Area of polygons
Surface Area
GCF, LCM, &
Word Problems
Word Problems
Prime Factorization
Ratios & Rates
100
What is the area of the figure below? Line DQ = 5 in, Line QC = 4in, and Line CB = 10 in. Line AB = 9.
90in2
100
Use the net to find the surface area of the solid below.
Square base (36) + Each triangle (27) (include all four)
36 + 27 + 27 + 27 + 27 = 144 ft2
36 + (4 x 27) = 144 ft2
100
Areli has two planks of plywood to make shelves. One of the planks is 4 2/3 feet long and the other plank is 5 1/6 long. How much plywood does she have to make the shelves?
4 2/3 + 5 1/6 = 4 4/6 + 5 1/6
9 5/6 feet of plywood total.
100
What is the prime factorization of 48?
2 x 2 x 2 x 2 x 3 or 24 x 3
100
This fall the ratio of Wiley basketball players to baseball players is 3:2. If there are 100 athletes playing either sport how many are playing basketball?
Hint: Use the ratio of basketball players to baseball players to total.
basketball:baseball:total
3:2:5
5 x 20 = 100 Do the same to the other terms in the ratio.
3 x 20 = 60 basketball players 2 x 20 = 40 baseball players.
200
How much wrapping paper is needed to wrap the gift below?
Credit: https://www.toppr.com/ask/question/find-the-surface-areain-cm2-of-the-square-pyramid-shown-below/
10 x 10 = 100
12 x 10 divided by 2 = 60
100 + 60 + 60 + 60 +60 = 340 cm2
200
You have 42 red cards and 63 blue cards. You are putting them into sets.
Each set has the same amount of red cards and each set has the same amount of blue cards.
How many sets can you make?
Challenge: How many red cards are in each set and how many blue cards are in each set?
You can make 7 sets.
Challenge: Each set has 6 red cards and 9 blue cards.
200
What is the prime factorization of 280?
2 x 2 x 2 x 5 x 7 or 23 x 5 x 7
200
Find the missing terms in the ratio table below.image credit: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-equivalent-ratios/v/solving-ratio-problems-with-tables-exercise
Term next to 80 = 48 because 40 x 2 =80 so 24 x 2 = 48.
Term next to 12 = 20 because 24 ÷ 2 = 12 and 40 ÷ 2 = 20.
Term next to 3 = 5 because 12 ÷ 4 = 3 and 20 ÷ 4 = 5.
300
What is the area of the figure below? Line AE is 12 km long.
Area of the bottom rectangle (48) + Area of top triangle (12).
48+12 = 60km2
300
How much paint is needed to paint the statue below?
Credit: https://www.slideshare.net/Kim199/surface-area-of-triangular-prism-1
Front Triangle (49.5) + Back Triangle (49.5) + Left Rectangle (192) + Right Rectangle (192) + Bottom Rectangle (144)
49.5 + 49.5 + 192 + 192 + 144 = 627 m2
300
Joanna bought cookies and cupcakes for a party. The cookies are sold in packs of 10 and the cupcakes are sold in packs of 12. Joanna bought as few packs as possible to have the same number of cookies and cupcakes.
How many total cupcakes did she buy?
Challenge: How many packs of cookies and cupcakes did she buy?
She bought 60 cupcakes.
Challenge: She bought 6 packs of cookies and 5 packs of cupcakes.
300
How many prime factors does the prime factorization of 1000 have?
6 prime factors: 2 x 2 x 2 x 5 x 5 x 5 or 23 x 53
300
In 2022 Wiley's softball team won at a rate of 6 wins to every 2 losses. In 2021 the softball team won 18 times and lost 7 times. Which year's team had the better wins to losses ratio?
Hint: to compare two or more ratios/rates one of the terms must be the same in both ratios.
2022 team 6:2 = 18:6
18:6 compared to 18:7
2022 team (18:6) had a greater wins to losses ratio than the 2021 team (18:7)
400
The theater crew is painting a board for a scene in their upcoming Beauty and the Beast musical performance. First they make a model design below.
How much paper will they need for the model design below?
Bottom rectangle (280) + Top rectangle (160) + Each triangle (10)
280 + 160 + 10 + 10 = 460 cm2
400
Which of the two nets represents a 3-d figure with a surface area of 52 units2?
Credit image 2: https://www.ixl.com/math/lessons/what-is-surface-area
Surface Area of cube's net is 54 in2. (3x3=9, 9 x 6 equal sides = 54)
Surface Area of rectangular prism's net is 52 in2.
Front/back 4 x 2 = 8, 2 equal sides so 2 x 8 = 16.
Left/Right 2 x 3 = 6, 2 equal sides so 2 x 6 = 12.
Top/Bottom 4 x 3 = 12, 2 equal sides so 2 x 12 = 24.
Surface Area Rectangular prism: 16 + 12 + 24 = 52 in2.
400
There are 84 boys and 72 girls going on a field trip.
The students are split into groups. Each group has an equal number of boys in it and an equal number of girls in it.
How many groups will the students be split into?
Challenge: How many boys and girls will be in each group?
The students are broken into 12 groups.
Challenge: There are 7 boys and 6 girls in each group.
400
How many prime factors does the prime factorization of 512 have?
9 prime factors: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 or 29
400
Jayden’s cookie recipe uses 4 cups of sugar to make 28 cookies. Olivia’s recipe uses 6 cups of sugar to make 36 cookies. Which cookie recipe is sweeter?
Hint: Which has a greater sugar/cookie ratio? Remember one term in the ratio must be the same in order to compare ratios and rates.
Problem Credit: https://imathworksheets.com/rate-worksheets/wp-comparing-ratios-2.pdf
Olivia's recipe is sweeter because there is more sugar in each cookie. 1/6 > 1/7
Jayden's recipe uses 1 cup of sugar for every 7 cookies or 1/7 of a cup of sugar per cookie.
Olivia's recipe uses 1 cup of sugar for every 6 cookies or 1/6 of a cup of sugar per cookie.
500
How much paint is needed to paint the billboard below?
Middle Rectangle (55) + Each triangle (6) + top/bottom rectangle (20)
55 + 6 + 6 + 6 + 6 + 20 + 20 = 119m2
55 + (4 x 6) + 20 + 20 = 119 m2
500
Darianis is building a model skate park she starts by making a plastic ramp below.
How much plastic is needed to build the model ramp below?
Front rectangle (90) + Right Rectangle (72) + Left Rectangle (54) + Top Triangle (24) + Bottom Triangle (24)
90 + 72 + 54+ 24 + 24 = 264 cm2
500
Damari had 4 1/6 lbs of apples. He made an apple turnover with 1 3/4 lbs of the apples. How many pounds of apples does he have left to make an apple pie?
4 1/6 - 1 3/4 = 4 2/12 - 1 9/12
You have to borrow 1 whole or 12/12 from the 4.
3 14/12 - 1 9/12
2 5/12 lbs of apples left to make apple pie.
500
What is the prime factorization of 630?
2 x 3 x 3 x 5 x 7 or 2 x 32 x 5 x 7
500
Alexander made $110.25 on an 7 hour shift as a supervisor at the local game shop. Cassandra made 146.25 on a 9 hour shift as a supervisor at the local bowling alley. Who makes more per hour and how much more do they make per hour?
Alexander $110.25/7 hours = $15.75/1 hour
Cassandra $146.25/9 hours = $16.25/ 1 hour
16.25 - 15.75 = $0.50
Cassandra makes $0.59 more per hour.