Grade 7

End-of-Unit Assessment

Select all the true statements about the angles in this diagram.

Angles $a$ and $b$ are supplementary angles.

Angles $a$ and $c$ are complementary angles.

Angles $a$ and $d$ are vertical angles.

Angles $a$ and $e$ are supplementary angles.

Angles $b$ and $e$ are complementary angles.

Answer: C, D

Teaching Notes

Students who select choice A may be confusing the terms "complementary" and "supplementary." Students who select choice B may remember that complementary angles have something to do with a right angle, but may not understand that the two angle measures added together make

90^\circ

. Students who select choice E may recognize that Angle

b

is complementary to another angle, but may not recognize which one.

A square pyramid is sliced parallel to the base and halfway up the pyramid.

Which of these describes the cross-section?

A square smaller than the base

A quadrilateral that is not a square

A square the same size as the base

A triangle with a height the same as the pyramid

Answer:

A square smaller than the base

Teaching Notes

Students who select choice B may have drawn the shape but did not notice or understand that it is still a square. Students who select choice C are likely to have pyramids and prisms confused, even though the pyramid is given. Students who select D have probably drawn a vertical cross-section.

Which of these describes a unique polygon?

A triangle with angles $30^\circ$ , $50^\circ$ , and $100^\circ$

A quadrilateral with each side length 5 cm

A triangle with side lengths 6 cm, 7 cm, and 8 cm

A triangle with side lengths 4 cm and 5 cm and a $50^\circ$ angle

Answer:

A triangle with side lengths 6 cm, 7 cm, and 8 cm

Teaching Notes

Students who select choice A need some refresher work on the activities of this unit, since a scaled copy of the triangle will have the same angle measures. Students who select choice B may have assumed that the shape is a square from its description, but it could also be a rhombus of many different angles. Students who select choice D did not recognize that the stated angle's location was not given, allowing there to be multiple triangles with this information.

Priya is trying to draw a triangle with side lengths 2 cm, 5 cm, and 1 cm. Explain why Priya’s drawing is not creating a triangle.

Answer: Sample response: Because the side lengths of 2 cm and 1 cm add up to 3 cm, and 3 cm is not longer than 5 cm, the circles will never cross. This means that there is no intersection point to use to create a triangle.

Teaching Notes

Students should apply their informal understanding that the lengths of two sides of a triangle must add up to a value greater than the length of the third side. They can explain their reasoning using this sum argument or the diagram of a compass and ruler construction to show that the two sides will never meet.

Draw as many different triangles as possible that have two sides of length 4 cm and a $\,45^\circ$ angle. Clearly mark the side lengths and angles given.

Answer:

There are 2 different triangles.

Minimal Tier 1 response:

Work is complete and correct.
Sample: Exactly 2 triangles are drawn; lengths and angles marked and reasonably accurate; no other lengths or angles are marked.
Acceptable errors: Other lengths and angles, besides the ones given, may be marked with reasonable approximations of their measures; sum of marked measures of three angles close to, but not equal to, 180 degrees.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: 3 triangles instead of 2; 45 degree angle drawn with significant inaccuracy; sides of length 4 cm drawn with significant inaccuracy, notably if they are significantly different in length; other lengths and angles, besides the ones given, measured or marked with significant inaccuracy.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: 0 triangles, 1 triangle, or more than 3 triangles drawn; two or more error types from Tier 2 response; an explanation of why the triangle cannot be drawn.

Teaching Notes

Some students may accidentally draw a third triangle (with the $45^\circ$ angle in a third position). If so,; they should attempt to verify that it is the same as one of the others (generally, it should be another of the triangles, flipped over). The given information forces 2 possible triangles and not 3, because the two given side lengths are equal.

What are the values of $x$ and $y$ ?

Three lines meet at a point, creating 3 sets of vertical angles. Their measures, counterclockwise, are x degrees, y degrees, y degrees, 35 degrees, blank, blank.

Answer:

$x = 35, y = 72.5$ (The angle marked $x$ and the angle marked as $35^\circ$ are vertical angles, so they have the same measure. The two angles marked $y$ , along with the angle marked as $35^\circ$ , form a straight line. Therefore, $2y + 35 = 180$ , and $y = 72.5$ .)

Teaching Notes

Give students credit for an answer for $y$ that is based on an incorrect answer for $x$ , since students may have used the relationship $x + 2y = 180$ to find $y$ .

Students should not be penalized for including the degree symbol in their answers.

Noah is building a planter box for the community garden near his school. The bottom of the box is wood, but the top of the planter box is left open for soil and plants. He plans to make the box 2 feet tall, with the base in this shape:

How much wood will Noah need to make the planter box?
If he fills the garden bed 1.5 feet deep with soil, how much soil will he need?

Answer:

43.5 ft²
17.25 ft³

Minimal Tier 1 response:

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

The area of the base is 11.5 ft². This may also be indicated by a decomposition into a rectangle, triangle, and trapezoid with areas 6 ft², 2 ft², and 3.5 ft², respectively, or other decompositions. The perimeter of the base is 16 ft. The area of the sides is $16\boldcdot2$ , or 32 ft². The total area of wood needed is $11.5+32$ , or 43 ft².
The area of the base is 11.5 ft². The soil is 1.5 ft deep. The volume of soil needed is $11\boldcdot 1.5$ , or 17.25 ft².

Tier 2 response:

Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification. Accept a volume for Part 2 based on an incorrect calculation of the area of the base in Part 1.
Sample errors: Incorrectly decomposing the base to calculate its area; including both top and bottom bases in the calculation of wood needed, or including neither base; incorrectly calculating perimeter of the base of the box; correctly calculating the quantities needed but using incorrect units to report, such as ft3 for area and surface area and ft2 for volume.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: Serious error(s) caused by a misunderstanding of one of the terms "volume," "area," or "base"; omission of one of the two parts.

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: Serious errors caused by misunderstanding of more than one of the terms; omission of the two parts.

Teaching Notes

Students determine whether a situation calls for surface area or volume of a prism, then calculate the corresponding values. They may need to deconstruct the base in order to calculate its area. Students may use the perimeter of the base in order to find the lateral surface area, or they may calculate the area of each rectangular face individually.