2. Build a Million: Helping Students Understand Large Numbers Sharon Moore and Nadine Bezuk San Diego City Schools San Diego State University CMC-NDec. 6, 2003

3. 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.

4. 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.

5. 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.

6. NCTM Standards In 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)

7. 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.

8. 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.

9. 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

10. Prerequisite Skills Making sense of smaller numbers (e.g. hundreds) An understanding of equivalent representations Experience with Base Ten Blocks

11. 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!

12. 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?

13. 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

14. 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