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1 1 of 2 8/8/ :03 AM Advice for Instruction 15. Solving linear inequalities Prepare instruction Goals and objectives Topic overview Resources Print resources Goals and objectives While equations are an easier medium through which to learn the mathematical concept of doing and undoing to solve for a variable, inequalities provide more interesting problem situations to solve. They more accurately represent scenarios in the real world since most solutions involve a range of acceptable values as opposed to the single solutions that represent equations. The goal of this topic is to use the parallels between solving equations and inequalities to develop a new skill while reinforcing an old one. In the topic Solving linear inequalities, students will describe functional relationships for given problem situations and write inequalities to answer questions arising from the situations; analyze situations involving linear functions and formulate linear inequalities to solve problems; investigate methods for solving linear inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the inequalities; interpret and determine the reasonableness of solutions to linear inequalities for given contexts. The Staying Sharp problems in Topic 15 are organized around several key ideas: Problems 1 and 2 (Practicing algebra skills and concepts): Inequalities and their solutions, and consolidating understanding of slope and linear equations Problems 3 and 4 (Preparing for upcoming lessons): Building skills for solving systems of equations using tables and graphs Problems 5 and 6 (Focus skill): Slope, slope triangles, and geometric connections Topic overview Lesson 15.1: The focus of this lesson is on using number lines to represent solutions to linear inequalities in one variable. Students will also investigate compound inequalities through number lines. Lesson 15.2: This lesson makes the connection between linear inequalities and linear functions. Students also extend what they know about different methods for solving equations to solving inequalities.

2 2 of 2 8/8/ :03 AM Lesson 15.3: Students learn how to use graphs and tables to solve linear inequalities in one variable. They use technology to help them construct tables and graphs. Lesson 15.4: Students investigate patterns related to inequalities. The focus of this lesson is on using inverse operations to solve linear inequalities in one variable. Lesson 15.5: Students explore how to graph solutions to linear inequalities in two variables. They also check their understanding of linear inequality concepts by completing an online assessment. Lesson 15.6: Students begin to explore compound inequalities in the plane. They are also given an opportunity to solidify their understanding of linear inequalities prior to taking the end-of-unit assessment. Lesson 15.7: One goal of this lesson is to check student understanding of linear inequalities through the end-of-unit assessment. Students also reflect on their effort to this point and set new goals for the next unit of study. Resources LESSON RESOURCES Computer with projection device and Internet connection Graphing calculators (Lesson 15.3) Computer lab (Lesson 15.5) Large chart paper Chart markers Masking tape Scissors Whiteboards, dry erase markers, and erasers Print resources Unit 5 Topic 15 Advice for instruction Unit 5 Topic 15 Student Activity Book (Updated 8/6/14) Unit 5 Topic 15 Student Activity Book Answer Key (Updated 8/6/2014) Card sort - Inequalities on a number line (Lesson 15.1) Card sort - Graphing compound inequalities (Lesson 15.7) Unit 5 end-of-unit assessment

3 1 of 3 8/8/ :04 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Solving linear inequalities: Student Activity Book Lesson 15.1 Inequalities on a number line Inequalities on a number line card sort (One copy for each pair of students) Scissors Lesson preview Suggested time Activity Goals 10 min Opener Understand the value of using the number line to represent inequalities 30 min Core activity Use number lines to depict inequalities 10 min Process homework Learn from reviewing the homework due today 25 min Consolidation activity Match inequalities and number line graphs 5 min Wrap up and introduce homework Reflect on the day s lesson and understand tonight s homework assignment Lesson activities OPENER (10 minutes) Online page 1 In this activity, students determine whether specific numbers make an inequality true. Then they identify other numbers that make the inequality true. Students will use the numbers from this activity to construct the graph of the inequality on a number line. [SAB, questions 1-5] To debrief, draw a number line on the board. Ask every student to offer one of their solutions or to pass if all their numbers were mentioned. Plot these on your number line. Ask: What do you notice about the solutions we plotted?

