Element Cards Measurement
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{{BACK TO|[[Element Cards]]}} | {{BACK TO|[[Element Cards]]}} | ||
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=Teaching Measurement= | =Teaching Measurement= | ||
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[http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | [http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | ||
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=CCC Mathematics: Measurement= | =CCC Mathematics: Measurement= | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS''': K.MD.A.2: Describe and compare measurable attributes.''' '''Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. ''For example, directly compare the heights of two children and describe one child as taller/shorter.'' |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||K.ME.1b2 |
− | | | + | ||Compare 2 objects with a measurable attribute in common to see which object has more/less of the attribute (length, height, weight). |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#E5DFEC;" colspan=2|'''Family:''' Sorting and Classifying | | style="background-color:#E5DFEC;" colspan=2|'''Family:''' Sorting and Classifying | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1b''' '''Comparing and ordering objects/events according to their specified attributes (using standard or non-standard units of measure), including indirectly by using a third object, or using common referents to estimate or compare'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Use connecting objects, e.g., cubes, to measure attributes of distance (length, height) by counting the number of objects needed to measure. | * Use connecting objects, e.g., cubes, to measure attributes of distance (length, height) by counting the number of objects needed to measure. | ||
* Use a scale to compare the weight of two objects. | * Use a scale to compare the weight of two objects. | ||
− | | | + | ||'''Representation:''' |
* Select representation of more and less, short and long, heavy and light; tall and short. | * Select representation of more and less, short and long, heavy and light; tall and short. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts (e.g., "Start by putting the shortest item in place like this…")<nowiki>*</nowiki> | * Least-to-Most prompts (e.g., "Start by putting the shortest item in place like this…")<nowiki>*</nowiki> | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Graphic organizer with more or less representations to prompt understanding | * Graphic organizer with more or less representations to prompt understanding | ||
* Unifix cube wands to compare lengths (same size same color – additional cubes in another color) | * Unifix cube wands to compare lengths (same size same color – additional cubes in another color) | ||
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* Yard sticks | * Yard sticks | ||
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|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 1.MD.A.1: Measure lengths indirectly and by iterating length units. Order three objects by length; compare the lengths of two objects indirectly by using a third object. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||1.ME.1b3 |
− | | | + | ||Order up to 3 objects based on a measurable attribute (height, weight, length). |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#E5DFEC;" colspan=2|'''Family:''' Sorting and Classifying | | style="background-color:#E5DFEC;" colspan=2|'''Family:''' Sorting and Classifying | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1b Comparing and ordering objects/events according to their specified attributes (using standard or non-standard units of measure), including indirectly by using a third object, or using common referents to estimate or compare'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Use connecting objects, e.g., cubes, to measure attributes of distance, length, and height | * Use connecting objects, e.g., cubes, to measure attributes of distance, length, and height | ||
* Use a scale to compare the weight of two objects. | * Use a scale to compare the weight of two objects. | ||
− | | | + | ||'''Representation:''' |
* Select representation of more and less, short and long, heavy and light; tall and short. | * Select representation of more and less, short and long, heavy and light; tall and short. | ||
* Apply understanding that if object 1 is longer/heavier than object 2 and object 2 is longer/heavier than object 3, then object 1 must be longer than object 3. | * Apply understanding that if object 1 is longer/heavier than object 2 and object 2 is longer/heavier than object 3, then object 1 must be longer than object 3. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts (e.g., "Start by putting the shortest item in place like this…")<nowiki>*</nowiki> | * Least-to-Most prompts (e.g., "Start by putting the shortest item in place like this…")<nowiki>*</nowiki> | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds''': |
* Sequencing Template for short - tall with graphic representations to prompt understanding | * Sequencing Template for short - tall with graphic representations to prompt understanding | ||
* Number line | * Number line | ||
* Measuring tools | * Measuring tools | ||
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|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 1.MD.A.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number''' '''of same-size length units that span it with no gaps or overlaps. ''Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.'' |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||1.ME.1c1 |
− | | | + | ||Compare 2 units of measurement and identify which unit would require more or less when measuring a selected object. (I can measure with paper clips or markers. Which unit will require more to measure the table?) |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
− | | | + | | colspan=2|'''Family:''' Measuring using Tools |
