How To Solve Scale Factor Problems

We might reason, “3 miles in 36 minutes means 1 mile in 12 minutes. So he can jog 5 miles.” We’ve used a : 12 minutes per mile. For Dwight, we used “within” reasoning, finding a ratio using his 3-mile numbers.For Dierdre, we used “between” reasoning, finding a ratio relating the 30-minute to the 60-minute jogs.The key is whether students understand what they are doing—that they’re reasoning about the situation and not simply following a recipe.

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For today’s lesson, the intended target is “I can determine scale factor.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

Activating Prior Knowledge: To get this lesson started, I like to pose the following problem: The scale of a blueprint is 1 inch = 10 feet.

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Mathematics This resource contains two packs of games, investigations, worksheets and practical activities. Activities relevant to this topic are: Pencils, comparing the lengths of different pencils, Walking to school, comparing distances students live from school, Introducing ratio comparing the number of beads on bracelets. Activities relevant to this topic are: Unibond mixtures, making mixtures of chemicals and water, International paper sizes, exploring the ratios involved in paper sizes. Contained in the starters section of phase one are activities which require students to review their knowledge of fractions, decimals, percentages, ratio and proportion.

Opener: As students enter the room, they will immediately pick up and begin working on the opener – Instructional Strategy - Process for openers This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3. I let tables discuss this problem for a few moments and take volunteers to share out their answers to the group.

Learning Target: After completion of the opener, I will address the day’s learning targets to the students. Key Points: Overall Conclusion If the scale factor is represented by k, then the area of the scale drawing is k times the corresponding area of the original drawing.Example 1 What percent of the area of the large square is the area of the small square?Determine the area of the shaded region in the smaller scale drawing.Example 4 Use Figure 1 below and the enlarged scale drawing to justify why the area of the scale drawing is k Exercise 1 1.Have students from both camps explain their reasoning.Your role may be to help compare the two approaches using some accessible scheme.On the other hand, with recipes, it usually makes more sense to think about the scaling factor—like Dierdre.If you’re tripling a recipe that takes 1 1/2 cups of flour and 1/3 cup of sugar, it’s easier to multiply both numbers by 3 than to keep in mind that there’s always going to be 4 1/2 times as much flour as sugar. With maps and scale drawings, you’re dealing with similarity and can go either way—but more often, scaling is what you want: as with a recipe, you figure out the scale factor (e.g., one inch = 10 miles) and use it repeatedly. Strategic Education Research Partnership1100 Connecticut Ave NW #1310 • Washington, DC 20036• (202) 223-8555 • [email protected] funding provided by The William and Flora Hewlett Foundation and S. Video solutions to help Grade 7 students solve area problems related to scale drawings and percent.


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