Read Confer Sizing up Measurement introduction (copy)
-What are the Big Ideas? Share out in a small group ExploreRead Big Ideas and levels of thinking. Discuss the levels of thinking and Big Ideas of measurement
5 Waysthinking. In your group, use math tools to Improve Children's Understandingmodel each of Length Measurement
You will do a series of math tasks involving length. The tasks progress in development. As you do the tasks, you will consider which concepts orthese levels of thinking the students may be learning.
Levels of Thinking
1. Unit iteration - the number of units = the distance being measured; placing the length of a small unit repeatedly along the length of an object being measured

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5. Transitive reasoning - ability to compare objects that are not side by side. If the length of object A is equal to the length of object B, and the length of object B is equal to the length of object C, the length of object A is equal to the length of object C.
6. Equal partitioning - the mental action of dividing an object into equal parts or units
Explore the levels of thinking and Big Ideas of measurement
5 Ways to Improve Children's Understanding of Length Measurement
You will do a series of math tasks involving length. The tasks progress in development. As you do the tasks, you will consider which concepts or levels of thinking the students may be learning.
Explore the levels of thinking and Big Ideas of measurement
Broken ruler - ability to use any two sets of marks on a ruler

of Measurement understandingin elementary grades
Understand the concepts needed to understand measurement
Explore the levels of thinking and Big Ideas of measurement

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Process of Measurement
If I were to ask you to measure an object for example an empty bucket, what would you need to know?

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to know.
Explore Measurement Concepts
Read Van de Walle Measurement introduction (K-2, 3-5, 6-8) first three pages

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Explore the levels of thinking and Big Ideas of measurement
5 Ways to Improve Children's Understanding of Length Measurement

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be learning.
Levels of Thinking
1. Unit iteration - the number of units = the distance being measured; placing the length of a small unit repeatedly along the length of an object being measured

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Broken ruler - ability to use any two sets of marks on a ruler
Can you measure the perimeter of a shape using only a broken ruler? UsingMeasure the length of string needed to wrap exactly around the shape.
Using only the

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and the perimeterperimeter.
Is the sum of the four sides the same as the length of string?
Measure the shape cutouts using your broken ruler
As you do the broken ruler task think about why students might have difficulty? What do they need to understand?
Explore the levels of thinking and Big Ideas of measurement

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Rectangles task
Measurement Relationships- Area and Perimeter Fencing tasks
Perimeters of different shapes
Explore the levels of thinking and Big Ideas of measurement
Structuring an array - Understanding the multiplicative formulas for area Perimeter vs. area - Understand the relationship between these two measures
Formula relationshipsArts Tasks
Levels of understanding
Measurement tasks with Tangrams
Preparation for presentations Geometry and Measurement
Work with 2-4 people at your grade level. Choose a measurement activity or geometry activity. Directions.
Measurement Standards
Common Core State Standards
Standards of Mathematical Practice
Standards Progressions
Homework
Read Van de Walle Chapter on Measurement

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Scaffolding Conceptual Understanding for Linear Measurement
Developmental progression for length measurement chart K-2 Dan Meyer 3-Act Tasks

Agenda
We use measurement daily. Why is Measurement so hard for students? AreLook at the Measurement standards at your grade level. Are the standards: major standards,

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or additional standards at your grade level?standards?
Share out the focus of measurement at your grade level
Focus standards by grade Concepts neededCommon Core State Standards
Process of Measurement
If I were to understand measurement
Bucket Activityask you to measure an object for example an empty bucket, what would you need to know?
In your group discuss what you would need to know.
Explore Measurement Concepts
Read Van de Walle Measurment IntroductionMeasurement introduction (K-2, 3-5, 6-8) first three pages
Read Confer Sizing up Measurement introduction (copy) What-What are the
Explore the levels of thinking and Big Ideas of measurement
5 Ways to Improve Children's Understanding of Length Measurement
You will do a series of math tasks involving length. The tasks progress in development. As you do the tasks, you will consider which concepts or levels of thinking the students may be learning.
Levels of Thinking
1. Unit iteration - the number of units = the distance being measured; placing the length of a small unit repeatedly along the length of an object being measured
2. Structuring Length - end-to-end, straight, no gaps or overlaps
3. Inverse relationship between the size of the unit and the # of units
4. Conservation of length - a different position does not change the length
5. Transitive reasoning - ability to compare objects that are not side by side. If the length of object A is equal to the length of object B, and the length of object B is equal to the length of object C, the length of object A is equal to the length of object C.
6. Equal partitioning - the mental action of dividing an object into equal parts or units
Explore the levels of thinking and Big Ideas of measurement
Broken ruler - ability to use any two sets of marks on a ruler
Can you measure the perimeter of a shape using only a broken ruler?
Using only the broken ruler section, find the lengths of the sides and the perimeter
As you do the broken ruler task think about why students might have difficulty? What do they need to understand?
Explore the levels of thinking and Big Ideas of measurement AreaPerimeter and Volume can be measured using only measures of length
Conservation of areaArea tasks - changingUnderstand the position o f a shape or subdividing it does not change the area
Area Partitioning - irregular polygons can be partitioned into shapes to determine overall arearelationship between these two measures
Rectangles task
Measurement Relationships- Area and Perimeter Fencing tasks
Structuring an array - Understanding the multiplicative formulas for area
Perimeter vs. area - Understand the relationship between these two measures

