Balance Equations
15 ➗ __ = 1 x 5
3
The Pet store just got 24 turtles. Petra is putting the turtles into terrariums. She puts 4 turtles in each terrarium. How many terrariums does she use?
Show your work and equation!
6 Terrariums
24 ➗ 4 = 6
Jenny has a tree house with a floor that is 4' by 6'.
Write an equation to show the area of her tree house.
Then write the REST of the equations for that fact family. (There will be 4 equations in all.)
4 x 6 = 24
6 x 4 = 24
24 ➗ 6 = 4
24 ➗ 4 = 6
The third graders are setting up the room for grandparents day. They are planning for 13 sets of grandparents. If they create 3 rows of chairs and put 9 chairs in each row, will that give every grandparent a seat?
Show all the steps of your thinking. Write 1 or more equations to prove your answer.
13 x 2 < 3 x 9
26 < 27
There will be 1 extra chair.
Area is what (10): Choose ALL the correct statements:
a. Area is measured in square units and found by multiplying length times width.
b. If you know the length of a rectangle, you can figure out its area.
c. You can find the area of a rug that is 5 feet long and 3 feet wide by solving 5 + 5 + 5.
d. When you measure the area of something, you find out how much space it takes up.
e. A tape measure is used to find perimeter, but not area. To find area, you have to use square tiles.
a, c, d
12 x b = 6 x 8
4
There are 36 fourth graders in the gym. The gym teacher divides them into 4 equal groups. How many forth graders are in each group?
Jami says she can solve the problem by thinking "4 times what number equals 36." Do you agree with her? Why or why not?
Show both equations as part of your answer, to prove your thinking!
Yes because 4 x 9 = 36
or 36 ➗ 4 = 9
Darron has a garden that is 8 feet long but half as wide as it is long. What is the area of his garden?
Show your thinking and solve.
8 x (half of 8) = area
8 x 4 = 32 square feet
Jeff and his sister picked 48 flowers. They put 6 flowers in each vase. How many vases did they use?
Write an equation to represent this story and solve!
48 flowers ➗ 6 flowers per vase = 8 vases used
OR 6 flowers x 8 vases = 48 flowers in all
Jack has a rectangular swimming pool in his backyard. Surrounding the pool is a flower garden taking up 36 square feet of the backyard. One side of Jack's swimming pool is 12 feet in length. The entire backyard (pool and garden combined) has an area of 132 square feet.
What are the dimensions (L and W) of Jack's swimming pool?
Show ALL the steps of your thinking, and be sure to write 1 or more equations that represent this problem.
Area = Pool + Garden
132 = (12 x P) + 36
- 36 - 36
96 = 12 x P = (10 x P) + (2 x P)
80 + 16 = (10 x 8) + (2 x 8)
96 = 12 x 8 The pool is 12 feet by 8 feet
16 ➗ 4 = ___ ➗ 5
20
The Pet Store had 10 puppies, and then two of them were adopted. Each puppy drinks seven cups of water every single day. Jim is getting ready to close the shop for two days, so he will need to leave plenty of water for the puppies.
Part A: How many cups of water does Jim need to leave for the puppies, so they don't run out of water before he returns?
Part B: If he buys the water in half-gallon jugs that cost $2.25, how much will he spend on this 2-day supply of water for the puppies?
Part A: 8 pups x 7 cups per day = 56 cups
Part B: 2 cups in a pint, 2 pints in a quart, 4 quarts in a gallon, so 2 quarts in a half-gallon
4 cups in a quart, so 8 cups per half-gallon.
He needs 7 jugs, so 7 x $2.25 = $14 + $1.75 = $15.75 is the cost of the water.
Sophie built an array out of centimeter cubes that had 9 rows and used 54 square centimeters in all.
What was the perimeter of her array?
54 ➗ 9 = ___ cm per row 6 x 9 = 54
(6 + 9) x 2 = 15 x 2 = 30 centimeters (Perimeter)
We have six third grade classrooms. Two classes have 26 students each, and the other four classes have 27 students each.
All six classes go to lunch at the same time. There are five long tables in the cafeteria, with an equal number of students sitting on each side of each table.
How many students will be sitting on one side of a table?
(26 x 2) + (27 x 4) = 52 + 108 = S (students)
5 tables x K (kids per table) = S (total students)
K ➗ 2 sides per table = H (kids sitting on one side)
S = 160 K = 32 H = 16
Mrs. Zurn's rug is 13 feet wide by 8 feet long.
What is the Perimeter of her rug?
Which equationS would help you solve this problem?
a. 13 x 8
b. (13 + 13) + (8 + 8)
c. 13 + 8
d. 2 x (13 + 8)
(L + W) x 2 = Perimeter
(13 + 8) x 2 = 21 x 2 = 42
b. (13 + 13) + (8 + 8)
d. 2 x (13 + 8)
The perimeter is 42 feet
2 x 12 = 4 x b
b = 6
Sophia has 4 bags of legos with 32 in each. John has 5 bags with 25 legos in each.
