator = part, and denominator = whole using a model. Types of models may include area or region models (e.g., pattern blocks, pie pieces, and grid or dot paper), length models (e.g., number lines, Cuisenaire rods, fraction rods, line segment drawings, etc.), and set models (e.g., drawings using X's and O's, two-color counters in loops on paper). | ||
− | * Time Delay | + | * Time Delay<nowiki>*</nowiki> |
* Have students demonstrate a fraction by shading in the correct number of units given a fraction bar with 2, 3, 4, 6 or 8, units | * Have students demonstrate a fraction by shading in the correct number of units given a fraction bar with 2, 3, 4, 6 or 8, units | ||
* Have students show a subset of a set (1 of the 6 objects are red/square/rough) | * Have students show a subset of a set (1 of the 6 objects are red/square/rough) | ||
− | * Use multiple exemplar training | + | * Use multiple exemplar training<nowiki>*</nowiki> |
− | * Use Least-to-Most prompting | + | * Use Least-to-Most prompting<nowiki>*</nowiki> |
* Have the student give fraction statements that are true for a provided group of objects. For example, say, "2/6 of the pencils are yellow. Show the corresponding/matching fraction." Using a shaded fraction bar, say "This show 2 parts out of 6/6 parts with 2 shaded/2 parts shaded out of 6. Show the corresponding/matching fraction." | * Have the student give fraction statements that are true for a provided group of objects. For example, say, "2/6 of the pencils are yellow. Show the corresponding/matching fraction." Using a shaded fraction bar, say "This show 2 parts out of 6/6 parts with 2 shaded/2 parts shaded out of 6. Show the corresponding/matching fraction." | ||
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* 2-dimensional rectangle segmented into parts (vs. a pizza) | * 2-dimensional rectangle segmented into parts (vs. a pizza) | ||
* Objects to model fractions | * Objects to model fractions | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 5.NBT.3a Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 | + | | colspan=3|'''CCSS:''' 5.NBT.3a Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., <math>347.392 = 3 * 100 + 4 * 10 + 7 * 1 + 3 * (1/10) + 9 * (1/100) + 2 * (1/1000)</math>. |
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||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family: '''Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family: '''Representing |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1b Extending place value understanding to reading (e.g., naming the values with number words, rather than "point four"), writing, comparing, and rounding decimals'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1b Extending place value understanding to reading (e.g., naming the values with number words, rather than "point four"), writing, comparing, and rounding decimals'' |
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− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach explicitly how to read and write decimals to the tenths (.1) and hundredths (.01). | * Teach explicitly how to read and write decimals to the tenths (.1) and hundredths (.01). | ||
* Teach explicitly the relative position of a number to the decimal point and its place value. | * Teach explicitly the relative position of a number to the decimal point and its place value. | ||
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** Ask the student read or select a recording of the decimal. | ** Ask the student read or select a recording of the decimal. | ||
** Complete for multiple decimals (.01 - .99). | ** Complete for multiple decimals (.01 - .99). | ||
− | * Use Model-Lead-Test | + | * Use Model-Lead-Test<nowiki>*</nowiki> |
* Match, write or say decimals that correspond to combinations of dollars and cents. | * Match, write or say decimals that correspond to combinations of dollars and cents. | ||
** Student will read a money amount card. (The amount could be written as a decimal, with words, or using a cent sign.) | ** Student will read a money amount card. (The amount could be written as a decimal, with words, or using a cent sign.) | ||
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− | + | | colspan=3|'''Suggested Supports and Scaffolds:''' | |
− | + | ||
* 10X10 grid paper | * 10X10 grid paper | ||
* Assistive technology | * Assistive technology | ||
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* Word cards, number cards, and grid cards for the same decimals (e.g., one tenth, .1, and a model) | * Word cards, number cards, and grid cards for the same decimals (e.g., one tenth, .1, and a model) | ||
− | |||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. ''For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram'' | + | | colspan=3|'''CCSS:''' 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. ''For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram'' |
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||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family: '''Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family: '''Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' |
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− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach explicitly that tenths have one digit after the decimal point (one digit to the right of the decimal point) and hundreds have two digits after the decimal point (two digits to the right of the decimal point). | * Teach explicitly that tenths have one digit after the decimal point (one digit to the right of the decimal point) and hundreds have two digits after the decimal point (two digits to the right of the decimal point). | ||
* Self-checking strategies using a calculator | * Self-checking strategies using a calculator | ||
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− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Place value chart | * Place value chart | ||
* Grids (with or without raised lines) | * Grids (with or without raised lines) | ||
* Grids with corresponding decimal number lines | * Grids with corresponding decimal number lines | ||
− | + | [[File:Element Cards Number Operations Fractions1.jpg|Grid of 100 squares marked in tenths]] | |
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* Calculator | * Calculator | ||
* Manipulatives such as base ten blocks to provide a visual representation (e.g. 8/10 is the same as .8 when represented with base ten blocks) | * Manipulatives such as base ten blocks to provide a visual representation (e.g. 8/10 is the same as .8 when represented with base ten blocks) | ||
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|} | |} | ||
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{|border=1 | {|border=1 | ||
− | || | + | |colspan =3| '''CCSS:''' 6.RP.3c Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. |
|- | |- | ||
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||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family:''' Representing | + | | colspan=2 style="background-color:#C6D9F1;"|'''Family:''' Representing |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems'' |
|- | |- | ||
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− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach a problem solving strategy to first find the whole, part (unknown), and then percent (e.g., Percentages can be thought of as rates per 100. We want to purchase something that originally cost $12.00 but has been reduced by 25%. We know the whole is $12.00. We want to know how much we can take off of the $12.00—this is the part or the unknown. We know that it is equal to 25%. 25% of $12.00 can be solved by writing the percent in hundredths and then multiplying by the quantity. 25/100 ×12=4. 25% of $12.00 is $4.00). | * Teach a problem solving strategy to first find the whole, part (unknown), and then percent (e.g., Percentages can be thought of as rates per 100. We want to purchase something that originally cost $12.00 but has been reduced by 25%. We know the whole is $12.00. We want to know how much we can take off of the $12.00—this is the part or the unknown. We know that it is equal to 25%. 25% of $12.00 can be solved by writing the percent in hundredths and then multiplying by the quantity. 25/100 ×12=4. 25% of $12.00 is $4.00). | ||
