DAY 2: Common Factors
Materials
Copies:
2.1 Greatest Common Factors
2.2 X Problems II
Ticket out the Door Day 2
Supplies:
Word Wall Cards: Greatest Common Factor
Multiplication chart(s) available for students to see/use
Objective
Students will look at orders for sets of three people where all orders contain 1 item in
common. They will learn to find the common item and factor this out to understand the
concept of factoring. They will apply this understanding to factoring algebraic
expressions by finding a common factor.
Student Talk Strategy
Three-way Interview for opening of 2.1
Report to a partner for 2.2
Academic Language Use
Area- The number of squares it takes to cover a rectangle. The teacher will introduce
and model this by giving the students squares, representing area.
Dimensions- In this unit, the two numbers being multiplied, the factors, will be used to
represent the dimensions, or the base and height of a rectangle. This term will be
introduced and modeled by the teacher throughout.
Factors- In this unit, the two numbers being multiplied, the base and height of the
rectangle, will be called factors. This will be modeled by the teacher throughout.
Product- In this unit, the answer to the multiplication problem, also the same as the area
of the rectangle, will be referred to as the product. This will be modeled by the
teacher throughout.
Greatest Common Factor- The largest monomial (integer and/or variable) that evenly
divides each term.
Activity Notes
15 minutes: Greatest Common Factor- Part 1
Pass out activity sheet 2.1. Give the students 1 minute to silently read the introduction.
Then use three-way interview to have each student find a partner, ask his/her partner
why 2 and 3 are factors of 6, and then call on 2-3 students to share what their partner
said. Explain to the class that you will be looking at another method to understand
factoring today. Direct the students’ attention to task 1. Explain that they need to look
for what is “common” to all items so they can save time in ordering. Point to example
#1 and give them 30 seconds to look at the word and pictures to decide what is
“common” to all the items being ordered. Use a chorale response to have the class tell
you what is common (the apples). Model how to record this in the space provided.
Teacher’s Guide Factoring & Solving Quadratics- Day 2
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Order:
Apples ( burger + nuggets +taco)
Have the class read the statement “What we just did was to pull out a common factor”
aloud together. Note: we will put up the word wall card later on, once they have a
better understanding. Set the timer for 10 minutes to have the students finish part 1 (#’s
1-5). Circulate to ensure the students understand and are doing the work correctly. If
time permits, use purposeful selection to have a few students share their answers. If
students are struggling with the language, feel free to draw pictures for each problem!
15 minutes: Greatest Common Factor- Part 2
Direct the students’ attention to part 2. Again, give them 1 minute to read the top
paragraph. Write up on the board: one #2 special, one #5 special and one #1 special.
Ask the class what is FOOD ITEM common to all the items- give them 10 seconds to
think and then call on a few students to share. They may point out “special”, but since
that is not a food item, we don’t know how to order it. Explain that we need to know
what comes IN each special to see if there is any food in common. Let the class know
that you will be uncovering the “specials” in this next part, by having them break down
each term into its factors. Go through examples 1 and 2 as a class, and ask the class, by
show of hands, who remembers doing factor trees. For example 2, while 6 and 2 are
factors, explain that the 6 has something “hidden” in the fact that it can be broken down
even more. Model how to circle the “prime factors”, the numbers that can only be
divided by 1 and the number itself or the numbers that can only be drawn as rectangles
with a base or height of 1. Put up the word wall card for Greatest Common Factor.
Ex 2: 12
6 • 2
3 •2
Prime Factors: 12 = 3 • 2 • 2
Set the timer for 5 minutes for the students to work alone on problems 1-8. Circulate to
ask guiding questions, such as, “what does x3 mean- how many x’s are being
multiplied?” Allow the students to use a multiplication chart to help them find factors!
After 5 minutes, have the students move their desk next to a partner to finish/check
work. Circulate to assess and question the students.
15 minutes: Greatest Common Factor- Part 3
Part 3 brings parts 1 and 2 together. Explicitly go over the 3 parts (a-c). Work through
problem #1 together, allowing the students 30 seconds to do part a, then calling on a
student to share, followed by 15 seconds to answer b. Use chorale response to have the
class say what is common. Finally, allow 30 seconds for the students to do part c and
have them check their work with a partner. Again, set the timer for 5 minutes for
Teacher’s Guide Factoring & Solving Quadratics- Day 2
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students to work alone. Note: a common mistake you may find on #2 is that the
students think “2x” is what is left as opposed to x 2. Then, set the timer for 5 minutes to
allow students to work with a partner. Use the last few minutes to have students come
share their solutions.
Note: we will revisit this topic at the beginning of Day 3.
10 minutes: X problems II
Pass out activity sheet 2.2. Go over example 1 as a class, pointing out the two side
numbers and asking the students how the two numbers were used to get the top
number. Have the class think for 10 seconds and then chorale reply “multiply”. Then
ask how the two side numbers were used to get the bottom number. Again, after 10
seconds to think, have the class chorale reply “add”. Give the class 1 minute to
complete example 2 and have them use report to a partner to share their answer. Call
on a volunteer to show his/her work. Then tell the students that example 3 is a bit
more challenging, as they now have the product and sum, but must figure out what the
numbers for the sides are. Give them 30 seconds to try to figure it out, and then use
report to a partner to have them share their ideas. Again, call on a volunteer to share.
Remind the class to be careful about the signs (negative and positive). Set the timer for
5 minutes for students to do as many as they can independently. Once the timer ends,
put up the answers for the class to check their work.
5 minutes: Ticket out the Door
Pass out the Ticket out the Door and collect it as soon as each student finishes (so that
you can discuss mistakes with students as they turn it in).
Teacher’s Guide Factoring & Solving Quadratics- Day 2
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