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K–12 teaching and learning · from the UNC School of Education

The factor game

http://illuminations.nctm.org/LessonDetail.aspx?ID=L620

A lesson plan for grades 3–4 and 6–7 Mathematics

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In this activity, students play a game in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Illuminations provides an activity sheet and an applet to complete this lesson. After the teacher demonstrates how to convert word problems to number sentences, students play the Factor Game in pairs. Then, students create a table of all the possible moves they could make when playing the game and evaluate the worst and best moves.

Students will:

  • Distinguish between numbers with many factors and numbers with few factors.
  • Define prime and composite numbers.
  • Play a strategy game which reinforces these concepts.

NCTM Standards and Expectations covered in this lesson include:

  • Using factors, multiples, prime factorization, and relatively prime numbers to solve problems.
  • Using the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 3

  • Goal 1: Number and Operations - The learner will model, identify, and compute with whole numbers through 9,999.
    • Objective 1.03: Develop fluency with multiplication from 1x1 to 12x12 and division up to two-digit by one-digit numbers using:
      • Strategies for multiplying and dividing numbers.
      • Estimation of products and quotients in appropriate situations.
      • Relationships between operations.

Grade 4

  • Goal 1: Number and Operations - The learner will read, write, model, and compute with non-negative rational numbers.
    • Objective 1.02: Develop fluency with multiplication and division:
      • Two-digit by two-digit multiplication (larger numbers with calculator).
      • Up to three-digit by two-digit division (larger numbers with calculator).
      • Strategies for multiplying and dividing numbers.
      • Estimation of products and quotients in appropriate situations.
      • Relationships between operations.

Grade 6

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.
    • Objective 1.05: Develop fluency in the use of factors, multiples, exponential notation, and prime factorization.

Grade 7

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.02: Develop fluency in addition, subtraction, multiplication, and division of rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.