Lesson Summary:
Students compare ratios of boys and girls in the class to the ratio of men and women in the US population. They then play a game in which different group “businesses” have different cost of goods/pricing ratios and compare how the ratios effect the distribution of money. They then use the business model to generalize the mathematics to simplifying ratios and finding equivalent ratios. Finally, they discuss other applications of ratios. Advanced students have the opportunity to compare the ratios of votes in five different presidential elections. Struggling students practice finding equivalent fractions in a cube game.
Lesson Objectives:
- Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities.
- Use ratio reasoning to solve problems.
- what a ratio is.
- how ratios are used in solving real-world problems.
- simplify ratios.
- find equivalent ratios.
- use ratio language.
- solve real-world mathematical problems using ratios.
Learning Styles Targeted:
Visual / Auditory / Kinesthetic/Tactile
Pre-Assessment:
1)Have students count the number of boys and girls in the class. Write the number on the board, for example 12 girls to 14 boys. Write the number as a fraction and simplify it if possible ().
2)Explain that after the 2000 Census, there were 144 million females and 138 million males in the United States. Write that as a fraction . Ask students to simplify the fraction () and compare the class ratio of girls to boys with that of the United States.
3)Make a note of students who cannot simplify fractions or understand the concept of equivalent fractions.
Whole-Class Instruction
Materials Needed:
Class Currency* master of play money that students can keep, counters, number cubes, or paper clips to represent merchandise.
Procedure:
Presentation
1)Explain that for a business to be profitable, it must buy or make merchandise at the lowest cost and sell it at a higher cost. Pricing the products for sale is a critical decision. If prices are too high, people won’t buy. If prices are too low, it is difficult to be profitable. The ratio of the cost of goods to the price is very important.
Guided Practice
2)Divide the class into groups of three to five students. One student will be the manufacturer, one the seller, and the other students are the customers. Give each manufacturer a handful (over 30) of “merchandise.” Give the seller $20. Give each customer $25.
3)Explain that the merchandise is a really hot item in great demand. The cost of goods that the manufacturer charges is always $1 for each item. Then assign each group a different pricing ratio. One seller should charge $1.00 for a ratio. Another group’s seller should charge $2.00 for a ratio. Other groups should charge $3.00, $4.00, and $5.00. Write the groups and the ratios on the board. (Group A: , Group B and so on).
4)Give the groups 10 minutes to play, having the sellers buy merchandise from the manufacturers and then sell it to the customers.
5)After 5 minutes, stop the interactions and have each group describe how the money shifted hands. In which group did the seller make the most money? Did the customers run out of money leaving the seller with excess inventory?
6)Have each group write the equivalent ratios for their group’s ratio of cost of goods to price for the initial 20 items that the seller purchased ( would be , would be , would be and so on.)
Independent Practice
7)Have the students play the game again, only this time set the cost of goods at $2 and give sellers $40 to buy from the manufacturer.
8)After 10 minutes, have each group describe how its ratio of price to cost changed.
Closing Activity
9)Write these ratios on the board: , , . Have students simplify them.
10)Write these ratios on the board: , , , . Have students find equivalent ratios that would represent additional sales, for example 100 items, 20 items, and 10 items.
11)Discuss other applications of ratios (vote tally in elections, price increases, and so on).
Advanced Learner
Election Results
Materials Needed: Internet access or almanac to find Presidential election results data.
Procedure:
1)Have students search for the results of five different United States Presidential elections.
2)Have them compare the results as ratios and discover which candidates among those they selected had the widest margin of victory.
3)Have them report their results to the class.
Struggling Learner
Equivalent Fraction Game
Materials Needed:Bags of chips each with 6 chips (half of the bags with chips labeled 0-5; half of the bags with chips labeled 5-10) for each group, paper and pencil
Procedure:
Divide groups of students into groups of three. Give each group a set of bags. Then give them these rules:
1)In turn each player picks a chip from each bag. (Pick again if the result is 0).
2)The player forms a fraction based on the numberspicked (, , , for example).
3)The player must calculate an equivalent fraction and present it to the group. Once it is accepted, the player can record it. The player at the end of a round with the largest equivalent fraction wins the round.
4)Play 2 rounds. Have students add their fractions, which will involve finding equivalent fractions for addition. The player with the highest total wins the game.
Class Currency
[Art:
- design “Mad Magazine” look bills and coins in denominations of $100, $10, $1, dimes, and pennies.
- On master include multiple copies of each denomination to fit 1 page]
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