1. Measurement training (grades k-3)
Michele Condap
MAT 657
National University
May 2, 2015

2. Today’s Goals Identify 4 Issues in Teaching Measurement
Connect Common Core State Standards: Math to Teaching Measurement
Content & Mathematical Practice Standards
Relationship to other contents
Increase knowledge of Strategies in Teaching Measurement
Practice Teaching & Learning Activities in Measurement
Have fun 

3. 4 Issues in Teaching Measurement
1) Building Conceptual Understanding
Visual Models
Tools and Manipulatives
Real-World Story Problems
Students Deriving Formulas
One huge focus in the shift to Common Core State Standards is the goal of teaching students Math with conceptual understanding. Conceptual understanding is characterized by a deep understanding of why and how a concept or process works. Prior to Common Core, students may have been traditionally taught a formula or algorithm and drilled in its step-by-step process. However, this is neither practical nor functional. If we want students to become competent and creative problem solvers in the workplace, we must allow students to develop their own new knowledge using exploration and visual models.

4. 4 Issues in Teaching Measurement
2) Role of ESTIMATION!
Focus on attribute & measuring process
Intrinsic Motivation
Familiarity with Standard units
Promotes multiplicative reasoning
Estimation plays a huge role in the development and use of measurement concepts and skills. For young learners, estimation gets students to really focus on the attribute they are measuring and what the process is for measuring it (repeating a unit of measure). In addition, the desire to be correct provides students intrinsic motivation to really think. When using standard units of measure, estimation getst studnets to really focus in on estimating that unit of measure. Finally, students naturally compare attributes of different measures which causes them to use the multiplicative property (ex. the.desk is three times the size of my pencil, the teacher is twice the height of Sally, etc.).

5. 4 Issues in Teaching Measurement
3) Non-Standard  Standard Units
Examples:
Non-standard- hands, pencils, body lengths, straws, string, toothpicks
Standard- inches, feet, meters, grams, minutes, dollars/cents
Tools- Rulers, yard sticks, tape measures, scales, clocks, nickel/dime
Progression
1) Non-Standard
Focus directly on attribute & measurement process
Confusing comparisons with different units of measure…
2) Standard
More accurate comparisons/relationships
Students in Pre-K through 1st grade work primarily in non-standard units of measurement. These students focus on comparing attributes, organizing attributes by measurement, and using iteration to determine a length. Students should be practicing measurement of length, weight, and time (1st grade).
Students in grades 2 and 3 will focus more on standard units of measure using formal tools of measurement. These students will focus on measuring and estimating length/volume/mass, telling time more accurately, solving word problems with money, squared units of measurement (3rd grade), and area/perimeter (3rd grade).

6. 4 Issues in Teaching Measurement
4) **TWO TYPES OF OBJECTIVES
Understanding meaning and technique of measuring a particular attribute
Learning about the standard units themselves to measure that attribute
Van de Walle states that one of the most common errors in teaching measurement is the failure to recognize this distinction (2014). It is imperative that teachers recognize the separation of the two types of objectives in measurement. Students should have time to focus on each when appropriate, however teachers must be clear in their instructional goals.

7. CCSSM- Main Topics (K-3)
Length
Non-Standard Units
Standard Units
Area
Square units
Relation to Perimeter
Money
Counting Sets
Making Change
Time
Digital & Analog
These are the four main topics in Measurement for K through 3rd graders.

8. CCSSM- Progression of Content Standards
Kindergarten
1st
2nd
3rd
Describe & compare measureable attributes
Measuring lengths indirectly by iterating length unit
Measure & estimate lengths in standard units
Solve problems with measurement & estimation for time, liquid volume, & mass
Tell & write time to hour & half hour
Tell & write time to nearest 5 minute
Tell & write time to nearest minute
Solve word problems with money
Relate addition & subtraction to length
Understand area in relation to multiplication/division
Recognize perimeter as an attribute of plane figures & distinguish between linear/area measurements
Similar to other content areas of CCSS, the measurement standards build upon one another through grade levels. Students’ knowledge and understanding deepens each year.
Visit < the complete listing of CCSS grade level Mathematics standards.

9. CCSSM- Connections to other Content Standards
Operations and Algebraic Thinking
Counting units of length/area
Multiplicative Property in Iteration
Building Area & Perimeter Formulas w/ multiplication
Multiplication/Division for Scaling
All Operations used in Time & Money manipulation
Numbers in Base Ten & Fractions (3rd grade)
Metric System
Area manipulation with division/fractions
Data
Colleting measurement data
Making sense of & Representing (graphs, plots, etc.)
Describe our world with measurement data
Geometry
Shape properties in relation to area/perimeter/volume/mass
Measurement and the CCSSM Measurement Standards are closely tied to all other Math Content Area Standards. For students to develop a deep, contextual understanding with practical application skills, teachers must integrate content area goals.

10. CCSSM- Mathematical Practice Standards (1-4)
How do we cover ALL MPs in Measurement?
MP.1 –Make sense of problems and persevere in solving them
Students have opportunities to determine the meaning and possible approaches to problems.
Ex. “How long is your desk?”
MP.2 - Reason abstractly & quantitatively
Students compare measureable attributes
Ex. “Which pumpkin is wider around?”
MP.3 – Construct viable arguments & critique the reasoning of others
Students justify their measurements and data
Ex. “Which pumpkin is wider around? How do you know?”
MP.4- Model with Mathematics
Students solve story problems involving measurement
Ex. “Tom owes Kim 65 cents. He gives her $1. What change would Kim give using the least amount of coins?”

