Check Your Readiness

1.

Which of these points is closest to the $y$ -axis?

A.

$(\text-6,0)$

B.

$(\text-2,12)$

C.

$(4,2)$

D.

$(5,1)$

Answer:

$(\text-2,12)$

Teaching Notes

In this unit, students work with rigid transformations and dilations, both with and without a grid. These transformations, especially when done on a grid, require familiarity with distance between a point and a line.

If most students struggle with this item, plan to use this problem and Unit 1 Lesson 5 to review distance on a coordinate grid. Students will have more opportunities to find distances on a coordinate grid in Lesson 4 Activity 3.

2.

Which of these points is closest to the point $(7,1)$ ?

A.

$(4,1)$

B.

$(7,\text-1)$

C.

$(7,4)$

D.

$(11,1)$

Answer:

$(7,\text-1)$

Teaching Notes

In this unit, students work with dilations by multiplying the distance between a point and the center of dilation by a scale factor.

If most students struggle with this item, plan to launch Lesson 4 Activity 3 by reviewing this problem and the concept of distance on the coordinate plane.

3.

Quantities $x$ and $y$ are in a proportional relationship. Complete the table.

$x$	$y$
4	16
3
	8

Answer:

$x$	$y$
4	16
3	12
2	8

Teaching Notes

In this unit, students will study similar triangles and slope. They will need to use proportional relationships to find other points on a line.

If most students struggle with this item, plan to use this problem in Lesson 11 Activity 2 to connect this context of a proportional relationship with points on a line.

4.

A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.

Line graphed on xy plane. horizontal axis, time in hours, scale 0 to 8, by 1's. vertical axis, distance in mile, 0 to 400, by 50's. Points on line: origin, 3 point 5 comma 210, 5 comma 300.

The point $(3.5, 210)$ is on the graph. Explain what this means in terms of the car.
Is the point $(1,60)$ on this graph? Explain how you know.

Answer:

It means that after 3.5 hours, the car has traveled a distance of 210 miles.
Yes, the car is traveling at a constant speed, and 300 miles in 5 hours means the car travels 60 miles each hour. That means the point $(1,60)$ is on the graph.

Teaching Notes

In this unit, students are introduced to the concept of slope, and build on their grade 7 work with proportional relationships and unit rate.

If most students struggle with this item, plan to support this thinking in Lesson 10 Activity 2 as students investigate why two triangles sharing one side along the same line are similar. Students will have several opportunities throughout this lesson to investigate this idea.

5.

Evaluate each expression.

$4\div \frac{1}{3}$
$\frac{3}{8}\div \frac{7}{2}$
$3\frac{1}{2}\div \frac{7}{4}$

Answer:

12
$\frac{3}{28}$ (or equivalent)
2

Teaching Notes

In this unit, students will use fraction division when they calculate unknown sides of similar triangles.

If most students struggle with this item, plan to use these problems and the ones in Lesson 1 Activity 1.

6.

The two triangles displayed are scaled copies of one another.

Find the scale factor.
What is the value of $x$ ?

Two triangles. Triangle on left, left side = x, bottom side = 4. Triangle on right, left side = 25, bottom = 10.

Answer:

$\frac 5 2$ or $\frac 2 5$ (or equivalent)
10

Teaching Notes

In this unit, students work with dilations and similar triangles, building on their grade 7 work with scaled copies and scale factors.

If most students struggle with this item, plan to do optional Lesson 1 Activity 3 to give students an opportunity to continue working with scaled copies and finding the scale factors.

7.

Is Figure B a scaled copy of Figure A? Explain how you know.

Answer:

No, the horizontal segments in Figure B are twice as long as the corresponding segments in Figure A, and the vertical segments are three times as long.

Teaching Notes

If most students struggle with this item, plan to spend time in Lesson 1 emphasizing the relationship between equivalent ratios and scaled copies. Plan to revisit this item in the synthesis of Lesson 1 Activity 2 and ask students how they could determine whether Figure B is a scaled copy of Figure A. Emphasize strategies that take advantage of the grid in looking for equivalent ratios.