Element Cards Number Operations Fractions
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=Teaching Fractions= | =Teaching Fractions= | ||
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| 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. | | 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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− | | 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., 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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* 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]] | ||
* 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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| colspan=3|'''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 | ||
− | * 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 Fractions2.jpg|Grid of 100 squares with 40 filled in, indicating 40%]] |
− | * Bundles of 10s and 100s [[File: | + | * 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]] | ||
* Number line | * Number line | ||
* Hundreds chart | * Hundreds chart | ||
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| colspan=3|'''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> | |
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| colspan=3|'''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> | |
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− | || | + | |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. | ||
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* Multiplication tables (e.g., 1 to 4 has the same ratio as 2 to 8) | * Multiplication tables (e.g., 1 to 4 has the same ratio as 2 to 8) | ||
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| 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'' | | 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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* 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]] | ||
* 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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{|border=1 | {|border=1 | ||
| 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. | | 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> | |
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||'''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;" |
− | hours | + | |- |
− | + | ||Inches of snow | |
− | 2 | + | ||hours |
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− | ? | + | ||? |
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* Vocabulary | * Vocabulary | ||
** ratio (e.g., 2:1, 1:1) | ** ratio (e.g., 2:1, 1:1) | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''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. | ||
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− | + | [[File:Element Cards Number Operations Fractions5.PNG|One shopping cart and two traffic cones. What is the ratio?]] | |
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||'''Representation:''' | ||'''Representation:''' | ||
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* 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.]] | ||
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| colspan=3|'''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.'' | ||
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| colspan=3|'''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.'' | ||
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<nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | <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 | ||
| 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. | | 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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* 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:''' | ||
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** Determine the relationship between "a" and "b" (a x __ = b) | ** Determine the relationship between "a" and "b" (a x __ = b) | ||
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− | Total Meals (b) | + | ||5 |
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− | 6 | + | |style="background-color:#D9D9D9;"|Total Meals (b) |
− | 9 | + | ||3 |
− | __ | + | ||6 |
− | __ | + | ||9 |
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+ | |} | ||
** 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). | ||
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* 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; " | + | {|border =1px solid black style="border-collapse:collapse;" |
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|style="background-color:#D9D9D9;"|Stamps | |style="background-color:#D9D9D9;"|Stamps | ||
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* Assistive Technology | * Assistive Technology | ||
* Highlight text using tape, pen, computer highlighting | * Highlight text using tape, pen, computer highlighting | ||
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<nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | <nowiki>*</nowiki>Refer to the NCSC Instructional Resource Guide for additional information about systematic instruction strategies. | ||
− | [[Category: | + | [[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:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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* 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:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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* 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:
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CCSS: 3.NF.2a and 2b Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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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:
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*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:
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*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:
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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.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 | ||
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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:
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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 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:
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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 | ||
Essential Understandings | Concrete Understandings:
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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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Representation:
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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 | ||
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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 | ||
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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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