Download Factors and Multiples Lesson Ideas

Factors and Multiples Lesson Ideas
Day 1: Factors vs. Multiples Exploration
1. Ask students to share what they know about factors and multiples. Have students
complete a “Rally Table” – give each table a blank sheet of paper. The first person writes
one fact they know and passes it to the next person who then writes one fact. The group
continues to pass the paper and write what they know for a few minutes. Next, have
groups share their facts, and have other groups check any facts that are said out loud by
any group. Make sure to highlight the big ideas/themes.
2. Distribute colored chips/blocks/manipulatives. Define “multiple.” For example, “List
some multiples of 3.” Ask students what “multiple” makes them think of. Students may
say, “many” or “more than 1.” Show students that if they have 3 blocks to represent 3,
multiples of 3 are simply “many sets of 3” (3, 6, 9, 12). Ask students how the numbers
change from each multiple of 3. Students should say +3. Ask students how else the
numbers are behaving. For example, “How are 3 and 6 related? How are 3 and 9 related?
How are 3 and 12 related?” Students should pick up the pattern that, “it is 3 x 2, 3 x 3, 3 x
4, etc.” In essence, to find multiples of 3, one can multiply 3 with another positive
integer to get a multiple. Ask students, “How many multiples does a number have?”
(Infinite!) Use examples of finding multiples of 5, 8, 10. To wrap up, ask students to
define in their own words what multiples of numbers are.
3. Define “factors.” For example, “List the factors of 8.” Ask students what “factors” mean
to them in a general setting. For example, “What are some factors that contribute to your
grades?” Discuss the components of a grade, for example homework, projects,
classwork, and tests. All of these items combined are the factors that make up the grade.
Similarly the factors of numbers are the numbers that combine (multiply) to make up the
number. Distribute Katie Cubes or square tiles to use for the following activity. Students
should have 8 blocks. Factors are simply smaller numbers that divide evenly into the
number. With manipulatives, students can think of it as creating rectangles or squares
with the given number. For example, 2 x 4 makes a perfect rectangle of 8. 8/2 = 4 and
8/4 = 2 (divides evenly!). Hence, 2 and 4 are factors of 8. 1 x 8 works as well. Hence, 1,
2, 4, and 8 are all factors of 8! Students may begin seeing that if you can multiply two
numbers to get 8, those two numbers are factors. Specifically, they are called “factor
pairs” (two factors that multiply to the number). Have students find factors of 12 and 18.
4. To help distinguish between factors and multiples, students can think of factors as smaller
parts that multiply to form a product and multiples as larger numbers that the numbers are
factors of.
5. On the board, make two columns: factors and multiples. Write the number 10 on the
board above the two columns. Ask students to come up and fill out numbers one by one
for each column and explain why. Students can critique and correct one another with
explanation.
6. Repeat the same exercise with numbers like 2, 9, 16, 30, 50, etc.
Day 2: Common Factors Card Game
1. Assign students to pairs. Using 2 decks of cards without aces and face cards, distribute
about 14 cards to each group. Write down 2 non-prime numbers from 2 - 100, and
students will determine to see if they have a common factor card of the two numbers.
Do one example with them.
Example- The two numbers are 8 and 18. Encourage students to write out factors of both
numbers and see if any factors are present in both! Then, they can see if one of their
cards is a common factor. If they have a 2, then they can put the card down, but only 1
card of 2 (they may have multiple 2s).
Examples to use:
9 and 21
14 and 21
30 and 40
18 and 27
60 and 90
(3)
(7)
(5, 10)
(3, 9)
(2, 3, 5, 6, 10)
24 and 32
18 and 36
15 and 30
4 and 28
56 and 84
(2, 4, 6, 8)
(2, 9)
(3, 5)
(4)
(2, 4, 7)


Students can find as many different factors, as long as they are valid factors!
Each card is worth 1 point, and after each card is put down, they may draw
another card from the deck.
 Whoever puts down the GREATEST COMMON FACTOR, however, gets an
extra point.
2. As a wrap-up, explain how the GCF (Greatest Common Factor) requires them to list out
all common factors. On the board, practice finding GCFs by giving examples such as
“The GCF between 8 and 12, (4), or 24 and 30 (6).”
For additional support materials and instructional activities for Greatest Common Factor, see
Moving with Math Fractions and Decimals (MH2) Lesson Plans (p. 7).
Day 3: Assign students to pairs and distribute Multiples Card Game resource and one deck of
cards without aces or face cards for each pair of students.
1. For each round, students will place a card down and record it under card 1 and card 2 (if
the numbers are the same, they are to draw another card so they are different). Under
each card, they are to write out 8 multiples of the number. Then they will circle common
multiples. Explain that common multiples are numbers that are multiples of both
numbers.
2. When rounds are finished, ask students to share and explain what they believe the “Least
Common Multiple” is for each of their rounds.
3. Distribute dry erase boards. Review examples that require them to practice finding the
Greatest Common Factor of two numbers, and finding Least Common Multiples of two
numbers.