Lesson plan
|Math Lesson: Ratio and Percent Models |Grade Level: 5 |
|Lesson Summary: Students will understand that ratios form proportions. Advanced students will solve world problems using ratios, proportions, and percents. |
|Struggling students will work to correct errors in a solution to a proportion. |
|Lesson Objectives: |
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|The students will know… |
|the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole. |
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|The students will be able to… |
|convert fractions and decimals to percents. |
|represent ratios as part-to-part and part-to-whole. |
|represent percents as part-to-whole. |
|Learning Styles Targeted: |
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|Visual |
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|Auditory |
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|Kinesthetic/Tactile |
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|Pre-Assessment: |
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|Use this quick assessment to see if students can write fractions in simplest form. |
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|1. [pic] ([pic]) 2. [pic] ([pic]) 3. [pic] ([pic]) |
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|Note students who do not get the correct answers. |
|Whole-Class Instruction |
|Materials Needed: classroom items (paper clips, tiles, number cubes, etc.), large container |
|Procedure: |
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|Explain how a ratio is two things compared to each other. A ratio can be written as |
|a to b a:b [pic] |
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|A ratio should always be written in simplest form. |
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|A proportion is an equation that states that two ratios are equal. A proportion is written as [pic] = [pic] where b and d are not equal to 0. |
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|Explain how a percent is a ratio whose second term is 100. The symbol % is used for percent. To solve a percent problem, write a percent as a fraction then use a |
|proportion to solve. [pic] = [pic]. |
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|Have a container filled with 100 items. There should be at least 3 different types of items in the container. Use paperclips, tiles, number cubes, etc. have |
|students separate the items into groups and record the number of each item. Then have them write the ratios and convert them to percents. |
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|Guided Practice: |
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|Have students write ratios in three different ways. |
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|1) There are 16 ducks and 9 geese in a pond. Express the ratio of ducks to geese in three ways. |
|(16:9, [pic], 16 to 9) |
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|2) There are 16 ducks and 9 geese in a pond. Express the ratio of geese to ducks in three ways. |
|(9:16, [pic], 9 to 16) |
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|3) The ratio of ducks to geese in a pond is 16 to 9. If there are 300 birds, how many are geese? |
|([pic] = [pic]; 108 geese) |
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|4) The ratio of ducks to geese in a pond is 16 to 9. If there are 192 ducks, how many are geese? |
|([pic] = [pic]; 108 geese) |
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|Independent Practice: |
|Provide students with survey results and have them write the responses as ratios to the whole. |
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|[pic] |
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|The pie chart shows a student survey of favorite colors. |
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|a. About what percent of students said that they preferred the color blue? |
|(40%) |
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|b. Suppose exactly 23% of the students said that red was their favorite color. Estimate how many students made this choice if 200 students took the survey. |
|([pic] = [pic]; about 46%) |
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|c. If 60 students said that their favorite color was blue, about how many students took the survey in all? |
|(40% = [pic] = [pic]; 60 divided by [pic] = 150; about 150 students) |
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|Closing Activity: |
|Have students write a fraction as a ratio in two other ways. Convert the ratio to a percent. |
|Advanced Learner |
|Materials Needed: 1 copy of the Worksheet* per student, writing utensils |
|Procedure: |
|Presentation: |
|Solve proportions like [pic] = [pic] using cross products. |
|10x + 5 = 2x + 4; 8x = –1; x = [pic] |
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|Have students complete the Worksheet. |
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|Emphasize that ratios must be written in simplest form. |
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|Write this expression on the board: [pic] = [pic]. Have students work in pairs to solve the expression for x. Have each group write out their work on the board or |
|on poster paper. Go over each one of the solutions. Make sure to identify any mistakes made by the students. |
|Struggling Learner |
|Materials Needed: paper, writing utensils |
|Procedure: |
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|Tell students that a picture can help them understand numbers. Draw a number map that shows many meanings of the decimal 0.25. |
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|[pic] |
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|Have students create a number map for the following numbers: 0.75, 0.1, and 0.5. Encourage them to use everyday meanings for numbers, like time and money. |
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|Remind students that if they are given the results of a survey in percents then they can find the number of people surveyed who preferred each category. |
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|The table shows the results of a survey of 300 movie rental customers. |
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|[pic] |
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|Have them find the number of customers who rent each type of movie. |
|(Action: [pic]= [pic] x = 132; Comedy: [pic] = [pic] x = 105; Drama: [pic] = [pic] x = 63) |
*see supplemental resources
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