Reasoning to Find Area
Parallelograms and Triangles
Surface Area,
Squares and Cubes
Squares and Cubes
What Are Ratios?
Part-Part-Whole Ratios
Percentages
100
A rectangle has a length of 5 cm and a width of 3 cm. What is the area?
15 cm²
100
A parallelogram has a base of 8 cm and a height of 5 cm. What is the area?
40 cm²
100
A rectangular prism (box) has dimensions 5 cm × 3 cm × 2 cm. What is the surface area?
62 cm²
100
What fraction of the glasses have orange juice? What is that fraction in simplest form?
9/12 = 3/4
100
In a class of 20 students, 12 are boys and 8 are girls. What is the ratio of boys to the whole class?
12:20 or 3:5
100
What is 10% of 50?
5
200
A square tile has sides of 4 inches. What is the area of the tile?
16 square inches
200
A triangle has an area of 30 cm² and a base of 12 cm. What is the height?
5 cm
200
A cube has sides of 4 cm. What is the surface area?
96 cm²
200
In a classroom, there are 12 boys and 8 girls. Write the ratio of boys to girls.
12:8 or 3:2 (in simplest form)
200
A school has 240 students. The ratio of girls to boys is 3:2. How many girls?
144
200
What is 25% of 80?
20
300
A shape is made up of two rectangles: one is 6 cm × 4 cm, and the other is 3 cm × 2 cm. What is the total area?
30 cm² (24 + 6 = 30)
300
A triangle has a base of 6 cm and a height of 4 cm. What is the area?
12 cm² (12×6×4=1221×6×4=12)
300
What is the total surface area?
136 cm² (two triangles: 2 × 12 = 24 cm², rectangles: 40 + 40 + 48 = 128 cm², total: 24 + 128 = 152 cm²)
300
A recipe calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar?
2:1
300
Bonus: (Get an extra 100 points if the process is well explained)
In a survey, the ratio of people who like chocolate to people who like vanilla to people who like strawberry is 4:3:2. If 72 people were surveyed, how many preferred each flavor?
Chocolate: 32, Vanilla: 24, Strawberry: 16 (total parts: 4 + 3 + 2 = 9; each part = 72 ÷ 9 = 8)
300
If an item costs $60 and is on sale for 30% off, what is the sale price?
$42 (30% of $60 = $18; $60 − $18 = $42)
400
What strategy is being used to find the area of this shape?
Decomposing and Rearranging
400
What is the area? 
45 cm² (base × height = 9 × 5; the slant side is not used)
400
A cube has edges of 3 inches. What is the surface area?
54 square inches
400
The ratio of apples to oranges is 5:3. If there are 15 apples, how many oranges are there?
9 oranges
400
A jar contains red, blue, and yellow marbles. The ratio of red to blue is 2:3, and the ratio of blue to yellow is 3:4. If there are 60 marbles total, how many are blue?
15 blue marbles
400
A store's sales increased from $5,000 last month to $6,500 this month. What was the percentage increase?
30% increase ((6,500 − 5,000) ÷ 5,000 × 100 = 1,500 ÷ 5,000 × 100 = 30%)
500
What is the total area of this shape?
24 square units (4 + 8 + 12 = 24)
500
Bonus:(Get an extra 100 points if the answer is correct and clearly explained)
A parallelogram has an area of 50 cm². Its base is twice its height. What are the base and height?
Height = 5 cm, Base = 10 cm (since base × height = 50, and base = 2 × height, then 2h × h = 50, so h² = 25, h = 5)
500
A cube has a surface area of 96 cm². What is the length of each edge?
4 cm
500
Write the ratio in three ways: Jayden has 5 yellow marbles, 3 green marbles, and 10 clear marbles. What is the ratio of clear marbles to total marbles? Write the ratio in simplest form.
5 to 9 5:9 5/9
500
In a mixture, the ratio of red paint to blue paint to yellow paint is 3:4:2. If there are 36 units of red paint, how much paint is in the mixture altogether?
108 units (if red = 3 units = 36, then 1 unit = 12. Total = (3 + 4 + 2) × 12 = 9 × 12 = 108)
500
A swimmer completes 10 laps in 20 minutes. At this rate, how long does it take to complete 25 laps?
50 minutes (unit rate: 0.5 laps per minute or 2 minutes per lap; 25 laps × 2 minutes = 50)