Name:______Class:______Date______
SWBAT solve problems using gcf in and out of context
Do Now[N1]Use prime factorization to find the gcf of 196 and 84
Answer:
Class Notes[N2]
Jasmine is making bead necklaces. She has 90 green beads and 108 blue beads.
a.)What is the greatest number of identical necklaces she can make if she wants to use all of the beads?
b.)How many blue beads will be in each necklace?
c.)How many green beads will be in each necklace?
I Do – You Help[N3]
The city of Clarksville is honoring 5 mothers and 10 fathers as winners of its "Best Parent" contest. The plan is to take several group photographs, each with the same combination of mothers and fathers and no parents left out. What is the greatest number of photos that can be taken?
How many mothers can be in each photograph?
How many fathers can be in each photograph?
You Do – I Help[N4]
At a party, the cheese pizza is cut into 45 slices and the veggie pizza is cut into 63 slices. If the host wants to serve identical platters that contain the same combination of cheese and veggie slices, with no slices left over, what is the greatest number of platters the host can prepare?
How many cheese slices on each platter?
How many veggie slices on each platter?
Bachelors Practice [N5]
1.) Kristen has two pieces of twine, one 60 inches long and the other 84 inches long. If she wants to cut them up to produce many pieces of twine that are all of the same length, with no twine left over, what is the greatest length, in inches, that she can make them?
Answer (In a complete sentence)
2.) With flu season coming up, Daron decides to make get-well-soon kits. He has 72 cans of chicken soup and 24 boxes of tissue, which he wants to use to make identical kits with no materials left over. What is the greatest number of get-well-soon kits Daron can make?
Daron can make ______get well soon kits.
There will be ______cans of chicken soup in each kit.
There will be ______boxes of Tissues in each kit.
3.) Deja is making stationery sets from 7 sheets of paper and 28 envelopes. If she wants all the sets to be identical without any paper or envelopes left over, what is the greatest number of sets Deja can make?
Deja can make______stationary sets
with ______sheets(s) of paper and ______
envelopes in each set.
4.) Mr. Koller, the science teacher, collected 36 sedimentary rocks and 96 metamorphic ones. Now he wants to create some identical kits for studying rocks, without having any rocks left over. What is the greatest number of kits he can create?
Mr. Koller can make ______kits.
Each kit will contain ______sedimentary rocks and ______
Metamorphic rocks.
Masters Practice (Challenge Problem) [N6]
Ms. Pandolfino has baked 84 raisin cookies, 106 muffins and 128 chocolate chip cookies, which all smell delicious! They smell so good she would like to keep 4 raisin cookies, 6 muffins and 8 chocolate chip cookies for herself though she know she has to cut down on sweets. She'll then put the rest into boxes with equal numbers of each type. What would be the largest number of cookies or muffins in each box?
GCF Problem Solving Exit Ticket
[N7]
Mastered Almost Not Yet
A choir director at your school wants to divide the choir into smaller groups. There are 24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each type of voice.
A. What is the greatest number of groups that can be formed?
_____groups can be formed. (1 pt)
B. How many sopranos , altos, and tenors will be in each group?
(3 pts)
______Sopranos ______Altos ______Tenors
GCF Problem Solving HomeworkMust show all work and answer all problems to get full credit
1.) Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white balloons, and 16 orange balloons. She wants each arrangement to have the same number of each color.
[N8]
a.)What is the greatest number of arrangements that she can make if every balloon is used?
Shannon can make ______balloon arrangements.
b.) How many orange balloons will be in each arrangement? ______
2.) Challenge! (Every student must try this problem)
Mrs. Bell owns a small grocery store. She has just received 3 sacks of sugar [N9]weighing 27kg, 36kg and 72kg and she wants to put them in equal-sized bags before she sells them. What's the least number of bags she would need if she doesn't want any sugar to be left without a bag?
Mrs. Bell will need ______bags if she does not want any sugar to be left over.
[N1]6 minutes
4 minutes work time
2 minutes to review
Do this one for students or look for a student who started this way.
Say, I knew that 14 x 14 is 196 because we call 196 a perfect square. That means you can multiply a number by itself to get this number.
196 = 14 x 14
196 = 2 x 2 x 7 x 7
Ask for a volunteer.
Ask: How did we know that 2 was a factor of 84?
Answer: 84 is an even number
84 = 42 x 2
84 = 6 x 7 x 2
84 = 2 x 2 x 3 x 7
Common Factors: 2 x 2 x 7
GCF = 28
[N2]6 minutes
Ask a student to read both the problem and part A
Say: This problem is really asking us to find the greatest common factor of 90 and 108?
Well how do I know that? I know that because the question is asking for the greatest number of identical necklaces.
That means that every necklace that Jasmine makes will have to all have the same number of green beads and each necklace will also have the same number of blue beads
We also know that Jasmine has to use all of the beads. That means there won’t be any beads left over. So the number of green beads Jasmine uses has to be a factor of 90 and the number of blue beads she uses has to be a factor of 108.
Ask: So how can wee find the gcf of 108 and 90? Use prime factorization
90 = 30 x 3 ( 2 x 3 x 3 x 5 )
108 -= 2 x 54 (2 x 2 x 3 x 3 x 3)
GCF = 18 (5 green and 6 blue beads)
[N3]4 minutes
Say: Ok, now lets try one together.
Ask: How did we say that we know this is a gcf word problem?
Great! Let’s underline the key words and phrases.
Awesome. Now what do we do?
Answer: Find the prime factorization of each number.
Point out that 5 is a prime number
so the prime factorization is 1 x 5.
GCF = 5
1 mother in each photo
2 fathers in each photo.
[N4]4 minutes
Use Equity Sticks
Say: “Ok ______now you take us through this one.”
Ask: How do we know this is a GCF word problem?
Direct students to underline key words and phrases
9 identicalplatters.
5 cheese slices on each platter
7 veggie slices on each platter
[N5]10 Minutes
8 Minutes Work Time
2 Minutes Review
1.) 12 inches long
2.) 24 get well kits
3 cans of chicken soup and 1 box of tissues
[N6]
GCF of 80, 100, and 120 is 20
[N7]10 minutes
6 minutes to complete and 4 minutes to grade and turn in
Differentiation: Possibly remove the Tenors for 623 and 624
12 groups
2 sopranos
5 altos
3 Tenors
[N8]8 arrangements
2 orange ballons
[N9]GCF of 27, 36, and 72 = 9
(27 + 36 + 72)/9 = 15 bags