* Teach explicitly three ways of expressing percent (e.g., 10 percent, 10%, 10/100). | * Teach explicitly three ways of expressing percent (e.g., 10 percent, 10%, 10/100). | ||
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|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* 10X10 grid and a number line to show relationship between a fraction and a percent (40% is the same as 40/100 | * 10X10 grid and a number line to show relationship between a fraction and a percent (40% is the same as 40/100 | ||
− | + | [[File:Element Cards Number Operations Fractions2.jpg|Grid of 100 squares with 40 filled in, indicating 40%]] | |
− | + | * Dual number line: For percent problems with one part missing, one side of the line is marked with the quantities and the other with the percentages; student organizes the given information and shows which information is missing.[[File:Element Cards Number Operations Fractions3.PNG|vertical line from 0% to 100% and 0 to 100. The student answers the question 30% equals blank units.]] | |
− | + | * Bundles of 10s and 100s [[File:Element Cards Number Operations Fractions4.PNG|4 bundles of 10]] | |
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− | * Dual number line: For percent problems with one part missing, one side of the line is marked with the quantities and the other with the percentages; student organizes the given information and shows which information is missing. | + | |
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− | * Bundles of 10s and 100s [[File: | + | |
* Number line | * Number line | ||
* Hundreds chart | * Hundreds chart | ||
Line 724: | Line 470: | ||
|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | + | | colspan=3|'''CCSS:''' 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
|- | |- | ||
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||'''Strand: '''Symbolic Expression | ||'''Strand: '''Symbolic Expression | ||
− | ||'''Family''': Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family''': Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator''':'' E.SE.1g Using symbols (=, >, <) to compare whole numbers, fractions, or decimals; write equations; and express inverse or related operations '' | + | | colspan=3|'''Progress Indicator''':'' E.SE.1g Using symbols (=, >, <) to compare whole numbers, fractions, or decimals; write equations; and express inverse or related operations '' |
|- | |- | ||
Line 757: | Line 504: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
− | * Multiple exemplars for equal, greater than, less than | + | * Multiple exemplars for equal, greater than, less than<nowiki>*</nowiki> |
* Explicit teaching of the rules of denominator and numerator | * Explicit teaching of the rules of denominator and numerator | ||
* Explicit teaching of comparisons (more of the same size parts, same number of parts but different sizes, more and less than ½ or 1 whole, distance from ½ or 1 whole) | * Explicit teaching of comparisons (more of the same size parts, same number of parts but different sizes, more and less than ½ or 1 whole, distance from ½ or 1 whole) | ||
Line 764: | Line 511: | ||
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Number line with fractions | * Number line with fractions | ||
* Illustrations | * Illustrations | ||
Line 774: | Line 521: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | + | | colspan=3|'''CCSS:''' 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
|- | |- | ||
Line 789: | Line 536: | ||
||'''Strand: '''Symbolic Expression | ||'''Strand: '''Symbolic Expression | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.SE.1g Using symbols (=, >, <) to compare whole numbers, fractions, or decimals; write equations; and express inverse or related operations '' | + | | colspan=3|'''Progress Indicator:''''' E.SE.1g Using symbols (=, >, <) to compare whole numbers, fractions, or decimals; write equations; and express inverse or related operations '' |
|- | |- | ||
Line 808: | Line 555: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
− | * Multiple exemplars for equal, greater than, less than | + | * Multiple exemplars for equal, greater than, less than<nowiki>*</nowiki> |
* Explicit teaching of the rules of denominator and numerator | * Explicit teaching of the rules of denominator and numerator | ||
* Explicit teaching of comparisons (more of the same size parts, same number of parts but different sizes, more and less than ½ or 1 whole, distance from ½ or 1 whole) | * Explicit teaching of comparisons (more of the same size parts, same number of parts but different sizes, more and less than ½ or 1 whole, distance from ½ or 1 whole) | ||
Line 815: | Line 562: | ||
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Number line with fractions | * Number line with fractions | ||
* Illustrations | * Illustrations | ||
Line 825: | Line 572: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. | + | | colspan=3|'''CCSS:''' 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. |
− | + | <ol type=lower-alpha><li> Represent a fraction 1/b on a number line diagram by defined the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.</li> | |
− | + | <li> Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.</li></ol> | |
|- | |- | ||
Line 842: | Line 589: | ||
||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' |
|- | |- | ||
Line 861: | Line 608: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Use sentence strips or string to fold to create their own number line. | * Use sentence strips or string to fold to create their own number line. | ||
* Explicitly teach that the denominator is the number of equal sections between 0 and 1. | * Explicitly teach that the denominator is the number of equal sections between 0 and 1. | ||
* Explicitly teach that the numerator is the number of equal sections from 0, e.g. - 3/5 means the space between 0 and 1 has 5 equal sections and 3/5 is at the end of the 3rd section from zero. | * Explicitly teach that the numerator is the number of equal sections from 0, e.g. - 3/5 means the space between 0 and 1 has 5 equal sections and 3/5 is at the end of the 3rd section from zero. | ||
− | * Time delay | + | * Time delay<nowiki>*</nowiki> |
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Interactive whiteboard | * Interactive whiteboard | ||
* Computer software | * Computer software | ||
Line 876: | Line 623: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. | + | | colspan=3|'''CCSS:''' 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. |
− | + | <ol type=lower-alpha><li> Represent a fraction 1/b on a number line diagram by defined the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.</li> | |
− | + | <li> Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.</li></ol> | |
|- | |- | ||
Line 893: | Line 640: | ||
||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers'' |
|- | |- | ||
Line 913: | Line 660: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Folding sentence strip or paper to have students generate a number line | * Folding sentence strip or paper to have students generate a number line | ||
* Use fraction cards to place and order on a number line. | * Use fraction cards to place and order on a number line. | ||
Line 920: | Line 667: | ||
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Start with 3<sup>rd</sup> grade concept of only ordering fractions with same numerator and same denominator Interactive whiteboard | * Start with 3<sup>rd</sup> grade concept of only ordering fractions with same numerator and same denominator Interactive whiteboard | ||
* Computer software | * Computer software | ||
Line 928: | Line 675: | ||
|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
− | || | + | |colspan=3|'''CCSS:''' 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. |
− | + | <ol type=lower-alpha><li> Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. </li> | |
− | + | <li> Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. </li> | |
− | + | <li> Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. ''Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.'' </li> | |
− | + | <li> Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. </li></ol> | |
+ | |||
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | ||
Line 947: | Line 696: | ||