4 2 of 3 8/8/ :04 AM Online page 2 How many possible numbers could we come up with that make the inequality true? Preview the activities and learning goals for the day s lesson. CORE ACTIVITY (30 minutes) This activity uses the problem from the Opener to help students understand how to depict inequalities on a number line. Students develop insights into building inequalities as well as setting the stage for the next lesson on solving inequalities. Online pages 3-4 Use these pages to launch the activity and introduce how inequalities are depicted on the number line. Page 3: Use the animation on this page to show students how to depict the inequality x > 7 and the other related inequalities. Page 4: Have students graph the inequalities on the number line in their activity books before discussing the solutions shown on the page. [SAB, question 1] Students should be familiar with graphing solutions on a number line from work in previous topics. Pages 5-7 Students are introduced to depicting compound inequalities involving the word or on the number line, then practice the skill. Page 5: Have students work with partners on solving a compound inequality involving the word "or." [SAB, questions 2-4] Page 6: Use the animation on this page to debrief students' work on question 3. Use the animation to address any misconceptions that arise, and to solidify students understanding. Page 7: Discuss the solution to the inequality shown on this page. Have students compare their graphs for question 4 with the one shown and discuss any differences, questions, or misconceptions that arise. Pages 8-10 Students depict compound inequalities involving the word and on the number line. Page 8: Have students work with partners on solving a compound inequality involving the word "and." [SAB, questions 5-7] Page 9: Use the animation on this page to debrief students' work on question 6. Use the animation to address any misconceptions that arise, and to solidify students' understanding. Page 10: Discuss the solution to the inequality shown on this page. Have students compare their graphs for question 7 with the one shown and discuss any differences, questions, or misconceptions that arise. Online page 11 Students practice graphing compound inequalities involving both the word or and the word and. Have students work with their partners on the remainder of this activity. [SAB, question 8] Classroom strategy. Encourage students to collaborate with their partners by listening to each other s contributions. In building knowledge as a community of learners, partners

5 3 of 3 8/8/ :04 AM explain, compare, test, and revise ideas with each other. Give students room to explore and resolve solutions among themselves without providing the correct solutions too soon. Facilitate this process by asking questions such as: Do you both agree on how each graph should look? If so, can you explain why your graph looks the way it does? If not, how are you thinking about the graph differently from each other? Can you test a few values of x to check if your solution works? PROCESS HOMEWORK (10 minutes) Online page 12 Students process the homework due today: Homework 14.3 and Staying Sharp Discuss the fundraiser problem from part I of the homework. Pay particular attention to questions 4 and 5 to make sure students can identify solutions on a graph given a problem situation and specific conditions. CONSOLIDATION ACTIVITY (25 minutes) In this activity, students work with their partners to match various inequalities (including compound inequalities) to their number line graphs. Then they write inequalities to match descriptions of number line graphs. For this activity, you will need to download the master for the cards from the Lesson materials section. Print one set of cards for each pair of students. You may want to cut the cards in advance to save class time. Online page 13 Have students work with their partners to match each inequality to its number line solution. Students record their matches in a table in their activity books, then answer related questions. [SAB, questions 1-4] WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 14 Homework 15.1 The first question in the homework asks students to match inequality statements to the number line solution. Then, students are asked to come up with inequalities that represent four different solution sets: empty set, some but not all real numbers, all real numbers, and exactly one number. Finally, given a graph, students determine appropriate inequality statements. Staying Sharp 15.1 The main concepts and skills in these problems are: 1. Comparing positive and negative fractions and decimals using inequality symbols 2. Ordering the slopes of lines given as graphs 3. Finding common coordinates between the x-y tables for two linear functions 4. Finding the coordinates of the point of intersection of the graphs of two linear functions 5. Computing the slope of a line given its graph with a slope triangle 6. Writing an equation for a linear function given its graph (and slope from question 5)