11. CCSSM- Mathematical Practice Standards (5-8)
MP.5- Use appropriate tools strategically
Students learn to use tools for standard units of measure
Ex. “Given a yardstick, balance scale, and a centimeter ruler. Determine the length of your fingernail.”
MP.6- Attend to precision
Student use standard units of measurement to record and manipulate data
Ex “My table is 4ft by 1ft long. How many squared inches of fabric will it take to cover?
MP.7 –Look for and make use of structure
Students use chunking and subdivision for estimation and measurement
Ex. “Estimate the height of the door.”
MP.8 – Look for and express regularity in repeated reasoning.
Students derive formulas for area and perimeter
Ex. “Is there a relationship between two rectangles with an area of 12 squared units if one has side lengths of 3 x 4 and one 2 x 6?”

12. Teaching Strategies in Measurement
ESTIMATION: Always start a measurement problem with estimation!
Allows students to focus on attribute and unit
Strategies:
Benchmarks for reference
“Chunking”
Subdivisions
Iterate mentally or physically
Benchmarks- students use mental reference points as examples for units of measure (i.e. a piece of paper or arms distance)
“Chunking”- students mentally split an attribute into smaller subdivisions or chunks
Subdivisions- students mentally split an attribute in half, quarters, eights, and so forth until they arrive at a manageable
piece
Iterate mentally or physically- students think or actually use a repeated number of units (non-standard) (i.e. walk & count
strides across room to estimate length)

13. Hands on Activity: Estimation (2nd grade)
Step 1- Without moving, estimate the length of this room in centimeters.
Step 2- Use one of the previous four estimation strategies to estimate the length of this room in centimeters. Explain and justify your estimation to another group
Step 3- Measure using a standard measurement tool of your choice. How many centimeters long is this room?
CCSSM Connections
ALL MP Standards!!!
Measurement and Data 2.MD
Measure and estimate lengths in standard units
1. Measure the length of an object by selecting and using appropriate tools
3. Estimate units of length uses inches, feet, centimeter, and meters
MP.1 –Make sense of problems and persevere in solving them
MP.2 - Reason abstractly & quantitatively
MP.3 – Construct viable arguments and critique the reasoning of others
MP.4- Model with Mathematics
MP.5- Use appropriate tools strategically
MP.6- Attend to precision
MP.7 –Look for and make use of structure
MP.8 – Look for and express regularity in repeated reasoning.

14. Hands on Activity: Estimation Reflection
What estimation strategy did you use?
How did it work?
Can you think of a more efficient way to estimate?
Based on your given data how would you estimate the length of our school?
One significant piece in this estimation activity comes from this reflection. Students reflect on their strategy and is practicality. Through this reflection students are making conclusions about which strategies work for them and in which types of situations

15. Teaching Strategies in Measurement
DEVELOPING AREA FORMULA
Why?
Students gain conceptual understanding!
Less likely to confuse area & perimeter
Understand how all area formulas are related
How?
Relate to multiplication
Arrays!
Row and columns  base and height
Row x column = area
Students must have opportunities to derive their own formulas in measurement and geometry because this representation of measureable attribute becomes meaningful to them. If students are simply given a formula, they confuse them easily and may not really understand why or how they work.
Students should be learning multiplication using arrays as visual representation. This is the perfect lead in to area.

16. Hands on Activity: Developing Area Formula (3rd grade)
Step 1- Estimate which of each set of rectangles is bigger.
Sets-
2 x 8 and 3 x 5
4 x 4 and 9 x 1
5 x 4 and 2 x 10
Step 2- Use square units &
rulers to determine each
area & fill in this chart:
Side
Area 2 8 16 3 5 15 4 9 1 20 10
Students first use estimation because it is motivating and stimulating. Next, students can use the unit squares and rulers to determine the square area of each shape. Students should not cut any of the rectangles, however they my draw on them to show each unit square or measurement unit they use.

17. Hands on Activity: Developing Area Formula Reflection
Step 3- Reflection
Write down any observations you made about the area of these shapes
Where my estimations accurate?
Where there any surprises?
Do I notice any relationships between units I measured today?
Share your reflection with another pair
CCSSM Connections
ALL MP Standards!!!
Measurement and Data 3.MD
Geometric Measurement: Understand concepts of area and relate to multiplication and addition
5. Recognize area as an attribute of plane figures and understand concepts of area measurement
6. Measure area by counting unit squares
7. Relate area to the operations of multiplication and addition
Using the chart may help students see a pattern similar to a multiplication algorithm. Students should come up with this idea on their own. If students do not instantly think of it, a classmate might suggest it. Some students may instantly relate this back to arrays.
Extension - For high-achieving students or a following lesson…Students do the same activity but with right triangles.

18. In Conclusion… Remember- Use Estimation!
Tools, Manipulatives, Visuals for Conceptual Understanding
Students derive own formulas
Focus on one objective
The process of measuring or
The unit of measure
Integrate multiple topics in Mathematics
Have Fun! 

19. Resources! Teacher Resources Websites Books
National Library of Virtual Manipulatives
Measurement Activities
Books
The Grouchy Lady Bug By: Eric Carle
What Time is it Mr. Crocodile? By: Judy Sierra
How Big is a Foot? By: Rolf Myller

20. More Resources! Student Resources PBS Kids Measurement Games
IXL w/ CCSS Math

21. References
California State Board of Education. (2013). California Common Core
State Standards for Mathematics. Retrieved from:
Van De Walle, J. A., Karp, & Bay-Williams. (2014). Elementary and
Middle School Mathematics: Teaching Developmentally (8th ed). London: Saffron House.