||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family: '''Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family: '''Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1m Composing and representing equivalent fractions in the form a/b'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1m Composing and representing equivalent fractions in the form a/b'' |
|- | |- | ||
Line 965: | Line 714: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach equivalency explicitly using bars of equal length with the same shaded amount (e.g., show that for bars of the same length, 1 part out of 2, two parts out of 4, and 3 parts out of six, are equal (the same amount of the bar is shaded broken into 1, 2 or 3 parts)). | * Teach equivalency explicitly using bars of equal length with the same shaded amount (e.g., show that for bars of the same length, 1 part out of 2, two parts out of 4, and 3 parts out of six, are equal (the same amount of the bar is shaded broken into 1, 2 or 3 parts)). | ||
* Teach equivalency explicitly by using bars (visual) to show that when both the numerator and the denominator are multiplied by the same "non-zero" number, the fractions remain equivalent (e.g., to remain equal, you will always multiply or divide by 1 represented in the form of a fraction (2/2). | * Teach equivalency explicitly by using bars (visual) to show that when both the numerator and the denominator are multiplied by the same "non-zero" number, the fractions remain equivalent (e.g., to remain equal, you will always multiply or divide by 1 represented in the form of a fraction (2/2). | ||
Line 991: | Line 740: | ||
** Explicitly state that when the numerator is doubled, by doubling the denominator, the fractions are equal. | ** Explicitly state that when the numerator is doubled, by doubling the denominator, the fractions are equal. | ||
** Provide additional examples to show that by splitting the bar, increasing all parts of the bars increases the number of shaded parts. | ** Provide additional examples to show that by splitting the bar, increasing all parts of the bars increases the number of shaded parts. | ||
− | * Use Model-Lead-Test | + | * Use Model-Lead-Test<nowiki>*</nowiki> |
− | * Multiple exemplars (e.g., "These fractions are equivalent. These fractions are equivalent. These fractions are not equivalent.") | + | * Multiple exemplars (e.g., "These fractions are equivalent. These fractions are equivalent. These fractions are not equivalent.")<nowiki>*</nowiki> |
|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Assistive Technology | * Assistive Technology | ||
* Virtual bars or tiles | * Virtual bars or tiles | ||
Line 1,006: | Line 755: | ||
* Pie diagrams | * Pie diagrams | ||
* Fraction bars that are ruled into certain fixed partitions and lined up for comparisons | * Fraction bars that are ruled into certain fixed partitions and lined up for comparisons | ||
− | * Multiplication tables (e.g., 1 to 4 has the same | + | * Multiplication tables (e.g., 1 to 4 has the same ratio as 2 to 8) |
+ | {|class=ThickBorder | ||
+ | |style="background-color:#D9D9D9;"| | ||
+ | |style="background-color:#D9D9D9;"|'''1''' | ||
+ | |style="background-color:#D9D9D9;"|'''2''' | ||
+ | |style="background-color:#D9D9D9;"|'''3''' | ||
+ | |style="background-color:#D9D9D9;"|'''4''' | ||
+ | |style="background-color:#D9D9D9;"|'''5''' | ||
+ | |style="background-color:#D9D9D9;"|'''6''' | ||
+ | |style="background-color:#D9D9D9;"|'''7''' | ||
+ | |style="background-color:#D9D9D9;"|'''8''' | ||
+ | |- | ||
− | '''1''' | + | |style="background-color:#D9D9D9;"|'''1''' |
− | '''2''' | + | |style="background-color:#CCC0D9;"|'''1''' |
− | '''3''' | + | |style="background-color:#C2D29B;"|'''2''' |
− | '''4''' | + | |style="background-color:#C2D29B;"|'''3''' |
− | '''5''' | + | |style="background-color:#CCC0D9;"|'''4''' |
− | '''6''' | + | |style="background-color:#C2D29B;"|'''5''' |
− | '''7''' | + | |style="background-color:#C2D29B;"|'''6''' |
− | '''8''' | + | |style="background-color:#C2D29B;"|'''7''' |
+ | |style="background-color:#C2D29B;"|'''8''' | ||
+ | |- | ||
+ | |style="background-color:#D9D9D9;"|'''2''' | ||
+ | |style="background-color:#CCC0D9;"|'''2''' | ||
+ | |style="background-color:#C2D29B;"|'''4''' | ||
+ | |style="background-color:#C2D29B;"|'''6''' | ||
+ | |style="background-color:#CCC0D9;"|'''8''' | ||
+ | |style="background-color:#C2D29B;"|'''10''' | ||
+ | |style="background-color:#C2D29B;"|'''12''' | ||
+ | |style="background-color:#C2D29B;"|'''14''' | ||
+ | |style="background-color:#C2D29B;"|'''16''' | ||
+ | |- | ||
+ | |style="background-color:#D9D9D9;"|'''3''' | ||
+ | ||'''3''' | ||
+ | ||'''6''' | ||
+ | ||'''9''' | ||
+ | ||'''12''' | ||
+ | ||'''15''' | ||
+ | ||'''18''' | ||
+ | ||'''21''' | ||
+ | ||'''24''' | ||
+ | |- | ||
+ | |style="background-color:#D9D9D9;"|'''4''' | ||
+ | ||'''4''' | ||
+ | ||'''8''' | ||
+ | ||'''12''' | ||
+ | ||'''16''' | ||
+ | ||'''20''' | ||
+ | ||'''24''' | ||
+ | ||'''28''' | ||
+ | ||'''32''' | ||
+ | |} | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fractions such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | + | | colspan=3|'''CCSS:''' 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fractions such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
|- | |- | ||
Line 1,079: | Line 828: | ||
||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.1n Comparing and modeling fractions, including with different denominators'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.1n Comparing and modeling fractions, including with different denominators'' |
|- | |- | ||
Line 1,096: | Line 845: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Compare fractions represented with models (e.g., circle divided in halves and in fourths with 1/2 and 3/4 shaded in). | * Compare fractions represented with models (e.g., circle divided in halves and in fourths with 1/2 and 3/4 shaded in). | ||
* Use rectangles that are the same size for students to partition and represent fractions. | * Use rectangles that are the same size for students to partition and represent fractions. | ||
Line 1,102: | Line 851: | ||
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* Assistive Technology | * Assistive Technology | ||
* Virtual bars or tiles | * Virtual bars or tiles | ||
Line 1,119: | Line 868: | ||
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 3.NF.1 Understand a fraction 1/''b ''as the quantity formed by 1 part when ''a ''whole is partitioned into ''b ''equal parts; understand a fraction ''a''/''b ''as the'' ''quantity formed by a parts of size 1/''b'' | + | | colspan=3|'''CCSS:''' 3.NF.1 Understand a fraction 1/''b ''as the quantity formed by 1 part when ''a ''whole is partitioned into ''b ''equal parts; understand a fraction ''a''/''b ''as the'' ''quantity formed by a parts of size 1/''b'' |
4.NF.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''. | 4.NF.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''. | ||
− | + | <ol type=lower-alpha><li> Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.</li> | |
− | + | <li> Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. </li> | |
+ | ''Examples: 3/8 = 1/8 + 1/8 + 1/8 | ||
+ | 3/8 = 1/8 + 2/8 | ||
+ | 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. | ||
|- | |- | ||
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||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.2g Recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.2g Recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions'' |
|- | |- | ||
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|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach explicitly using manipulatives that can be partitioned into equal sections. | * Teach explicitly using manipulatives that can be partitioned into equal sections. | ||
* Use a number line to model decomposing fractions. | * Use a number line to model decomposing fractions. | ||
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** Explicitly state that when the numerator is doubled, by doubling the denominator, the fractions are equal. | ** Explicitly state that when the numerator is doubled, by doubling the denominator, the fractions are equal. | ||
