Price Combinations
13. Explanations will vary, but the steps in Joe’s reasoning are as follows:
• Divide the second picture by two (one of each for $1.70).
• Then multiply that by three to find the price of three tall and three short candles ($5.10).
• Then compare the three tall and three short candles to those in the first picture (three tall and five short).
• Subtract to find the price of two short candles ($2.20).
• The price of one short candle is $1.10.
• Substitute the price of one short candle into the first line to calculate the price of one tall candle ($1.70 $1.10 $0.60).
0 1 2 3 4
+ .35 – 1.25
– 1.25
+.35
5 0
1 2 3 4
2.05
3.30 4.90 4.55
.45
.80 1.60 0
Cups of Peanuts Costs of Combinations
(in dollars)
Cups of Raisins + .80
Finding Prices C
$4.20
$4.35
Finding Prices
C
You can use different strategies to solve shopping problems.
If you can find a pattern in a picture, you can use the fair exchange method. To do so, continue exchanging until a single item is left so you can find its price. If not, combining information may help you find the price of a single item.
Another strategy is to make a combination chart and look for a pattern in the prices. Use the pattern to find the price of a single item. You may also use the fair exchange method with a combination chart.
1. Felicia and Kenji want to buy candles. The candles are available in different combinations of sizes.
a. Without calculating prices, determine which is more expensive, the short or the tall candle.
b. What is the difference in price between one short and one tall candle?
c. Draw a new picture that shows another combination of short and tall candles. Write the price of the combination.
d. What is the price of a single short candle?
Notes
Check Your Work problems are provided so students can review the concepts taught in this section. They can be assigned as home-work.
Reaching All Learners
Extension
You may ask students to look for an example for each strategy described in the Summary. They can select appropriate problems they have solved in this section. You may assign them to write these examples in their journals.
Parent Involvement
Have parents review the section with their child to relate the Check Your Work problems to the problems in the section.
Assessment Pyramid
1
Assesses Section C Goals
20 Comparing Quantities
Section C: Finding Prices 20T d. One short candle costs $0.90. Different
strategies are possible. Discuss your strategy with a classmate.
An example of one strategy follows:
Exchange each tall candle for a short candle.
(See pictures in answer c.)
When you have five short candles, the total price is $4.50.
$4.50 5 $0.90
Solutions and Samples
Answers to Check Your Work
1. a. You can have different explanations that are correct. One example is:
• In both pictures there are five candles, but the price is higher in the second picture.
Since there are more short candles in the picture below, they must be more expensive.
• When one tall candle is replaced by one short candle, the price increases $0.15.
The short candles are more expensive than the tall candles.
b. The short candles are $0.15 more expensive than the tall candles.
c. Compare your answer with your classmates.
There are several possible combinations. You can add all the candles and prices to get one combination:
Some other examples you get when you exchange candles are below.
$8.55
$3.75
$4.05
$4.20
$4.35
$4.50
$3.90
Hints and Comments
Overview
Students read in the Summary the two strategies they used in this section to solve shopping problems. Then they start with the Check Your Work problems.
Students use these Check Your Work problems as self-assessment. The answers to these problems are also provided in the Student Book.
Planning
You may wish to conclude this section with a discussion to assess whether students understand how to find patterns in combination charts, as well as how to extend them by manipulating the numbers. You may plan to do this before students start with the Check Your Work problems.
15¢
15¢
15¢
Finding Prices C
2. Roberto bought two drinks and two bagels for $6.60.
Anne bought four drinks and three bagels for $11.70.
Use a combination chart to find the cost of a single drink.
3. The prices of drinks and bagels have changed.
a. Use any strategy to find the new cost of a drink.
b. How much is a single bagel now?
Write several sentences describing the differences between using the method of fair exchange and using combination charts to solve problems.
$5.80
$10.20
Notes
2Struggling students may want to try this problem using the compensation strategy. Then have them put the combinations in a combination chart to help them see the patterns.
For Further Reflection Reflective questions are meant to summarize and discuss important concepts.
Reaching All Learners
Extension
Have students try solving problem 3 using a different strategy.
Accommodation
Provide copies of Student Activity Sheet 4 or graph paper.
Assessment Pyramid
FFR 2
2, 3
Assesses Section C Goals
21 Comparing Quantities
Section C: Finding Prices 21T For Further Reflection
Answers may vary. Sample response:
When I use the method of fair exchange, I look at the combinations of the pictures and try to find out how to exchange the items, how many of one item for how many of the other item. And then of course I look at how the price changes.
When I use a combination chart, I look just at the numbers in the chart and try to find out how to make moves to get at the bottom side or left side of the chart.
Solutions and Samples
2. One strategy is to subtract the price of one bagel