The World of Math

AREA-ana Grande

Express Yo'Self

Equationator

Decimacito

Miscellaneous

100

Here are two copies of the same figure. Show two different ways for finding the area of the shaded region. All angles are right angles.

100

Do 4x and 15+x have the same value when x is 5?

Yes, they both have the value of 20.

100

What is the value of x?

x = 7

100

Mai had $14.50. She spent $4.35 at the snack bar and $5.25 at the arcade. What is the exact amount of money Mai has left?

$4.90

100

A recipe for orange water says, “Mix 3 teaspoons yellow water with 1 teaspoon red water.” For this recipe, we might say: “The ratio of teaspoons of yellow water to teaspoons of red water is 3:1.”

Write a ratio for 2 batches of this recipe.
Write a ratio for 4 batches of this recipe.

1. 6:2

2. 12:4

200

Find the area of each shaded region. Show your reasoning.

A = 22 square units

B = 28 square units

C = 18 square units

200

Select all the expressions that are equivalent to 16x+36.

16(x+20)
x(16+36)
4(4x+9)
2(8x+18)
2(8x+36)

3 and 4

200

Mai's water bottle had 24 ounces in it. After she drank x ounces of water, there were 10 ounces left. Select all the equations that represent this situation.

24÷10=x
24+10=x
24−10=x
x+10=24
10x=24

4 and 5

200

A large cheese pizza costs $7.50. Diego has $40 to spend on pizzas. How many large cheese pizzas can he afford? Explain or show your reasoning.

5 pizzas. Sample reasoning: Each pizza costs about $8, and 8⋅5=40.

200

Bottles of sparkling water usually cost $1.69 each. This week they are on sale for 4 for $5. You bought one last week and one this week. Did you pay more or less for the bottle this week? How much more or less?

I paid $0.44 less this week. Possible strategy: Since 4 bottles cost $5, each bottle costs $5÷4, or $1.25 this week. The difference is $0.44, because 1.69−1.25=0.44.

300

Find the area of each shaded region for diagram C.

Figure C = 96 sq. cm

150-54 = 96

300

Select all the expressions that are equivalent to 4b.

b+b+b+b
b+4
2b+2b
b⋅b⋅b⋅b
b÷14

1, 3, and 5

300

Priya has 5 pencils, each x inches in length. When she lines up the pencils end to end, they measure 34.5 inches. Select all the equations that represent this situation.

5+x=34.5
5x=34.5
34.5÷5=x
34.5−5=x
x=(34.5)⋅5

2 and 3

300

Compute the following sums. If you get stuck, you can draw base-ten diagrams.

0.027+0.004

0.203+0.1

1.2+0.145

0.031
0.213
1.345

300

Write down a number that has the same value as each number:

|-12.9|

1. 5 or |-5|

2. 12.9 or |12.9|

400

Find the area of the parallelogram.

30 sq cm.

400

Choose the expressions that do not represent the total area of the rectangle. Select all that apply.

5t+4t
t+5+4
9t
4⋅5⋅t
t(5+4)

2 and 4

400

For the equation 2n−3=7

What is the variable?
What is the coefficient of the variable?
Which of these is the solution to the equation? 2, 3, 5, 7, n

1. n

2. 2

3. 5

400

Find each product. Show your reasoning.

(1.2)⋅(0.11)
(0.34)⋅(0.02)
120⋅(0.002)

1. 0.132

2. 0.0068

3. 0.24

400

What is the greatest common factor of 24 and 64? Show your reasoning.

8. The common factors of 24 and 64 are 1, 2, 4, and 8, and 8 is the greatest.

500

Find the area of the shaded triangle. Show your reasoning.

18 square units

500

For each expression, use the distributive property to write an equivalent expression.

4(x+2)
(6+8)⋅x

4(2x+3)
6(x+y+z)

4x+4⋅2
6x+8x
8x+4⋅3
6x+6y+6z

500

Solve each equation.

10=4y

5y=17.5

1.036=10y

0.6y=1.8

15=0.1y

y=2.5
y=3.5
y=0.1036
y=3
y=150

500

Here is an area diagram that represents (3.1)⋅(1.4).

Find the areas of sub-rectangles A and B.

What is the area of the 3.1 by 1.4 rectangle?

Rectangle A: 3.1 square units, Rectangle B: 1.24 square units
4.34 square units (3.1+1.24=4.34)

500

Jada and Diego are practicing the piano for an upcoming rehearsal. The tables list the number of minutes each of them practiced in the past few weeks.

Jada's practice times:

Diego's practice times:

Find the median of each data set.

Jada's = 20 minutes

Diego's = 22.5 minutes