Finding Factors

Abstract

The following discussions and activities are designed to give students practice in finding the factors of whole numbers. The activities provide ample practice opportunities to reinforce the information from the discussions

Objectives

Upon completion of this lesson, students will:

  • have learned about factors
  • have visually seen how factorizations make up various numbers

Standards Addressed

Grade 3

  • Functions and Relationships

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

  • Geometry

    • The student solves problems using perimeter or area.

  • 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.

  • Geometry

    • The student solves problems using perimeter or area.

  • 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.

  • Geometry

    • The student solves problems (including real-world situations) using perimeter or area.

  • 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).

  • Numeration

    • The student demonstrates conceptual understanding of fractions (proper or mixed numbers), decimals, percents (whole number), or integers.

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

  • Measurement and Data

    • Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

  • Operations and Algebraic Thinking

    • Represent and solve problems involving multiplication and division.

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

Grades 6-8

  • Geometry

    • Use visualization, spatial reasoning, and geometric modeling to solve problems

  • Numbers and Operations

    • Compute fluently and make reasonable estimates
    • Understand meanings of operations and how they relate to one another

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.

Grade 6

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

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

Grade 7

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

    • COMPETENCY GOAL 1: The learner will understand and compute with 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

  • Algebra

    • The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

  • 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.

6th Grade

  • Number and Operation

    • Content Standard 1.0 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.

7th 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.

8th 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.

8th Grade

  • Computation and Estimation

    • 8.5 The student, given a whole number from 0 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies.

Textbooks Aligned

Grade Six

  • Prime Time

    • Investigation One: The Factor Game
    • Investigation Three: Factor Pairs
    • Investigation Four: Common Factors and Multiples
    • Investigation Five: Factorizations

Book 1

  • Module 4 - Mind Games

    • Section 2: Prime Factors

Book 2

  • Module 3 - A Universal Language

    • Section 1: Prime Factorization
    • Section 1: Common Factors

6th

  • Module 3 - Mind Games

    • Section 3: Factors and Divisibility

7th

  • Module 3 - Codes

    • Section 2: Factors, Divisibility, and Multiples

8th

  • Module 7 - The Algebra Connection

    • Section 4: Polynomials and Factoring

Grade 8

  • Reflections on Number

    • Divisibility and Prime Factorization

Student Prerequisites

  • Arithmetic: Students must be able to:
    • perform basic operations on whole numbers
    • understand visual representations of numbers
  • 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
  • pencil and paper

Key Terms

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

Lesson Outline

  1. Focus and Review

    Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

    • Ask students if anyone knows what a factor is
    • Using either the defintion a student gives, or one you provide yourself, ask if anyone knows what it means to factorize a number.

  2. Objectives

    Let the students know what it is they will be doing and learning today. Say something like this:

    • Today, class, we will be talking about factors
    • We are going to use the computers to learn about factors, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about this activity first.

  3. Teacher Input

    • Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.
    • Open your browser to Factorize in order to demonstrate this activity to the students.

  4. Guided Practice

    • Work through the first few questions on the Factorize Questions worksheet and then let them finish it on their own.
    • When you begin using the Factorize activity you may want to have students take turns giving answers to the problems and work through one or two games as a class until students are ready to try it on their own

  5. Independent Practice

    • Allow the students to work in groups of two. Monitor the room for questions and to be sure that the students are on the correct web site.

  6. Closure

    • You may wish to bring the class back together to discuss any problems that were especially hard for students to solve. Once the students have been allowed to share what they found, summarize once more the main points of the lesson.

Alternate Outline

This lesson can be rearranged in several ways if there is only one available computer:

  • This lesson can be rearranged in several ways if there is only one available computer: Have students complete paper worksheets that ask them to find the factors of certain numbers and use Factorize as a reward for two students at a time who have shown proficiency in solving the problems on paper.
  • Alternatively, select students who need additional practice to use the game. Teams of one strong student and one who needs help work well with this activity.