Grade 7

Readiness Check

Check Your Readiness
1.

What is a 90∘90^\circ angle called?

A.

acute

B.

obtuse

C.

right

D.

straight

Answer:

C

Teaching Notes

Early in the unit, students are introduced to the terms “complementary” and “supplementary” as they pertain to angles. Later, students will write equations to solve for the measure of an unknown angle, in which one of the givens is that two angles together form a right angle.

If most students struggle with this item, reinforce the fact that we call an angle with a measure of 90 degrees a “right angle.”

2.

Use a protractor to measure each of the 5 numbered angles. Write the measure of each angle to the nearest whole degree.

<p>A figure.</p>

Answer:

1 = 120∘120^\circ, 2 = 60∘60^\circ, 3 = 90∘90^\circ, 4 = 30∘30^\circ, and 5 = 60∘60^\circ. Measurements within +/-5 degrees should be accepted.

Teaching Notes

Throughout the unit, students are expected to measure angles with a protractor in order to make conjectures such as “vertical angles are equal.”

If most students struggle with this item, incorporate practice with a protractor before Lesson 2 Activity 2. An optional activity in Lesson 1 might also be a good place to revisit how a protractor is used to measure angles.

3.

Use a protractor to draw an angle of each measure.

  1. 120∘120^\circ
  2. 50∘50^\circ

Answer:

  1.  
    <p>A figure.</p>
  2.  
    <p>A figure.</p>

Teaching Notes

In this unit, students investigate the number of distinct polygons or triangles that can be drawn with given information: for example, with two sides and an angle. In some cases, students use a protractor as a tool in constructing these shapes.

If most students struggle with this item, incorporate drawing angles on tracing paper into earlier activities to verify the measures of angles that are given. Students can place their tracing paper over the printed angles to check their drawings.

4.
  1. Draw a pair of perpendicular lines.
  2. Draw a pair of parallel lines.
  3. Draw a right triangle.
  4. Draw an acute angle.

Answer:

Answers vary.

Teaching Notes

The vocabulary words in the Student Task Statement are all background for the geometric work of this unit.

If most students struggle with the term “parallel,” plan to discuss in Lesson 9 Activity 3 that one of the triangles is impossible to draw because two sides end up being parallel. In Lesson 11, students may not have experience with parallel planes. Connect the idea of parallel lines with parallel planes.

If most students struggle with the term ”perpendicular,” define it in Lesson 2 Activity 2, where students are told that they do not need to make a cut "perpendicular to the side of the paper." Perpendicular lines come up again in Lesson 3 Activity 3, as students learn that intersecting lines need not be perpendicular.

If most students struggle with the terms “acute” and “obtuse,” define those terms in Lesson 1 Activity 1. Consider making an anchor chart with names and types of angles that will be used throughout this unit.

5.

Draw a right rectangular prism with a volume of 90 cm3. Label the edges you used to calculate the volume. Determine the area of the base. Include units in your results.

Answer:

Answers vary. Sample response: a base with length 5 cm and width 2 cm, and height 9 cm. The base area is 10 cm2.

Teaching Notes

In this unit, students study volume and surface area. In grade 6, they learned to calculate the volume of a rectangular prism. They also learned to calculate the surface area of prisms and other solids by adding up the area of each face.

If most students struggle with this item, revisit it with students prior to Lesson 12, helping them to recall what they know about finding the volume of right rectangular prisms. You may also choose to present right rectangular prisms with given side lengths to find the volume, in addition to this item which has a volume given.

If most students do well with this item, Optional Activity 4 in Lesson 12 gives students an opportunity to explore the same idea but with prisms other than right rectangular prisms.

6.

A right rectangular prism has a length of 0.25 feet and a width of 5 inches.

  1. Find a height so its volume is between 30 and 45 cubic inches.
  2. What is the volume of your prism? Include units of measure in your response.

Answer:

Answers vary. Sample response: a height of 2 inches will produce a volume of 30 cubic inches.

Teaching Notes

The volume formula for the area of a rectangular prism will be familiar to students from grade 6. They will not have had as much experience solving for height given volume. However, this problem provides students with an opportunity to connect their sixth-grade work with their more recent work solving equations. Watch for students making the error of ignoring the change in units (feet vs. inches).

If most students struggle with this item, plan to discuss in Part 2 of Activity 1 what we can tell about unknown side lengths of a right rectangular prism if we know something about the volume. You may connect this to the equation-solving work students did in a prior unit. If students struggle to convert between feet and inches, that is not an expectation of this unit and does not need to be addressed for success.

7.

What is the area of this trapezoid?

<p>A trapezoid.</p>

Answer:

312 square units

Teaching Notes

In this unit, when studying volume and surface area, students will need to find the area of a trapezoidal base for a prism.

If most students struggle with this item, review these strategies, and spend extra time discussing Lesson 13 Activity 2. Revisit this item and invite students to share how they could use these strategies to find the area of the trapezoid, during the Activity Synthesis of Lesson 13 Activity 2.