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1c''' '''Recognizing that the smaller the unit, the more units are needed to measure an object; and that units can be decomposed/partitioned into smaller units'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Understand that smaller units will require more to measure an object than using larger units to measure the same object. | * Understand that smaller units will require more to measure an object than using larger units to measure the same object. | ||
* Use connecting objects, e.g., cubes, to measure attributes of distance, length, and height. | * Use connecting objects, e.g., cubes, to measure attributes of distance, length, and height. | ||
− | | | + | ||'''Representation:''' |
* Select the number that represents the number of units used to measure the length of an item. | * Select the number that represents the number of units used to measure the length of an item. | ||
* Understand the concept of more and less. | * Understand the concept of more and less. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts (e.g., "Start by filling in the first row of the template with paperclips like this…")<nowiki>*</nowiki> | * Least-to-Most prompts (e.g., "Start by filling in the first row of the template with paperclips like this…")<nowiki>*</nowiki> | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds''': |
* Measuring template (i.e., length of item being measured: 1<sup>st</sup> row segmented into sections for paperclips; 2<sup>nd</sup> row segmented into sections for markers) | * Measuring template (i.e., length of item being measured: 1<sup>st</sup> row segmented into sections for paperclips; 2<sup>nd</sup> row segmented into sections for markers) | ||
* Measuring stick made of Unifix cubes | * Measuring stick made of Unifix cubes | ||
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|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS''': 1.MD.A.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number''' '''of same-size length units that span it with no gaps or overlaps. ''Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.'' |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||1.ME.2a1 |
− | | | + | ||Measure using copies of one object to measure another. |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#7030A0;" colspan=2|'''Family:''' Scaling and Unit Conversions | | style="background-color:#7030A0;" colspan=2|'''Family:''' Scaling and Unit Conversions | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.2a Applying nonstandard and common standard units to measure or estimate (length, height, weight, time)'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Counting up to --- objects | * Counting up to --- objects | ||
* Identify the beginning and end point that needs to be measured. | * Identify the beginning and end point that needs to be measured. | ||
* Recognize that an object can be measured by lining up multiple objects of the same size without gaps or overlaps. | * Recognize that an object can be measured by lining up multiple objects of the same size without gaps or overlaps. | ||
− | | | + | ||'''Representation:''' |
* Select the numeric symbol that represents the number of units used to measure the length of an item. | * Select the numeric symbol that represents the number of units used to measure the length of an item. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts (e.g., "Start by placing a paperclip next to the item like this…")<nowiki>*</nowiki> | * Least-to-Most prompts (e.g., "Start by placing a paperclip next to the item like this…")<nowiki>*</nowiki> | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds''': |
* Measuring template (i.e., length of item being measured –segmented into sections the size of paperclips) | * Measuring template (i.e., length of item being measured –segmented into sections the size of paperclips) | ||
* Measuring stick made of Unifix cubes | * Measuring stick made of Unifix cubes | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS''': 2.MD.A.1: Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||2.ME.1a3 |
− | | | + | ||Select appropriate unit of measurement to measure an object (ruler or yard stick; inches or feet). |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#E5DFEC;" colspan=2|'''Family:''' Sorting and Classifying | | style="background-color:#E5DFEC;" colspan=2|'''Family:''' Sorting and Classifying | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1a Recognizing, identifying, and describing the measurable attributes of objects'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Understand that smaller units are part of larger units within the same system (12 inches = 1 foot). | * Understand that smaller units are part of larger units within the same system (12 inches = 1 foot). | ||
* Identify the smaller and/or larger unit (e.g., inches are smaller than feet). | * Identify the smaller and/or larger unit (e.g., inches are smaller than feet). | ||
* Understand that they should use the unit of measure that will require fewer units to measure objects. | * Understand that they should use the unit of measure that will require fewer units to measure objects. | ||
− | | | + | ||'''Representation:''' |
* Select the numeric symbol that represents the number of units that make up a larger unit of measure. | * Select the numeric symbol that represents the number of units that make up a larger unit of measure. | ||
* Select representation of larger units of measure within a system of measurement. | * Select representation of larger units of measure within a system of measurement. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
''<nowiki>*</nowiki> This should be to "nearest whole unit" – in grade 2 we do not measure fractions/parts of a unit'' | ''<nowiki>*</nowiki> This should be to "nearest whole unit" – in grade 2 we do not measure fractions/parts of a unit'' | ||
* Model-Lead-Test ("Watch me…do together….you try") | * Model-Lead-Test ("Watch me…do together….you try") | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds''': |
* Foldable ruler | * Foldable ruler | ||
* Measuring stick made of Unifix cubes | * Measuring stick made of Unifix cubes | ||
