build a million: helping students understand large numbers sharon moore and nadine bezuk san diego...

Build a Million: Helping Students Understand Large

Numbers

Sharon Moore and Nadine Bezuk

San Diego City Schools

San Diego State University

CMC-N Dec. 6, 2003

Session Overview What do students need to know?

Concepts/Big Ideas NCTM & CA Standards

Build A Million Place Value Chart How to use the chart to develop,

rebuild, and extend place value understanding.

What Do Students Need to Know about Place Value? Sets of ten (and tens of tens) must be

perceived as single entities. These sets can then be used to describe how many.

The positions of digits in numbers determine what they represent--which size group they count.

There are patterns to the way numbers are formed.

What Do Students Need to Know about Place Value? The groupings of ones, tens, and

hundreds can be taken apart in different ways. For example, 256 can be 1 hundred, 14 tens, and 16 ones.

“Really big” numbers are best understood in terms of familiar real- world referents.

NCTM StandardsIn Grades 3-5, all students should: understand the place-value structure of the

base-ten number system and be able to represent and compare whole numbers and decimals;

recognize equivalent representations for the same number and generate them by decomposing and composing numbers.(NCTM, 2000, p. 148)

What Do the CA Standards Say?

Grade 2: NS 1.0 Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.

Grade 3: NS 1.3 Identify the place value for each digit in numbers to 10,000.

Grade 4: NS 1.1: Read and write whole numbers in the millions.

More from the CA Standards Grade 4: NS 1.2: Order and compare

whole numbers in the millions. Grade 5, NS 1.0 Students . . .

understand the relative magnitudes of numbers: 1.1 Estimate, round, and manipulate

very large. . . numbers.

Why Build a Million? To build a visual representation of one

million to help conceptualize the magnitude of large numbers

To develop, extend, and rebuild place value understanding in the base ten number system

To create a tool rich with opportunities for number sense and place value routines

Prerequisite Skills Making sense of smaller numbers (e.g.

hundreds)

An understanding of equivalent

representations

Experience with Base Ten Blocks

Introduction Teaching for understanding vs. “blue

digit” and “fill in the chart” work

Literature connections provide context

for thinking about large numbers

Let’s get busy with the chart!

Making It Work in Your Classroom

Establishing classroom culture

The “ready-made” million

Making a smaller version

To cut or not to cut?

Making use of the chart over time

Connection to decimals

Questions?

Revisiting the Big Ideas The positions of digits in numbers

determine what value they represent There are patterns to the way numbers

are formed in the base ten system Numbers can be expressed by a variety

of equivalent representations

Resources Literature Connections Bibliography

Slideshow and handouts are posted in the

“Resources” section of our website:

pdc.sdsu.edu

Contact us:

smoore@sciences.sdsu.edu

nbezuk@mail.sdsu.edu