Class Dates- Sept 16, Sept 30, October 14, October 28
September 16, Sept 30

Day One

  • 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

1. 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?
Share out the focus of measurement at your grade level
Focus standards by grade
Common Core State Standards

2. 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

3. 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

4. Math Workshop with length
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.

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?
  • Measure the length of string needed to wrap exactly around the shape.
  • Using only the broken ruler section, find the lengths of the sides and the perimeter.
  • Is the sum of the four sides the same as the length of string?
  • Measure the shape cutouts using your broken ruler

6. Perimeter/Area

Understand the relationship between these two measures
  • Rectangles task
  • Measurement Relationships- Area and Perimeter Fencing tasks
  • Perimeters of different shapes

7. Day two prep

Work with 2-4 people at your grade level. Choose a measurement activity or geometry activity.

8. Day one homework

Read Van de Walle Chapter on Measurement
Read Essential Understandings at your grade band- Measurement understandings
Prepare for presentation

9. Measurement Sources
  • 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

Day Two

  • Explore the big ideas of measurement in area, surface area and volume
  • Use the coherence map to develop understanding within your grade and grade band

Exploring Area and levels of understanding

Area and Arrays

  • Structuring an array - Understanding the multiplicative formulas for area
  • Arts Tasks - Levels of understanding

Surface Area and Volume

  • 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