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* Color coded units (inches=red, feet=blue, yards=green) | * Color coded units (inches=red, feet=blue, yards=green) | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS''': 2.MD.A.2: Measure and estimate lengths in standard units. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. |
|- | |- | ||
− | | | + | ||'''CCC''': |
− | | | + | ||2.ME.1c3 |
− | | | + | ||Recognize that standard units can be decomposed into smaller units. |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
− | | | + | | colspan=2|'''Family:''' Measuring using Tools |
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1c''' '''Recognizing that the smaller the unit, the more units are needed to measure an object; and that units can be decomposed/partitioned into smaller units'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Understand that smaller numbers are part of larger numbers (e.g., 5 can be made of 4 and 1 or 3 and 2, etc.). | * Understand that smaller numbers are part of larger numbers (e.g., 5 can be made of 4 and 1 or 3 and 2, etc.). | ||
* Within the same system of measurement identify the smaller or larger unit—inches are shorter than feet, feet are shorter than yards, etc. | * Within the same system of measurement identify the smaller or larger unit—inches are shorter than feet, feet are shorter than yards, etc. | ||
− | | | + | ||'''Representation:''' |
* Select the numeric symbol that represents the number of units that make up a larger unit of measure. | * Select the numeric symbol that represents the number of units that make up a larger unit of measure. | ||
* Understand that multiple units make up a larger unit of measure (12 inches in 1 foot). | * Understand that multiple units make up a larger unit of measure (12 inches in 1 foot). | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts (e.g., "Put an inch on the ruler like this…")<nowiki>*</nowiki> | * Least-to-Most prompts (e.g., "Put an inch on the ruler like this…")<nowiki>*</nowiki> | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Foldable ruler | * Foldable ruler | ||
* Measuring stick made of Unifix cubes | * Measuring stick made of Unifix cubes | ||
* Interactive whiteboard or other technology | * Interactive whiteboard or other technology | ||
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|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS''': 2.MD.A.4: Measure and estimate lengths in standard units. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. |
|- | |- | ||
− | | | + | ||'''CCC''': |
− | | | + | ||2.ME.2a4 |
− | | | + | ||Solve one step subtraction problems involving the difference of the lengths of 2 objects in standard length units |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#B2A1C7;" colspan=2|'''Family:''' Problem Solving using Measurement Process | | style="background-color:#B2A1C7;" colspan=2|'''Family:''' Problem Solving using Measurement Process | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.2a Applying nonstandard and common standard units to measure or estimate (length, height, weight, time)'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Understand that smaller numbers are part of larger numbers (e.g., 5 can be made of 4 and 1 or 3 and 2, etc.). | * Understand that smaller numbers are part of larger numbers (e.g., 5 can be made of 4 and 1 or 3 and 2, etc.). | ||
* Identify the smaller unit (e.g., inches are smaller than feet). | * Identify the smaller unit (e.g., inches are smaller than feet). | ||
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* Recognize that when we compare lengths we want to answer "How much longer is object 1 than object 2?" | * Recognize that when we compare lengths we want to answer "How much longer is object 1 than object 2?" | ||
− | | | + | ||'''Representation:''' |
* Represent the numeric symbol by breaking the whole into the corresponding number of parts. | * Represent the numeric symbol by breaking the whole into the corresponding number of parts. | ||
* Select the numeric symbol that represents the differences. | * Select the numeric symbol that represents the differences. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts to use the foldable ruler<nowiki>*</nowiki> | * Least-to-Most prompts to use the foldable ruler<nowiki>*</nowiki> | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Foldable ruler | * Foldable ruler | ||
* Measuring stick made of Unifix cubes (use two colors to reflect those taken away) | * Measuring stick made of Unifix cubes (use two colors to reflect those taken away) | ||
* Talking ruler | * Talking ruler | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||3.ME.1d2 |
− | | | + | ||Measure area of rectilinear figures by counting squares. |
|- | |- | ||
− | | | + | ||'''Strand: '''Measurement |
− | | | + | | colspan=2|'''Family:''' Measuring Using Tools |
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1d''' '''Describing and demonstrating: unit attributes, iterating, tiling, identical units, number line intervals, standardization, proportionality, additivity, and origin'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Count up to 20 objects. | * Count up to 20 objects. | ||
* Identify the area on a surface (e.g., piece of paper). | * Identify the area on a surface (e.g., piece of paper). | ||
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* Decompose rectangles within a rectilinear figure. | * Decompose rectangles within a rectilinear figure. | ||
− | | | + | ||'''Representation:''' |
* Select the numeric symbol that represents the number of squares used to find area of a figure. | * Select the numeric symbol that represents the number of squares used to find area of a figure. | ||
* Count to find the area of a rectangle when given a picture or array. | * Count to find the area of a rectangle when given a picture or array. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Use Least Intrusive Prompts (e.g., "Put a tile on like this…")<nowiki>*</nowiki> | * Use Least Intrusive Prompts (e.g., "Put a tile on like this…")<nowiki>*</nowiki> | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* 1 inch tiles | * 1 inch tiles | ||
