Lesson plan

In this lesson, students will learn how to solve scaling problems. Students will begin by using a map to find the length of a trail. Students will then be introduced to different types of scaling problems and explain the strategies they use to solve them. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 7

Rates And Proportional Relationships

7.G.A.1

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Students will be able to solve scaling problems.

- Teacher slideshow
- Student Resource Sheet
- Online Practice

Students should be given a copy of the __student resource sheet__ so they can use the string, rulers, or other resources they find to help them answer the question. The __student resource sheet__ can potentially be reused for each class if they are placed in a sheet protector.

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Allow students to work together to use their problem-solving skills and prior knowledge to estimate and solve the scaling problem. As students work, listen to their conversations and strategies used. Some students may use the string to follow the path and get the length of the whole path, then use the scale factor to set up a proportion. Other students may use the scale factor given to estimate how many sections would fit between the two parking areas.

Once students have their answers, it is important to have them explain their process. Ideally, you can have multiple students share who all used different strategies so that students can hear the different methods that worked. This can help them expand what they already know and understand about scaling problems. It may also be helpful to ask students to reflect on the different methods people used and think about the pros and cons for each.

You can let students know that solving scaling problems will be similar to this problem; however, there may not always be an image given to help them.

In this example, students will have the scale factor given as a ratio.

Sometimes, when students might try to express the dimensions in meters by converting centimeters to meters or the other way around instead of applying the scale factor.

In solving scaling problems, students should figure out ways of organizing the information. They could use a ratio table or a proportion - make sure that they use labels for any tool.

*Ratio table*

*Proportion*

`\frac{\text{Model (cm)}}{\text{Real life (m)}}=1/120 =8/?`

Students should explain their reasoning, and you may find that some students use visual cues, such as drawing a small rectangle and a large rectangle to help them grasp that there are two sizes.

Some students might just multiply the original by the scale factor. The issue with this strategy is that when the original is missing, they tend to apply the same formula.

To help connect scaling problems to application problems, students will need to find the area of the park based on the model. Students should ideally use the new length and width they found previously to find the perimeter of the park.

This problem gives you an opportunity to expose students to solving scaling problems that require them to find the scale factor and then identify unknown measurements. It also allows students to see how a more complicated problem can be broken down into smaller pieces.

When finding the scale of the drawing, students may divide the values in the wrong order or think they do not have enough information to answer the question. When determining the height of the ship knowing the height of the drawing, students may struggle to work with the fraction and the scale.

The key in solving scaling problems is to organize the information using a tool. Once they have done it, students might notice that since `4/5` is `4` divided by `5`, they can find the actual height by dividing the actual length by `5`.

For this example, students should be encouraged to use what they already know to try and solve the problem. Encourage students to draw a picture if it will help them visualize the information they are given. Students should be able to explain the reasoning they used to solve the scaling problem.

When students are given the actual measurements and have to find the scaled measurements, organizing the information can help them figure out what is given and what is unknown.

Students struggle with finding the area of a polygon when there is a scale factor. They tend to scale the area using the scale factor instead of scaling the dimensions. You can use an error analysis problem with area at the end of the class or beginning of the next class to help catch common misconceptions with application problems.

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for solving scaling problems. Check out the online practice and assign to your students for classwork and/or homework!

Solving Scaling Problems Practice

Problem 1 of 5

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