** Provide additional examples to show that by splitting the bar, increasing all parts of the bars increases the number of shaded parts. | ** Provide additional examples to show that by splitting the bar, increasing all parts of the bars increases the number of shaded parts. | ||
− | * Use Model-Lead-Test | + | * Use Model-Lead-Test<nowiki>*</nowiki> |
− | * Multiple exemplars (e.g., "These fractions are equivalent. These fractions are equivalent. These fractions are not equivalent.") | + | * Multiple exemplars (e.g., "These fractions are equivalent. These fractions are equivalent. These fractions are not equivalent.")<nowiki>*</nowiki> |
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* Assistive technology | * Assistive technology | ||
* Manipulatives | * Manipulatives | ||
Line 1,176: | Line 928: | ||
|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. ''For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.'' | + | | colspan=3|'''CCSS:''' 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. ''For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.'' |
|- | |- | ||
Line 1,190: | Line 943: | ||
||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family: '''Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family: '''Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' |
|- | |- | ||
Line 1,208: | Line 961: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach explicitly that the tenths place is the first digit after the decimal point and hundredths place is the second digit after the decimal point. | * Teach explicitly that the tenths place is the first digit after the decimal point and hundredths place is the second digit after the decimal point. | ||
− | * Time delay | + | * Time delay<nowiki>*</nowiki> |
* Self-checking strategies using a calculator | * Self-checking strategies using a calculator | ||
** Divide the top of the fraction by the bottom, and read off/record the answer | ** Divide the top of the fraction by the bottom, and read off/record the answer | ||
Line 1,218: | Line 971: | ||
|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Place value chart | * Place value chart | ||
* Grids (with or without raised lines) | * Grids (with or without raised lines) | ||
* Grids with corresponding decimal number lines | * Grids with corresponding decimal number lines | ||
− | + | [[File:Element Cards Number Operations Fractions1.jpg|Grid of 100 squares with 50 colored green and marked .50]] | |
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* Calculator | * Calculator | ||
* Manipulatives such as base ten blocks to provide a visual representation (e.g. 8/10 is the same as .8 when represented with base ten blocks) | * Manipulatives such as base ten blocks to provide a visual representation (e.g. 8/10 is the same as .8 when represented with base ten blocks) | ||
Line 1,354: | Line 983: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. ''For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.'' | + | | colspan=3|'''CCSS:''' 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. ''For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.'' |
|- | |- | ||
Line 1,369: | Line 998: | ||
||'''Strand''': Number Operations (Fractions, Ration, Proportions) | ||'''Strand''': Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' |
|- | |- | ||
Line 1,386: | Line 1,015: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies''': | + | | colspan=3|'''Suggested Instructional Strategies''': |
* Explicitly teach using a task analysis. | * Explicitly teach using a task analysis. | ||
** Write down the decimal. | ** Write down the decimal. | ||
Line 1,392: | Line 1,021: | ||
** Multiply top and bottom by 100 (e.g., 50/1 x 100 + 50/100). | ** Multiply top and bottom by 100 (e.g., 50/1 x 100 + 50/100). | ||
** Simplify the fraction (e.g., 50/100, divided by the greatest common factor which is 50. 50/100 ÷50/50 =1/2). | ** Simplify the fraction (e.g., 50/100, divided by the greatest common factor which is 50. 50/100 ÷50/50 =1/2). | ||
− | * Teach using Least-to-most prompting. | + | * Teach using Least-to-most prompting.<nowiki>*</nowiki> |
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* 10x10 decimal grid | * 10x10 decimal grid | ||
* Assistive Technology | * Assistive Technology | ||
Line 1,405: | Line 1,034: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. ''For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.'' | + | | colspan=3|'''CCSS:''' 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. ''For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.'' |
|- | |- | ||
Line 1,421: | Line 1,050: | ||
||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family: '''Problem Solving | + | | colspan=2 style="background-color:#548DD4;"|'''Family: '''Problem Solving |
|- | |- | ||
− | ||'''Progress Indicator:''''' .NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' | + | | colspan=3|'''Progress Indicator:''''' .NO.1c Using a variety of fractional and decimal representations and locating them on a number line'' |
|- | |- | ||
Line 1,446: | Line 1,075: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach explicitly how to express a verbal description of a fraction ("one-fourth" as 1/4). | * Teach explicitly how to express a verbal description of a fraction ("one-fourth" as 1/4). | ||
* Task analysis: | * Task analysis: | ||
Line 1,455: | Line 1,084: | ||
* Teach explicitly how to represent the total number of objects in a word problem as an array by creating sets based on the denominator of the provided fraction in a word problem (e.g., ½ of the 20 students would be a group of 20 objects shown as two arrays of 10 each). | * Teach explicitly how to represent the total number of objects in a word problem as an array by creating sets based on the denominator of the provided fraction in a word problem (e.g., ½ of the 20 students would be a group of 20 objects shown as two arrays of 10 each). | ||
* Teach explicitly how to use a number line/conversion tables to solve a word problem. | * Teach explicitly how to use a number line/conversion tables to solve a word problem. | ||
− | * Use Model-Lead-Test. | + | * Use Model-Lead-Test.<nowiki>*</nowiki> |
* Give students problems to model such as these: Charlene ate 1/4 of the sandwich at breakfast and 2/4 of the sandwich at lunch. How much of the sandwich did she eat? | * Give students problems to model such as these: Charlene ate 1/4 of the sandwich at breakfast and 2/4 of the sandwich at lunch. How much of the sandwich did she eat? | ||
|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Use arrays to represent the denominator as sets. | * Use arrays to represent the denominator as sets. | ||
* Number line | * Number line | ||
Line 1,470: | Line 1,099: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 6.RP.3a Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | + | | colspan=3|'''CCSS:''' 6.RP.3a Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. |
− | + | <ol type=lower-alpha><li> Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.</li></ol> | |
|- | |- | ||
Line 1,486: | Line 1,115: | ||
||'''Strand''': Number Operations (Fractions, Ration, Proportions) | ||'''Strand''': Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems'' |
|- | |- | ||
Line 1,501: | Line 1,130: | ||
||'''Representation:''' | ||'''Representation:''' | ||
* Create a table showing equivalent ratios based on a given ratio. | * Create a table showing equivalent ratios based on a given ratio. | ||
− | Inches of snow | + | {|border=1px solid black style="border-collapse:collapse;" |
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* Vocabulary | * Vocabulary | ||
** ratio (e.g., 2:1, 1:1) | ** ratio (e.g., 2:1, 1:1) | ||
Line 1,521: | Line 1,152: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies''': | + | | colspan=3|'''Suggested Instructional Strategies''': |
* When looking at a table, identify the pattern in each column. | * When looking at a table, identify the pattern in each column. | ||
* Teach explicitly how to problem solve for proportional relationships: | * Teach explicitly how to problem solve for proportional relationships: | ||
Line 1,530: | Line 1,161: | ||
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* Calculator | * Calculator | ||
* Table of values | * Table of values | ||
Line 1,540: | Line 1,171: | ||
|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 7.RP.2 Recognize and represent proportional relationships between quantities. | + | | colspan=3|'''CCSS:''' 7.RP.2 Recognize and represent proportional relationships between quantities. |