* 1 inch tiles that are numbered | * 1 inch tiles that are numbered | ||
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* Counting sheet that allows students to mark the tiles that have been counted | * Counting sheet that allows students to mark the tiles that have been counted | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. |
4.MD.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. ''For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.'' | 4.MD.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. ''For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.'' | ||
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||4.ME.1g2 |
− | | | + | ||Solve word problems using perimeter and area where changes occur to the deminsions of a rectilinear figure. |
|- | |- | ||
− | | | + | ||'''Strand: '''Measurement |
| style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | | style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''E.ME.1g''' '''Exploring what happens to 2‐dimensional measurements (perimeter or area) when the dimensions of the figure are changed '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Decompose a rectilinear figure into rectangles | * Decompose a rectilinear figure into rectangles | ||
* Identify the perimeter of a rectilinear figure | * Identify the perimeter of a rectilinear figure | ||
* Identify the area of a rectilinear figure | * Identify the area of a rectilinear figure | ||
− | | | + | ||'''Representation:''' |
* Understand the following concepts and vocabulary (pictures/symbols): area, perimeter, length, width, side, +, -, X, ÷ | * Understand the following concepts and vocabulary (pictures/symbols): area, perimeter, length, width, side, +, -, X, ÷ | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis (solving problems using formulas); isolate each step of the solution process | * Task analysis (solving problems using formulas); isolate each step of the solution process | ||
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
Line 439: | Line 441: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Premade formula worksheets | * Premade formula worksheets | ||
* Calculator | * Calculator | ||
Line 450: | Line 452: | ||
* Interactive whiteboard, PowerPoint, or other visual demonstrating how squares change to rectangles when 2 sides are elongated | * Interactive whiteboard, PowerPoint, or other visual demonstrating how squares change to rectangles when 2 sides are elongated | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
− | |||
===Additional Resource=== | ===Additional Resource=== | ||
+ | |||
[http://www.khake.com/page47.html http://www.khake.com/page47.html] | [http://www.khake.com/page47.html http://www.khake.com/page47.html] | ||
+ | |||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||5.ME.2a1 |
− | | | + | ||Solve problems involving conversions of standard measurement units of area, volume, time, mass in the same system. |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#7030A0;" colspan=2|'''Family:''' Scaling and Unit Conversions | | style="background-color:#7030A0;" colspan=2|'''Family:''' Scaling and Unit Conversions | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.2a Selecting and applying appropriate standard units, tools,and level of precision in real-world measurment problems (e.g., area, surface area, volume, rate) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Match like units of measurement within a measurement system (e.g., hours to minutes, inches to feet). | * Match like units of measurement within a measurement system (e.g., hours to minutes, inches to feet). | ||
− | | | + | ||'''Representation:''' |
* Use various strategies to add, subtract, multiply, and divide. | * Use various strategies to add, subtract, multiply, and divide. | ||
* Use a pictorial representation of a ratio to make conversions. | * Use a pictorial representation of a ratio to make conversions. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis for problem solving | * Task analysis for problem solving | ||
* Model-Lead-Test<nowiki>*</nowiki> | * Model-Lead-Test<nowiki>*</nowiki> | ||
Line 495: | Line 498: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Calendar | * Calendar | ||
* Calculator | * Calculator | ||
Line 506: | Line 509: | ||
* Cups and buckets to measure volume | * Cups and buckets to measure volume | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||5.ME.1b2 |
− | | | + | ||Convert standard measurements of length. |
|- | |- | ||
− | | | + | ||'''Strand: '''Measurement |
| style="background-color:#7030A0;" colspan=2|'''Family: '''Scaling and Unit Conversions | | style="background-color:#7030A0;" colspan=2|'''Family: '''Scaling and Unit Conversions | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.1b''' '''Recognizing relationships among units and using proportional reasoning to convert measurements from one unit to another within the same system '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Recognize that in the same system, I can measure the same object with 2 different units (e.g., I can measure the height of a desk in both inches and feet). | * Recognize that in the same system, I can measure the same object with 2 different units (e.g., I can measure the height of a desk in both inches and feet). | ||
− | | | + | ||'''Representation:''' |
* Understand the following concepts and vocabulary: conversion, inch, foot, yard | * Understand the following concepts and vocabulary: conversion, inch, foot, yard | ||
* Understand standard units and abbreviations (e.g., feet=ft) | * Understand standard units and abbreviations (e.g., feet=ft) | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Multiple exemplar training (e.g., "This is an inch, this is an inch…this is not an inch, show me an inch.")<nowiki>*</nowiki> | * Multiple exemplar training (e.g., "This is an inch, this is an inch…this is not an inch, show me an inch.")<nowiki>*</nowiki> | ||
* Task analysis steps to convert from inches to feet using a table | * Task analysis steps to convert from inches to feet using a table | ||
