Grade 8

Readiness Check

Check Your Readiness
1.

A line contains the points (-1,4)(\text-1,4) and (5,-3)(5,\text-3).

  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 negative. One way to see this is to plot the two points. Another is to note that as the xx-coordinate increases, the yy-coordinate decreases.
  2. -76\text-\frac76 (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.

Lin has some money in her bank account before she starts a summer job. She deposits the money from the summer job in her bank account and doesn’t spend any of it. After working 4 hours, she has $85 in the account. After working 15 hours, she has $217 in the account. How much money does Lin earn per hour?

Answer:

Lin earns $12 per hour. She earns $132 by working 11 hours, so she earns $12 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.

<p>A graphed line.</p>
Graph in first quadrant. Balance in dollars on y-axis from 0 to 160 by tens. Time in weeks on x axis from 0 to 17 by ones. Graphed line starts at 0 comma 40 and slants up to pass through 15 comma 130.

  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. b=6t+40b=6t+40 (or equivalent)
  2. The slope of 6 means the balance in the account is increasing by $6 each week.
  3. The vertical intercept of 40 means this person started the year with $40 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.

Determine each answer to the nearest tenth of a percent.

  1. 8 out of 32 football teams are on the East Coast. What percentage of football teams are on the East Coast?
  2. It rained 4 out of 7 days this week. What percentage of days did it rain?

Answer:

  1. 25.0%
  2. 57.1%

Teaching Notes

In this unit, students will frequently calculate percentages and should be capable of rounding to the nearest percent or tenth of a percent.

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 this item can also be revisited as part of the Warm-up for Activity 10.

5.

Students voted for their favorite pizza toppings. Kiran recorded the results in this bar graph. 

<p>A bar graph.</p>

  1. Which topping won the contest?
  2. How many votes did pepperoni get?
  3. Which topping got more votes: mushrooms or green peppers?

Answer:

  1. Cheese
  2. 28
  3. Green peppers

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 Andre’s school were polled about the mascot they would most like to have. This table shows the results:

mascot number of votes
badger 14
hornet 25
viking 67
cardinal 49
wildcat 83

Make a bar graph that displays this information.

Answer:

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

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.