− | + | <ol type=lower-alpha><li> Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.</li> | |
− | + | <li> Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.</li> | |
− | + | <li> Represent proportional relationships by equations. ''For example, if total cost t is proportional to the number n of items purchased at a constant price p, the as t = pn.''</li></ol> | |
Explain what a point (''x'', ''y'') on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, ''r'') where r is the unit rate. | Explain what a point (''x'', ''y'') on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, ''r'') where r is the unit rate. | ||
Line 1,558: | Line 1,190: | ||
||'''Strand: '''Number Operations (Fractions/ratios/Proportions) | ||'''Strand: '''Number Operations (Fractions/ratios/Proportions) | ||
− | ||'''Family: '''Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family: '''Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.2f Describing proportional relationships and solving related problems'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.2f Describing proportional relationships and solving related problems'' |
|- | |- | ||
Line 1,573: | Line 1,205: | ||
− | + | [[File:Element Cards Number Operations Fractions5.PNG|One shopping cart and two traffic cones. What is the ratio?]] | |
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− | + | ||
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||'''Representation:''' | ||'''Representation:''' | ||
Line 1,587: | Line 1,215: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
− | * Multiple Exemplar Training | + | * Multiple Exemplar Training<nowiki>*</nowiki> |
** Example: There are three chairs for one/each table. The ratio is '''3 to 1'''. The ratio is '''3:1'''. The ratio is '''3/1.''' The ratio is not '''1 to 3.''' Show me the proportion/ratio for three chairs for one table. | ** Example: There are three chairs for one/each table. The ratio is '''3 to 1'''. The ratio is '''3:1'''. The ratio is '''3/1.''' The ratio is not '''1 to 3.''' Show me the proportion/ratio for three chairs for one table. | ||
* Teach explicitly three ways to represent a proportion. | * Teach explicitly three ways to represent a proportion. | ||
Line 1,600: | Line 1,228: | ||
|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Use real-life contexts such as recipes and piano keys (black to white) that are relevant to students. | * Use real-life contexts such as recipes and piano keys (black to white) that are relevant to students. | ||
* Draw pictures and use tables to determine proportions. | * Draw pictures and use tables to determine proportions. | ||
Line 1,609: | Line 1,237: | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. ''For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."'' | + | | colspan=3|'''CCSS:''' 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. ''For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."'' |
|- | |- | ||
Line 1,624: | Line 1,252: | ||
||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||'''Strand:''' Number Operations (Fractions, Ration, Proportions) | ||
− | ||'''Family:''' Determining Equivalency | + | | colspan=2 style="background-color:#8DB3E2;"|'''Family:''' Determining Equivalency |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems'' |
|- | |- | ||
Line 1,636: | Line 1,264: | ||
* Represent the proportion of a subgroup of objects (e.g., red hats) to the total number of objects (red and green hats). | * Represent the proportion of a subgroup of objects (e.g., red hats) to the total number of objects (red and green hats). | ||
* Use a table with visuals or objects to represent proportions to determine if two numbers (i.e., 10:1) are the same proportional relationship as previous numbers (2:1, and 4:2). | * Use a table with visuals or objects to represent proportions to determine if two numbers (i.e., 10:1) are the same proportional relationship as previous numbers (2:1, and 4:2). | ||
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+ | [[File:Element Cards Number Operations Fractions6.PNG|Table with inches of snow in the first column and hours in the second. Row 1, 2 inches of snow, 1 hour. Row 2, 4 inches of snow, 2 hours. Row 3, 10 inches of snow, 1 hour.]] | ||
Line 1,661: | Line 1,273: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies''': | + | | colspan=3|'''Suggested Instructional Strategies''': |
* Use counters or objects to demonstrate a proportion. | * Use counters or objects to demonstrate a proportion. | ||
* Generate a graph of values that are proportional. | * Generate a graph of values that are proportional. | ||
Line 1,667: | Line 1,279: | ||
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* Calculator | * Calculator | ||
* Assistive Technology | * Assistive Technology | ||
Line 1,675: | Line 1,287: | ||
|- | |- | ||
− | ||'''CCSS:''' 4.NF.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''. | + | | colspan=3|'''CCSS:''' 4.NF.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''. |
− | + | <ol type=lower-alpha><li> Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.</li> | |
− | Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. ''Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2'' ''1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.'' | + | <li>Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. </li></ol> |
+ | |||
+ | ''Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2'' ''1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.'' | ||
|- | |- | ||
Line 1,689: | Line 1,303: | ||
||'''Strand:''' Number Operations (Fractions, Ratios, Proportions). | ||'''Strand:''' Number Operations (Fractions, Ratios, Proportions). | ||
− | | style="background-color:#00B0F0;"|'''Family:''' Performing Operations | + | | style="background-color:#00B0F0;" colspan=2|'''Family:''' Performing Operations |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.2h Adding, subtracting, and multiplying fractions, including mixed numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.2h Adding, subtracting, and multiplying fractions, including mixed numbers'' |
|- | |- | ||
Line 1,711: | Line 1,325: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies''': | + | | colspan=3|'''Suggested Instructional Strategies''': |
− | * Model-Lead-Test | + | * Model-Lead-Test<nowiki>*</nowiki> |
* Teach explicit rules for adding and subtracting fractions. | * Teach explicit rules for adding and subtracting fractions. | ||
* Pizza Fractions: Cut 'pizza' circles the same size then cut them into a variety of fractions and use them to add/subtract mixed numbered fractions (e.g., add one half pizza to two 1/4 pieces to make a whole or subtract 1/3 pizza from 6/6). | * Pizza Fractions: Cut 'pizza' circles the same size then cut them into a variety of fractions and use them to add/subtract mixed numbered fractions (e.g., add one half pizza to two 1/4 pieces to make a whole or subtract 1/3 pizza from 6/6). | ||
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* Fraction strips | * Fraction strips | ||
* Fraction tiles | * Fraction tiles | ||
Line 1,729: | Line 1,343: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 4.NF.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''. | + | | colspan=3|'''CCSS:''' 4.NF.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''. |
− | + | <ol type=lower-alpha><li> Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.</li> | |
− | + | <li> Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. </li> | |
+ | ''Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2'' ''1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.'' | ||
|- | |- | ||
Line 1,746: | Line 1,361: | ||
||'''Strand:''' Number Operations (Fractions, Ratios, Proportions). | ||'''Strand:''' Number Operations (Fractions, Ratios, Proportions). | ||
− | | style="background-color:#00B0F0;"|'''Family:''' Performing Operations | + | | style="background-color:#00B0F0;" colspan=2|'''Family:''' Performing Operations |
|- | |- | ||
− | ||'''Progress Indicator:''''' E.NO.2h Adding, subtracting, and multiplying fractions, including mixed numbers'' | + | | colspan=3|'''Progress Indicator:''''' E.NO.2h Adding, subtracting, and multiplying fractions, including mixed numbers'' |
|- | |- | ||
