1. Foundations of Geometric Measurement
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
Monday July 18, 2016
10:45-12:00

2. Learning Intention Learning Intention:
We are learning the foundations of measurement.
Success Criteria:
We will be successful when we can
Describe the process of measurement, both in general and in the specific context of measuring length;
Make sense of measurements using personal benchmarks;
Explain the difference between “quantity” and “number.”

3. How would you determine the length of this room?
Work with your table group. Find a way to measure the length of the room. You may NOT use the ceiling or floor tiles. Share your process by recording it on the whiteboard.
Kevin
Add grid to poster or white board for groups to record their lengths
Group Measurement
Be done in 10 minutes

4. What did we find out?
How does the information on the whiteboard help us understand the length of the room? Do any of these measurement results help you conceptualize the length of the room better than others? How could you carry out the measurement so as to best communicate the length of this room to someone who has never seen it?
The aim of the last question on this slide is to surface the idea of standard units

5. What does it mean to measure?
Measurement is the process of assigning a number to a magnitude of some attribute shared by some class of objects, such as length, relative to a unit.
K-5, Geometric Measurement Progressions p. 2

6. Measurement Process
1. Define an attribute of an object. 2. Identify a unit of measure. 3. Count the number of units

7. All Physical Objects have attributes that can be measured
Make a list of objects and an “attribute” that you—or someone else—might want to measure. What units could be used to measure each attribute in your list. (Both standard and non-standard units.)
Emphasize (again) that we will focus on geometric measurement. Ask participants, which of the attributes they identified are geometric,
We will be focusing on Geometric Measurement this summer. Which of the attributes you identified are geometric, and which are not?

8. Using Personal Benchmarks to Make Sense of Standard Units
What are some ways you make sense of standard units? How do you think of a yard? Meter? Pounds? Kilograms? A cubic centimeter?
Personal benchmarks are in essence based on comparison.

9. Development of Units
Long ago units were derived from natural resources.
1 inch  3 barley corns 1 foot  length of a human foot. 1 acre  amount of land a horse could plow in 1 day.

10. Standardizing Measurement: A Need Recognized Long Ago
This weight was one of the First Emperor’s of China’s new standards. King Qin [Chin] issued an edict that all weights will be standardized. “…where they are not uniform or where there are any doubts, let them be standardized and clarified!”

11. Evolution of the Meter
Over time, standard units have been given ever more accurate definitions. For example:
1 meter (1795)  1 ten-millionth of the distance from the North Pole to the Equator (along the meridian passing through Paris) 1 meter (1927)  distance between two marked lines on a specific platinum-iridium bar (kept in Paris) 1 meter (1983)  distance travelled by light (in vacuum) in 1/299,792,458 of a second.

12. Quantity Helps Us Understand “How Much”
Quantity  Number + Unit 135 miles to Grandmas kilometers to Grandmas. A movie was 120 minutes. A movie was 7200 seconds. Turn and talk.. What is the effect of choosing two different units?
What’s the effect of choosing these two different units. Note that the numbers are different, but the quantities are the same.

13. Progressions Document: K-5 Geometric Measurement
Open your K-5 Geometric Measurement Progressions document to page 2
Read the overview through the bottom of page 3.
Highlight crucial ideas that help define the study of Geometric Measurement.
 Check in with your shoulder partners about the crucial ideas and why you thought they were important.
Chart big ideas they are listing from the progressions doc
Length is continuous, it connects to, but is different from cardinality
Kids have to understand what an attribute is
Indirect vs. direct comparison
Creating personal benchmarks
Overarching concept of a unit
Geometric measurement connects the 2 most critical domains of early math- geometry and number

14. Learning Intention Learning Intention:
We are learning the foundations of measurement.
Success Criteria:
We will be successful when we can
Describe the process of measurement, both in general and in the specific context of measuring length;
Make sense of measurements using personal benchmarks;
Explain the difference between “quantity” and “number.”
Turn & Talk about the 1st and 3rd success criteria- make sure you can make sense of and explain

15. Length: The Basic Geometric Measurement
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
Monday July 18, 2016
1:00 – 2:30

16. Learning Target & Success Criteria
We are learning to…
Understand length as a core concept in Geometric Measurement.
We will be successful when we can…
describe the process used to measure length in order to quantify the distance between the endpoints of an object.

