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