6 1 of 3 8/8/ :04 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Student Activity Book Lesson 15.2 Introduction to solving linear inequalities Chart paper and markers Lesson preview Suggested time Activity Goals 10 min Opener Determine the solution set to a problem situation involving an inequality 30 min Core activity Use methods for solving equations to solve inequalities 10 min Process homework Learn from reviewing the homework due today 25 min Consolidation activity Find solution sets when comparing two pricing schemes 5 min Wrap up and introduce homework Reflect on the day s lesson and understand tonight s homework assignment Lesson activities OPENER (10 minutes) Students model a problem situation with a function rule and revisit the familiar notion of finding function inputs given particular outputs. [SAB, questions 1-2] Online page 1 To debrief, ask a few students to share their solutions and explain how they arrived at these answers. An animation at the beginning of the next activity will further this debriefing and set up learning in the rest of the lesson. Online page 2 Preview the activities and learning goals for the day s lesson.

7 2 of 3 8/8/ :04 AM CORE ACTIVITY (30 minutes) In this activity, you will guide students through the same four methods explored in Solving linear equations. The notable difference is that you will be looking at all possible solutions for the inequality representing a problem situation, rather than just focusing on a one-number solution. Solving a linear inequality can be thought of as finding all the possible input values that make the inequality statement true. Connecting the writing and solving of linear inequalities to tabular, graphical, and symbolic representations of linear functions not only gives students different strategies for solving inequalities, but can also develop a deeper understanding of why they are solving them. Online page 3 Students work on the Opener is extended with the use of an animation. The animation helps to transition to the core algebraic learning of the lesson, setting up and solving inequalities. Before showing the animation, ask students to write an inequality that they think represents the problem situation. [SAB, question 1] Use panel 1 to reinforce that the constant rate of change in the problem situation suggests the use of a linear model. Use panels 2 and 3 to confirm students thinking about the graph and to remind students of the input-output relationship described by the function. Draw students attention to the notion that there are many possible input values that will result in an output value less than $75. After playing panel 3, ask: How many possible solutions do you think there are to this inequality? Online pages 4 and 5 Students are introduced to the concept of a linear inequality in one variable. They then solve a problem involving the car rental situation using one of four solution methods. Page 4: Reinforce that the linear inequality in one variable came from a linear function. Ask: What does it mean to solve an inequality? How is solving an inequality different than solving an equation? Page 5: Partners work to solve a car rental problem. Assign each pair of students a particular problem solving method: using undoing, using a table, using a graph, or using algebraic operations. Ask partners to create a poster that shows how they would use their method to solve the problem. Have partners hang their posters on the wall. [SAB, question 2] Online pages 6-9 Each of the four methods for solving the car rental problem is debriefed. Review the solution methods used by the different pairs to prepare their posters. As different methods are discussed, refer to students posters to connect to what students already know how to do. Students will utilize all four methods presented as they explore linear inequalities. Online page 10 Students reflect on what they learned in the discussion of the four solution methods. Have students record the four solution strategies in their activity books and complete a math journal entry to reflect on the meaning of linear inequality. [SAB, questions 3-4] PROCESS HOMEWORK (10 minutes)

8 3 of 3 8/8/ :04 AM Online page 11 Students process the homework due today: Homework 15.1 and Staying Sharp Go over questions 2 through 5 with students. Ask students to give you examples of what a number line graph would look like for each type of solution set. Then have students relate the graph to an inequality statement. CONSOLIDATION ACTIVITY (25 minutes) Students work in pairs to solve another car rental problem, using the methods of their choice. They prepare a report of their solution. Online page 12 Organize students in pairs. Have partners read the problem, solve it, and present their solution in a report. [SAB, questions 1-2] Language strategy. Building literacy skills across the content might be a focus on your campus or in your district. Point out that the final product for this assignment is a report in which recommendations need to be written. The recommendations are being sent to the boss so encourage students to use complete sentences. WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 13 Homework 15.2 Students practice solving a few simple linear inequalities using any method they choose. Then students explain how an inequality describes a certain problem situation and solve that inequality. Staying Sharp 15.2 The main concepts and skills in these problems are: 1. Comparing positive integers (presented as exponents) using inequality symbols 2. Sketching and calculating the slope of a line given its x- and y-intercepts 3. Computing the rates of change of two linear functions from their x-y tables 4. Finding common coordinates between the x-y tables for two linear functions 5. Computing the slope of a line given its graph with two different slope triangles 6. Explaining the constant slope of a line

