+ — =¢
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MATH THAT MAKES
¢ ENTS
GRADE
5
worksheet 11 - TOYS TO GO
Toys To Go is having a big sale.
Sam is in charge of changing the price tags on the scooters.
They usually sell for $55. Help Sam decide what the sale price
should be based on the other discounts advertised.
Extra:
Pedal Cars are on sale for $120. What was their original
selling price?
MATH STANDARDS ALIGNMENT:
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction
models or equations to represent the problem.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
Personal Finance Big Ideas:
What is Money
METHOD 1: EXAMINE DIFFERENCES, NOTICE FACTORS
I wondered if the prices were all decreased by the same amount. I listed the prices and differences:
ItemOriginal priceSale price
Difference
Skates
$20
$16
$4
Wagons
$75
$60
$15
Pogo Sticks
$40
$32
$8
Bicycles
$135
$108
$27
None of the differences were the same, but I noticed something about them. For the skates, the difference (4) is a
factor of the original price (20) and the sale price (16). For the pogo sticks, the difference (8) is a factor of the original
price (40) and the sale price (32), and these are all twice the numbers for the skates. I discovered these relationships:
Skates
5 * 4 = 20
4 * 4 = 16
Pogo sticks
5 * 8 = 40
4 * 8 = 32
In both cases 5 * difference = original 4 * difference = sale
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MATH THAT MAKES
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worksheet 11 - TOYS TO GO
GRADE
5
I checked to make sure that my rule worked for the other toys:
Wagons
5 * 15 = 75
4 * 15 = 60
Bicycles
5 * 27 = 135
4 * 27 = 108
To find the sale price of the scooters, I need to find the difference. What number multiplied by 5 gives me 55? I can
divide, since that is the opposite of multiplication.
55/5 = 11 [the difference between the original price and the sale price]
55 - 11 = 44 [the sale price]
So Sam should price the scooters at $44.
Extra: I need to find the differences again. Since I know the sale price, what number multiplied by 4 gives me 120?
120/4 = 30 [the difference between the original price and the sale price]
120 + 30 = 150 [the sale price]
The original price of the pedal cars was $150.
METHOD 2: FRACTIONS
I tried to find out if the sale prices were all the same fraction of the original prices.
ItemOriginal priceSale price
Fraction
Skates
$20
$16
16/20 = 4/5
Wagons
$75
$60
60/75 = 4/5
Pogo Sticks
$40
$32
32/40 = 4/5
Bicycles
$135
$108
108/135 = 4/5
I reduced all the fractions to their lowest form. The sale prices are all 4/5 of the original price. I needed to find 4/5 of
$55, the original price of the scooters.
1/5 of 55 is 11, so 4/5 of 55 is 4 * 11, or 44. So the sale price of scooters is $44.
Extra: $
120 must be 4/5 of the original price. 120/4 = 30, so 1/5 of the original price is $30. The original price must be
5 * $30 or $150.
[Note: S
ome students may use the differences as a basis for their fractions, finding that they are all 1/5 of the original
price. Those who have been introduced to formal operations with ratios might apply that skill.]
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MATH THAT MAKES CENTS
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x —
MATH THAT MAKES
¢ ENTS
GRADE
5
worksheet 11 - TOYS TO GO
METHOD 3: PERCENTS
I wanted to find out if the prices were all discounted by the same percentage. I found the differences between the
original price and the sale price and divided by the original price to find the percent discount. The differences were all
20% of the original price.
Item
Original price
Sale price
Difference
Difference as % of original price
Skates
$20
$16
$4
4/20 = 20%
Wagons
$75
$60
$15
15/75 = 20%
Pogo Sticks
$40
$32
$8
8/40 = 20%
Bicycles
$135
$108
$27
27/135 = 20%
I found 20% of $55 by multiplying. 55 * 0.2 = 11
So the sale price of scooters should be $11 less than the original price. $55 - $11 = $44
So Sam should price the scooters at $44.
Extra: P
edal cars were discounted by 20% to a sale price of $120. That means 120 represents 80% of the original
price. What number multiplied by 80% yields 120? I can divide because it is the inverse of multiplication.
120/0.8 = 150
The original price of pedal cars is $150.
To check this answer I found 20% of $150 to find the discount and subtracted the result from $150.
0.2 * 150 = 30
150 - 30 = 120
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MATH THAT MAKES CENTS
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x —
MATH THAT MAKES
¢ ENTS
worksheet 11 - TOYS TO GO
4
GRADE
5
MATH THAT MAKES CENTS