Line 547: | Line 550: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Conversion table, adapted or un-adapted measuring tools | * Conversion table, adapted or un-adapted measuring tools | ||
* Calculator | * Calculator | ||
Line 556: | Line 559: | ||
* Rulers with limited measurement (e.g., only 1 inch and ½ inch tabs) | * Rulers with limited measurement (e.g., only 1 inch and ½ inch tabs) | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||6.ME.2b2 |
− | | | + | ||Decompose complex shapes (polygon, trapezoid, pentagon) into simple shapes (rectangles, squares, triangles) to measure area. |
|- | |- | ||
− | | | + | ||'''Strand: '''Measurement |
| style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | | style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.2b Using a variety of strategies (decomposing complex shapes, using formulas and models) to measure area (triangles, quadrilaterals, polygons) and volume (rectangular prisms) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Recognize simple shapes within a larger shape. | * Recognize simple shapes within a larger shape. | ||
* Identify the dimensions (base, height, length, width, etc.) of smaller shapes. | * Identify the dimensions (base, height, length, width, etc.) of smaller shapes. | ||
* Multiply fractions and whole numbers. | * Multiply fractions and whole numbers. | ||
− | | | + | ||'''Representation:''' |
* Given a picture identify the dimensions of 2-D and 3-D shapes. | * Given a picture identify the dimensions of 2-D and 3-D shapes. | ||
* Understand the following concepts and vocabulary: polygon, trapezoid, pentagon, rectangles, squares, triangles, area. | * Understand the following concepts and vocabulary: polygon, trapezoid, pentagon, rectangles, squares, triangles, area. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis to apply strategies for taking apart shapes | * Task analysis to apply strategies for taking apart shapes | ||
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
Line 601: | Line 604: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* 1 inch tiles | * 1 inch tiles | ||
* Raised grid with numbered squares | * Raised grid with numbered squares | ||
Line 611: | Line 614: | ||
* Use real-world examples (cutting a magazine clipping to fit onto a card that is a simple shape) | * Use real-world examples (cutting a magazine clipping to fit onto a card that is a simple shape) | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 6.RP.A.3b Use ratio and rate reasoning to solve real-world and mathematical problems, (e.g., by reasoning about tables of equivalent rations, tape diagrams, double number line diagrams, or equations). Solve unit rate problems including those involving unit pricing and constant speed. ''For example, if it took 7 hours to mow 4 lawns, then at that rate how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?'' |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||6.ME.2a2 |
− | | | + | ||Solve one step real-world measurement problems involving unit rates with ratios of whole numbers when given the unit rate (3 inches of snow falls per hour, how much in 6 hours) |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#7030A0;" colspan=2|'''Family: '''Scaling and Unit Conversions | | style="background-color:#7030A0;" colspan=2|'''Family: '''Scaling and Unit Conversions | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.2a''' '''Selecting and applying appropriate standard units, tools,and level of precision in real-world measurment problems (e.g., area, surface area, volume, rate) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Multiply using concrete objects. | * Multiply using concrete objects. | ||
* Divide using concrete objects. | * Divide using concrete objects. | ||
* Use a ratio to solve a measurement conversion problem. | * Use a ratio to solve a measurement conversion problem. | ||
− | | | + | ||'''Representation:''' |
* Multiply whole numbers. | * Multiply whole numbers. | ||
* Divide whole numbers. | * Divide whole numbers. | ||
Line 647: | Line 650: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis for problem solving (formula) | * Task analysis for problem solving (formula) | ||
* Model-Lead-Test<nowiki>*</nowiki> | * Model-Lead-Test<nowiki>*</nowiki> | ||
Line 655: | Line 658: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Premade function table | * Premade function table | ||
* Conversion chart | * Conversion chart | ||
Line 662: | Line 665: | ||
* Counters and graphic representation of ratios | * Counters and graphic representation of ratios | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||7.ME.2d1 |
− | | | + | ||Apply formula to measure area and circumference of circles. |
|- | |- | ||
− | | | + | ||'''Strand: '''Measurement |
| style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | | style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.2d Using various strategies (decomposing complex shapes, using formulas) to measure volume (cones, cylinders, spheres) and area and circumference of circles '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Identify the radius and diameter of a circle. | * Identify the radius and diameter of a circle. | ||
* Multiply decimals and whole numbers. | * Multiply decimals and whole numbers. | ||
− | | | + | ||'''Representation:''' |
* Recognize the meaning of terms used in formulas as labeled representations related to circles. | * Recognize the meaning of terms used in formulas as labeled representations related to circles. | ||
* Understand the following concepts and vocabulary: circumference, area, pi, and radius. | * Understand the following concepts and vocabulary: circumference, area, pi, and radius. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis with formula | * Task analysis with formula | ||
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
Line 703: | Line 707: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Calculator | * Calculator | ||
* Graphic of circle | * Graphic of circle | ||
Line 712: | Line 716: | ||
