**"Factors"**

Edwina R. Justice Gunsaulus Scholastic Academy

4420 South Sacramento Ave.

Chicago IL 60632

(312) 535-7215

**Objectives**:

Demonstrate a phenomenological approach to teaching mathematics

Inspire others to use the approach

**Objectives (Grades 5-7)**:

Show and record groups formed by using pennies

Define factor, product, prime, and composite

Write related number sentences

Find the factors of whole numbers

Classify numbers as prime or composite

Identify abundant, deficient, and perfect numbers

**Materials Needed**:

paper coins (actual coins??)

worksheet for analyzing first moves

**Recommended Strategy**:

Ask: "How many ways can you make change for $1.00 using only groups of the

same coin?"

Expected responses: 1 group of 100 pennies

20 groups of nickels

10 groups of dimes

4 groups of quarters

2 groups of half-dollars

"How many ways can you make equal groups of 100 pennies?"

Expected responses: 1 group of 100 pennies

2 groups of 50 pennies

4 groups of 25 pennies

10 groups of 10 pennies

20 groups of 5 pennies

Discuss similarities in responses to both questions

Show one penny - Write "1 group of 1 = 1"

Show two pennies - Write "1 group of 2 = 2"

Show three pennies - Write "1 group of 3 = 3"

Show four pennies - Write "1 group of 4 = 4"

Show two groups of two pennies - Write "2 groups of 2 = 4"

Show and record all equal groups for 5 to 12 pennies

Write number sentences: 1 x 1 = 1; 1 x 2 = 2; 1 x 3 = 3; 1 x 4 = 4;

2 x 2 = 4; 1 x 5 = 5; 1 x 6 = 6; 2 x 3 = 6;

... 1 x 12 = 12; 2 x 6 = 12; 3 x 4 = 12

Define factor and product

Analyze number of factors for products 1 - 12

Identify and define prime and composite numbers for products 1 - 20

Play "Factor Game" - List the numbers 1 - 36 as a 6 x 6 grid.

Circle a number. Students draw a box around each proper factor

of the number. Students select a number and draw a box around it.

Teacher circles proper factors of the number. Continue process until

no moves are possible. Add the teacher's and students' numbers. The

highest total wins.

Analyze first moves for the factor game - List the factors for numbers

1 - 36. Compare the sum of the proper factors to each number.

Define abundant, deficient, and perfect numbers

**Performance Assessment**:

Select a two-digit number greater than 50.

Identify its factors.

Write related number sentences using the factors and the number.

Explain why the number is prime or composite.

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