Angle Pair Relationships

TERM DEFINITION DIAGRAMacute angle

obtuse angle

right angle

straight angle

vertical angles

TERM DEFINITION DIAGRAM MEMORY TRICKS

complementary angles

supplementary angles

linear pair

adjacent pair

(12q)°

112°43°

47°

30°

60°

65°

(3x)°

52°

18°105°

(5z)°

(2y)°

40°

(6a)° (25c)°

Using patty paper, trace pairs of angles that you think are complemenatary/supplementary angles. Once you have traced the angle pair, use the straight/right angle below to help you identify the angle pair. You must find the value of each variable using your angle pair relationships, there is room provided on the next page for you to show your work.

Use the space provided below to setup an equation and solve for each variable.

Solve for a.1.

Solve for q.2.

Solve for x.3.

Solve for y.4.

Solve for z.5.

Solve for c.6.

Detroit City Map

Map Activity

1. Using one of your three colored pencils locate and highlight 4 different linear pairs (only 1 linear pair should consist of right angles).

2. Using your second colored pencil locate and highlight 2 different complementary angles.

3. Using your third colored pencils locate and highlight 3 different adjacent angles (none linear pairs).

4. Given the NW corner of Brush and Gratiot Ave. form a 60° angle. What would be the measure of the complement angle? What is the measure of the supplement angle?

5. Locate the SE corner of Cass Ave. and Michigan Ave. Estimate the measure of the its complement and supplement angles? Explain how you arrived at your estimate.

6. Critical Thinking – locate one pair of supplementary angles (Cannot be a linear pair). Explain the decision making process you used to choose the two supplementary angles.

zyx

32°x 135°

x74°x

73°

(10x-18)°

(4x+16)°

B

A

C

E

F

D

Angle Pair Relationships HW Day 1 Name ______________________________

Solve for the missing angle(s). SHOW ALL YOUR WORK.

1. 2. 3. 4.

5. What is the measure of the supplement angle to 57 ?

6. What is the measure of the complement angle to 47 ?

7. and are supplementary angles. Find the and .

(10y - 74)°

(4y - 8)°

B

C

D

A

F

E

Solve for the variable and give the measure of angle.

8. 9. 10. 11.

Use the picture below to answer questions 12 – 15. Be sure to use the proper symbol when naming each figure.

12. Name two acute adjacent angles. ______________

13. Name two angles that form a linear pair.

14. Name two obtuse vertical angles. ______________

15. Solve for all of the missing angles in the picture to the right.

6p + 14

8p + 4

5p + 15

7p + 45

2x + 15

13p + 61 5p – 7

Mixed Review: Name one of each figure from the picture to the right using the proper symbols.

16. Line _______________________

17. Ray ________________________

18. Right Angle _________________

19. Linear Pair __________________

20. 3 Collinear Points _____________

Day 2 Warm-Up

Using the word bank below, choose the word that best completes each statement. Explain each answer with a diagram or written response.

SOMETIMESALWAYSNEVER

1. 2 acute angles __________ form complementary angle pairs.

2. 2 acute angles __________ form supplementary angle pairs.

3. A complementary angle pair ___________ includes an obtuse angle.

4. A supplementary angle pair ___________ includes an obtuse angle.

5. One right angle ___________ forms a complementary angle pair.

6. Two right angles ____________ form a complementary angle pair.

7. 2 right angles ____________ form a supplementary angle pair.

8. A supplementary angle pair ___________ includes an acute angle pair.

Angle Pair Relationships HW Day 2 Name ______________________________

Using algebra, solve each of the following. Remember to show work for credit and circle your answers.

Examples

a. The measure of one angle is twice the measure of its complement. Find the measures of both angles.

b. The measure of the supplement of an angle is 30 more than twice the measure of the angle. Find the measure of the angles.

c. The measure of the supplement of an angle is 30 more than twice the measure of the angle. Find the measures of the angles.

Using algebra, solve each of the following. Remember to show work for credit and circle your answers.