9 1 of 3 8/8/ :04 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Solving linear inequalities: Student Activity Book Lesson 15.3 Solving inequalities using tables and graphs Graphing calculators Lesson preview Suggested time Activity Goals 10 min Opener Solve an equation using graphs and tables 30 min Core activity Solve inequalities using graphs and tables 10 min Process homework Learn from reviewing the homework due today 25 min Consolidation activity Analyze the advantages and disadvantages of the table and graph methods 5 min Wrap up and introduce homework Reflect on the day s lesson and understand tonight s homework assignment Lesson activities OPENER (10 minutes) Students review how to use graphing technology to create tables and graphs in order to find a solution to a linear equation. Students will recall how to use technology to find the point of intersection of the two related functions from their work in the topics Solving linear equations and Problem solving in a community of learners. Online page 1 Students solve the equation using the table and graphing features of their calculators. [SAB] In debriefing, ask: Which method do you prefer to use? For how many values for x is this equation true? How do you know?

10 2 of 3 8/8/ :04 AM Online page 2 What is the difference between an inequality and an equation? Preview the activities and learning goals for the day s lesson. CORE ACTIVITY (30 minutes) Students first explore using graph technology to solve inequalities. The new learning here is the ability to use the information given in the inequality to determine solution sets. Though the point of intersection is an interesting point, since it is the solution to the related linear equation, it is not part of the solution set for either of the inequalities explored in this activity. Then, students investigate the use of table technology to solve inequalities and connect this work to graphing technology. Online pages 3-5 Page 3: Have students use their sketches of the graph and table displays from the Opener to answer these questions in pairs. [SAB, questions 1-3] Pages 4-5: Use the animations on these pages to debrief responses to questions 1 and 2. Page 6: Use the calculator screen images and first discussion question to connect the table and graphing methods for solving inequalities. In the second discussion question students consider how a displayed solution would change if the inequality were written with the symbol, instead of <. This will be further explored in the next lesson and in upcoming lessons. Have students complete the math journal entry in their activity books to reflect on what they learned in this activity. [SAB, question 4] PROCESS HOMEWORK(10 minutes) Online page 7 Students process the homework due today: Homework 15.2 and Staying Sharp Review question 2 with students. Focus on students ability to interpret the meaning of the inequality and solution in terms of the situation. For part a, ask questions such as: What does the variable represent in the inequality? What do the 5 and 200 represent? Why is the expression on the right less than or equal to $150? For part c, ask: What would it mean in this situation if 50 tickets were sold? What would it mean if 100 tickets were sold? CONSOLIDATION ACTIVITY (25 minutes) Students solve inequalities using both the table and graphing features of their calculators. Then they compare the methods. Online page 8 Have student work in pairs to find the solutions to the inequalities, then compare the methods of graphing and using a table. [SAB, questions 1-3] To debrief, discuss the advantages and disadvantages of each method. You may want to point out, for example, that using a table can be time consuming if the solution is not an integer or another nice number or if the solution is very large.

11 3 of 3 8/8/ :04 AM WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 9 Homework 15.3 Students practice using tables and graphs to find solutions to inequalities. Staying Sharp 15.3 The main concepts and skills in these problems are: 1. Testing an inequality to understand the effect of multiplying by a negative value 2. Ordering the slopes of lines given as graphs 3. Graphing lines on the coordinate plane from their algebraic rules 4. Identifying and verifying the point of intersection of two lines in their algebraic rules 5. Marking two lattice points on the graph of a line 6. Using lattice points to draw a slope triangle and calculate the slope of a line

