The factor game
http://illuminations.nctm.org/LessonDetail.aspx?ID=L620
A lesson plan for Grades 3–8 Mathematics
About this resource
- Appropriate grades
- 3–8
- Subjects
- mathematics (arithmetic, number sense)
- Provider
- National Council of Teachers of 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 1.02: Develop fluency with multi-digit addition and subtraction through 9,999 using:
- Strategies for adding and subtracting numbers.
- Estimation of sums and differences in appropriate situations.
- Relationships between operations.
- 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.
- Objective 1.04: Use basic properties (identity, commutative, associative, order of operations) for addition, subtraction, multiplication, and division.
- Objective 1.05: Use area or region models and set models of fractions to explore part-whole relationships.
- Represent fractions concretely and symbolically (halves, fourths, thirds, sixths, eighths).
- Compare and order fractions (halves, fourths, thirds, sixths, eighths) using models and benchmark numbers (zero, one-half, one); describe comparisons.
- Model and describe common equivalents, especially relationships among halves, fourths, and eighths, and thirds and sixths.
- Understand that the fractional relationships that occur between zero and one also occur between every two consecutive whole numbers.
- Understand and use mixed numbers and their equivalent fraction forms.
- Objective 1.06: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
- Objective 1.02: Develop fluency with multi-digit addition and subtraction through 9,999 using:
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.
- Objective 1.03: Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions involving halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, hundredths, and mixed numbers.
- Objective 1.05: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
- Objective 1.02: Develop fluency with multiplication and division:
Grade 5
- Goal 1: Number and Operations - The learner will understand and compute with non-negative rational numbers.
- Objective 1.02: Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).
- Develop and analyze strategies for adding and subtracting numbers.
- Estimate sums and differences.
- Judge the reasonableness of solutions.
- Objective 1.03: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
- Objective 1.02: Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).
Grade 6
- Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
- Objective 1.03: Compare and order 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.
- Objective 1.07: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
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.
- Objective 1.03: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
- Objective 1.02: Develop fluency in addition, subtraction, multiplication, and division of rational numbers.
Grade 8
- Goal 1: Number and Operations -The learner will understand and compute with real numbers.
- Objective 1.02: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