* Real-world materials | * Real-world materials | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and mathematical problems. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||8.ME.2d2 |
− | | | + | ||Apply the formula to find the volume of 3-dimensional shapes (i.e., cubes, spheres, and cylinders) |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#5F497A;" colspan=2|'''Family:''' Perimeter, Area, and Volume Problems | | style="background-color:#5F497A;" colspan=2|'''Family:''' Perimeter, Area, and Volume Problems | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.2d''' '''Using various strategies (decomposing complex shapes, using formulas) to measure volume (cones, cylinders, spheres) and area and circumference of circles '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Recognize attributes of a 3-dimensional shape. | * Recognize attributes of a 3-dimensional shape. | ||
* Multiply whole numbers, fractions, and decimals. | * Multiply whole numbers, fractions, and decimals. | ||
− | | | + | ||'''Representation:''' |
* Recognize that volume of 3-D shapes can be found by finding the area of the base and multiplying that by the height. | * Recognize that volume of 3-D shapes can be found by finding the area of the base and multiplying that by the height. | ||
* Understand the following concepts and vocabulary: volume, cylinder, cone, height, radius, circumference, cube, sphere, side, pi | * Understand the following concepts and vocabulary: volume, cylinder, cone, height, radius, circumference, cube, sphere, side, pi | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis for applying formula | * Task analysis for applying formula | ||
* Model-Lead-Test<nowiki>*</nowiki> | * Model-Lead-Test<nowiki>*</nowiki> | ||
Line 754: | Line 758: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Cones, cylinders, cubes, and spheres in differing sizes and textures | * Cones, cylinders, cubes, and spheres in differing sizes and textures | ||
* Cardboard models that can be folded to make 3-dimensional shapes | * Cardboard models that can be folded to make 3-dimensional shapes | ||
Line 760: | Line 764: | ||
* Calculator | * Calculator | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 8.G.C.4 Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||8.ME.1e1 |
− | | | + | ||Describe the changes in surface area, area, and volume when the figure is changed in some way (e.g., scale drawings). |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#7030A0;" colspan=2|'''Family: '''Scaling and Unit Conversions | | style="background-color:#7030A0;" colspan=2|'''Family: '''Scaling and Unit Conversions | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''M.ME.1e Exploring what happens to 2‐ and 3‐ dimensional measurements (such as surface area, area, and volume) when the figure is changed in some way (e.g., scale drawings)'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Recognize how the space inside a figure increases when the sides are lengthened. | * Recognize how the space inside a figure increases when the sides are lengthened. | ||
* Multiply whole numbers, fractions, and decimals. | * Multiply whole numbers, fractions, and decimals. | ||
* Apply formulas to find surface area, area, volume of figures. | * Apply formulas to find surface area, area, volume of figures. | ||
− | | | + | ||'''Representation:''' |
* Given a picture, identify dimensions needed to calculate surface area, area, and volume. | * Given a picture, identify dimensions needed to calculate surface area, area, and volume. | ||
* Compare greater than, less than, equal/same squares and rectangles in 2 and 3 dimensions. | * Compare greater than, less than, equal/same squares and rectangles in 2 and 3 dimensions. | ||
Line 796: | Line 800: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | * Model-Lead-Test ("Watch me…do together….you try")<nowiki>*</nowiki> | ||
* Least-to-Most prompts <nowiki>*</nowiki> | * Least-to-Most prompts <nowiki>*</nowiki> | ||
Line 803: | Line 807: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Hollow square and rectangular boxes | * Hollow square and rectangular boxes | ||
* Blocks or tiles to place in the boxes | * Blocks or tiles to place in the boxes | ||
Line 813: | Line 817: | ||
* Real-world materials | * Real-world materials | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3|'''CCSS:''' HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||H.ME.1a2 |
− | | | + | ||Solve real-world problems involving units of measurement. |
|- | |- | ||
− | | | + | ||'''Strand:''' Measurement |
| style="background-color:#B2A1C7;" colspan=2|'''Family: '''Problem Solving Using Measurement Processes | | style="background-color:#B2A1C7;" colspan=2|'''Family: '''Problem Solving Using Measurement Processes | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''H.ME.1a''' '''Making decisions about units and scales that are appropriate for problem‐solving situations within or across mathematics disciplines or real-world contexts'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Determine what units are used in problem (e.g., money, time, units of measurement, etc.). | * Determine what units are used in problem (e.g., money, time, units of measurement, etc.). | ||
* Match the action of combining with vocabulary (i.e., in all; altogether) or the action of decomposing with vocabulary (i.e., have left; take away, difference) in a word problem. | * Match the action of combining with vocabulary (i.e., in all; altogether) or the action of decomposing with vocabulary (i.e., have left; take away, difference) in a word problem. | ||
− | | | + | ||'''Representation:''' |
* Apply conversions of units while solving problems (e.g., Recognize that monetary units can be combined to equal other monetary units). | * Apply conversions of units while solving problems (e.g., Recognize that monetary units can be combined to equal other monetary units). | ||
* Translate wording into numeric equation. | * Translate wording into numeric equation. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis | * Task analysis | ||
* Model-Lead-Test <nowiki>*</nowiki> | * Model-Lead-Test <nowiki>*</nowiki> | ||
