We included **HMH Into Math Grade 7 Answer Key PDF** **Module 12 Proportional Reasoning with Samples **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 12 Answer Key Proportional Reasoning with Samples

**Sampling and Data Analysis**

**Research Assistant**

A research assistant collects or verifies information in a laboratory setting, or even in an office for a field such as law or media. The responsibilities of a research assistant may include conducting surveys, analyzing data, providing quality control, managing information storage, and preparing results for presentation or publication. Research assistants often use computers to help them perform these tasks.

**STEM Task:**

Work as a class to record the birth month of each class member. Assign the number 1 to represent January, the number 2 to represent February, and so on. Use the class data to make a dot plot. What observations and conclusions can you make by looking at the dot plot? What questions do the data raise? Explain your thinking.

**Learning Mindset Resilience Manages the Learning Process**

Resilience is the ability to move forward when obstacles arise. Developing resilience allows you to identify a barrier, learn from it, and overcome the challenges it presents. Here are some ways you can increase your resilience.

- Consider where you are within the learning process. Do you think you may encounter barriers to completing a task? If so, try to identify them.
- Review the steps you are taking to direct your learning. Monitor your feelings, motivation, and interest level to keep yourself on task.
- If necessary, modify learning situations and activities so that they lead to successful conclusions.

**Reflect**

Question 1.

What strategies did you use to overcome barriers you encountered during the STEM Task?

Answer: By collecting and analyzing the data you can overcome the barriers encountered during the STEM task.

Question 2.

What steps can you take to direct your learning and better understand how to collect and analyze data?

Answer:

1. Determining the data you need.

2. Collect the data using different strategies.

3. Analyse the type of data on what you want to know.

4. Direct observation

**WHICH FRACTION DOES NOT BELONG?**

Each diagram represents a fraction. All but one of the fractions can be matched with a partner, but not based on the shapes of the models.

Write the fraction that each model represents.

A.

Answer:

The above figure is a 10×10 grid.

10 rows and 4 columns are shaded.

40 are shaded among 100.

Thus the fraction is 40/100 or 4/10.

B.

Answer:

The name of the shape is a circle.

It is equally divided into 5 parts.

Among the 5 parts, 2 are shaded.

So, the fraction is 2/5.

C.

Answer:

The name of the shape is a rectangle that is divided into 14 equal shares.

Now we can see that 4 parts are shaded among 14.

So, the fraction of the shaded part is 4/14.

D.

Answer:

The above figure is a 10×10 grid.

10 rows and 1 column are shaded.

10 are shaded among 100.

Thus the fraction is 10/100 or 1/10.

E.

Answer:

The name of the shape is a rectangle that is divided into 7 equal shares.

Now we can see that 2 parts are shaded among 7.

So, the fraction of the shaded part is 2/7.

**Turn and Talk**

How can you pair up the fractions? Which is the fraction that does not belong? Explain your answers.

Answer: You can pair up the fractions by writing the shaded part in the numerator and the total number of parts in the denominator.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**Statistical Data Collection**

**For Problems 1 and 2, tell whether the question is a statistical question. Explain your reasoning.**

Question 1.

How many days are in the month of March?

Answer: There are 31 days in the month of March.

It is not statistical. This question is answered by counting the number of days in March. This produces a single number. This question is not answered by collecting data that vary.

Question 2.

How tall are the giraffes at the zoo?

Answer: The given question is a statistical question because the height of all giraffes are not same . Height of some giraffes are same and some giraffes have the same height.

Question 3.

Write a statistical question about your school.

Answer: “How old are the students in your school?” is a statistical question.

**Representing Equivalent Ratios**

**Complete the table of equivalent ratios.**

Question 4.

Answer:

The actual ratio is 4:1

The equivalent ratios are 8:2, 10:2.5, 12:3

Question 5.

Answer:

The ratio is 1:42

The equivalent ratios are 2:84, 3:126, 5:210 and 8:336

**Use Ratio and Rate Reasoning**

**Write an equation to model each proportional relationship. Then solve the problem.**

Question 6.

The ratio of tables x to chairs y in a restaurant is 2 to 7. The restaurant has a total of 12 tables. How many chairs does it have?

Equation: ___________

Solution: __________ chairs

Answer:

Given,

The ratio of tables x to chairs y in a restaurant is 2 to 7. The restaurant has a total of 12 tables.

2 tables = 7 chairs

12 tables = x chairs

2x = 12 × 7

2x = 84

Thus the equation is 2x = 84

x = 84/2

x = 42

Thus there are 42 chairs.

Question 7.

Let x represent the number of batteries and y represent the cost of the batteries. A package of 8 rechargeable batteries costs $12. At this rate, how much would a package of 20 rechargeable batteries cost?

Equation: ___________

Solution: $ ___________

Answer:

Given,

Let x represent the number of batteries and y represent the cost of the batteries.

A package of 8 rechargeable batteries costs $12.

8 batteries = $12

20 batteries = x

x × 8 = 12 × 20

8x = 240

The equation would be 8x = 240

x = 240/8

x = 30

Thus the cost of 20 batteries is $30.