Concepts needed to understand measurement
Bucket Activity
Read Van de Walle Measurment Introduction
Read Confer Sizing up Measurement introduction (copy)
What are the Big Ideas? Share out in a small group
Explore the levels of thinking and Big Ideas of measurement
5 Ways to Improve Children's Understanding of Length Measurement

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Formula relationships
Preparation for presentations

Understanding standard units of measure
Measuring Length
Research Summary Measurement of Geometric Objects
Scaffolding Conceptual Understanding for Linear Measurement
Developmental progression for length measurement chart K-2

Explore the levels of thinking and Big Ideas of measurement
Agenda WhyWe use measurement daily. Why is Measurement
Are Measurement standards major standards, supporting standards or additional standards at your grade level?
Share out the focus of measurement at your grade level

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Perimeter vs. area - Understand the relationship between these two measures
Formula relationships s
Preparation for presentations Resources for Sept 16 Class
StandardsWork with 2-4 people at your grade level. Choose a measurement activity or geometry activity.
Directions.
Measurement Standards
Common Core State Standards
Standards of Mathematical Practice unpacked geometry and measurement standards
Standards Progressions
Homework

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5 Ways to Improve Children's Understanding of Length Measurement
Understanding standard units of measure
Measuring Length
Scaffolding Conceptual Understanding for Linear Measurement
Developmental progression for length measurement chart K-2

Agenda
Why is Measurement so hard for students? Progressions Activity- What do students need to knowAre Measurement standards major standards, supporting standards or additional standards at your grade level?
unpacked
Share out the focus of measurement at your grade level
Focus standards
Gr K
Gr 1
Gr 2
Gr 3
Gr 4
Gr 5
Gr 6
Gr 7
Gr 8 by grade
Concepts needed to understand measurement
Bucket Activity

Class Dates- Sept 16, Sept 30, October 14, October 28
September 16- Understanding Measurement K-516, Sept 30
Outcomes
Understand K-5mathematical progression of Measurement
Consider misconceptions or errors students may have
Consider ways to develop understanding
Big Ideas
Understand the process and components ofconcepts needed to understand measurement
process p271 math matters and article Copy p271 to 275
components
Measurement Involves a comparison of an attribute of an item or situation with a unit that has
Explore the same attribute
Estimationlevels of measuresthinking and the developmentBig Ideas of benchmarks for frequently used unit of measure help students increase their familiarity with units
Measurement instruments group multiple units so that you do not have to iterate a single unit multiple timesmeasurement
Agenda Measurement Big IdeasWhy is Measurement so hard for students?
Progressions Activity- What do students need to know at your grade level?
unpacked standards

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Gr 7
Gr 8 Bucket Activity - What do students needConcepts needed to know?understand measurement
Bucket Activity
Explore the levels of thinking and Big Ideas of measurement
5 Ways to Improve Children's Understanding of Length Measurement There are many underlying concepts that contributeLevels of Thinking
Explore the levels of thinking and Big Ideas of measurement
Broken ruler - ability to being able to measure. Describe these concepts.
Measuring Space in One, Twouse any two sets of marks on a ruler
Explore the levels of thinking and Three Dimensions
Chapter 4
Case StudiesBig Ideas of measurement
Area and VideosVolume can be measured using only measures of length
Conservation of area - changing the position o f a shape or subdividing it does not change the area
Area Partitioning - irregular polygons can be partitioned into shapes to determine overall area
Structuring an array - Understanding the multiplicative formulas for area
Perimeter vs. area - Understand the relationship between these two measures
Formula relationships
s
Preparation for presentations
Resources for Sept 16 Class

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Homework
Read Van de Walle Chapter on Measurement Read Case Studies 12-17 and answer activity questions
Prepare for presentation
Measurement Sources

Measurement Big Ideas
Progressions Activity- What do students need to know at your grade level?
unpacked standards
Gr K
Gr 1
Gr 2
Gr 3
Gr 4
Gr 5
Gr 6
Gr 7
Gr 8
Bucket Activity - What do students need to know?
5 Ways to Improve Children's Understanding of Length Measurement
There are many underlying concepts that contribute to being able to measure. Describe these concepts.
Measuring Space in One, Two and Three Dimensions
Chapter 4
Case Studies and Videos
Preparation for presentations

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Common Core State Standards
Standards of Mathematical Practice
unpacked geometry and measurement standards
Standards Progressions
Homework