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 complementary angles.

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

Answer:

A, D, E

Teaching Notes

Students who select choice B may be confusing the terms "complementary" and "vertical." Students who select choice C may remember that vertical angles appear to be across from each other, but may not understand that the two angles are created from two intersecting straight lines.

A rectangular pyramid is sliced. The slice passes through the vertex of the pyramid and is perpendicular to the base of the pyramid.

Which of these describes the cross-section?

A rectangle smaller than the base

A quadrilateral that is not a rectangle

A rectangle the same size as the base

A triangle with a height the same as the pyramid

Answer:

Teaching Notes

Students who select choice A, B, or C have probably drawn a different cross-section that isn’t going from the top of the pyramid down to the base.

Which of these describes a unique polygon?

A quadrilateral with 4 right angles

A triangle with angles $30^\circ$ , $80^\circ$ , and $70^\circ$

A triangle with side lengths 7 cm and 8 cm and a $70^\circ$ angle

A triangle with each side length 5 inches

Answer:

Teaching Notes

Students who select choice A or B need some refresher work on the activities of this unit, since a scaled copy of any polygon will have the same angle measures. Students who select choice C did not recognize that the stated angle's location was not given, allowing there to be multiple triangles with this information.

Mai is trying to draw a triangle with side lengths 1 cm, 6 cm, and 3 cm using a compass and ruler. Explain why Mai’s drawing is not creating a triangle.

Answer: Sample response: Because the side lengths of 1 cm and 3 cm add up to 4 cm, and 4 cm is not longer than 6 cm, the circles will never cross. This means 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 a side of length 5 units, a $45^\circ$ angle, and a $90^\circ$ 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; the third angle is drawn and labeled as something else other than a 45 degree angle; 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

The given information forces 2 possible triangles and not 3. Some students may accidentally draw a third triangle (with the 5m length 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 the same as one of the other triangles, flipped over).

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

Answer:

$x=30$ , $y=120$ (The angle marked $x$ and the angle marked as $30^\circ$ are vertical angles, so they have the same measure. The angles marked x and y, along with the angle marked as $30^\circ$ , form a straight line. Therefore, $x+y+30=180$ , and $y=120$ .)

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 $x + y + 30 =180$ to find $y$ . Students should not be penalized for including the degree symbol in their answers.

Kiran 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 3 feet tall, with the base in this shape:

How much wood will Kiran need to make the planter box?
If he fills the garden bed 2.5 feet deep with soil, how much soil will he need?

Answer:

39 ft²
15 ft³

Minimal Tier 1 response:

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

The area of the base is 6 ft². This may also be indicated by a decomposition into a rectangle and trapezoid with areas 1.5 ft² and 4.5 ft², respectively, or other decompositions. The perimeter of the base is 11 ft. The area of the sides is $11\boldcdot3$ , or 33 ft². The total area of wood needed is $33+6$ , or 39 ft².
The area of the base is 6 ft². The soil is 2.5 ft deep. The volume of soil needed is $6\boldcdot 2.5$ , or 15 ft³.

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.