12 1 of 3 8/8/ :05 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Solving linear inequalities: Student Activity Book Lesson 15.4 "Solving inequalities with algebraic operations" Student whiteboards Lesson preview Suggested time Activity Goals 10 min Opener Explore inequality relationships involving adding and subtracting a quantity 30 min Core activity Learn methods to find solutions to inequalities that have a negative coefficient 10 min Process homework Learn from reviewing the homework due today 25 min Consolidation activity Check for errors in solutions to inequalities and correct the mistakes you find 5 min Wrap up and introduce homework Reflect on the day s lesson and understand tonight s homework assignment Lesson activities OPENER (10 minutes) Students look for relationships when adding or subtracting equal quantities from both sides of an inequality. In the core lesson today, they will learn two methods for solving inequalities when there is a negative coefficient. Keep the focus in this activity on noticings and wait for the core to explore and discuss the two methods. Online page 1 Students complete the inequalities and look for patterns. [SAB, questions 1-3] To debrief,

13 2 of 3 8/8/ :05 AM solicit a few responses from the students and record their observations on the board. You can refer to these during the rest of the lesson. If a misconception comes up, be sure to address it during the lesson. Students should notice that the inequality remains intact when adding or subtracting equal quantities. Online page 2 Preview the activities and learning goals for the day s lesson. CORE ACTIVITY (30 minutes) Students investigate the addition and multiplication properties as they apply to inequalities. Then, students practice using algebraic operations to solve inequalities in one variable. Online pages 3-5 Use these pages to guide a whole-class discussion about using algebraic properties to solve inequalities. Page 3: Before working through the online puzzle, have student pairs complete the puzzle in their activity books and answer the reflective question. [SAB, questions 1-2] Then ask for volunteers to come up to the classroom computer and fill in pieces of the online puzzle. Discuss students' responses to question 2, highlighting the idea that when multiplying or dividing by a negative number, the inequalities will reverse directions. Page 4: Use the balance scale animation to show students how they can use the same symbolic manipulation in working with inequalities that they used when solving inequalities. Ask students to answer the questions in their activity books as they view the animation. [SAB, questions 3-4] Page 5: Before playing the animation, ask student pairs to use what they learned in the last animation to solve the inequality 8 2x 14 by first subtracting 8 from both sides of the inequality. [SAB, question 5] Then, play panels 2 and 3. Ask students to try a different approach to solving the inequality, first adding 2x to both sides of the inequality. [SAB, question 6] Finish playing the animation. ask: What did you notice about the process you used in getting the answers for questions 5 and 6? [SAB, question 7] What did you notice about the solutions when you used the two different methods? Which method do you prefer? Why? Online page 6 Students practice using algebraic operations to solve inequalities in one variable. Have student pairs practice what they ve learned by completing the problems in their activity books. [SAB, question 8] After students complete the problems, select one or two inequalities and ask one or two pairs of students present their solutions for those inequalities to the class. Address any questions and misconceptions that arise in the discussions that follow. PROCESS HOMEWORK (10 minutes) Online page 7 Students process the homework due today: Homework 15.3 and Staying Sharp Discuss question 2 as a class. Ask students to share some of their responses. This will help

14 3 of 3 8/8/ :05 AM students develop their mathematical communication skills. Students should realize that the tables do not show the solution to the inequality and that neither Amber nor Nikki is correct. The solution to the equation x + 5 = -3x 1 occurs at x = Thus, the inequality will be true for values of x < CONSOLIDATION ACTIVITY (25 minutes) Students build their understanding of using algebraic properties to solve inequalities by looking for errors in another student's solutions. Students will also use their whiteboards to write inequalities for their partners to solve. Online page 8 Have students work with partners to analyze Jacob's solutions to four different inequalities, then create their own inequalities to solve. [SAB, questions 1-2] As student pairs work on Jacob's solutions, ask them questions such as: What was Jacob trying to do in this step? Why is it not correct? What algebraic property is Jacob not using properly in this step? How could this step have been done correctly? Would you have arrived at the same answer? Prove it. In debriefing question 1 with the whole class, ask students to share their answers to some of the question prompts listed above. To debrief question 2, ask a few students to share their inequalities and solutions. WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 9 Homework 15.4 Students continue to practice solving linear inequalities using algebraic operations. Students are also asked to verbalize a solution method and confront some common misconceptions about solving linear inequalities. Staying Sharp 15.4 The main concepts and skills in these problems are: 1. Sketching a horizontal line through a given point and writing an equation for the line 2. Sketching a vertical line through two given points and writing an equation for the line 3. Computing the rates of change of two linear functions from their x-y tables 4. Identifying that there are no common coordinates in the x-y tables for parallel lines 5. Writing an equation for a line from its graph, with slope triangles given 6. Finding the y-coordinate of a point on a line given an x-coordinate and the line s graph

