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Action Research

This video spotlights instances where students' words and actions seem to indicate understanding. On further investigation the apparent understanding was revealed to be different from or more fragile than what might have been assumed from the evidence. This is a situation in which teachers frequently find themselves.

The teacher reflects on this issue and follows up on some questions she has about students' prior knowledge.

All clips originate from the same group of students working with Bits and Pieces II and Bits and Pieces III.

As you view the video, consider the following:

• What are the goals of Bits and Pieces II, Problems 3.1, 3.2?
• How would you expect students to think about 2/3 of 3/4 and 3/4 of 2/3 after their experiences with Problems 3.1 and 3.2?
• What are the goals of Bits and Pieces II, Problem 3.3, 3.4?
• From their experience with Bits and Pieces II, 3.3 and 3.4, what strategies would you expect students to develop for multiplying mixed numbers?
• What are the goals of Bits and Pieces III, 2.1?
• What do students have to know in order to be successful with Bits and Pieces III, 2.1?
• How does Bits and Pieces III 2.1 relate to the development of an algorithm for multiplying decimals?
• CMP2 Goals
• 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
• CMP3 Goals
• 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.
• Video Transcript