Grade 7

Readiness Check

Check Your Readiness

Plot and label each number on the number line.

0.75, $\frac14$ , 0.2, 0.5, $\frac{8}{10}$

Answer:

Teaching Notes

Students should be fairly comfortable with placing a list of numbers in order and on a number line. This problem is intended to familiarize students with fractions and decimals between 0 and 1, which are useful in probability.

If most students struggle with this item, plan to take extra time for the Launch of Lesson 2, Activity 4. Display a blank number line and call on students to place benchmark fractions, decimals, and percents on the number line. Ask students to share their strategies for making the placement. Connect this to the questions “Which is closer to 1?” and “Which has the largest value?”

Teachers held a basketball shooting contest. Their goal was to make 60 baskets. For each teacher, determine what percentage of the goal they achieved.

Teacher A made 12 baskets.
Teacher B made 42 baskets.
Teacher C made 66 baskets.
Teacher D made 9 baskets.

Answer:

20%. 12 is 20% of 60, because $12\div6 = 2$ , and $2\boldcdot10 = 20$ .
70%. 42 is 70% of 60, because $42\div6 = 7$ , and $7\boldcdot10 = 70$ .
110%. 66 is 110% of 60, because $66\div6 = 11$ , and $11\boldcdot10 = 110$ .
15%. 9 is 15% of 60, because $9\div6 = 1.5$ , and $1.5\boldcdot10 = 15$ .

Teaching Notes

Calculating and making sense of percentages will come up throughout the unit as students study probability and sampling.

Watch for students struggling with the percentages that are greater than 100%. Encourage students to use fractions, benchmarks, or proportional reasoning to help. Since 6 baskets are 10% of the goal, any percentage can be determined by dividing the baskets by 6 and then multiplying by 10.

If most students struggle with this item, plan to emphasize the Lesson Synthesis of Lesson 2, Activity 3, where percentages are used and interpreted with probability. During the unit, students have choices of reporting probabilities as fractions or percentages, but they need to interpret percentages. For example, a 30% chance means we expect success in 3 out of 10 trials. Offer tape diagrams and double number lines as tools for helping students recall and calculate percentages. Additional practice can be found in Grade 6, Unit 3, Lessons 11–16.

A survey was conducted of a random sample of 15 sports team coaches in a school district and found that 6 of them were in favor of a shorter season for their sport.

The school district has 132 sports team coaches. Make an estimate for the number of coaches in the school district who are in favor of a shorter season for their sport.
Do you think it would be surprising if 99 coaches were in favor? Explain your reasoning.
Do you think it would be surprising if 60 coaches were in favor? Explain your reasoning.

Answer:

Answers vary. Sample response: 53 coaches. 40% of the coaches surveyed were in favor, and 40% of 132 is 52.8.
Yes, this would be surprising. Sample reasoning: 99 is 75% of 132, so having 75% in favor instead of something close to the 40% from the sample would be surprising.
No, this would not be surprising. Sample reasoning: 60 is about 45% of 132, so having 45% in favor instead of 40% would not be surprising.

Teaching Notes

This problem mainly tests students’ understanding of proportional relationships, while preparing for some of the concepts about using samples to draw inferences that will be presented in the upcoming unit.

If most students struggle with this item, it is not necessary to take any specific action. Students start off Lesson 3 with some additional examples of sample populations so that they can start to practice this new concept. Attend to students who struggle with this problem and make sure they are able to follow the proportional reasoning they are using. More practice with this concept is found in Lesson 16.

Select all the measures of center.

mean

IQR (interquartile range)

MAD (mean absolute deviation)

median

range

Answer:

A, D

Teaching Notes

This item tests students’ ability to distinguish measures of center from measures of spread. This is also an opportunity to determine whether students are familiar with these terms from their work in grade 6. All of these terms are needed in the second half of the unit, both when using samples to make inferences about populations and when testing whether there is a significant difference between two populations. Review of mean, MAD, and dot plots will come in this unit.

Students who do not select choice A or choice D have a significant gap in understanding about the meaning and use of mean and median, or they simply may not remember the terms. Students who select choice B or choice C do not fully understand the differences between measures of center and measures of spread. Students who select choice E may not know what range is or may not recognize it as a measure of spread.

If most students struggle with this item, plan to spend additional time on the Lesson Synthesis of Lesson 11, Activity 2. Review both MAD and IQR as well as mean and median. Focus on what MAD and IQR tell us about data sets, not how to calculate them. If extra practice interpreting MAD and IQR is needed, Grade 6, Unit 8, has additional work on calculating mean, median, MAD, and IQR.

Jada completed 11 homework assignments. This list shows her scores for each assignment.

10, 9, 8, 10, 7, 9, 8, 6, 10, 10, 8

What is the median score?
What are the first quartile and the third quartile?
What is the interquartile range?

Answer:

The median is 9. The ordered list is 6, 7, 8, 8, 8, 9, 9, 10, 10, 10, 10.
Quartile 1 is 8. The half of the data with smaller values lower than the median is 6, 7, 8, 8, 8, and its middle value is 8. Quartile 3 is 10. The half of the data with greater values than the median is 9, 10, 10, 10, 10, and its middle value is 10.
The IQR is 2, because $10 - 8 = 2$ .

Teaching Notes

This question more specifically tests whether students remember how to calculate range and quartiles of data. Watch for students attempting to answer the question without first sorting the data, and for students who have significant trouble understanding the question because they do not recognize or understand the vocabulary.

If most students struggle with this item, plan to review it, or a similar item using small data sets, during the Launch of Lesson 18, Activity 3.

Two students compared their test scores. Here are the scores for each student.

Student A: 91, 100, 82, 90, 93, 85

Student B: 80, 70, 58, 98, 75, 81

Construct two box plots, one for the data for each student.
Which student’s scores show greater variability? Explain how you know.

Answer:

Student B shows greater variability. Sample reasoning: Student B’s scores have a greater IQR.

Teaching Notes

This problem tests students' prior knowledge of box plots, and provides an opportunity for students to demonstrate how they are thinking about variability.

If students have difficulty, they will need a quick refresher on constructing box plots when this concept first appears in the unit. Students may argue variability by appealing to range (whether they use the term or not), but the IQR is the more important measure of spread for the work of this unit.

If most students struggle with this item, plan to review it during the Launch of Lesson 18, Activity 4. If students are struggling to understand how to construct box plots, Grade 6, Unit 8, Lesson 16, has activities to help students understand and construct them.

The data set shows the number of shells that 12 people collected.

4, 5, 5, 4, 1, 6, 8, 2, 2, 2, 4, 5

What is the mean number of shells collected?
What is the MAD (mean absolute deviation) of this data? Explain how you know.

Answer:

The mean is 4.
The MAD is 1.5 shells. Sample reasoning: First, calculate the mean. The total number of shells is 48. The mean is 4 shells, because $48 \div 12 = 4$ . The absolute deviations are 0, 1, 1, 0, 3, 2, 4, 2, 2, 2, 0, 1. The total of these is 18, and $18 \div 12 = 1.5$ .

Teaching Notes

This problem tests students’ fluency with a list of data, mean, and MAD. Look at students’ explanations to see which incorrect answers come from a misunderstanding of mean and MAD and which are simply arithmetic errors.

If most students struggle with this item, plan to review it during the Activity Synthesis of Lesson 11, Activity 2, to help students recall how to use the dot plot to find the mean and MAD. If students struggle with both this item and Item 4, plan to use activities from grade 6 to do a more thorough review of interpreting and estimating measures of center and spread to compare data sets represented in box plots.