17. How would you answer the question, “What is length
How would you answer the question, “What is length?” Jot down your ideas in your notebook. Turn and share with a shoulder partner. Use items on your table to justify your definition of length and come to a consensus. Be prepared to share out.
(don’t chart, just share)

18. Length is…
Length is a characteristic of an object found by quantifying how far it is between the endpoints of the object. K-6, Measurement Progressions What do young learners have to understand to measure the length of an object?

19. Length Answers the Questions “How Long”, or “How Far?”
Work as a trio.
Identify the attribute of your table you will measure.
Identify a unit to determine the length of the table.
Large paper clips
Drinking straws
Estimate the length and record the number of units anticipated.
Measure, and record the total number of units.
Additional instructions: measure the length of the table using one of your tools. Then measure the drinking straw in units of the paper clip, and estimate how many of the second tool you will need to measure the table.
Measurement Tool
Estimate Number of Units Needed
Total Number of Units
Drinking Straws
Large paper clips

20. Checking in with your thinking…
Units Are A
Big Deal!
Check in with your table… What did you have to understand about measurement in order to complete the task?
Units must have equal length.
Units must be placed on the path to be measured.
Units are placed end-to-end…No gaps or overlaps.
Counting the units leads to a total quantity.
The number of units needed depends on the size of the unit used to measure.
Chart out tables’ thinking
Chart title: Measuring Length
Make connection to multiplicative comparison (Can we use the “times as many” language)

21. Adding to Our Thinking: Length
Read the first two paragraphs of p. 4 in the K-6, Geometric Measurement Progressions. Share connections between the reading and the activity you completed. How does this information help to refine your definition of length measurement?

22. Big Ideas for children
The process of measuring length involves developing understanding of two ideas…
Partitioning – mentally subdividing an object into congruent units.
Unit iteration – is translating a unit successfully alongside an object being measured without leaving space.
Refer to our charting
How do these ideas relate to the Measurement Process we discussed this morning?

23. Grade 1: Which Path Should the Worm Take?
The worm has two paths, A and B. Estimate: About how long is each path? Next: Use no more than 5 paper clips to figure out how long each path is. Don’t forget! Make a representation to document how you kept track of your measurements.
Use large paper clip.
Be ready to share out: How did you know which path was longer?

24. 1.MD.1 and 1.MD.2
Measure lengths indirectly and by iterating length units.
1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.2 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.
Standards grid…
Turn and share
Do we see the measurement process in the standards?

25. Comparison: An Essential Idea
The purpose of measurement is to allow indirect comparisons of…an attribute using numbers. An attribute of an object is measured (i.e., assigned a number) by comparing it to an amount of that attribute held by another object. K-5, Geometric Measurement Progressions, p. 3
The big idea is the comparison (not the assigning of a number) and we compare 2 ways directly and indirectly
Note here that comparison is going to be developmentally prior to quantitative measurement.

26. Looking at Student Work
How do students represent their measurements? How do students identify the quantity? What understandings do you see? What misconceptions do you see? Is this typical of students at the end of first grade?
What challenged student thinking between path A and path B?

27. 1.MD.1 & 1.MD.2
Identify work samples that meet the expectations of the standards.
Identify work samples that does not meet the standards.

28. Learning Target & Success Criteria
We are learning to…
Understand length as a core concept in geometric measurement.
We will be successful when we can…
describe the process used to measure length in order to quantify the distance between the endpoints of an object.

29. PRR: Measurement
Open your K-5, Geometric Measurement progression: Read pp. 8-9 through the bottom of the first full paragraph.
Reflect on the big ideas and concepts young learners need to understand about length and length measurement and make connections to the Worm Task and/or to your own grade level work.

30. Core Mathematics Partnership Project
Disclaimer
Core Mathematics Partnership Project
University of Wisconsin-Milwaukee,
This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors.
This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.