Line 1,768: | Line 1,383: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies''': | + | | colspan=3|'''Suggested Instructional Strategies''': |
− | * Model-Lead-Test using representations | + | * Model-Lead-Test using representations<nowiki>*</nowiki> |
* Teach explicit rules for adding and subtracting fractions. | * Teach explicit rules for adding and subtracting fractions. | ||
* Pizza Fractions: Cut 'pizza' circles the same size then cut them into a variety of fractions and use them to add/subtract mixed numbered fractions (e.g., add one half pizza to two 1/4 pieces to make a whole or subtract 1/3 pizza from 6/6). | * Pizza Fractions: Cut 'pizza' circles the same size then cut them into a variety of fractions and use them to add/subtract mixed numbered fractions (e.g., add one half pizza to two 1/4 pieces to make a whole or subtract 1/3 pizza from 6/6). | ||
|- | |- | ||
− | ||'''Supports and Scaffolds''': | + | | colspan=3|'''Supports and Scaffolds''': |
* Fraction strips | * Fraction strips | ||
* Fraction tiles | * Fraction tiles | ||
Line 1,787: | Line 1,402: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | + | | colspan=3|'''CCSS:''' 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. |
|- | |- | ||
Line 1,802: | Line 1,417: | ||
||'''Strand:''' Number Operations (Fractions, Ratios, Proportions). | ||'''Strand:''' Number Operations (Fractions, Ratios, Proportions). | ||
− | | style="background-color:#00B0F0;"|'''Family:''' Performing Operations | + | | style="background-color:#00B0F0;" colspan=2|'''Family:''' Performing Operations |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.2c Using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.2c Using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)'' |
|- | |- | ||
Line 1,820: | Line 1,435: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach problem solving strategies to determine operations'''.''' | * Teach problem solving strategies to determine operations'''.''' | ||
* Use task analytic instruction to teach steps to solve word problems. | * Use task analytic instruction to teach steps to solve word problems. | ||
− | * Teach using Least to Most prompts | + | * Teach using Least to Most prompts<nowiki>*</nowiki> |
− | * Use Model-Lead-Test | + | * Use Model-Lead-Test<nowiki>*</nowiki> |
* Have students self-check their answers. Start by modeling this process. | * Have students self-check their answers. Start by modeling this process. | ||
* To demonstrate addition, gather several representations labeled with the decimal (circles, squares, pattern blocks, Cuisenaire rods) and identify how many of the pieces make one whole (e.g., .5 + .5). | * To demonstrate addition, gather several representations labeled with the decimal (circles, squares, pattern blocks, Cuisenaire rods) and identify how many of the pieces make one whole (e.g., .5 + .5). | ||
|- | |- | ||
− | ||'''Supports and Scaffolds:''' | + | | colspan=3|'''Supports and Scaffolds:''' |
* 10x10 hundreds grids | * 10x10 hundreds grids | ||
* Place value chart | * Place value chart | ||
Line 1,839: | Line 1,454: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. ''For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples.'' | + | | colspan=3|'''CCSS:''' 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. ''For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples.'' |
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | ||
Line 1,855: | Line 1,470: | ||
||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||
− | | style="background-color:#00B0F0;"|'''Family: '''Performing Operations | + | | style="background-color:#00B0F0;" colspan=2|'''Family: '''Performing Operations |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.2c Using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.2c Using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)'' |
|- | |- | ||
Line 1,873: | Line 1,488: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
− | * Use multiple exemplar training to teach part to whole. | + | * Use multiple exemplar training to teach part to whole.<nowiki>*</nowiki> |
− | * Task analysis | + | * Task analysis<nowiki>*</nowiki> |
− | * Teach using Least Intrusive Prompts. | + | * Teach using Least Intrusive Prompts.<nowiki>*</nowiki> |
− | * Use Model-Lead-Test. | + | * Use Model-Lead-Test.<nowiki>*</nowiki> |
* Have students self-check their answers. Start by modeling this process. | * Have students self-check their answers. Start by modeling this process. | ||
* To demonstrate addition, gather several representations of halves (circles, squares, pattern blocks, Cuisenaire rods) and identify how many of the pieces make one whole. Discuss that adding one more half makes the sum bigger than the whole. | * To demonstrate addition, gather several representations of halves (circles, squares, pattern blocks, Cuisenaire rods) and identify how many of the pieces make one whole. Discuss that adding one more half makes the sum bigger than the whole. | ||
Line 1,883: | Line 1,498: | ||
|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Provide meaningful manipulatives, counters and/or picture representations with symbol included. | * Provide meaningful manipulatives, counters and/or picture representations with symbol included. | ||
* Templates with formulas | * Templates with formulas | ||
Line 1,898: | Line 1,513: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
{|border=1 | {|border=1 | ||
− | || | + | |colspan=3|'''CCSS:''' 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. |
Apply properties of operations as strategies to add and subtract rational numbers. | Apply properties of operations as strategies to add and subtract rational numbers. | ||
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. | 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. | ||
Line 1,915: | Line 1,530: | ||
||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||'''Strand: '''Number Operations (Fractions/Ratios/Proportions) | ||
− | | style="background-color:#00B0F0;"|'''Family: '''Performing Operations | + | | style="background-color:#00B0F0;" colspan=2|'''Family: '''Performing Operations |
|- | |- | ||
− | ||'''Progress Indicator:''''' M.NO.2i Using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line'' | + | | colspan=3|'''Progress Indicator:''''' M.NO.2i Using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line'' |
|- | |- | ||
Line 1,934: | Line 1,549: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Prime background knowledge and connections by using real-world context. | * Prime background knowledge and connections by using real-world context. | ||
* Task analysis of steps to solve two-step word problems (this could include using Least Intrusive Prompts) | * Task analysis of steps to solve two-step word problems (this could include using Least Intrusive Prompts) | ||
** When solving word problems, teach how to determine which part of the problem is given and which part needs to be determined/solved | ** When solving word problems, teach how to determine which part of the problem is given and which part needs to be determined/solved | ||
− | * Use Model-Lead-Test (This involves model solving a word problem while thinking out loud. For example, pointing out the key words and the operations they call for. For example, "To find the whole, we add. Then, to find a part, we subtract." Next follow the steps as a group with the teacher leading as needed. Last, give students an opportunity to complete the steps without help.) | + | * Use Model-Lead-Test (This involves model solving a word problem while thinking out loud. For example, pointing out the key words and the operations they call for. For example, "To find the whole, we add. Then, to find a part, we subtract." Next follow the steps as a group with the teacher leading as needed. Last, give students an opportunity to complete the steps without help.)<nowiki>*</nowiki> |
* Teach explicitly the rules for solving problems involving computation providing templates/formulas | * Teach explicitly the rules for solving problems involving computation providing templates/formulas | ||
