Grade 7

End-of-Unit Assessment

Quadrilateral $ABCD$ is a scaled copy of quadrilateral $EFGH$ . Select all of the true statements.

<p>A figure. quadrilateral EFGH. Quadrilateral ABCD.</p>

Segment $BC$ is half the length of segment $EF$ .

Segment $CD$ is half the length of segment $GH$ .

The measure of angle $ADC$ is equal to the measure of angle $EHG$ .

The length of segment $AB$ is 3 units.

The area of $ABCD$ is half the area of $EFGH$ .

Answer:

B, C, D

Teaching Notes

Students who select choice A are missing the fact that the two segments are not corresponding. Students who select choice E are making a common mistake: when a figure is scaled by a factor of $\frac12$ , the scaled copy has $\frac14$ the area (not $\frac12$ ).

Rectangle A measures 8 inches by 2 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

40 inches by 10 inches

10 inches by 2.5 inches

9 inches by 3 inches

7 inches by 1 inch

6.4 inches by 1.6 inches

Answer:

A,B,E

Teaching Notes

The correct answer choices all involve side lengths that are in a $8:2$ ratio. Students who select choice C or choice D may believe that adding or subtracting one from both lengths will maintain their ratio.

A scale drawing of a rectangular parking lot is 6 inches long and 5 inches wide. The actual parking lot is 240 feet long. What is the area of the actual parking lot, in square feet?

48,000

1,200

200

Answer:

Teaching Notes

Students who select choice D have calculated the area of the scale drawing rather than of the park. Students who select choice C have found the correct length of the park, but not the area. Students who select choice B have multiplied the area of the drawing by the scale factor, neglecting the fact that both the length and the width of the park are scaled by a factor of 40, so the area of the park will be 1,600 times greater than the area of the drawing.

Here is a polygon. Draw a scaled copy of the polygon using a scale factor of $\frac13$ .

Answer:

Minimal Tier 1 response:

Work is complete and correct.
Sample: See above. Acceptable differences from sample: Figure is somehow in a different orientation; figure overlaps original.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Correct drawing with scale factor 3 instead of scale factor $\frac13$ ; minor error in determining dimensions of figure, such as a pair of segments 1 unit longer than they should be.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Drawing shows lack of use of any scale factor; multiple errors in determining dimensions; incorrect attempt at drawing with scale factor 3.

Teaching Notes

Students draw a scaled copy of a figure on a grid.

The scale of a map says that 3 cm represents 5 km.

What distance on the map represents an actual distance of 15 km?
What actual distance is represented by 15 cm on the map?

Answer:

9 cm (or equivalent)
25 km (or equivalent)

Teaching Notes

Students are given the scale of a map and asked to find lengths and distances using that scale. Common errors for this problem may include reversing the numbers (5 cm represents 3 km) and other errors typical of calculating and using unit rates such as multiplying rather than dividing.

There are two different maps of California.

On the first map, the scale is 1 cm to 20 km. The distance from Fresno to San Francisco is 15 cm.
On the second map, the scale is 1 cm to 100 km.

What is the distance from Fresno to San Francisco on the second map? Explain your reasoning.

Answer:

The distance is 3 cm. Sample explanations:

On the 1 cm : 20 km scale map, each centimeter represents 5 times as much actual distance as on the 1 cm: 100 km map. That means that on the 1 cm : 5 km map the distance from Fresno to San Francisco will be one fifth as much, 3 cm.
The actual distance from Fresno to California is 300 km, because $15 \boldcdot 20=300$ . The distance on the second map that represents 300 km is 3 cm, because $300 \div 100=3$ .

Minimal Tier 1 response:

Work is complete and correct.
Sample: Lengths on the second map are five times smaller because 1 cm represents 20 km instead of 100 km. Divide 15 cm by 5 to get 3 cm.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Multiplication or division errors in otherwise correct work; work involves a correct substantive intermediate step (such as the actual distance from Fresno to San Francisco) but goes wrong after that; one mistake involving an “upside down” scale factor (or multiplying when division is called for); a correct answer without explanation.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Work does not involve proportional reasoning; an incorrect answer without explanation, even if close; multiple mistakes that involve inversion of scale factors.

Teaching Notes

Students reason about maps drawn at two different scales. This problem can be solved using a variety of approaches, including tables and double number lines.

Mai’s kitchen is a rectangle with length 6 meters and width 2 meters.

Make a scale drawing of Mai’s kitchen, using a scale of 1 to 40. Be sure to label the dimensions of your drawing.
Mai’s kitchen door is 1.2 meters wide. How wide should the door be on the scale drawing? Explain how you know.
Mai’s kitchen table measures 4 centimeters by 2.5 centimeters on the scale drawing. What are the actual measurements of her table?

Answer:

A rectangle, labeled with length 15 cm and width 5 cm (or equivalent units, such as 0.15 m and 0.05 m).
3 cm (or equivalent units). Sample reasoning: 1.2 m is 120 cm. At 1 to 40, the width of the door is 3 cm, because $120\div40=3$ .
160 cm by 100 cm (or equivalent units). Actual measurements are 40 times as long as the corresponding measurements on the drawing.

Minimal Tier 1 response:

Work is complete and correct, with complete explanation or justification.
Sample:

A rectangle, labeled 15 cm and 5 cm, with the larger side labeled 15 cm.
3 cm. Because the scale is 1 to 40, the door’s 120 cm width becomes $120\div40$ cm in the scale drawing.
1.6 m by 1 m

Tier 2 response:

Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
Sample errors: One calculation or conversion error; clear error in relative shape of rectangle; incomplete explanation of 3 cm calculation; describing instead of drawing and labeling the scale drawing.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: Two or more error types from Tier 2 response; multiple calculation and conversion errors; scaling in wrong direction (multiplying or dividing when inappropriate); using incorrect scale factor.

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: Two or more error types from Tier 3 response; adding or subtracting when working with scale factor; misunderstanding of the meaning and use of “1 to 40.”

Teaching Notes

Students make a scale drawing of a kitchen using a given scale. They then use that scale to calculate lengths of various objects.