Check Your Readiness

1.

There is a proportional relationship between $x$ and $y$ . Complete the table with the missing values.

$x$	$y$
4.5	3
18	12
	30
15

Answer:

$x$	$y$
4.5	3
18	12
45	30
15	10

Teaching Notes

In this unit, students review previous work with proportional relationships as a lead-in to linear equations.

If most students struggle with this item, plan to use this problem or a similar one as an additional warm-up activity. During Lessons 1 and 2 plan to emphasize multiple ways to identify whether a relationship is proportional, such as finding a constant of proportionality using a table of values and using coordinates of points on the graph.

2.

To mix a particular shade of pink paint, white paint and red paint are mixed in the ratio $4:3$ . If 12 gallons of red paint are mixed with some white paint to make this same shade of pink, how many total gallons of pink paint result?

A.

48

B.

36

C.

28

D.

16

Answer:

28

Teaching Notes

Students move from scale factors to proportional relationships in preparation for linear relationships. If most students struggle with this item, before beginning Lesson 1, do Grade 6, Unit 2, Lesson 16, Activity 2 to practice the concept of generating equivalent ratios.

3.

At a grocery store, 2 gallons of milk cost $7.20, and 5 gallons of milk cost $18. Which equation relates the total cost, $t$ , to the gallons of milk purchased, $m$ ?

A.

$m=7.2t$

B.

$t = 7.2m$

C.

$m = 3.6t$

D.

$t = 3.6m$

Answer:

$t = 3.6m$

Teaching Notes

In grade 7, students wrote equations to describe proportional relationships. The graphs of these equations were lines through the origin. In this unit, students will write equations for proportional relationships as well as other linear relationships.

If most students struggle with this item, plan to do Lesson 1 Activity 3. During the Activity Synthesis spend some extra time sharing student equations and making connections to the tick-mark diagram.

4.

Plot and label 3 different points with $y$ -coordinate -4.
Plot and label 3 different points with $x$ -coordinate 2.

Answer:

Any 3 points with $y$ -coordinate -4 plotted and labeled. Sample responses: $(0,\text-4)$ , $(\text-2,\text-4)$ , $(1,\text-4)$
Any 3 points with $x$ -coordinate 2 plotted and labeled. Sample responses: $(2,0), (2,\text -3), (2,5)$

Teaching Notes

Students will need to be familiar with the coordinate plane to graph lines.

If most students struggle with this item, plan to pause students as they are working on Lesson 1, Activity 2, Question 4 to ensure that they can plot and mark points once they have identified the bug's location at the given time. If students need additional practice, refer to Grade 6, Unit 7, Lesson 11, Activity 1.

5.

Which graph is a translation of line $n$ ?

Answer:

Line D

Teaching Notes

In this unit, students are presented with various forms of linear equations and various ways of thinking about those forms. One interpretation is to consider nonproportional linear equations as vertical translations of the line $y=mx$ .

If most students struggle with this item, plan to use Activity 1 in Lesson 8 to review translations. If students need additional practice recalling translations, especially translations of lines, refer to Unit 1, Lesson 9, Activity 2.

6.

At a sandwich shop, any sandwich costs $4.50, plus $0.25 for each extra topping.

How much does a sandwich cost with 3 extra toppings?
How much does a sandwich cost with 13 extra toppings?
If Andre’s sandwich cost $2.00 more than Clare’s sandwich, how many more toppings did Andre add to his sandwich?

Answer:

$5.25
$7.75
8 toppings

Teaching Notes

Another interpretation of a linear equation is to start with a given amount and thereafter increase the amount at a constant rate. Students are asked to engage in repeated reasoning in anticipation of this way of thinking.

If most students struggle with this item, plan to review it with students before beginning Lesson 6, Activity 2 and amplify vocabulary such as “constant of proportionality” and “rate of change” starting in Lesson 3, Activity 1.