* Model addition/subtraction equations by placing the appropriate numbers of chips on a graphic organizer. Using the notion of opposites, demonstrate how to simplify by removing pairs of opposite colored chips. | * Model addition/subtraction equations by placing the appropriate numbers of chips on a graphic organizer. Using the notion of opposites, demonstrate how to simplify by removing pairs of opposite colored chips. | ||
|- | |- | ||
− | ||'''Suggested Supports and Scaffolds:''' | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Highlight text using tape, pen, computer highlighting that provide important information | * Highlight text using tape, pen, computer highlighting that provide important information | ||
* Provide visual representations (e.g., grids) of problem with symbols | * Provide visual representations (e.g., grids) of problem with symbols | ||
Line 1,957: | Line 1,572: | ||
|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | |
− | [[File: | + | [[File:Element Cards Number Operations Fractions7.PNG|Equation Prompt where blank plus or minus blank equals blank]] |
{|border=1 | {|border=1 | ||
− | ||'''CCSS:''' 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. | + | | colspan=3|'''CCSS:''' 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. |
|- | |- | ||
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||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||'''Strand:''' Number Operations (Fractions/Ratios/Proportions) | ||
− | ||'''Family:''' Problem Solving | + | | colspan=2 style="background-color:#548DD4;"|'''Family:''' Problem Solving |
|- | |- | ||
− | ||'''Progress Indicator:''''''' M.NO.2f Describing proportional relationships and solving related problems'''' | + | | colspan=3|'''Progress Indicator:''''''' M.NO.2f Describing proportional relationships and solving related problems'''' |
|- | |- | ||
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* Relate the placement of numbers in a ratio to the given context (the meaning of 46:1, 46 equals miles, 1 equals a gallon of gas). | * Relate the placement of numbers in a ratio to the given context (the meaning of 46:1, 46 equals miles, 1 equals a gallon of gas). | ||
* Use a table with visuals or objects to represent proportions to solve ratio problem. | * Use a table with visuals or objects to represent proportions to solve ratio problem. | ||
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+ | [[File:Element Cards Number Operations Fractions6.PNG|Table with inches of snow in the first column and hours in the second. Row 1, 2 inches of snow, 1 hour. Row 2, 4 inches of snow, 2 hours. Row 3, 10 inches of snow, 1 hour.]] | ||
||'''Representation:''' | ||'''Representation:''' | ||
Line 2,011: | Line 1,609: | ||
|- | |- | ||
− | ||'''Suggested Instructional Strategies:''' | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Help students access background knowledge and connections by using real world context. | * Help students access background knowledge and connections by using real world context. | ||
* Task analysis of steps to solve word problems (this could include using Least Intrusive Prompts) | * Task analysis of steps to solve word problems (this could include using Least Intrusive Prompts) | ||
** When solving word problems, teach how to determine which part of the problem is given and which part needs to be determined/solved. | ** When solving word problems, teach how to determine which part of the problem is given and which part needs to be determined/solved. | ||
− | * Use Model-Lead-Test | + | * Use Model-Lead-Test<nowiki>*</nowiki> |
* Teach explicitly the rules for solving problems involving ratios providing templates/formulas. | * Teach explicitly the rules for solving problems involving ratios providing templates/formulas. | ||
− | * Use multiple exemplar training. | + | * Use multiple exemplar training.<nowiki>*</nowiki> |
* Task Analysis example: | * Task Analysis example: | ||
** Read the story problem/situation: "In one (1) day, Jack eats three meals. How many meals will Jack eat in 5 days? | ** Read the story problem/situation: "In one (1) day, Jack eats three meals. How many meals will Jack eat in 5 days? | ||
Line 2,026: | Line 1,624: | ||
** Determine the relationship between "a" and "b" (a x __ = b) | ** Determine the relationship between "a" and "b" (a x __ = b) | ||
− | Day (a) | + | {|border =1px solid black style="border-collapse:collapse;" |
− | 1 | + | |- |
− | 2 | + | |style="background-color:#D9D9D9;"|Day (a) |
− | 3 | + | ||1 |
− | 4 | + | ||2 |
− | 5 | + | ||3 |
− | + | ||4 | |
− | Total Meals (b) | + | ||5 |
− | 3 | + | |- |
− | 6 | + | |style="background-color:#D9D9D9;"|Total Meals (b) |
− | 9 | + | ||3 |
− | __ | + | ||6 |
− | __ | + | ||9 |
− | + | ||__ | |
+ | ||__ | ||
+ | |} | ||
** Here is a way to show the ratio / compare the two numbers. The first row is a and the second row is b (<u>a</u>/<u><u>b</u></u>, 5/b, 5/15). | ** Here is a way to show the ratio / compare the two numbers. The first row is a and the second row is b (<u>a</u>/<u><u>b</u></u>, 5/b, 5/15). | ||
Line 2,045: | Line 1,645: | ||
|- | |- | ||
− | || | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Highlight text that provide important information. | * Highlight text that provide important information. | ||
* Provide visual representations (e.g., grids) of problem with symbols. | * Provide visual representations (e.g., grids) of problem with symbols. | ||
* Tables (vertical or horizontal) with two labeled columns/rows to illustrate the ratio (e.g., Maria stamps three letters every minute which we write as 3:1. Show me the letters she stamps in a minute.). | * Tables (vertical or horizontal) with two labeled columns/rows to illustrate the ratio (e.g., Maria stamps three letters every minute which we write as 3:1. Show me the letters she stamps in a minute.). | ||
− | + | {|border =1px solid black style="border-collapse:collapse;" | |
− | Minutes | + | |- |
− | + | |style="background-color:#D9D9D9;"|Stamps | |
− | 3 | + | |style="background-color:#D9D9D9;"|Minutes |
− | 1 | + | |- |
− | + | ||3 | |
− | __ | + | ||1 |
− | 2 | + | |- |
− | + | ||__ | |
− | __ | + | ||2 |
− | 3 | + | |- |
− | + | ||__ | |
+ | ||3 | ||
+ | |} | ||
* Voice output devices or talking software | * Voice output devices or talking software | ||
* Calculator | * Calculator | ||
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* Assistive Technology | * Assistive Technology | ||
* Highlight text using tape, pen, computer highlighting | * Highlight text using tape, pen, computer highlighting | ||
+ | |} | ||
+ | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | ||
− | + | [[Category: Element Cards]] | |
− | + | [[Category: Math]] | |
− | + |
Latest revision as of 14:54, 29 May 2014
BACK TO Element Cards
Contents |
[edit] Teaching Fractions
All of the CCCs in this document relate to teaching Fractions. Below are some additional resources that may be helpful: NCSC Curriculum Resource Guide: Fractions and Decimals NCSC Content Module: Fractions and Decimals
[edit] Websites
http://www.teachingideas.co.uk/maths/contents_fractions.htm
http://www.mathsisfun.com/converting-decimals-fractions.html
http://www.mathplayground.com/
[edit] Other Resources
http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf
http://www.ncpublicschools.org/acre/standards/common-core-tools/
[edit] CCC Mathematics: Number Operations (Fractions)
CCSS: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | ||
CCC: | 3.NO.1l1 | Identify the number of highlighted parts (numerator) of a given representation (rectangles and circles). |
Strand: Number Operations (Fractions, Ratios, Proportions) | Family: Representing | |
Progress Indicator: E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | ||
CCC: | 3.NO.1l2 | Identify the total number of parts (denominator) of a given representation (rectangles and circles). |
Strand: Number Operations (Fractions, Ratios, Proportions) | Family: Representing | |
Progress Indicator: E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitions into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | ||
CCC: | 3.NO.1l3 | Identify the fraction that matches the representation (rectangles and circles; halves, fourths, and thirds, eighths). |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Representing | |
Progress Indicator: E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
CCSS: 3.NF.2a and 2b Understand a fraction as a number on the number line; represent fractions on a number line diagram.
