Element Cards Measurement
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==Websites== | ==Websites== | ||
[http://www.mathsisfun.com/ http://www.mathsisfun.com/] | [http://www.mathsisfun.com/ http://www.mathsisfun.com/] | ||
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[http://www.mathplayground.com/ http://www.mathplayground.com/] | [http://www.mathplayground.com/ http://www.mathplayground.com/] | ||
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[https://www.khanacademy.org/ https://www.khanacademy.org/] | [https://www.khanacademy.org/ https://www.khanacademy.org/] | ||
− | [http://www.mathhelp.com/ http://www.mathhelp.com/] | + | |
+ | [http://www.mathhelp.com/ http://www.mathhelp.com/] | ||
==Other Resources == | ==Other Resources == |
Revision as of 17:18, 13 November 2013
Contents |
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 NCSC Content Module: Ratios and Proportions
Websites
http://www.mathplayground.com/
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/
CCC Mathematics \| Measurement
CCSS: K.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.MD-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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.MD.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
* This should be to "nearest whole unit" – in grade 2 we do not measure fractions/parts of a unit
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.MD.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 3.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 4.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
Additional Resource
http://www.khake.com/page47.html
CCSS: 5.MD.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 5.MD.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 6.G.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 6.RP.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 7.G.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 8.G.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 8.G.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: N.Q.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 | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: A.REI.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) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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'Suggested Supports and Scaffolds:'
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