Getting Down to the Basics with Length

Measurement

Lorraine Males, Funda Gonulates,

& Jack Smith

STEM Project,

Michigan State University

MiCTM Conference

August 6, 2009

• Welcome!• Your presenters & you• A bit about the STEM project• A problem & NAEP data• Three Activities• Putting together the key length

measurement ideas• Feedback

2

Introduction and Overview

A Bit About Our Project• STEM – Strengthening Tomorrow's

Education in Measurement• Premise: Part of the problem may be our

curriculum materials• Carefully examine 3 elementary programs

• Everyday Mathematics• Scott-Foresman/Addison-Wesley Mathematics• Saxon Mathematics

• We are not aiming to evaluate these curricula – we are looking to provide a description of the opportunity to learn measurement

3

A Bit About Our Project

• Look for every instance of measurement content

• Code each as an “opportunity” to learn some bit of conceptual or procedural knowledge

• Length analysis is complete for K through Grade 3

4

• Lots of different conceptual and procedural elements

• We found that these curricula provide tasks that mostly have a procedural focus

• We found some examples that may be used to introduce some key ideas related with length measurement

5

Some Results

The Toothpick Problem

“What is the length of the toothpick?”

6

Into the Content

[NAEP, Grade 4, 2003, Open response]

[Grade 4, large national sample]

Response % Responding

2.5 inches (correct) 2010.5 inches 14

3.5 inches 23

Other 42

Omitted 2

7

The Toothpick Problem Data

What lessons can we take from the toothpick problem?

• students• teaching• content• curriculum

8

We will do three length measurement activities• Buttons• Footprint• Funny Rulers

As we do these activities think about:• the key length measurement ideas• possible connections between these

activities and ideas9

Come Potentially Useful Activities

Question:

What is the width of the paper you are given in buttons?

1. Sketch possible ways that a student may solve this task.

10

Buttons

Question:

What is the height of the desk you are sitting at?

How long is it?

1. Trace you footprint on the paper provided in your bag, cut it and determine the height and length of your desk.

2. Sketch possible ways students might come up with.

11

Footprint

Question:

How long is the paperclip provided in your bag?

1. Examine the rulers in your envelope to answer the following questions:

• Which rulers could give you an accurate measure?

• Which rulers you should not use?  

For each, explain why the ruler will not give an accurate measure.  

12

Funny Rulers

Think back to the following questions:

What were some of the key length

measurement ideas in these activities?

What are some possible connections between

these activities and ideas?

13

Reflecting on Activities

• In all those three activities there is an exhaustion of the space but• If we skip tiling ……………….• If we always provide sufficient materials

but do not provide opportunities for unit iteration …………

• If we start with measurement with ruler without providing an enough experience with tiling and unit iteration ………..

• Rulers embed units14

Key Ideas

15

Percentages of Selected Conceptual Knowledge Elements Across Grades

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Percentages of Selected Procedural Knowledge Elements Across Grades

What happens if we don’t show strange and

incorrect ways of doing something?

Is it good if we just show students correct

procedures?

Think back to the toothpick problem

Some things may be worth investing more time

on than others because of the benefit these

things may provide 17

Overall

Thank you for coming & engaging

Please let us know if youare interested in free

professional developmentaround measurement ideas

18

Closing

Engage with us• Feedback form• Indicate an interest in measurement• Are you using one of our target curricula?• Look for us around the state, at NCTM, and in

NCTM’s journalsLorraine Males (maleslor@msu.edu) Funda Gonulates (gonulate@msu.edu)Jack Smith (jsmith@msu.edu)

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Closing