| ||
CCC: | 3.NO.1l4 | Identify that a part of a rectangle can be represented as a fraction that has a value between 0 and 1. |
Strand: Number Operations (Fractions, Ratios, Proportions) | Family: Representing | |
Progress Indicator: E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | ||
CCC: | 4.NO.1n1 | Select a model of given fraction (halves, thirds, fourths, sixths, eighths). |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Representing | |
Progress Indicator: E.NO.1n Comparing and modeling fractions, including with different denominators | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Instructional Strategies:
| ||
Supports and Scaffolds:
|
*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 5.NBT.3a Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., . | ||
CCC: | 5.NO.1b1 | Read, write, or select a decimal to the hundredths place. |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Representing | |
Progress Indicator: M.NO.1b Extending place value understanding to reading (e.g., naming the values with number words, rather than "point four"), writing, comparing, and rounding decimals | ||
Essential Understandings | Concrete Understandings:
|
Representation:
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Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram | ||
CCC: | 5.NO.1c1 | Rewrite a fraction as a decimal |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Determining Equivalency | |
Progress Indicator: M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
CCSS: 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | ||
CCC: | 3.SE.1g1 | Use =, <, or > to compare 2 fractions with the same numerator or denominator. |
Strand: Symbolic Expression | Family: Determining Equivalency | |
Progress Indicator: E.SE.1g Using symbols (=, >, <) to compare whole numbers, fractions, or decimals; write equations; and express inverse or related operations | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | ||
CCC: | 4.SE.1g2 | Use =, <, or > to compare 2 fractions (fractions with a denominator of 10 or less). |
Strand: Symbolic Expression | Family: Determining Equivalency | |
Progress Indicator: E.SE.1g Using symbols (=, >, <) to compare whole numbers, fractions, or decimals; write equations; and express inverse or related operations | ||
Essential Understandings | Concrete Understandings:
|
Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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CCC: | 4.NO.1l6 | Locate fractions on a number line |
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |
Progress Indicator: E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers | ||
Essential Understandings | Concrete Understandings:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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CCC: | 4.NO.1l7 | Order fractions on a number line |
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |
Progress Indicator: E.NO.1l Identifying and locating fractions on the number line or as regions, or parts of a set or unit, and recognizing that whole numbers are a subset of rational numbers | ||
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CCSS: 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | |||||||||||||||||||||||||||||||||||||||||||||||
CCC: | 4.NO.1m1 | Determine equivalent fractions. | |||||||||||||||||||||||||||||||||||||||||||||
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Determining Equivalency | ||||||||||||||||||||||||||||||||||||||||||||||
Progress Indicator: E.NO.1m Composing and representing equivalent fractions in the form a/b | |||||||||||||||||||||||||||||||||||||||||||||||
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fractions such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | ||
CCC: | 4.NO.1n2 | Compare 2 given fractions that have different denominators. |
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |
Progress Indicator: E.NO.1n Comparing and modeling fractions, including with different denominators | ||
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CCSS: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Examples: 3/8 = 1/8 + 1/8 + 1/8 3/8 = 1/8 + 2/8 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. | ||
CCC: | 4.NO.2g1 | Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼). |
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |
Progress Indicator: E.NO.2g Recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions | ||
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CCSS: 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | ||
CCC: | 5.NO.1c1 | Rewrite a fraction as a decimal. |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Determining Equivalency | |
Progress Indicator: M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line | ||
Essential Understandings | Concrete Understandings:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | ||
CCC: | 5.NO.1c2 | Rewrite a decimal as a fraction. |
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |
Progress Indicator: M.NO.1c Using a variety of fractional and decimal representations and locating them on a number line | ||
Essential Understandings | Concrete Understandings:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. | ||
CCC: | 5.NO.2c2 | Solve word problems involving the addition, subtraction, multiplication or division of fractions. |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Problem Solving | |
Progress Indicator: .NO.1c Using a variety of fractional and decimal representations and locating them on a number line | ||
Essential Understandings | Concrete Understandings:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 6.RP.3a Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
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CCC: | 6.NO.1f4 | Find a missing value (representations, whole numbers, common fractions, decimals to hundredths place, percent) for a given ratio. | ||||||||||
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |||||||||||
Progress Indicator: M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems | ||||||||||||
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CCSS: 7.RP.2 Recognize and represent proportional relationships between quantities.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. | ||
CCC: | 7.NO.2f1 | Identify the proportional relationship between two quantities. |
Strand: Number Operations (Fractions/ratios/Proportions) | Family: Determining Equivalency | |
Progress Indicator: M.NO.2f Describing proportional relationships and solving related problems | ||
Essential Understandings | Concrete Understandings:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." | ||
CCC: | 7.NO.2f2 | Determine if two quantities are in a proportional relationship using a table of equivalent ratios or points graphed on a coordinate plane. |
Strand: Number Operations (Fractions, Ration, Proportions) | Family: Determining Equivalency | |
Progress Indicator: M.NO.1f Recognizing equivalence of representations using fractions, decimals, and percents and using them solve ratio problems | ||
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CCSS: 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. | ||
CCC: | 4.NO.2h1 | Add and subtract fractions with like denominators of (2, 3, 4, or 8). |
Strand: Number Operations (Fractions, Ratios, Proportions). | Family: Performing Operations | |
Progress Indicator: E.NO.2h Adding, subtracting, and multiplying fractions, including mixed numbers | ||
Essential Understandings | Concrete Understandings:
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. | ||
CCC: | 4.NO.2h2 | Add and subtract fractions with like denominators (2, 3, 4, or 8) using representations. |
Strand: Number Operations (Fractions, Ratios, Proportions). | Family: Performing Operations | |
Progress Indicator: E.NO.2h Adding, subtracting, and multiplying fractions, including mixed numbers | ||
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | ||
CCC: | 5.NO.2c1 | Solve 1 step problems using decimals. |
Strand: Number Operations (Fractions, Ratios, Proportions). | Family: Performing Operations | |
Progress Indicator: M.NO.2c Using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths) | ||
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | ||
CCC: | 6.NO.2c3 | Solve one step, addition, subtraction, multiplication, or division problems with fractions or decimals. |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Performing Operations | |
Progress Indicator: M.NO.2c Using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths) | ||
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. | ||
CCC: | 8.NO.2i4 | Solve two step addition, subtraction, multiplication, and division problems with fractions, decimals, or positive/negative numbers. |
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Performing Operations | |
Progress Indicator: M.NO.2i Using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line | ||
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*Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies.
CCSS: 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. | ||||||||||||||
CCC: | 7.NO.2f6 | Solve word problems involving ratios. | ||||||||||||
Strand: Number Operations (Fractions/Ratios/Proportions) | Family: Problem Solving | |||||||||||||
'Progress Indicator:'' M.NO.2f Describing proportional relationships and solving related problems' | ||||||||||||||
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