Line 854: | Line 858: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* $1, $5, and $10 bills | * $1, $5, and $10 bills | ||
* Number line labeled with $1/unit, $5/unit, and $10/unit | * Number line labeled with $1/unit, $5/unit, and $10/unit | ||
Line 860: | Line 864: | ||
* Graph paper where each square equals a unit | * Graph paper where each square equals a unit | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||H.ME.1b2 |
− | | | + | ||Solve a linear equation to find a missing attribute given the area, surface area, or volume and the other attribute. |
|- | |- | ||
− | | | + | ||'''Strand: '''Measurement |
| style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | | style="background-color:#5F497A;" colspan=2|'''Family: '''Perimeter, Area, and Volume Problems | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator: '''''H.ME.1b Investigating the results when linear dimensions of objects change by some factor (e.g., area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube)'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Understand concepts of area, volume, width, length, height, equals. | * Understand concepts of area, volume, width, length, height, equals. | ||
* Identify the unknown quantity when given an equation and labeled figure. (E.g., Provide a labeled prism and the equation V=L×H. Ask the student to draw/indicate the label on the prism to the letter in the equation.) | * Identify the unknown quantity when given an equation and labeled figure. (E.g., Provide a labeled prism and the equation V=L×H. Ask the student to draw/indicate the label on the prism to the letter in the equation.) | ||
Line 891: | Line 895: | ||
* Multiply and divide to find measurement. | * Multiply and divide to find measurement. | ||
− | | | + | ||'''Representation:''' |
* Given a picture, identify dimensions needed to calculate surface area, area, and volume. | * Given a picture, identify dimensions needed to calculate surface area, area, and volume. | ||
* Understand formula representation (e.g., "h" in the equation means height). | * Understand formula representation (e.g., "h" in the equation means height). | ||
Line 899: | Line 903: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Tiling/fill-in space and count | * Tiling/fill-in space and count | ||
* Sequence: 1. Area 2. Volume 3. Missing attribute | * Sequence: 1. Area 2. Volume 3. Missing attribute | ||
Line 909: | Line 913: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Supports and Scaffolds:''' |
* Pre-made formula | * Pre-made formula | ||
* Use of calculator | * Use of calculator | ||
Line 915: | Line 919: | ||
* Counters (e.g., tally counter) and counting mechanism (e.g., number line) | * Counters (e.g., tally counter) and counting mechanism (e.g., number line) | ||
|} | |} | ||
+ | |||
+ | |||
+ | |||
[[Category: Element Cards]] | [[Category: Element Cards]] | ||
− | [[Category:Math]] | + | [[Category: Math]] |
Latest revision as of 10:49, 16 September 2014
BACK TO Element Cards
Contents |
[edit] Teaching Measurement
All of the CCCs in this document relate to teaching Measurement. Below are some additional resources that may be helpful:
NCSC Curriculum Resource Guide: Measurement and Geometry
NCSC Content Module: Perimeter, Area and Volume Content Module
NCSC Content Module: Ratios and Proportions Content Module
[edit] Websites
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: Measurement
CCSS: K.MD.A.2: Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. | ||
CCC: | K.ME.1b2 | Compare 2 objects with a measurable attribute in common to see which object has more/less of the attribute (length, height, weight). |
Strand: Measurement | Family: Sorting and Classifying | |
Progress Indicator: E.ME.1b Comparing and ordering objects/events according to their specified attributes (using standard or non-standard units of measure), including indirectly by using a third object, or using common referents to estimate or compare | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.MD.A.1: Measure lengths indirectly and by iterating length units. Order three objects by length; compare the lengths of two objects indirectly by using a third object. | ||
CCC: | 1.ME.1b3 | Order up to 3 objects based on a measurable attribute (height, weight, length). |
Strand: Measurement | Family: Sorting and Classifying | |
Progress Indicator: E.ME.1b Comparing and ordering objects/events according to their specified attributes (using standard or non-standard units of measure), including indirectly by using a third object, or using common referents to estimate or compare | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.MD.A.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | ||
CCC: | 1.ME.1c1 | Compare 2 units of measurement and identify which unit would require more or less when measuring a selected object. (I can measure with paper clips or markers. Which unit will require more to measure the table?) |
Strand: Measurement | Family: Measuring using Tools | |
Progress Indicator: E.ME.1c Recognizing that the smaller the unit, the more units are needed to measure an object; and that units can be decomposed/partitioned into smaller units | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.MD.A.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | ||
CCC: | 1.ME.2a1 | Measure using copies of one object to measure another. |
Strand: Measurement | Family: Scaling and Unit Conversions | |
Progress Indicator: E.ME.2a Applying nonstandard and common standard units to measure or estimate (length, height, weight, time) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.MD.A.1: Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | ||
CCC: | 2.ME.1a3 | Select appropriate unit of measurement to measure an object (ruler or yard stick; inches or feet). |
Strand: Measurement | Family: Sorting and Classifying | |
Progress Indicator: E.ME.1a Recognizing, identifying, and describing the measurable attributes of objects | ||
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* This should be to "nearest whole unit" – in grade 2 we do not measure fractions/parts of a unit