15 1 of 3 8/8/ :05 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Solving linear inequalities: Student Activity Book Lesson 15.5 Inequalities in the plane Computer lab Lesson preview Suggested time 10 min Opener Activity 25 min Core activity Determine solution regions Goals Use inequalities to describe coordinates of points on a coordinate plane 5 min Process homework Learn from reviewing the homework due today 35 min Online assessment 5 min Wrap up and introduce homework Assess your understanding of key ideas and skills of this topic Reflect on the day s lesson and understand tonight s homework assignment Lesson activities OPENER (10 minutes) Students locate coordinate pair solutions to compound inequalities. Online page 1 Students match points and descriptions of coordinates. [SAB, questions 1-4] In debriefing, ask students to come up to the class computer and drag tiles to match points to the descriptions. For each point, you might ask: Are there other compound inequalities that could describe that point? What inequalities? Online page 2

16 2 of 3 8/8/ :05 AM Preview the activities and learning goals for the day s lesson. CORE ACTIVITY (25 minutes) Students investigate how to graph linear inequalities in the plane through the context of a problem situation. Online pages 3-4 Students are introduced to the problem situation. They work with their partners to complete the activity in their activity books. Then the first two questions are debriefed. Page 3: Have students read the problem situation, then work with their partners to complete the activity. [SAB, questions 1-7] Use the check reveal to verify students expressions. Page 4: Use the two reveals to debrief questions 1 and 2. Online pages 5-11 Students are formally introduced to the concept of an inequality in two variables. Then the remainder of students work on the activity is debriefed. Page 5: Compare the form of an inequality in two variables with that of an inequality in a single variable. Ask: If A or B were zero, why would we not have an inequality in two variables? What does it mean to be an ordered pair solution for an inequality in two variables? Page 6: Use this page to debrief question 3 in the Student Activity Book. Page 7: Use this page to debrief question 4. Ask: How would you write 2 boxes of candy and 1 combo as an ordered pair? Does this ordered pair satisfy the inequality? Can you find other ordered pairs that satisfy this inequality? How many can you find? Page 8: Use this page to verify students responses to question 5. To debrief, ask students to come up and solve the puzzle. Page 9: Use this page to verify students responses to question 6. Ask: What do all of the "solution" points have in common? Where would you look to find other solutions? Page 10: Use this page to debrief question 7 and develop a strategy for graphing a linear inequality in two variables. Page 11: Use this page to show how the graphical solution looks in the context of the problem situation. Ask: Why doesn t it make sense to include negative values for x and y? Can you think of the inequality that would represent the constraints on the x-values? On the y-values? [Students may not be able to come up with the inequalities x 0 and y 0. This question is meant to seed the learning for an upcoming lesson, so try not to give too much away. Students will be coming back to this problem.] Online page 12 Students complete a puzzle to reinforce the learning in this Exploring. Have students complete the puzzle in their activity books. [SAB, question 8] Then invite students up one at a time to match the inequalities with the correct graph. PROCESS HOMEWORK (5 minutes) Online page 13

