Model Drawing Strategy
In this article, the lesson objectives are:
- Drawing models to help us solve word problems involving increase in the subject(s)
Model drawing is a useful skill which is used to understand complex word problems visually.
Question 1:
Timmy had 128 fewer stickers than Chloe. After Chloe bought another 132 stickers, she had thrice as many stickers as Timmy. How many stickers did Chloe have at first?
Solution:
Difference between Chloe and Timmy’s stickers in the end
\(\begin{align} &= 128 + 132\\[2ex] &= 260 \end{align}\)
\(\begin{align} 2 \text{ units} &= 260 \\[2ex] 1 \text{ units} &= 260 \div 2\\[2ex] &= 130 \end{align}\)
Number of stickers Chloe had at first
\(\begin{align} &= 1 \text{ unit} + 128\\[2ex] &= 130 + 128\\[2ex] &= 258 \end{align}\)
Answer:
258 stickers
Question 2:
Phoebe had 812 more stamps than Rachel at first. After Phoebe bought 804 more stamps, she had 5 times as many stamps as Rachel.
- How many stamps did Rachel have?
- How many stamps would Rachel need to buy in order to have twice as many stamps as Phoebe in the end?
Solution:
Difference between Phoebe and Rachel’s stamps in the end
\(\begin{align} &= 812 + 804\\[2ex] &= 1616 \end{align}\)
\(\begin{align} 4 \text{ units} &= 1616 \\[2ex] 1 \text{ units} &= 1616 \div 4\\[2ex] &= 404 \end{align}\)
Number of stamps Rachel had
\(\begin{align} &=1 \text{ units} \\[2ex] &= 404 \end{align}\)
Answer:
404 stamps
In order for Rachel to have twice as many stamps as Phoebe in the end,
Number of units Rachel must have in the end
\(\begin{align} &=2 \times 5 \text{ units} \\[2ex] &= 10 \text{ units} \end{align}\)
Number of stamps Rachel need to buy
\(\begin{align} &= 10 \text{ units } – 1 \text{ units} \\[2ex] &= 9 \text{ units} \\[2ex] &= 9 \times 404\\[2ex] &= 3636 \end{align}\)
Answer:
3636 stamps
Question 3:
Julian and Ken had some stickers at first. After Julian bought 24 more stickers, Ken's stickers became 4 times that of Julian's stickers. The total number of stickers Julian and Ken had in the end was 405. How many stickers did Julian have at first?
Solution:
\(\begin{align} 5 \text{ units} &= 405 \\[2ex] 1 \text{ units} &= 405 \div 5\\[2ex] &= 81 \end{align}\)
Number of stickers Julian had at first
\(\begin{align} &= 1 \text{ units } – 24\\[2ex] &= 81 – 24\\[2ex] &= 57 \end{align}\)
Answer:
57 stickers
Question 4:
Maddy had $24 more than Han at first. After Han received $284, Han had thrice as much as Maddy. Find the total amount of money they had in the end.
Solution:
Difference between Maddy and Han’s money in the end
\(\begin{align} &= $284 – $24\\[2ex] &= $230 \end{align}\)
\(\begin{align} 2 \text{ units} &= $230 \\[2ex] 1 \text{ units} &= $230 \div 2\\[2ex] &= $115 \end{align}\)
Total amount of money they had in the end
\(\begin{align} &= 3 \text{ units} + 1 \text{ unit} \\[2ex] &= 4 \text{ units} \\[2ex] &= 4 \times $115\\[2ex] &= $460 \end{align}\)
Answer:
$460
Question 5:
Jason had $230 less than Doris. After Jason received $1500 from his mother, he had 3 times as much money as Doris. How much did both of them have in total at first?
Solution:
Difference between Jason’s and Doris’s money in the end
\(\begin{align} &= $1500 \;–\; $230\\[2ex] &= $1270 \end{align}\)
\(\begin{align} 2 \text{ units} &= $1270 \\[2ex] 1 \text{ units} &= $1270 \div 2\\[2ex] &= $635 \end{align}\)
Total number of stickers both of them had at first
\(\begin{align} &= 1 \text{ unit} + 1 \text{ unit} \;–\; $230 \\[2ex] &= $635 \;+\; $635 \;–\; $230 \\[2ex] &= $1040 \end{align}\)
Answer:
$1040
Continue Learning | |
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Multiplication | Whole Numbers |
Multiplication And Division | Decimals |
Model Drawing Strategy | Division |
Fractions | Factors And Multiples |
Area And Perimeter 1 | Line Graphs |
Time |