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 10

Estimation and Computation

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

Numeration

The student demonstrates conceptual understanding of real numbers.

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 4

Number Sense

4.0 Students know how to factor small whole numbers

Algebra

Arithmetic with Polynomials and Rational Expressions

Use polynomial identities to solve problems

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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.