+ — =¢
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MATH THAT MAKES
¢ ENTS
GRADE
3
worksheet 7 - shop til you drop
Jason earned $600 over the summer by babysitting. It took him 10
shopping trips to purchase the things he needed for the new school year
– school supplies, new clothes and soccer gear. On each trip he spent
$10 more than on the previous trip. After the 10th trip, he had spent all his
summer earnings.
(a) How much did Jason spend on the first shopping trip?
(b) Jason wanted to buy a new phone also. He figured out that if he saved
1/3 of his money and earned $4 in interest each month he would have
enough for his phone in 8 months. How much does the phone he wants cost?
MATH STANDARDS ALIGNMENT:
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based
on place value and properties of operations.
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts;
understand a fraction a/b as the quantity formed by a parts of size 1/b.
Personal Finance Big Ideas:
Delayed Gratification; Scarcity
METHOD 1: GUESS AND CHECK
(a) I decided to test $10 for a starting amount for Jason’s first shopping trip, since it’s easy to work with mentally.
I made a table to keep track of what he spent each trip.
Trip
Spent
1 $10
2 $20
3 $30
4 $40
5 $50
6 $60
7 $70
8 $80
9 $90
10 $100
Total
$550
1
MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
GRADE
3
worksheet 7 - shop til you drop
If Jason spent $10 on his first trip, he would have spent only $550 by the end of the week. I needed to increase my
starting guess. Since I need to account for $50 more over the course of 10 trips, I decided to try $15 for his first trip.
Here are my results.
Trip
Spent
1 $15
2 $25
3 $35
4 $45
5 $55
6 $65
7 $75
8 $85
9 $95
10 $105
Total
$600
So Jason spent $15 on his first trip.
(b) First I need to figure out what 1/3 of $600 is. I decided to break $600 into 3 equal pieces.
$200$200$200
Looking at my drawing, I can see that 1/3 of $600 is $200.
To figure out the cost of the phone I need to add in the $4 per month that Jason is earning for 8 months.
Months
Total
1 $204
2 $208
3 $212
4 $216
5 $220
6 $224
7 $228
8 $232
After 8 months, Jason would have $232 and so the cost of the phone Jason wants is $232.
2
MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
worksheet 7 - shop til you drop
GRADE
3
METHOD 2: TOTAL THE 10s
(a) I found out the total of the extra $10 amounts. Since he spent $10 more on each trip than the previous trip I added
9 numbers that increased by $10.
10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = $450
I noticed that I could make 4 groups of 100 (90 + 10, 80 + 20, etc.) plus one 50, making a total of 450. The other $150
represents the amount he spent on the first trip and each other trip, too.
$150/10 = $15, so Jason spent $15 on his first trip. I made a chart [or spreadsheet] to show how much he spent on
each trip to check my answer.
TripSpentTotal Spent
1$15$15
2$25$40
3$35$75
4$45$120
5$55$175
6$65$240
7$75$315
8$85$400
9$95$495
10$105$600
Total
$600
(b) To find the cost of the phone, first I calculated 1/3 of Jason’s total earnings.
(1/3) ($600) = $200
I know Jason earns $4 per month for 8 months, so I figure her earns $4 per/month*8 months which equals $32.
At the end of 8 months, Jason will have $232, so the cost of the phone is $232.
3
MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
worksheet 7 - shop til you drop
GRADE
3
METHOD 3: ALGEBRAIC
(a) I let m stand for the amount Jason spent the first trip. Each trip he spent $10 more, so on the second trip he spent
(m + 10), on the third trip (m + 20), etc. I knew the total was $600, so I made an equation:
m + (m+10) + (m+20) + (m+30) + (m+40) + (m+50) + (m+60) + (m+70) + (m+80) + (m+90) = 600
10m + 450 = 600 [gather like terms]
10m = 150 [subtract 450 from both sides]
m = 15 [divide both sides by 10]
Jason spent $15 on his first trip. I checked by adding 15 + 25 + 35 + . . . = 600
(b) I figured this one out logically. I know that 1/3 of $600 is $200. And I know that $4 per month for 8 months is $32.
So $200+$32 = $232, so the cost of the phone is $232.
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MATH THAT MAKES CENTS