Unit 7 Angles And Angle Measurement — Unit Plan

Title	Takeaways	Assessment
Lesson 1 How Would You Describe These Figures?	—	Lines and More (1 problem) Here is a drawing on a card: image of a rectangle with 4 lines drawn inside. First line goes from lower left corner to top right corner. Second line goes from lower right corner to top left corner. Third line goes vertically through the middle of the rectangle through the point of intersection of the previous two lines. The lower half darken. Fourth line goes from bottom right corner to the middle of the top side. Write a description of the drawing that could be used by a classmate to make a copy. Show Solution Sample response: Draw two diagonal lines: one from the top left corner to the bottom right, and another from the bottom left corner to the top right. Draw a line that goes up and down through the point where the two diagonal lines cross. From the top of that line, draw a line to the bottom right corner. The bottom segment of the up-and-down line is thicker than the rest of the lines. The lines make a lot of triangles of different sizes.
Lesson 2 Points, Lines, Rays, and Segments	—	True or False: What’s the Point? (1 problem) Decide if each statement is true or false. If it is false, correct it. A point marks a place. This is a drawing of a ray. A line can be curved or straight. This is a drawing of a segment. The length of a ray can be measured. Show Solution True True False. A line is always straight. False. Sample responses: A line segment is a part of a line and has two endpoints. The drawing shows a line or two rays pointing in opposite directions. This is a drawing of a segment: False. A ray goes on forever in one direction so the length cannot be measured.
Lesson 3 Two or More Lines	—	Parallel and Not Quite Parallel (1 problem) Explain why these lines are not parallel. Sketch a line that is parallel to this line. Show Solution Sample responses: The two lines get closer to each other in one direction. If we extend them, they eventually will intersect. The two lines are not the same distance apart everywhere. The gap between the two lines is noticeably wider on one side and narrower on the other, so the two lines will cross if they’re extended. Sample responses:
Lesson 4 Points and Lines All Around	—	Word Fun (1 problem) Which letters in the phrase FUN KITES have: parallel segments no parallel segments Here is a field of dots. Use it to draw 2 pairs of parallel lines, each pair pointing in a different direction. Show Solution F, U, N, and E K, I, T, and S Sample response:
Lesson 5 What Is an Angle?	—	Spot the Angles (1 problem) Jada says Figure A shows an angle, but Figure B does not. Do you agree? Explain your reasoning. Mark the angles in each letter, and draw the rays to show each angle. two figures resembling the capital letters L and Y. The letter L consists of 2 line segments that meet at a right angle. The letter Y consists of 3 segment that all meet in the middle. The bottom line segment is slightly longer than the other two. Show Solution Yes. Sample responses: Figure A is made up of two rays with the same starting point. Figure B is a continuous curve, so it doesn’t count as an angle. Sample response:
Section A Check Section A Checkpoint		Problem 1 Identify a line, a ray, and a line segment in the figure by tracing those parts and labeling them. Show Solution Sample response: Problem 2 On the grid, draw a number or a letter that has at least two line segments that are parallel and two line segments that intersect. Draw a shape that has at least two pairs of line segments that are parallel. Show Solution Sample response: Problem 3 Mark as many angles as you can find in the diagram. Show Solution

Lesson 6 Compare and Describe Angles	—	Compare Two Angles (1 problem) Here are two angles. Describe at least one way they are alike. Describe at least one way they are different. Show Solution Sample response: Alike: Both show 2 rays that share a common starting point. Both have one ray that is pointing in the same direction. Different: Each has one ray pointing in a different direction. The angle on the right looks wider than the other angle.
Lesson 7 The Size of an Angle on a Clock	—	Which Angle Is Greater? By How Much? (1 problem) The hands on each clock form an angle. A B Which angle is greater? How much greater than the other angle is it? Explain how you know. Show Solution The angle on Clock A is greater by about 5 minutes. Sample response: In Clock A, the minute hand would have to turn 13 or 14 minutes to get to where the hour hand is. In Clock B, the minute hand would have to turn only 8 or 9 minutes.
Lesson 8 The Size of An Angle, in Degrees	—	Estimate Angle Size in Degrees (1 problem) Use the tool you created to estimate the size of each angle in degrees. a b c Show Solution 90 degrees 45 degrees 150 degrees
Lesson 9 Use a Protractor to Measure Angles	—	Measure the Angles (1 problem) An angle is composed of seventeen $1^\circ$ angles. How many degrees is the angle? What is the measurement of each angle? Show Solution $17^\circ$ $18^\circ$ $65^\circ$
Lesson 10 Angle Measurement and Perpendicular Lines	—	Size Up Angles (1 problem) Which figures show perpendicular lines or rays? image of 4 figures. A. 2 intersecting lines forming 2 acute and 2 obtuse angles. B. Two rays connected at the endpoint to form a right angle. C. 2 rays. One ray connected to the other ray at its endpoint to form 2 right angles. D. 2 intersecting lines to form 4 right angles. Use a protractor to measure the labeled angles in the figure. Show Solution B, C, and D Angle X is $53^\circ$ . Angle Y is $117^\circ$ .
Lesson 11 Use a Protractor to Draw Angles	—	A Ray or Two (1 problem) Draw a new ray, starting from point Z, to create a $25^\circ$ angle. Draw two rays to create an angle that is $165^\circ$ . Show Solution Sample responses: Sample response:
Section B Check Section B Checkpoint		Problem 1 What is the measurement of each angle? a. b. Show Solution $37^\circ$ , because $180 - 143 = 37$ . $130 ^\circ$ , because $160 - 30 = 130$ . Problem 2 Use a protractor to draw a 135-degree angle. Show Solution Sample response:

Lesson 12 Types of Angles	—	Obtuse, Acute, and Straight Angles (1 problem) Here is a ray. Draw another ray from point P to make an acute angle. Here are some labeled angles. Identify all angles that are obtuse. An angle is formed by four $35^\circ$ angles. Is that angle a straight angle? Explain how you know. Show Solution Sample response: Angles B, E, and D No. Sample response: A straight angle is $180^\circ$ . Four $35^\circ$ angles make $140^\circ$ ( $4 \times 35 = 140$ ).
Lesson 13 Find Angle Measurements	—	Sets of Three Angles (1 problem) Noah cuts out 3 copies of Angle P and 3 copies of Angle Q. He arranges them side by side. Three copies of Angle P make a straight line. How many degrees is Angle P? Explain or show your reasoning. Three copies of Angle Q make a right angle. How many degrees is Angle Q? Explain or show your reasoning. Noah puts Angle P and Angle Q together. How many degrees is the resulting angle? Explain or show your reasoning. Show Solution $60^\circ$ .Sample response: Three times the measure of P is $180^\circ$ , so P must measure $60^\circ$ . $30^\circ$ . Sample response: $90 \div 3 = 30$ . $90^\circ$ . Sample response: $60 + 30 = 90$ .
Lesson 14 Reasoning about Angles (Part 1)	—	One Angle at a Time (1 problem) How many degrees is each marked angle on the clock? Explain or show your reasoning. A B Show Solution $60^\circ$ . Sample response: Every time the minute hand moves from one number to the next, it turns $30^\circ$ . The angle between the hands is 2 numbers apart, so it is $2 \times 30$ , which is 60. $150^\circ$ . Sample responses: $5 \times 30 = 150$ If it was 6 o'clock, the angle would be $180^\circ$ . The angle for 5 o'clock is $30^\circ$ less than $180^\circ$ .
Lesson 15 Reasoning about Angles (Part 2)	—	Heart to Heart (1 problem) Find the measurement of each labeled angle. Show your reasoning. Show Solution The measure of Angle C is $45^\circ$ and that of Angle D is $135^\circ$ . Sample response: Angle C and the $135^\circ$ angle together make a straight angle, which is $180^\circ$ , so the measure of C is $180 - 135$ , which is $45^\circ$ . Angle D, the right angle, and the $135^\circ$ angle make $360^\circ$ . $90+135 = 225$ and $360-225 = 135$ , which is $135^\circ$ .
Lesson 16 Angles, Streets, and Steps	—	No cool-down
Section C Check Section C Checkpoint		Problem 1 Angle S and the angle that is $138^\circ$ make a straight angle. What are the measurements of Angles S and T? Explain or show your reasoning. Show Solution Angle S is $42 ^\circ$ . Sample response: Angle S and the $138 ^\circ$ angle make a straight angle, and $180 - 138 = 42$ . Angle T is $160 ^\circ$ . Sample response: $180 - 20 = 160$ Problem 2 Decide if each angle in the triangle is acute, right, or obtuse. Draw a triangle with one right angle. Label the right angle B. Show Solution Sample responses: a. b. Problem 3 What are the measurements of Angles A and B if all of the angles add up to 180 degrees? Explain or show your reasoning. Show Solution Angle A is $90^\circ$ because the rays that create the angle are perpendicular. Angle B is $15 ^\circ$ because six of them make a $90^\circ$ angle ( $180 - 90 = 90$ ), so each of them is $90 \div 6$ or 15 degrees.
Unit 7 Assessment End-of-Unit Assessment