advice for instruction | 15. solving linear inequalities...

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 throughwhich to learn the mathematical concept of“doing and undoing” to solve for a variable,inequalities provide more interesting problemsituations to solve. They more accuratelyrepresent scenarios in the real world since mostsolutions involve a range of acceptable values as opposed to the single solutions that representequations. The goal of this topic is to use the parallels between solving equations and inequalitiesto 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 answerquestions arising from the situations;analyze situations involving linear functions and formulate linear inequalities to solveproblems;investigate methods for solving linear inequalities using concrete models, graphs, and theproperties of equality, select a method, and solve the inequalities;interpret and determine the reasonableness of solutions to linear inequalities for givencontexts.

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, andconsolidating understanding of slope and linear equationsProblems 3 and 4 (Preparing for upcoming lessons): Building skills for solving systems ofequations using tables and graphsProblems 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 linearinequalities in one variable. Students will also investigate compound inequalities through numberlines.

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 solvinginequalities.

Agile Mind http://tng.agilemind.com/LMS/com.agilemind.common.Print/Print.html

1 of 2 8/8/2014 11:03 AM

Lesson 15.3: Students learn how to use graphs and tables to solve linear inequalities in onevariable. 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 onusing inverse operations to solve linear inequalities in one variable.

Lesson 15.5: Students explore how to graph solutions to linear inequalities in two variables. Theyalso 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 anopportunity to solidify their understanding of linear inequalities prior to taking the end-of-unitassessment.

Lesson 15.7: One goal of this lesson is to check student understanding of linear inequalitiesthrough the end-of-unit assessment. Students also reflect on their effort to this point and set newgoals for the next unit of study.

Resources

LESSON RESOURCES

Computer with projection device and Internet connectionGraphing calculators (Lesson 15.3)Computer lab (Lesson 15.5)Large chart paperChart markersMasking tapeScissorsWhiteboards, dry erase markers, and erasers

Print resources

Unit 5 Topic 15 Advice for instructionUnit 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


2 of 2 8/8/2014 11:03 AM

Advice for Instruction | 15. Solving linear inequalities | Deliver instruction

Lesson materials Lesson preview Lesson activities

Lesson materials

Solving linear inequalities:

Student Activity BookLesson 15.1 “Inequalities on a numberline”Inequalities on a number line card sort(One copy for each pair of students)Scissors

Lesson preview

Suggestedtime

Activity Goals

10 min OpenerUnderstand the value of using the number line torepresent 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 minWrap up and introducehomework

Reflect on the day’s lesson and understand tonight’shomework assignment

Lesson activities

OPENER (10 minutes)

Online page 1In this activity, students determine whether specific numbers make an inequality true. Then theyidentify other numbers that make the inequality true. Students will use the numbers from thisactivity 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 theirsolutions 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?


1 of 3 8/8/2014 11:04 AM

How many possible numbers could we come up with that make the inequality true?

Online page 2

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 depictinequalities on a number line. Students develop insights into building inequalities as well as settingthe stage for the next lesson on solving inequalities.

Online pages 3-4Use these pages to launch the activity and introduce how inequalities are depicted on the numberline.

Page 3: Use the animation on this page to show students how to depict the inequality x > 7and the other related inequalities.: Have students graph the inequalities on the number line in their activity books beforediscussing the solutions shown on the page. [SAB, question 1] Students should be familiarwith graphing solutions on a number line from work in previous topics.

Pages 5-7Students are introduced to depicting compound inequalities involving the word “or” on the numberline, then practice the skill.

Page 5: Have students work with partners on solving a compound inequality involving theword "or." [SAB, questions 2-4]Page 6: Use the animation on this page to debrief students' work on question 3. Use theanimation 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 comparetheir graphs for question 4 with the one shown and discuss any differences, questions, ormisconceptions that arise.

Pages 8-10Students depict compound inequalities involving the word “and” on the number line.

Page 8: Have students work with partners on solving a compound inequality involving theword "and." [SAB, questions 5-7]Page 9: Use the animation on this page to debrief students' work on question 6. Use theanimation 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 comparetheir graphs for question 7 with the one shown and discuss any differences, questions, ormisconceptions that arise.

Online page 11Students 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 toeach other’s contributions. In building knowledge as a community of learners, partners


2 of 3 8/8/2014 11:04 AM

explain, compare, test, and revise ideas with each other. Give students room to explore andresolve 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 12Students process the homework due today: Homework 14.3 and Staying Sharp 14.3.