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.MD.A.2: Measure and estimate lengths in standard units. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | ||
CCC: | 2.ME.1c3 | Recognize that standard units can be decomposed into smaller units. |
Strand: Measurement | Family: Measuring using Tools | |
Progress Indicator: E.ME.1c Recognizing that the smaller the unit, the more units are needed to measure an object; and that units can be decomposed/partitioned into smaller units | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.MD.A.4: Measure and estimate lengths in standard units. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | ||
CCC: | 2.ME.2a4 | Solve one step subtraction problems involving the difference of the lengths of 2 objects in standard length units |
Strand: Measurement | Family: Problem Solving using Measurement Process | |
Progress Indicator: E.ME.2a Applying nonstandard and common standard units to measure or estimate (length, height, weight, time) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | ||
CCC: | 3.ME.1d2 | Measure area of rectilinear figures by counting squares. |
Strand: Measurement | Family: Measuring Using Tools | |
Progress Indicator: E.ME.1d Describing and demonstrating: unit attributes, iterating, tiling, identical units, number line intervals, standardization, proportionality, additivity, and origin | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. | ||
CCC: | 4.ME.1g2 | Solve word problems using perimeter and area where changes occur to the deminsions of a rectilinear figure. |
Strand: Measurement | Family: Perimeter, Area, and Volume Problems | |
Progress Indicator: E.ME.1g Exploring what happens to 2‐dimensional measurements (perimeter or area) when the dimensions of the figure are changed | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
[edit] Additional Resource
http://www.khake.com/page47.html
CCSS: 5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems. | ||
CCC: | 5.ME.2a1 | Solve problems involving conversions of standard measurement units of area, volume, time, mass in the same system. |
Strand: Measurement | Family: Scaling and Unit Conversions | |
Progress Indicator: M.ME.2a Selecting and applying appropriate standard units, tools,and level of precision in real-world measurment problems (e.g., area, surface area, volume, rate) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | ||
CCC: | 5.ME.1b2 | Convert standard measurements of length. |
Strand: Measurement | Family: Scaling and Unit Conversions | |
Progress Indicator: M.ME.1b Recognizing relationships among units and using proportional reasoning to convert measurements from one unit to another within the same system | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | ||
CCC: | 6.ME.2b2 | Decompose complex shapes (polygon, trapezoid, pentagon) into simple shapes (rectangles, squares, triangles) to measure area. |
Strand: Measurement | Family: Perimeter, Area, and Volume Problems | |
Progress Indicator: M.ME.2b Using a variety of strategies (decomposing complex shapes, using formulas and models) to measure area (triangles, quadrilaterals, polygons) and volume (rectangular prisms) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 6.RP.A.3b Use ratio and rate reasoning to solve real-world and mathematical problems, (e.g., by reasoning about tables of equivalent rations, tape diagrams, double number line diagrams, or equations). Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? | ||
CCC: | 6.ME.2a2 | Solve one step real-world measurement problems involving unit rates with ratios of whole numbers when given the unit rate (3 inches of snow falls per hour, how much in 6 hours) |
Strand: Measurement | Family: Scaling and Unit Conversions | |
Progress Indicator: M.ME.2a Selecting and applying appropriate standard units, tools,and level of precision in real-world measurment problems (e.g., area, surface area, volume, rate) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | ||
CCC: | 7.ME.2d1 | Apply formula to measure area and circumference of circles. |
Strand: Measurement | Family: Perimeter, Area, and Volume Problems | |
Progress Indicator: M.ME.2d Using various strategies (decomposing complex shapes, using formulas) to measure volume (cones, cylinders, spheres) and area and circumference of circles | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and mathematical problems. | ||
CCC: | 8.ME.2d2 | Apply the formula to find the volume of 3-dimensional shapes (i.e., cubes, spheres, and cylinders) |
Strand: Measurement | Family: Perimeter, Area, and Volume Problems | |
Progress Indicator: M.ME.2d Using various strategies (decomposing complex shapes, using formulas) to measure volume (cones, cylinders, spheres) and area and circumference of circles | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 8.G.C.4 Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. | ||
CCC: | 8.ME.1e1 | Describe the changes in surface area, area, and volume when the figure is changed in some way (e.g., scale drawings). |
Strand: Measurement | Family: Scaling and Unit Conversions | |
Progress Indicator: M.ME.1e Exploring what happens to 2‐ and 3‐ dimensional measurements (such as surface area, area, and volume) when the figure is changed in some way (e.g., scale drawings) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | ||
CCC: | H.ME.1a2 | Solve real-world problems involving units of measurement. |
Strand: Measurement | Family: Problem Solving Using Measurement Processes | |
Progress Indicator: H.ME.1a Making decisions about units and scales that are appropriate for problem‐solving situations within or across mathematics disciplines or real-world contexts | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | ||
CCC: | H.ME.1b2 | Solve a linear equation to find a missing attribute given the area, surface area, or volume and the other attribute. |
Strand: Measurement | Family: Perimeter, Area, and Volume Problems | |
Progress Indicator: H.ME.1b Investigating the results when linear dimensions of objects change by some factor (e.g., area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube) | ||
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