Who has more legos? How many more do they have?
Sophia: 4 x 32 = 128
John: 5 x 28 = 125
Sophia has 3 more legos because 128-125 = 3
Jordan has two rugs in his room. The area of rug one is 24 square feet, and the area of rug two is 32 square feet. Laying side by side, the two rugs completely cover the floor of his room, with no gaps or overlaps.
Since the two rugs do not have the same area, we know they cannot have the same dimensions. But since the floor is covered completely, we know that the two rugs have either the same width OR the same length.
If no side of either rug is less than 3 feet in length, what could the dimensions of each rug be?
Draw a labelled diagram with equations to show your thinking and solution.
24 square feet could be ... 3 x 8 or 4 x 6
32 square feet could only be ... 4 x 8.
Option 1: The two rugs are 4 x 8 and 4 x 6, laid end to end, with their 4-ft ends touching. That room would be 4 by 14. (Really long and skinny!)
Option 2: The two rugs are 8 x 3 and 8 x 4, laid end to end, with their 8-ft ends touching. That room would be 7 x 8.
There are six classes (of 24 kids each) going to the museum. Each class has a teacher and two parent volunteers. Each bus has 1 driver. If everyone going to the museum were split evenly among nine buses, how many persons were on each bus?
Show ALL the steps of your thinking.
Write 1, 2, or more equations to represent the solution to this problem.
(24 + 1 + 2) x 6 = 27 x 6 = 120 + 42 = 162
162 ➗ 9 = 18 museum goers per bus
So, 19 persons on each bus (You didn't forget the driver, did you??)
Monique just finished a diamond dot painting of a rainbow unicorn! She wants to glue a border of gold ribbon all the way around the outside edge of her painting. The ribbon is sold in lengths that are multiples of 10, so she bought 120 inches, knowing that would give her 4 extra inches of ribbon. If the short side of her painting is 22 inches, what is the length of the longer side? Show how you know.
22 by M inches is her painting
(22 + M) x 2 = 120 - 4
22 + 22 + M + M = 116
44 + M + M = 116
- 44 - 44
M + M = 72 so 72 ➗ 2 = M
72 = 60 + 12 = (30 x 2) + (6 x 2)
Half of 60 is 30 Half of 12 is 6
30 + 6 = 36, so the long side is 36 inches
(4x6) ➗ 3 = (5 x 8) ➗ M
M = 5 ... because
(4x6) ➗ 3 = (5 x 8) ➗ M
24 ➗ 3 = 40 ➗ M
8 = 40 ➗ M ----> 8 x M = 40
M = 5
CHALLENGE!
Mr. Garner gathered $7.50 each from the 12 students going to a music festival. He hires a bus driver plus two people to run the festival. He will . How much money did each person receive for helping with the festival?
Show your equation and solve.
$22.50 to each helper & himself
(7.50 x 12) ➗ 4 = M
$90 ➗ 4 = M -----> 4 x M = 90
I know (4 x 20) + (4 x 2) = $88 = 22 x 4
the remaining $2.00 split 4 ways is 50 cents each.
So $22.50 is each person's pay.
Maggie used 45 square-inch tiles to build an array.
The perimeter of this rectangle was 28 inches.
What were the dimensions of her array?
Prove how you know with one or more equations.
It was a 5 by 9 array.
The area was 45 square inches, so the dimensions had to be factors of 45. L x W = 45
The perimeter was 28 inches, so L + W = 14.
The only two numbers that sum to 14 AND also give us a product of 45 are 5 and 9.
A: 5 x 9 = 45 in2 P: (5 + 9) x 2 = 28 in.
A t-shirt costs $11.50 at Walmart. The exact same t-shirt costs four times as much at the mall!
How much will two of these t-shirts cost me if I buy them at the mall?
Choose the equation that best represents this problem, then use it to find the answer.
a. ($11.50 + 4) ➗ 2 = P
b. 4 x $11.50 x 2 = P
c. ($11.50 x 4) ➗ 2 = P
d. ($11.50 + 4) x 2 = P
b. 4 x $11.50 x 2 = P
4 x 2 x $11.50 = (8 x $11) + (8 x 50 cents)
$88 + (4 x $1) = 88 + 4 = $92
Jason has a basketball court at his apartment building. The length of the court is 50 feet and the Width is 30 feet. What is the perimeter of his basketball court?
**Bonus - Jason wants to put a fence around the court and leave 2 openings in the fence of 3 feet each for an entrance and exit. If the fence is priced at $15 per foot, how much will the fence cost Jason?
(L + W) x 2 = Perimeter
(50 + 30) x 2 = 160 feet
160 - (3x2) = 154 feet of fence needed
154 x $15 = (154 x 10) + [(154 x 10) ➗ 2]
1,540 + (1,540 ➗ 2) = 1540 + (500 + 250 + 20) = 1540 + 770 = 1510 + 800 = 1310 + 1000 = $2,310 to build the fence