Discuss the fundraiser problem from part I of the homework. Pay particular attention toquestions 4 and 5 to make sure students can identify solutions on a graph given a problemsituation and specific conditions.

CONSOLIDATION ACTIVITY (25 minutes)In this activity, students work with their partners to match various inequalities (includingcompound inequalities) to their number line graphs. Then they write inequalities to matchdescriptions of number line graphs. For this activity, you will need to download the master for thecards from the Lesson materials section. Print one set of cards for each pair of students. You maywant 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 relatedquestions. [SAB, questions 1-4]

WRAP UP AND INTRODUCE HOMEWORK (5 minutes)

Online page 14

Homework 15.1The first question in the homework asks students to match inequality statements to thenumber line solution. Then, students are asked to come up with inequalities that representfour different solution sets: empty set, some but not all real numbers, all real numbers, andexactly one number. Finally, given a graph, students determine appropriate inequalitystatements.Staying Sharp 15.1The main concepts and skills in these problems are:

Comparing positive and negative fractions and decimals using inequality symbols1.Ordering the slopes of lines given as graphs2.Finding common coordinates between the x-y tables for two linear functions3.Finding the coordinates of the point of intersection of the graphs of two linear functions4.Computing the slope of a line given its graph with a slope triangle5.Writing an equation for a linear function given its graph (and slope from question 5)6.


3 of 3 8/8/2014 11:04 AM



Lesson materials

Student Activity BookLesson 15.2 “Introduction to solving linear inequalities”Chart paper and markers

Lesson preview

Suggestedtime

Activity Goals

10 min OpenerDetermine the solution set to a problem situationinvolving an inequality

30 min Core activity Use methods for solving equations to solve inequalities


25 min Consolidation activity Find solution sets when comparing two pricing schemes



Lesson activities

OPENER (10 minutes)Students model a problem situation with a function rule and revisit the familiar notion of findingfunction 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 theseanswers. An animation at the beginning of the next activity will further this debriefing andset up learning in the rest of the lesson.

Online page 2



1 of 3 8/8/2014 11:04 AM

CORE ACTIVITY (30 minutes)In this activity, you will guide students through the same four methods explored in Solving linearequations. The notable difference is that you will be looking at all possible solutions for theinequality 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 theinequality statement true. Connecting the writing and solving of linear inequalities to tabular,graphical, and symbolic representations of linear functions not only gives students differentstrategies for solving inequalities, but can also develop a deeper understanding of why they aresolving them.

Online page 3Students’ work on the Opener is extended with the use of an animation. The animation helps totransition 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 representsthe problem situation. [SAB, question 1]Use panel 1 to reinforce that the constant rate of change in the problem situation suggeststhe use of a linear model.Use panels 2 and 3 to confirm students’ thinking about the graph and to remind students ofthe input-output relationship described by the function. Draw students’ attention to thenotion 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 5Students are introduced to the concept of a linear inequality in one variable. They then solve aproblem 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 particularproblem solving method: using “undoing,” using a table, using a graph, or using algebraicoperations. Ask partners to create a poster that shows how they would use their method tosolve the problem. Have partners hang their posters on the wall. [SAB, question 2]

Online pages 6-9Each 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 differentmethods are discussed, refer to students’ posters to connect to what students already knowhow to do. Students will utilize all four methods presented as they explore linear inequalities.

Online page 10Students 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 mathjournal entry to reflect on the meaning of linear inequality. [SAB, questions 3-4]



2 of 3 8/8/2014 11:04 AM


Go over questions 2 through 5 with students. Ask students to give you examples of what anumber line graph would look like for each type of solution set. Then have students relate thegraph to an inequality statement.

CONSOLIDATION ACTIVITY (25 minutes)Students work in pairs to solve another car rental problem, using the methods of their choice. Theyprepare a report of their solution.

Online page 12

Organize students in pairs. Have partners read the problem, solve it, and present theirsolution in a report. [SAB, questions 1-2]Language strategy. Building literacy skills across the content might be a focus on yourcampus or in your district. Point out that the final product for this assignment is a report inwhich recommendations need to be written. The recommendations are being sent to the bossso encourage students to use complete sentences.

WRAP UP AND INTRODUCE HOMEWORK (5 minutes)Online page 13

Homework 15.2Students practice solving a few simple linear inequalities using any method they choose. Thenstudents explain how an inequality describes a certain problem situation and solve thatinequality.Staying Sharp 15.2The main concepts and skills in these problems are:

Comparing positive integers (presented as exponents) using inequality symbols1.Sketching and calculating the slope of a line given its x- and y-intercepts2.Computing the rates of change of two linear functions from their x-y tables3.Finding common coordinates between the x-y tables for two linear functions4.Computing the slope of a line given its graph with two different slope triangles5.Explaining the constant slope of a line6.


