Grade 8

Readiness Check

Check Your Readiness
1.

A line contains the points (-3,-2)(\text-3,\text-2) and (7,2)(7,2).

  1. Without doing any calculations, determine whether the slope of this line is positive or negative. Explain or show your reasoning.
  2. Calculate the slope of the line.

Answer:

  1. The slope is positive. One way to see this is to plot the 2 points. Another is to note that as the xx-coordinate increases, the yy-coordinate also increases.
  2. 25\frac{2}{5} (or equivalent)

Teaching Notes

In this unit, students will need to eyeball the data in scatter plots to determine if the data points show a positive association, a negative association, or neither. Lines fitted to data showing positive association have positive slope, and lines fitted to data showing negative association have negative slope.

If most students struggle with this item, plan to reinforce language about positive and negative slopes, specifically "as the value of one variable increases, the value of the other increases" for positive slope, and "as the value of one variable increases, the value of the other decreases" for negative slope.

2.

Diego has some money in his bank account before he starts a summer job. He deposits the money from the summer job in his bank account and doesn’t spend any of it. After working 3 hours, he has $71 in the account. After working 12 hours, he has $134 in the account.

How much money does Diego earn per hour?

Answer:

Diego earns $7 per hour. He earns $63 by working 9 hours, so he earns $7 by working 1 hour.

Teaching Notes

Though this problem does not use the word “slope,” students need to find the rate of change for the situation. If most students struggle with this item, plan to have students show their calculations and perhaps revisit this item during Activity 1.

3.

Here is a graph showing the balance in someone's savings account since the beginning of the year.

A line in an x y plane. 
A line in an x y plane. Origin 0. Vertical axis, dollars, from 0 to 140 by 10s. Horizontal axis, weeks, from 0 to 16 by 1s. The line passes through the points 0 comma 110, 5 comma 90, and 10 comma 70.

  1. Write an equation for the line shown on the graph.
  2. What does the slope mean in this situation?
  3. What does the vertical intercept mean in this situation?

Answer:

  1. d=-4w+110d = \text-4w + 110 (or equivalent)
  2. The slope of -4 means that each week, this person is spending $4 more than they are earning.
  3. The vertical intercept of 110 means that this person started the year with $110 in the account.

Teaching Notes

In this unit, students will draw lines that fit data in a scatter plot and estimate the slope, intercepts, and equation for the line they drew.

If most students struggle with this item, beginning in Lesson 4 when students begin connecting the meaning of slope to models, review how slope can be seen on graphs. In Lessons 5, 6, and 7, continue to ask students how the slope and intercepts of any given linear model can be seen in the equation and in the graph. When students draw lines of best fit, give them opportunities to practice estimating slope and intercepts by referring to how slope can be seen on the graph. Help students connect the visual of a slope triangle to the language “For every 1 unit increase in [the independent variable], the [dependent variable] increases/decreases by . . . .” Make sure students attend to the scale of the axes as they estimate and describe slopes.

4.

In many schools, students have the choice between taking art, music, or some other elective.

  1. At Euclid Middle School, there are 200 students in the eighth grade. Of those students, 40 students are taking art. What percentage of eighth graders at Euclid Middle School are taking art? Explain or show your reasoning.
  2. At Newton Middle School, there are 320 students in the eighth grade. Of those students, 54 are taking music. What percentage of eighth graders at Newton Middle School are taking music? Explain or show your reasoning.

Answer:

  1. 20%. Sample reasoning: 100:20 and 200:40 are equivalent ratios.
  2. 16.875%. Sample reasoning: 54 can be divided by 320 to find the percentage.

Teaching Notes

In this unit, students will be introduced to two-way tables. Many questions that come up in the context of two-way tables are of this form: “What percentage of _____ are _____?”

If most students struggle with this item, plan to spend time during the Launch of Activity 3 helping students verify that the percentage of 10-to-12 year olds that have a cell phone is 42%. Students will have more practice finding percentages in Lesson 10, but you may choose to revisit this item as part of the Warm-up for Activity 10.

5.

Students voted for their favorite entry in a kids' Halloween costume contest. Jada recorded the results in a bar graph:

  1. Who got more votes: the pumpkin or the crayon?
  2. How many votes did the unicorn get?
  3. Who won the contest?

Answer:

  1. The pumpkin
  2. 18 votes
  3. The dog

Teaching Notes

Bar graphs should be familiar to students from grade school, but it has been a long time since students have used this representation. In this unit, students will learn to use segmented bar graphs as a way of representing categorical data.

If most students struggle with this item, plan to ask students in Activity 2 to connect each number in the two-way table to the graph. As students do the card sort in the activity, you may wish to check in with those who struggled with this item to ask them to map the numbers from the two-way tables to the bar graph it matches.

6.

Students at Elena’s school were polled about the animal they would most like to have as a pet.

animal votes
bird 22
cat 45
dog 55
fish  37
rabbit 15

Make a bar graph that displays this information.

Answer:

Students should use a scale of 5 or 10 on the vertical axis. Sample response:

<p>Bar graphs of different animals.</p>

Teaching Notes

Students will have to think about how many bars are needed and how to scale the vertical axis.

If most students struggle with this item, plan to ask students in Activity 1 to work with a partner to create a bar graph from the data. Each partner should use one category as the xx-axis label. Partners can trade and check each other’s graphs.