Let's Be Rational
Standards & Objectives | |
File Size: | 325 kb |
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Goals for Let's Be Rational
Students should...
- Understand that estimation is a tool used in a variety of situations including checking answers and making decisions, and develop strategies for estimating results of arithmetic operations
- Revisit and continue to develop meanings for the four arithmetic operations and skill at using algorithms for each
- Variables and Equations Use variables to represent unknown values and equations to represent relationships
Investigation 1
Investigation 1 Vocabulary | |
File Size: | 222 kb |
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Investigation 1 focuses on estimating sums of fractions and decimals, and then moves to finding algorithms for precise computations. It builds on Comparing Bits and Pieces by extending skills with benchmarks, equivalent fractions, and the relationship between decimals and fractions.Students play a game in which they estimate the size of sums. Students also explore estimation as a strategy to reason about contextual situations. They identify whether their estimate is an underestimate or an overestimate.
This Investigation also focuses on developing computational understanding and skill in adding and subtracting fractions. Students are not given algorithms for computation. Instead, students figure out how to add and subtract fractions by being flexible in finding equivalent fractions. This Investigation serves as an important formative assessment of students’ understanding of fractions.
In the course of solving the problems, students develop strategies for adding and subtracting fractions and mixed numbers. Through class discussion, these strategies are made more explicit and efficient.
This Investigation also focuses on developing computational understanding and skill in adding and subtracting fractions. Students are not given algorithms for computation. Instead, students figure out how to add and subtract fractions by being flexible in finding equivalent fractions. This Investigation serves as an important formative assessment of students’ understanding of fractions.
In the course of solving the problems, students develop strategies for adding and subtracting fractions and mixed numbers. Through class discussion, these strategies are made more explicit and efficient.
Investigation 2
Investigation 2 Vocabulary | |
File Size: | 155 kb |
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Investigation 2 focuses on developing computational skill with and understanding of fraction multiplication. Various contexts and models are introduced to help students make sense of when multiplication is appropriate.In Problem 2.1 students develop an understanding of multiplication with simple fractions. Problems 2.2 and 2.3 focus on multiplication with fraction, mixed number, and whole-number combinations.
Estimation is used across the Problems so that students can determine the reasonableness of their answers. Also, students develop the idea that multiplication does not always lead to a larger product. Within these Problems, students form a general algorithm for fraction multiplication.
Estimation is used across the Problems so that students can determine the reasonableness of their answers. Also, students develop the idea that multiplication does not always lead to a larger product. Within these Problems, students form a general algorithm for fraction multiplication.
Investigation 3
Investigation 3 Vocabulary | |
File Size: | 154 kb |
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Investigation 3 explores the operation of division. Problem 3.1 emphasizes estimation. The context involves measurements that provide a familiar setting for the first interpretation of division. Students are asked to consider How much of this is in that? using fractional dividends and divisors. Everyday situations are used to help students make sense of when division is an appropriate operation. The first two Problems in the Investigation involve the measuring interpretation of division, and the third involves the sharing interpretation. The last Problem uses presorted division problems to develop a general algorithm for fraction division.
Investigation 4
Investigation 4 Vocabulary | |
File Size: | 214 kb |
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Investigation 4 concludes Let’s Be Rational’s exploration of the four arithmetic operations with fractions, first by considering more abstract relationships among the four operations, and second by considering what kinds of contexts lead to each of the operations in order to highlight their structure. Problems 4.1 and 4.2 have students use fact families to express additive and multiplicative relationships among fractional quantities. In doing so, students also work on the ideas of inverse and decomposition, each of which is an important numerical precursor to algebra work. Problem 4.3 presents students with a variety of contextual problems. Students have to sort out for themselves which operations apply in each situation. Being able to recognize which operation is called for in a problem situation strengthens students’ understanding of the meaning of each operation.