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Bits And Pieces II

Bits And Pieces II  
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Bits And Pieces II
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Bits And Pieces III

Bits And Pieces II
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Bits And Pieces III
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Bits and Pieces I, II, III

Decimals

Fractions

Percents


CMP Parents
Bits and Pieces I

(University of Michigan Overview)
Concept with Explanation
Selected Homework from ACE
In Bits and Pieces I students will investigate and make sense of rational numbers and operations with rational numbers. The investigations in this unit will help students to:

  • Build an understanding of fractions, decimals, and percents and the relationships between and among these concepts and their representations;
  • Develop ways to model situations involving fractions, decimals, and percents;
  • Understand and use equivalent fractions to reason about situations;
  • Compare and order fractions;
  • Move flexibly between fraction, decimal, and percent representations;
  • Use benchmarks such as 0, 1/2 , 1, and 1/4 to help estimate the size of a number or sum;
  • Develop and use benchmarks that relate different forms of representations of rational numbers (for example, 50% is the same as 1/2 and 0.5);
  • Use physical models and drawings to help reason about a situation;
  • Look for patterns and describe how to continue the pattern;
  • Use context to help reason about a situation; and
  • Use estimation to understand a situation..

Bits and Pieces II
Concept with Explanation
Selected Homework from ACE
Bits and Pieces II was created to help students make sense of one aspect of rational number: fraction operations. The investigations in this unit will help students to:

  • Use benchmarks and other strategies to estimate the reasonableness of results of operations with fractions;
  • Develop ways to model sums, differences, products, and quotients with areas, strips, and number lines;
  • Use estimates and exact solutions to make decisions;
  • Look for and generalize patterns in numbers;
  • Use knowledge of fractions and equivalence of fractions to develop algorithms for adding, subtracting, multiplying and dividing fractions;
  • Recognize when addition, subtraction, multiplication, and division is the appropriate operation to solve a problem;
  • Write fact families to show the inverse relationship between addition and subtraction, and between multiplication and division;
  • Solve problems using arithmetic operations on fractions; and
  • Look for and generalize patterns.

Bits and Pieces III
Concept with Explanation
Selected Homework from ACE
Bits and Pieces III, along with Bits and Pieces I and Bits and Pieces II, completes the development of meaning of, and operations on, fractions, decimals, and percents. This unit will help students to:

  • Connect to what students already know about operations on fractions and whole numbers;
  • Develop and use benchmarks and other strategies to estimate the answers to computations with decimals;
  • Develop meaning of and algorithms for operations with decimals;
  • Use the relationship between decimals and fractions to develop and understand why decimal algorithms work;
  • Use the place value interpretation of decimals to make sense of short-cut algorithms for operations;
  • Generalize number patterns to help make sense of decimal operations;
  • Understand when addition, subtraction, multiplication or division is an appropriate operation to use to solve a problem;
  • Understand that decimals are often associated with measurements in real world situations;
  • Solve problems using operations on decimals;
  • Use understanding of operations and the meaning of percents to solve percent problems of the form a% of b equals c for any one of the variables a, b, or c; and
  • Create and interpret circle graphs