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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
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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 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)
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