Factors

Abstract

Students learn about factoring by using manipulatives and computer applets.

Objectives

Upon completion of this lesson, students will:

  • understand the concept of a factor
  • identify factors of whole numbers
  • explain the relationship between factors, multiplication, divisors, and division

Standards Addressed

Grade 3

  • Functions and Relationships

    • The student demonstrates conceptual understanding of functions.
    • The student demonstrates algebraic thinking.

  • Numeration

    • The student demonstrates conceptual understanding of whole numbers up to one thousand.

Grade 4

  • Functions and Relationships

    • The student demonstrates conceptual understanding of functions, patterns, or sequences.
    • The student demonstrates algebraic thinking.

  • Numeration

    • The student demonstrates conceptual understanding of whole numbers to ten thousands.

Grade 5

  • Functions and Relationships

    • The student demonstrates conceptual understanding of functions, patterns, or sequences.
    • The student demonstrates algebraic thinking.

  • Numeration

    • The student demonstrates conceptual understanding of whole numbers to millions.

Grade 6

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

Grade 7

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

Grade 8

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

Grade 9

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.

Grade 10

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.

Grade 4

  • Number Sense

    • 4.0 Students know how to factor small whole numbers

Third Grade

  • Operations and Algebraic Thinking

    • Represent and solve problems involving multiplication and division.
    • Understand properties of multiplication and the relationship between multiplication and division.
    • Multiply and divide within 100.

Fourth Grade

  • Operations and Algebraic Thinking

    • Use the four operations with whole numbers to solve problems.
    • Gain familiarity with factors and multiples.

Sixth Grade

  • The Number System

    • Compute fluently with multi-digit numbers and find common factors and multiples.

Algebra

  • Arithmetic with Polynomials and Rational Expressions

    • Use polynomial identities to solve problems

Grades 3-5

  • Numbers and Operations

    • Compute fluently and make reasonable estimates

Grade 3

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will model, identify, and compute with whole numbers through 9,999.

Grade 4

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will read, write, model, and compute with non-negative rational numbers.

Grade 5

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 1: The learner will understand and compute with non-negative rational numbers.

3rd Grade

  • Number and Operations

    • The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.

6th Grade

  • Numbers and Operations

    • The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

Elementary Algebra

  • Elementary Algebra

    • Standard EA-2: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.
    • Standard EA-6: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

5th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

3rd Grade

  • Numbers and Operations

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

4th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Student Prerequisites

  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag
    • use a browser for experimenting with the activities

Teacher Preparation

  • access to a browser
  • access to pencil and paper

Key Terms

division

The inverse operation of multiplication

factor

Any of the numbers or symbols in mathematics that when multiplied together form a product. For example, 3 is a factor of 12, because 3 can be multiplied by 4 to give 12. Similarly, 5 is a factor of 20, because 5 times 4 is 20

multiples

The product of multiplying a number by a whole number. For example, multiples of 5 are 10, 15, 20, or any number that can be evenly divided by 5

multiplication

The operation by which the product of two quantities is calculated. To multiply a number b by c is to add b to itself c times

Lesson Outline

  1. Focus and Review

    • Pass out 2 pieces of graph paper to each student.
    • Instruct the students to draw all possible rectangles with an area of 10 squares.
    • The students should draw squares with dimensions of 1x10, 2x5, 5x2, and 10x1.
    • Call on several students to draw their rectangles on the board.
    • Next, instruct the students to draw all possible rectangles with an area of 24 squares.
    • Continue having the students draw rectangles for different size areas until they recognize that there is a connection between the dimensions of the rectangles and the area of the rectangles.
    • Call on a student to explain this connection to the class.

  2. Objectives

    Students will demonstrate their ability to list the factors for different numbers.

  3. Teacher Input

    Explain to the class the term "factor."

  4. Guided Practice

    Work a few problems with the class demonstrating how to using the Factorize and the Factorize 2 applets.

  5. Independent Practice

    Instruct the students to work 10 computer generated problems from each applet.

  6. Closure

    Review the term factor and some different methods that can be used to find the factors of a given number.