1. Find the measure of an angle that is half the measure of its complement.

2. The measure of one angle is eight times the measure of its supplement. Find the measures of the angles.

3. The difference in the measures of two supplementary angles is 38. Find the measures of the two angles.

4. The difference in the measures of two complementary angles is 39. Find the measures of the two angles.

5. Find the expression that represents the complement and supplement of for each of the following.a. b. c.

6. Two angles are complementary. of the smaller is 7 more than half the larger. Find the measure of each angle.

7. The measure of the supplement of an angle is 7 times greater than its complement, find the measure of its supplement.

8. The measure of an angle is 20 less than the measure of its supplement. Find the measure of the angle.

9. The measure of the supplement of an angle is 10 more than 5 times the measure of its complement. Find the measure of the complement.

10. Find the measure of the complement and the supplement of an angle if the angle measure is (a – 20).

11. Two times the complement of an angle is 23 less than the supplement of the angle. Find the supplement of the angle.

12. The measure of the supplement of an angle is 5 times the measure of its complement. Find the measure of its supplement.

13. The measure of the supplement of an angle is 30 more than twice the measure of the angle. Find the measure of the angles.

14. Create your own accurate complementary and supplementary word problem, then solve.

Planning to Create a Math-Talk Communitygeneral outline of lesson activities including homework assignment and formative assessment

Lesson Title: Angle Pair Relationships Grade Level/Course: 9-10 Source Credit (if applicable):

Sub-unit: complementary & supplementary angles

Connection to Content Standards (include prior grade level standards if applicable) : Secondary: 7.G.5

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Connection to Mathematical Practice Standards: Secondary: #1 Make sense of problems and persevere in solving them.

o Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.

#2 Reason abstractly and quantitativelyo They bring two complementary abilities to bear on problems involving quantitative

relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.

#4 Model with mathematicso They are able to identify important quantities in a practical situation and map their

relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. #5 Use appropriate tools strategically

o Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper.

o They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data.

#6 Attend to precisiono Mathematically proficient students try to communicate precisely to others. They try to use

clear definitions in discussion with others and in their own reasoning.o They calculate accurately and efficiently, express numerical answers with a degree of

precision appropriate for the problem context. #7 Look for and make use of structure

o They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

What prior knowledge is important for students to understand before starting this lesson?

Students will need to know the definition of an angle. Students should also be familiar with acute, obtuse, right and straight angles.

Materials Needed by Students and by Teachers (including worksheets, solution keys, power points, etc): patty paper worksheet colored pencils

PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK

(i) What are your mathematical goals for the lesson (i.e., what do you want students to know and understand about mathematics as a result of this lesson)? Students will know and understand the characteristics of complementary and supplementary angles as well adjacent and vertical angles.

(ii) What is the rich task that students will explore? Students will use manipulatives to explore the relationship between special angle pairs.

(iii) In what ways does the task build on students’ previous knowledge, life experiences, and culture? What definitions, concepts, or ideas do students need to know to begin to work on the task? What questions will you ask to help students access their prior knowledge and relevant life and cultural experiences?Students will bring their knowledge of reading maps, the downtown Detroit area, as well as previously-taught material on acute, obtuse, right, and straight angles to this lesson.

(iv) What are all the ways the task can be solved?When looking for angle pairs on the map, there are multiple ways to look at street intersections to compose complementary angles, supplementary angles, linear pairs, and adjacent angles.

(v) Which of these methods do you think your students will use? What misconceptions might students have? What errors might students make?Students could misunderstand the difference between a linear pair and supplementary angles. Students might not realize that only some angles have a complement.

(vi) What particular challenges might the task present to struggling students? to students who are English Language Learners (ELL)? How will you address these challenges?The task is quite visual, so verbal challenges should be kept to a minimum to those students who are English Language Learners. This task could be challenging to those students who have difficulty with tasks requiring visualization/attending to only necessary information (while separating out the rest). Reducing the amount of the map that these students see could help. It could also help to use patty paper and trace angles or even to cut up the map. It may be useful to model solving the first couple problems together.

