Accentuate the Negative
Standards & Objectives | |
File Size: | 205 kb |
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Goals for Accentuate the Negative
Students should...
- Develop an understanding that rational numbers consist of positive numbers, negative numbers, and zero
- Develop understanding of operations with rational numbers and their properties
Investigation 1
Vocabulary | |
File Size: | 221 kb |
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This Investigation gives students experiences with rational numbers, ordering numbers, and informal operation computations in a variety of contexts. Subsequent formal work can therefore be based on “what makes sense.” Positive and negative numbers in the form of integers, fractions, and decimals are represented on a number line. Students use horizontal and vertical number lines when representing positive and negative numbers. They also reinforce skills in graphing inequalities when exploring relationships between rational numbers.
Students informally develop methods for adding integers by working on problems that have real-life contexts, such as money or scores in a game. They connect the operations of addition and subtraction (including the relationships between these two operations) to actions on chip-board displays. Students extend their work around comparing and ordering positive and negative integers to rational numbers.
Students informally develop methods for adding integers by working on problems that have real-life contexts, such as money or scores in a game. They connect the operations of addition and subtraction (including the relationships between these two operations) to actions on chip-board displays. Students extend their work around comparing and ordering positive and negative integers to rational numbers.
Investigation 2
Vocabulary | |
File Size: | 222 kb |
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This Investigation gives students experience with adding and subtracting positive and negative rational numbers. Students experiment with addition and subtraction by modeling real-world situations on chip boards with black and red chips representing positive and negative integers. Students also use the more sophisticated model of a number line. These experiences build the foundation for developing algorithms for addition and subtraction with positive and negative rational numbers. Students will use these operations with whole numbers, fractions, and decimals.
They examine the Commutative Property of Addition with rational numbers and then use it to simplify more complicated problems. The usefulness of fact families is revisited with positive and negative rational numbers.
They examine the Commutative Property of Addition with rational numbers and then use it to simplify more complicated problems. The usefulness of fact families is revisited with positive and negative rational numbers.
Investigation 3
Vocabulary | |
File Size: | 216 kb |
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This Investigation gives students experience with multiplying and dividing rational numbers. The Investigation uses time, distance, speed, and direction to think about multiplication and division of rational numbers. Students also examine number patterns and develop algorithms for multiplying and dividing rational numbers. Problem 3.1 focuses on multiplication patterns with positive and negative integers. Problem 3.2 builds on the first problem by examining algorithms for multiplying rational numbers that include fractions. Problem 3.3 looks at positive and negative fractions and fact families to develop multiplication and division further. Finally, students play the Integer Product Game to solidify their experiences with positive and negative integers.
Investigation 4
Vocabulary | |
File Size: | 222 kb |
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This Investigation focuses on properties of operations. Problem 4.1 reviews the Order of Operations convention that students learned in Grade 6 and extends it to include integers. Problem 4.2 examines the Distributive Property over subtraction. Students encounter more complicated strings of computations in which they have to use their knowledge of the Order of Operations to carry out the needed computations. Problem 4.2 also challenges students to work in both directions with expressions. Students expand and factor expressions that involve positive and negative numbers.
Problem 4.3 gives students an opportunity to use their knowledge of and experience with operations to solve problem situations. These problem situations have no labels suggesting a particular algorithm to use. Students have to decide which of the algorithms they have studied are appropriate.
Problem 4.3 gives students an opportunity to use their knowledge of and experience with operations to solve problem situations. These problem situations have no labels suggesting a particular algorithm to use. Students have to decide which of the algorithms they have studied are appropriate.