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 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.

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 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

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.

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.

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.

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

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.

Objectives

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

Teacher Input

Explain to the class the term "factor."

Guided Practice

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

Independent Practice

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

Closure

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