Fractions as Quotients
Fractions of Whole Numbers
Area and Fractional Side Lengths
Word Problems
Mystery
5
Draw a rectangle and shade 3/4 of the rectangle. Explain or show your reasoning.
Sample response:
There are 4 equal parts and 3 of them are shaded so that is 3/4 of the rectangle.
5
Find the value of 1/2 x 6.
3 or 6/2 equivalent.
5
What is the area of the rectangle? Explain or show your reasoning.
96 square centimeters since 12 x 8 = 96.
5
There are 36 fish in 4 aquariums. There are the same number of fish in each aquarium. How many fish are in each aquarium? Show or explain your reasoning.
There are 9 fish in each aquarium since 4 x 9 = 36.
5
3 x 20 = ?
60
10
- Locate on the number line.
- Explain or show why your point represents 6/4.
- The tick marks are equally spaced and there are 4 of them in 1 so each tick mark is 1/4 and 6/4 is at the sixth tick mark.
10
Find the value of 1/8 x 11.
11/8 or equivalent.
10
What is the area of the shaded region? Explain or show your reasoning.
12/5 square units since there are 3 x 4 rectangles shaded and each is 1/5 of a square unit.
10
Mayra ran 1/5 the length of a road, which is 9 miles long. How far did Mayra run? Show or explain your thinking.
9/5 mile or 1 4/5 mile. Sample response: 9 ÷ 5 = 9/5.
10
5 x 24 = ?
120
15
Explain or show why 4/3 = 4 x 1/3.
The drawing shows that there are 4 equal groups of 1/3 in 4/3 so 4/3 = 4 x 1/3.
15
Find the value of 1/3 x 34.
11 1/3 or 34/3 or equivalent.
15
Find the area of the shaded region. Explain or show your reasoning.
12 3/4 or equivalent. There are 12 full squares (3 x 4) and then 3 rectangles that are each 1/4 square are also shaded.
15
A regular sheet of paper is 8 1/2 inches wide and 11 inches long. What is the area of the paper in square inches?
93 1/2 square inches or 88 11/2 or equivalent.
15
1/8 x 32 = ?
4
20
A bottle holds 7/10 liter of water. How much water do 6 bottles hold? Explain or show your reasoning.
42/10 or 4 2/10 liters or equivalent: 6 x 7 = 42 so there are 42/10 liters of water in the 6 bottles.
Sample picture:
20
Find the value of 2/5 x 6.
2 2/5 or 12/5 or equivalent.
20
A banner at a sporting event is 8 feet long and 2 1/3 feet wide.
- Sketch and label a diagram of the banner.
- Find the area of the banner.
18 2/3 or 56/3 square feet or equivalent.
20
There are 8 ounces of pasta in the package. Jessie cooks 2/3 of the pasta. How many ounces of pasta did Jessie cook?
Jessie cooked 5 1/3 ounces of pasta or 16/3 or equivalent because 8 x 2/3 = 16/3 = 5 1/3.
20
Use a ruler to measure the side lengths of something in the classroom and find the area. Must have side lengths less than 12 inches or 30 cm. BONUS 5 points added to your total if you have a fractional side length (Example: 3 1/2 in x 4 in).
Solutions will vary.
25
Describe a situation that represents the equation 4 ÷ 6 = 4/6.
Sample response: There are 4 quarts of apple cider that 6 friends split equally. How many quarts of apple cider does each friend get?
25
Damien cuts a 15-foot piece of rope into 4 equal parts. Decide whether each expression represents the length of each part of the rope in feet. Explain or show your reasoning.
1. 15 ÷ 4
2. 4 x 15
3. 3 3/4
- Yes, this is 1 of four equal groups making 15.
- No, this is 4 times as long as the piece of rope.
- Yes, because 12 feet of the rope gives 4 equal groups of 3 and then there are 3 feet left and dividing that into 4 equal parts is 3/4 more feet.
25
Find the value of 8 x 14/3. Show or explain your reasoning.
112/3 or equivalent. I multiplied 8 and 14 and have that many 1/3's.
25
A hiking trail is 5 miles long. Kevin B. hikes 1/2 of the trail and then stops for water. Luciano hikes 2/3 of the trail and then stops for water.
1. How many miles did Kevin B. hike before stopping for water? Explain or show your reasoning.
2. How many miles did Luciano hike before stopping for water? Explain or show your reasoning.
1. Kevin B. hiked 2 1/2 miles or 5/2 or equivalent because 1/2 x 5 = 5/2 = 2 1/2.
2. Luciano hiked 3 1/3 miles or 10/3 or equivalent because 1/3 of 5 miles is 5/3 mile. 2/3 of 5 miles is 10/3 mile.
25
Write as many expressions as you can to represent the shaded area in square feet. For each correct expression, add 5 points to your point total (PLUS the 25). You have 5 minutes. GO!
Answers vary. Teacher double-check! Possible responses:
3 x 5 3/4
3 x (5 + 3/4)
3 x 6 - (3 x 1/4)
15 + 2 1/4