UNIT 1 BRIDGES TO MATHEMATICS DIFFERENTIATED INSTRUCTION Scaffold Brainstorm situations that are proportional relationships and list them on the board. Pick one of these situations or use the ratio of two hours of homework for every three classes. Work with students to represent the ratio using a colon, in words, as a picture, and in a table. Take turns having the students read the ratio in different ways. Connect the ratio representations to the ratio concepts and vocabulary from the lesson. Amplify Have students create their own ratio situation. Then have them represent the ratio using a colon, in words, as a picture, and in a table. Have students create another ratio situation and write it on an index card. Have them trade situations with a classmate. Each student will represent the ratio using a colon, in words, as a picture, and in a table. Instructional Routine: Mathematics p. Txxxiv Applying Ratios and Proportions Essential Question: How can we use ratios and proportional relationships to make sense of real-life situations? Participate in academic discussions Use the Essential Question as a warm-up. Ask students to work in pairs to brainstorm relationships between numbers. Lead students to discuss numbers that have a proportional relationship (i.e., they change together in the same way). A • Read and comprehend academic informational texts Ask students to read the text silently. Then ask a different student to read aloud each paragraph. Stop after each paragraph and ask questions to confirm comprehension. • Use knowledge of context to understand domain-specific vocabulary Ask students to call out the bold words and phrases in the text. Show that these words are defined in a glossary and explained in the text. Ask students to identify clues in the text and the graphic that help them understand their meaning. For example, for proportional relationship, point out the chart of water and rice in the graphic. Show how the amounts for each increase proportionally. • Understand ratios Create a chart on the board for other ingredients, such as lemonade mix and water. Change the ratio to different amounts, such as 3 to 1 or 4 to 3. Ask students to explain how to scale the ingredients up and down. • Represent ratios Once students have created their own chart of proportional ingredients, ask them to write the proportions in the different ways shown in the graphic. • Develop understanding of proportional relationships Ask: Why are proportional relationships important? Have students explain what would happen if the ratio of ingredients were changed or proportioned incorrectly. • Represent proportional relationships Show students how the graph shows the relationship between rice and water. If students have experience graphing, ask them to graph their own ingredients on the chart. EXPLORE AND LEARN A Mathematics also involves relationships. Read the informational text about relationships between numbers. Applying Ratios and Proportions Water Rice 1 2 1 4 2 12 6 0 x y Water Rice Representing Ratios Writing Ratios 2:1 2 to 1 2 cups for every 1 cup Unit Rates: Examples • price per pound • miles per hour (mph) • miles per gallon (mpg) Representing Proportional Relationships Two quantities are in a proportional relationship when they change in the same way. A ratio compares amounts. It says how much of one thing there is compared to another thing. A ratio can be scaled up or scaled down. If you multiply one part of the ratio, you need to multiply the other part by the same factor. You can also divide both parts by the same divisor. A unit rate tells how much of one quantity there is for one unit of the other quantity. We read unit rates as one quantity per the other quantity. To make one portion of rice, you need 2 cups of water and 1 cup of rice. When you want to make two portions of rice, you multiply the number of cups of water by two. You also multiply the number of cups of rice by two. 2 cups of water x 2 = 4 cups of water 1 cup of rice x 2 = 2 cups of rice Ratios and Proportional Relationships 1 2 proportional relationship a description of two quantities that change in the same way ratio a number that shows the relationship between two amounts scale up to multiply each part of a ratio by the same factor scale down to divide each part of a ratio by the same divisor unit rate a ratio that compares a quantity of a unit to one unit of another quantity GLOSSARY UNIT 1 34 ESSENTIAL QUESTION How can we use ratios and proportional relationships to make sense of real-life situations? ? BRIDGES TO MATHEMATICS BLC23_SE_LB_U01_034-035_BM.indd 34 9/15/21 12:26 PM 34 | Teacher’s Edition • UNIT 1
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