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# Missing Factors

## Developing an Algorithm for Decimal Multiplication

For CMP2, Bits and Pieces III, Problem 2.2.

The CMP3 Decimal Ops Unit is substantially different than the corresponding Unit in CMP2. This roughly corresponds to Investigation 3 of Decimal Ops.

The focus of this video is on the progress made by students towards understanding and using an efficient algorithm for multiplying decimals. At the end of Problem 2.1 at least two different students have proposed algorithms, but it is not clear that everyone has understood why these work.

Real time is 1.5 class periods.

As you view the video, consider the following:

- What is the evidence of students’ understanding and reasoning? What prior understandings do you see students using or building upon?
- What is the evidence of students’ use of the Mathematical Practices from the Common Core State Standards for Mathematics (CCSSM)? To what extent are students growing in their sophistication of their use of the Mathematical Practices?
- Were there any “aha moments” in the video?
- How is the teacher facilitating the development of students’ understanding and reasoning?
- As a teacher, how would you use the information from this lesson to plan the next lesson?

- Full Length Video (29:18)
- Problem 2-2
- Goals for CMP2 Missing Factors, Bits and Pieces III, Problem 2.2
- Estimate the relative size of a decimal product prior to finding an exact answer
- Develop place-value understanding of decimal multiplication
- Solve problems that require decimal multiplication
- Consider how finding a decimal part of and a fraction part of a quantity affects the relative size of a product
- Use place value to reason about decimal multiplication
- Explore the relationship between factors and products in decimal multiplication
- Develop estimation strategies for finding decimal products
- Use estimation as a strategy for locating the position of the decimal in finding exact decimal products
- Generalize an approach to placing the decimal point into a product that involves counting and adding decimal places
- Consider when various strategies are useful for finding decimal products
- Understand what happens to place value and the position of the decimal when you multiply by powers of ten
- Develop at least one efficient algorithm for multiplying decimals

- Goals for CMP3 Missing Factors, Bits and Pieces III, Problem 2.2
- Numeric Estimation
- Understand that estimation can be used as a tool in a variety of situations, including as a way to check answers and make decisions. Use estimates to solve problems and check answers.

- Decimal Operations
- Revisit and continue to develop meanings for the four arithmetic operations on rational numbers, and practice using algorithms to operate on decimals. Recognize when addition, subtraction, multiplication, or division is the appropriate operation to solve a problem. Use place value to develop understanding of algorithms and to relate operations with decimals to the same operations with fractions. Extend understanding of multiplication and division of multidigit whole numbers Develop standard algorithms for multiplying and dividing decimals with the aid of, at most, paper and pencil. Find a repeating or terminating decimal equivalent to a given fraction Solve problems using arithmetic operations on decimals, including finding unit rates.

- Variables and Number Sentences
- Use variables to represent unknown values and number sentences to represent relationships between values. Write number sentences to represent relationships between both real-world and abstract values. Use fact families to write and solve equivalent number sentences. Use multiplication sentences to check division sentences.

- Numeric Estimation
- Video Transcript
- Suggestions for organizing Professional Development