17 3 of 3 8/8/ :05 AM Students process the homework due today: Homework 15.4 and Staying Sharp You may want to review a few of the problems from question 1. Asking students to verbalize their problem solving strategy, as in question 2, helps build communication skills and conceptual understanding. ONLINE ASSESSMENT (35 minutes) Online pages 14 Students complete the online Guided assessment in the online services for this topic. You will need to reserve a computer lab for this activity. Completion of the items in the Guided assessment will provide you and your students with formative assessment data related to student understanding of the key ideas in this topic, and will help students prepare for the upcoming mid-unit assessment. To view and analyze data from this assessment, you will need to create an assignment for your class, and then view the assignment report. WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 15 Homework 15.5 Students will practice writing and graphing linear inequalities in two variables. Staying Sharp 15.5 The main concepts and skills in these problems are: 1. Solving a two-step inequality in one variable 2. Writing an equation for a line from its slope and a point, then finding another point on it 3. Interpreting the point of intersection of two lines in the context of the situation 4. Identifying lines as parallel from their equations 5. Graphing a line from its y-intercept and slope using slope triangles 6. Writing an equation for a line from its y-intercept and slope and/or its graph

18 1 of 3 8/8/ :05 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Solving linear inequalities: Student Activity Book Lesson 15.6 Compound inequalities in the plane Assessment reports Lesson preview Suggested time 10 min Opener Activity Goals Build intuition for graphing compound inequalities in the plane 30 min Core activity Graph compound inequalities in the plane 10 min Process homework Learn from reviewing the homework due today 25 min Review online assessment Analyze and learn from performance on the online assessment 5 min Wrap up and introduce homework Reflect on the day s lesson and understand tonight s homework assignment Lesson activities OPENER (10 minutes) Students build intuition for graphing compound inequalities in the plane by graphing compound inequalities on a number line. Students will connect their understanding of or statements, as used in compound inequalities in one variable, to the use of or statements when graphing compound inequalities in the plane. Online page 1 Students graph the compound inequality on a number line and predict what the graph looks like in the plane. [SAB, questions 1-3] In debriefing, discuss the connection between number line graphs and coordinate plane graphs. Ask:

19 2 of 3 8/8/ :05 AM How is the number line graph of x < -1 similar to the coordinate plane graph of x < -1? What do you expect the graph of x < -1 or x > 4 to look like in the coordinate plane? Why? Is there something about the number line graph of x < -1 or x > 4 that leads you to think the coordinate plane graph would look a certain way? An animation on online page 3 shows the graphing of x < -1 or x > 4 in the plane, so you can finish debriefing then. Online page 2 Preview the activities and learning goals for the day s lesson. CORE ACTIVITY (30 minutes) Students extend their understanding from the Opener to graphing and statements in the plane. Online pages 3-5 Page 3: Use the animation to debrief the Opener and solidify students understanding of how to graph or statements in the coordinate plane. [SAB, question 1] Page 4: Before showing the animation depicting the graphing of the and statement, give students time to complete questions 2 and 3 in their activity books. [SAB, questions 2-3] Then use the animation to debrief. Page 5: Have students work with their partners on the remainder of this activity. [SAB, questions 4-5] Once students have had time to work, use the check reveal to allow students to verify their solutions. PROCESS HOMEWORK (10 minutes) Online page 6 Students process the homework due today: Homework 15.5 and Staying Sharp Discuss question 5 as a class. Ask students to translate their answers to parts a through c into equations or inequalities. Students will most likely use phrases such as above the line or below the line. Ask students haw they would represent these statements symbolically (< and >). Also, ask students if there were parts of the regions they described that do not make sense in the context of the problem. (For example, it does not make sense to buy negative boxes of candy, so this variable must be greater than or equal to 0.) REVIEW ONLINE ASSESSMENT (25 minutes) Students analyze class performance on the Guided assessment. Online page 7 Display the class report for the Guided assessment questions. Have students identify the items the class did well on and those the class did not do well on. Instruct students to write the question numbers in the table provided in the activity book. Work as a class to identify the mathematics of problems the class did well on, and discuss these concepts and skills. Be prepared to project particular Guided assessment questions. Then identify and discuss the mathematics involved for problems on which the class did not perform well. Be prepared to project particular questions (perhaps two questions) from the

