Factor – a number multiplied by another number to find a product
Prime number – a number with exactly two factors, 1 and the number itself
Composite number – a number with more than two factors
Divisibility – the ability to be divided without a remainder
DAY 1
1 2 3 6 9 18
How did you know these numbers were factors of 18?
What do you know about factors? What does it mean to find the factors of a number?
How do you know that there are not more pairs of whole numbers whose product is 18?
Seating Problem
Can you use a rectangular area model with your color tiles to solve this problem? Explain
Could the students be arranged in one row? (Yes)
What would that look like? (1 row with 24 students (tiles) in a row)
How many different area models did you form with the 24 tiles? (8 area models)
What are they? (1 x 24, 2 x 12, 3 x 8, 4 x 6, 24 x 1, 12 x 2, 8 x 3, and 6 x 4)
How many ways can the students be seated onstage? Explain. (8 ways, because there are 8 different area models
or arrangements.)
What are some things the students might consider when deciding which arrangement to use? Answers may vary.
How the students will look at the audience; how big the stage is, etc.
How many factor pairs can be made from 24? Explain.
Factor Pair Area Model Practice
Use color tiles to create an area model for each problem. Record each area model on
centimeter grid paper and label each model. Use your drawings to help you answer the
questions. List all factors and describe the factors with a written description.
DAY 2
What are some of the ways you can find the factors of a number? Answers may vary. You can
use area models, grouping, etc.
How can an area model help find factors? Answers may vary. An area model demonstrates the
possible groupings of a number, etc.
When would an area model not be helpful? Answers may vary. When the numbers get really
large; if you did not have enough color tiles to build it, etc.
Prompt students to brainstorm other possible ways, besides using area models, to find all the
factors of a number. Discuss as a class. Discussion should include multiplication/division facts,
basic number concepts, etc.
Explain that they are going to look at the divisibility rules as another strategy to find the factors of
a number. Have students discuss what they think the word “divisibility” means and then use
the vocabulary note at right to give the formal definition. Be sure to discuss the meaning of a
whole number.
Divisible: A whole number is divisible by another number if the quotient is a whole number and the remainder is zero.
Whole Number: a number that does not have a decimal or a fraction
Divisibility: the ability to be divided without a remainder
Divisibility Rules- POSTER IN ROOM!!
Am I a Factor? Table 30
Am I a Factor? Practice 36
Find the Factor Practice 12
For students who are still struggling with basic facts, have them use a Multiplication Table to help find all the factors of a number.
DAY 3
Factor Rainbow Practice
MISCONCEPTION
Some students may think that there is only one way to represent factor pairs. Factor pairs can be represented multiple ways: factors pairs of
12 are (1,12), (2,6), (3,4), list of factors: (1,2, 3, 4, 6, 12), multiplication (1 x 12, 2 x 6, 3 x 4), factored tree pairs (
charts or tables.
Example:
12
1 12
2 6
3 4
), and/or T-
When factors in the first column begin to repeat the factors in the second column, students know that they have found all the factors for the
given number. Still another way to organize factors might include using a factor tree.
Example:
Point out to students that there is a special name for numbers that have only one factor pair or one “rainbow.” They are called prime
numbers. Numbers that have more than one factor pair or more than one “rainbow” are called composite numbers.
TEXTEAMS: Rethinking Elementary Mathematics Part I: Multiple Towers may be used to reinforce the concepts of prime and
composite numbers.