(vi) What are your expectations for students as they work on and complete this task?

What resources or tools will students have to use in their work that will give them entry into, and help them reason through, the task?In order to be successful in the map task, students will access their knowledge from the patty paper activity.

How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work individually or in small groups or pairs? Will students be partnered in a specific way? If so, in what way?

Students can complete this activity independently or in pairs. Total lesson should take 2 class periods. Map task should take 1 class period. How will students record and report their work?

Students will complete the problems within the worksheets.

(vii) How will you introduce students to the exploration task so as to provide access to all students while maintaining the cognitive demands of the task? How will you ensure that students understand the context of the problem? What will you hear that lets you know students understand what the task is asking them to do?

Teacher will explain in accordance to the educational level of the students. Different type of questions will be posed to students based on their ability levels.

PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK

(i) As students work independently or in small groups, what questions will you ask to— help a group get started or make progress on the task?Find a pair of complementary angles.Find a pair of supplementary angles.Find a linear pair.Are there any vertical angles on this map?

focus students’ thinking on the key mathematical ideas in the task? State, in your own words, what are complementary angles, etc.

assess students’ understanding of key mathematical ideas, problem-solving strategies, or the representations? Physically walk around the room and check that students are identifying correct angle pairs on their map.

advance students’ understanding of the mathematical ideas?Can you find examples of these special types of angles within your own community?

encourage all students to share their thinking with others or to assess their understanding of their peers’ ideas? At different intervals, students share with individual or group next to them. Encourage students to ask each other for help before asking the teacher.

(ii) How will you ensure that students remain engaged in the task? What assistance will you give or what questions will you ask a student (or group) who becomes quickly

frustrated and requests more direction and guidance in solving the task? Teacher will simplify the task to a smaller subset of angles and have students identify the angles within that smaller area of the map.

What will you do if a student (or group) finishes the task almost immediately? How will you extend the task so as to provide additional challenge?

Ask students to create their own map where these special types of angles are located within their street intersections.

What will you do if a student (or group) focuses on non-mathematical aspects of the activity (e.g., spends most of his or her (or their) time making a poster of their work)?

Teacher will redirect the student regarding the task required.

PART 3: SHARING AND DISCUSSING THE TASK

(i) How will you orchestrate the class discussion so that you accomplish your mathematical goals? Which solution paths do you want to have shared during the class discussion? In what order will the

solutions be presented? Why? In what ways will the order in which solutions are presented help develop students’ understanding of the mathematical ideas that are the focus of your lesson?

The worksheets have been developed in the logical manner that they should be followed.

What specific questions will you ask so that students will—o make sense of the mathematical ideas that you want them to learn? o expand on, debate, and question the solutions being shared? o make connections among the different strategies that are presented?o look for patterns? begin to form generalizations?

Teacher will ask different groupings of students to present their supplementary angle pairs. Students will explain the different ways they determined these pairs (patty paper, protractor, estimation, cutting up of the map).

(ii) How will you ensure that, over time, each student has the opportunity to share his or her thinking and reasoning with their peers? At regular intervals, students will be asked to discuss their solutions with a group of their peers.

(iii) What will you see or hear that lets you know that all students in the class understand the mathematical ideas that you intended for them to learn?Correct responses will be verified on their maps.

(iv) What closure will you bring to the lesson? If the lesson is a multi-day lesson, what are some possible stopping points? What closure will you bring at these stopping points?

Brainstorm 5 things you learned today. Give me an intersection within ________ city that forms a linear pair, etc.

(v) What assignment will you give students to do before the next class?Basic algebra review problems will be given that will lead into tomorrow’s lesson.

(vi) What will you do tomorrow that will build on this lesson?Students will engage in an activity that requires them to solve more complex problems that illustrate their knowledge of the difference between complementary and supplementary angles.