ࡱ>  Jbjbj ԇCJ J 8DtV((3G SVVVVVVVX>[hV["3[[VH.V[:V[V+P U[:7R:VDV0tVqRR[U[U@[[[[[[[VV[[[tV[[[[[[[[[[[[[[J S:  Math Lesson: ProportionsGrade Level: 6Lesson Summary: Students experience different types of proportions beginning with calculating fair pay based on hours worked and then observing pictures that are not in proportion. They then calculate different proportions for recipes using charts and mathematical formulas. Advanced students have the opportunity to create a scale model of a classroom object after calculating proportions. Struggling students practice using map scales to calculate distances in proportion.Lesson Objectives: Understand the concept of a proportion. Use proportional reasoning to solve problems. The students will know what a proportion is. how proportions relate to equivalent ratios. The students will be able to find equivalent ratios. solve a proportion for an unknown. create a table and/or graph of equivalent ratios.Learning Styles Targeted:  FORMCHECKBOX  Visual  FORMCHECKBOX  Auditory  FORMCHECKBOX  Kinesthetic/Tactile Pre-Assessment: Pose this problem. Five students worked hard helping to plant flowers in front of the school. One worked four hours, two worked two hours each, and the other two had to leave after one hour. The school got a donation of $100 and decided to use it to pay the students for their work in proportion to how long each worked. How much should each student receive? Give students a minute to think about this, and then invite students to explain how they might go about solving it. Question reasoning, but do not solve the problem at this time. Make a note of students who do not recognize that they must think proportionally. Whole-Class InstructionMaterials Needed: Lighthouse Proportions*, Homemade Play Dough Recipe*Procedure: Presentation Hand out or display Lighthouse Proportions. Ask students to describe the differences between the first row of lighthouses and the second row. Guide them to recognize the differences in proportionthat in the second row, the pictures are bigger or smaller, but the lighthouses are all in proportion. In the first row, the lighthouses are out of proportion and are distorted. Discuss what happens when things are out of proportion. For example, people may not be paid fairly, pictures or features are distorted, or recipe ingredients may be wrong. Guided Practice Provide the Homemade Play Dough Recipe. Have students use the chart to convert the recipe in proportion for different amounts. Start by asking how they would double the recipe for two batches and guide them to see that they would have to multiply all the ingredients by 2. Ask what would happen if they doubled the water but not the flour? Then give them 5 minutes to complete the chart. Discuss student results. If any answers differ, have students explain their reasoning to discover why there are differences. Write the ratio for the amount of cream of tartar in one batch as 2/1 (two teaspoons for 1 batch). Then present a second question of how to find how many teaspoons you would need for 25 batches, and represent the problem using the proportion 2/1 = ?/25. Ask how students could solve the problem mathematically instead of creating a table. Guide them to recognize that they can divide the denominator in the first fraction into the denominator of the second fraction and then multiply that result by the numerator of the first fraction to find the equivalent ratio fraction and proportion. Independent Practice Write the recipe for six servings of lemonade on the board: 1 cup of sugar, 1 cup hot water to dissolve the sugar, juice of 5 lemons, and 4 cups of cold water. Have students convert the recipe to make enough for 120 people for a school event. After 10 minutes, have pairs of students compare their answers and then present how they found them by using tables, multiplying, or multiplying fractions. Closing Activity Review the Pre-Assessment problem and discuss how to solve that problem mathematically: $100/10 = ?/4, ?/2, ?/1. Discuss other applications of proportions and equivalent ratios. Advanced LearnerScale Models Materials Needed: Ruler, paper, glue, scissorsProcedure: Scale models are in proportion to the real objects. Have students select an object in the classroom such as a table, chair, door, or clock and create a scale model of it out of paper. Have them present their models and explain the proportions between the model and the real object.Struggling LearnerMap Scales Materials Needed: MapsProcedure: Explain that maps show locations in proportion. Provide students with a local, state, country, or world map. Have students locate the scale on the map. Then have them choose two locations on the map and use the scale to calculate how many miles or kilometers it is between the locations. 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