20 3 of 3 8/8/ :05 AM Guided assessment. Next, allow students several minutes to work with their partners to re-do these problems in their activity books, and then discuss as a class. Share with students their individual score reports. Tell students they should take some time outside of class to revisit problems from the Guided assessment, in particular those for which they did not get the correct answers. WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 8 Homework 15.6 This lesson s homework helps students prepare for the end-of-unit assessment. Students will also be taking the online More practice in the topic Solving linear inequalities. Students will need to bring their Student Activity Books home and will also need online access in order to complete Parts I and II of the homework. Remind students where and when they can get online access in school or in the community. Staying Sharp 15.6 The main concepts and skills in these problems are: 1. Finding solutions of inequalities in one variable and understanding a common sign error 2. Writing an equation for a line from two points 3. Completing a three-column input-output table for two linear function rules 4. Explaining the use of an input-output table to find and check an intersection point 5. Graphing a line from a point and its slope using slope triangles 6. Writing an equation for a line from a point and its slope and/or its graph

21 1 of 3 8/8/ :06 AM Advice for Instruction 15. Solving linear inequalities Deliver instruction Lesson materials Lesson preview Lesson activities Lesson materials Solving linear inequalities: Student Activity Book Lesson 15.7 Checking for understanding Unit 5 end-of-unit assessment Card sort - Graphing compound inequalities (live link) Lesson preview Suggested time 10 min Opener Activity Goals Review linear inequality concepts prior to taking the end of unit assessment 10 min Process homework Learn from reviewing the homework due today 50 min End-of-unit assessment Demonstrate your understanding of important mathematical skills and concepts from the unit 10 min Consolidation activity Graph compound inequalities by completing a card sort activity 5 min Wrap up and introduce homework Reflect on the day's lesson and understand tonight's homework assignment Lesson activities OPENER (10 minutes) Students review the concepts related to linear inequalities in the context of a problem situation. Online page 1 Students write an inequality to describe the problem situation and solve it. [SAB, questions 1-3] In debriefing, find out which methods students used to solve the inequality and ask them to describe how they used a particular method to arrive at the solution. Online page 2

22 2 of 3 8/8/ :06 AM Preview the activities and learning goals for the day s lesson. PROCESS HOMEWORK (10 minutes) Online page 3 Students process the homework due today: Homework 15.6 and Staying Sharp Ask students if they recorded any questions or challenges they encountered as they completed the More practice. Discuss these questions as a class. END-OF-UNIT ASSESSMENT (50 minutes) Students take the end-of-unit assessment. Online page 4 Distribute a copy of the assessment to students. Allow students approximately 50 minutes to complete the assessment. Students who finish the assessment early can work on the next activity in their Student Activity Book. CONSOLIDATION ACTIVITY (10 minutes) In this activity, students work with their partners to match various compound inequalities to their coordinate plane graphs. For this activity, you will need to download the master for the cards from the Lesson materials section. Print one set of cards for each pair of students. You may want to cut the cards in advance to save class time. Students will also reflect on their performance and effort this unit and write a goal for the next unit of study. Online page 5 Have students work with their partners to match each inequality to its coordinate plane solution. Students record their matches in their activity books. [SAB, question 1] Before class concludes for the day, direct students attention to question 2 on their activity sheet. Have them reflect on their performance and effort over the course of this unit and write a goal they have for themselves for the next unit of study. [SAB, question 2] If necessary, use Lesson 8.3 to remind students of what a SMART goal is and what enabling goals are. Students will have an opportunity to revise their goal when they receive feedback on their end-of-unit assessment in the next topic. WRAP UP AND INTRODUCE HOMEWORK (5 minutes) Online page 6 Homework 15.7 Students practice graphing compound inequalities in the plane. Staying Sharp 15.7 The main concepts and skills in these problems are: 1. Writing an equation for a line from its slope and a point 2. Identifying points that are on a line from their coordinates, given the equation of the line 3. Graphing lines from their algebraic rules and identifying their point of intersection 4. Identifying a point of intersection of two linear functions by completing x-y tables

23 3 of 3 8/8/ :06 AM Graphing lines from their algebraic rules using slope triangles Identifying the quadrant of the point of intersection of two lines

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