Check Your Readiness

1.

How far away is the point $(\text-5,2)$ from the $x$ -axis?

A.

7 units

B.

5 units

C.

3 units

D.

2 units

Answer:

D

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.

Select all the points that are 5 units away from $(6,2)$ .

A.

$(1,2)$

B.

$(6,5)$

C.

$(11,7)$

D.

$(30,10)$

E.

$(6,\text-3)$

F.

$(11,2)$

Answer:

A, E, F

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.

The point $(5,15)$ is on a graph representing a proportional relationship. Give the coordinates of two other points on the same graph.

Answer:

Sample responses: $(1, 3), (2, 6), (3, 9), (4, 12), (10, 30)$ . Any point of the form $(5a, 15a)$ , where $a$ is any number except 1.

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

<p>A graph. Distance. Miles. Time. Hours.</p>

The point $(1, m)$ is on the graph. Find the value of $m$ and explain how you know.
What does the value of $m$ mean in this situation?

Answer:

80. Sample reasoning: 4 divided by 4 is 1, and 320 divided by 4 is 80.
The train is moving 80 miles per hour.

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.

$3\div\frac{1}{8}$
$\frac{7}{10}\div\frac{3}{2}$
$3\frac{1}{3}\div\frac{5}{6}$

Answer:

24
$\frac{7}{15}$ (or equivalent)
4

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.
Sketch a new triangle that is also a scaled copy of these triangles using a different scale factor.

Answer:

$\frac43$ or $\frac34$ (or equivalent)
Answers vary. The side lengths of the new triangle must all be $k$ times the side lengths of one of the original triangles for some positive number $k$ where $k \ne 1$ .

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.

Which figure is a scaled copy of Figure A? Explain how you know.

<p>Polygons. Figure A. Figure B. Figure C.</p>

Answer:

Figure C is a scaled copy because each side of Figure C is twice as long as the corresponding side of Figure A. Figure B is not a scaled copy because the bottom side of Figure B is three times as long as the bottom side of Figure A, but the left side of Figure B is twice as long as the left side of Figure A.

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.