Measuring Length
Day Two Understand mathematical progressionExplore the big ideas of Measurementmeasurement in elementary grades
Understandarea, surface area and volume
Use the concepts neededcoherence map to understand measurement
Explore the levels of thinkingdevelop understanding within your grade and Big Ideas of measurementgrade band
Exploring Area and levels of understanding
Area and Arrays
Structuring an array - Understanding the multiplicative formulas for area
Arts Tasks
Levels - Levels of understanding
Measurement tasks with Tangrams
Area
Surface Area and Volume
Unit Dog
Determine the surface area and volume of cubes
Explore how the surface area and volume of an irregularyly shaped objec, "unit dog," change as the dimensions are scaled
Presentations

Read Essential Understandings at your grade band- Measurement understandings
Prepare for presentation

...

Measurement Sources
Essential Understanding of Geometry and Measurement into Practice K-2
Essential Understanding of Geometry and Measurement into Practice 3-5

...

Explore the levels of thinking and Big Ideas of measurement
Exploring Area and levels of understanding Explore the levels of thinkingArea and Big Ideas of measurementArrays
Structuring an array - Understanding the multiplicative formulas for area
Arts Tasks
Levels of understanding
Measurement tasks with Tangrams
Area and Volume
Unit Dog
Presentations

Class Dates- Sept 16, Sept 30, October 14, October 28
September 16, Sept 30 SessionDay One Outcomes
Understand mathematical progression of Measurement in elementary grades
Understand the concepts needed to understand measurement
Explore the levels of thinking and Big Ideas of measurement Day One Agenda
Measurement1. Measurement Standards
We use measurement daily. Why is Measurement so hard for students?
Look at the Measurement standards at your grade level.

...

Focus standards by grade
Common Core State Standards Read Measurement Concepts2. Readings
Read Van de Walle Measurement introduction (K-2, 3-5, 6-8) first three pages
Read Confer Sizing up Measurement introduction (copy)
Read Big Ideas and levels of thinking. Discuss the levels of thinking. In your group, use math tools to model each of these levels of thinking Measurement -levels3. Levels of thinkingThinking
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

...

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 Measurement-4. Math Workshop with length tasks
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.
Read, 5 Ways to Improve Children's Understanding of Length Measurement. Measurement -5. Broken Ruler Activity
Ability to use any two sets of marks on a ruler
Can you measure the perimeter of a shape using only a broken ruler?

...

Is the sum of the four sides the same as the length of string?
Measure the shape cutouts using your broken ruler Measurement-Perimeter/Area6. Perimeter/Area
Understand the relationship between these two measures
Rectangles task
Measurement Relationships- Area and Perimeter Fencing tasks
Perimeters of different shapes Prep for session7. Day two prep
Work with 2-4 people at your grade level. Choose a measurement activity or geometry activity. Homework for September 308. Day one homework
Read Van de Walle Chapter on Measurement
Read Essential Understandings at your grade band- Measurement understandings
Prepare for presentation Measurement9. Measurement Sources and Articles
Essential Understanding of Geometry and Measurement into Practice K-2
Essential Understanding of Geometry and Measurement into Practice 3-5
5 Ways to Improve Children's Understanding of Length Measurement
Measuring Length SessionDay Two Outcomes
Understand mathematical progression of Measurement in elementary grades
Understand the concepts needed to understand measurement

Measurement Standards
We use measurement daily. Why is Measurement so hard for students?

...

grade level.
Are the standards: major standards, supporting standards or additional standards?
Share out the focus of measurement at your grade level

...

Read Confer Sizing up Measurement introduction (copy)
Read Big Ideas and levels of thinking. Discuss the levels of thinking. In your group, use math tools to model each of these levels of thinking
Measurement Levels-levels of Thinkingthinking
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

...

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 Big Ideas of MeasurementMeasurement- length tasks
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.
Read, 5 Ways to Improve Children's Understanding of Length Measurement. Big Ideas of Measurement
Broken rulerMeasurement - abilityBroken Ruler
Ability to use
Can you measure the perimeter of a shape using only a broken ruler?
Measure the length of string needed to wrap exactly around the shape.

...

Is the sum of the four sides the same as the length of string?
Measure the shape cutouts using your broken ruler Big Ideas of Measurement
Perimeter and Area tasks - UnderstandMeasurement-Perimeter/Area
Understand the relationship
Rectangles task
Measurement Relationships- Area and Perimeter Fencing tasks
Perimeters of different shapes PreparationPrep for Geometry and Measurement presentationssession two
Work with 2-4 people at your grade level. Choose a measurement activity or geometry activity.
Homework for September 30

Class Dates- Sept 16, Sept 30, October 14, October 28
September 16, Sept 30 OutcomesSession One Outcomes
Understand mathematical progression of Measurement in elementary grades
Understand the concepts needed to understand measurement
Explore the levels of thinking and Big Ideas of measurement AgendaDay One Agenda
Measurement Standards
We use measurement daily. Why is Measurement so hard for students?
Look at the Measurement standards at your grade level. Are the standards: major standards, supporting standards or additional standards?

...

Focus standards by grade
Common Core State Standards Process of Measurement
If I were to ask 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.
ExploreRead Measurement Concepts
Read Van de Walle Measurement introduction (K-2, 3-5, 6-8) first three pages
Read Confer Sizing up Measurement introduction (copy) -What are the Big Ideas? Share out in a small group
ReadRead Big Ideas

...

of thinking
Levels
Measurement 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

...

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 BigBig Ideas of measurement
5 Ways to Improve Children's Understanding of Length Measurement
You

...

be learning.
Explore the levels
Read, 5 Ways to Improve Children's Understanding of thinking and BigLength Measurement.
Big Ideas of measurementMeasurement
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?

...

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 BigBig Ideas of measurementMeasurement
Perimeter and Area tasks - Understand the relationship between these two measures
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 formulasPreparation for area
Arts Tasks
Levels of understanding
Measurement tasks with Tangrams
Preparation for presentations Geometry and Measurement presentations
Work with 2-4 people at your grade level. Choose a measurement activity or geometry activity.
Homework for September 30
Read Van de Walle Chapter on Measurement
Read Essential Understandings at your grade band- Measurement understandings
Prepare for presentation
Measurement Sources and Articles
Essential Understanding of Geometry and Measurement into Practice K-2 Putting Essential Understanding of Geometry and Measurement into Practice 3-5
Essential Understanding of Geometry and Measurement into Practice 3-5 Putting Essential Understanding of Geometry and Measurement into Practice 3-5
Measurement Articles
5 Ways to Improve Children's Understanding of Length Measurement Understanding standard units of measure
Measuring Length Research SummarySession Two Outcomes
Understand mathematical progression of Measurement in elementary grades
Understand the concepts needed to understand measurement
Explore the levels of Geometric Objects
Scaffolding Conceptualthinking and Big Ideas of measurement
Exploring Area and levels of understanding
Explore the levels of thinking and Big Ideas of measurement
Structuring an array - Understanding the multiplicative formulas for Linear Measurement
Developmental progression for length measurement chart K-2 area
Arts Tasks
Levels of understanding
Measurement tasks with Tangrams

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

...

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

...

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

...

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

...

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

...

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

...

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

...

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

...

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

...

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