3 of 3 8/8/2014 11:04 AM



Lesson materials


Student Activity BookLesson 15.3 “Solving inequalities using tables and graphs”Graphing calculators

Lesson preview

Suggestedtime

Activity Goals

10 min Opener Solve an equation using graphs and tables

30 min Core activity Solve inequalities using graphs and tables


25 min Consolidation activityAnalyze the advantages and disadvantages of the tableand graph methods



Lesson activities

OPENER (10 minutes)Students review how to use graphing technology to create tables and graphs in order to find asolution to a linear equation. Students will recall how to use technology to find the point ofintersection of the two related functions from their work in the topics Solving linear equationsand 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?


1 of 3 8/8/2014 11:04 AM

What is the difference between an inequality and an equation?

Online page 2


CORE ACTIVITY (30 minutes)Students first explore using graph technology to solve inequalities. The new learning here is theability to use the information given in the inequality to determine solution sets. Though the pointof intersection is an interesting point, since it is the solution to the related linear equation, it isnot part of the solution set for either of the inequalities explored in this activity. Then, studentsinvestigate the use of table technology to solve inequalities and connect this work to graphingtechnology.

Online pages 3-5

Page 3: Have students use their sketches of the graph and table displays from the Opener toanswer 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 tableand graphing methods for solving inequalities. In the second discussion question studentsconsider how a displayed solution would change if the inequality were written with thesymbol ≤, instead of <. This will be further explored in the next lesson and in upcominglessons. Have students complete the math journal entry in their activity books to reflect onwhat they learned in this activity. [SAB, question 4]

PROCESS HOMEWORK(10 minutes)


Review question 2 with students. Focus on students’ ability to interpret the meaning of theinequality 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. Thenthey compare the methods.

Online page 8

Have student work in pairs to find the solutions to the inequalities, then compare themethods of graphing and using a table. [SAB, questions 1-3] To debrief, discuss theadvantages and disadvantages of each method. You may want to point out, for example, thatusing a table can be time consuming if the solution is not an integer or another “nicenumber” or if the solution is very large.


2 of 3 8/8/2014 11:04 AM


Online page 9

Homework 15.3Students practice using tables and graphs to find solutions to inequalities.Staying Sharp 15.3The main concepts and skills in these problems are:

Testing an inequality to understand the effect of multiplying by a negative value1.Ordering the slopes of lines given as graphs2.Graphing lines on the coordinate plane from their algebraic rules3.Identifying and verifying the point of intersection of two lines in their algebraic rules4.Marking two lattice points on the graph of a line5.Using lattice points to draw a slope triangle and calculate the slope of a line6.


3 of 3 8/8/2014 11:04 AM



Lesson materials


Student Activity BookLesson 15.4 "Solving inequalities with algebraic operations"Student whiteboards

Lesson preview

Suggestedtime

Activity Goals

10 min OpenerExplore inequality relationships involving adding andsubtracting a quantity

30 min Core activityLearn methods to find solutions to inequalities thathave a negative coefficient


25 min Consolidation activityCheck for errors in solutions to inequalities and correctthe mistakes you find



Lesson activities

OPENER (10 minutes)Students look for relationships when adding or subtracting equal quantities from both sides of aninequality. In the core lesson today, they will learn two methods for solving inequalities whenthere is a negative coefficient. Keep the focus in this activity on noticings and wait for the core toexplore and discuss the two methods.

Online page 1

Students complete the inequalities and look for patterns. [SAB, questions 1-3] To debrief,


1 of 3 8/8/2014 11:05 AM

solicit a few responses from the students and record their observations on the board. You canrefer to these during the rest of the lesson. If a misconception comes up, be sure to address itduring the lesson. Students should notice that the inequality remains intact when adding orsubtracting equal quantities.

Online page 2


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 3-5Use these pages to guide a whole-class discussion about using algebraic properties to solveinequalities.

Page 3: Before working through the online puzzle, have student pairs complete the puzzle intheir activity books and answer the reflective question. [SAB, questions 1-2] Then ask forvolunteers 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 ordividing by a negative number, the inequalities will reverse directions.Page 4: Use the balance scale animation to show students how they can use the samesymbolic 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 lastanimation to solve the inequality 8 – 2x ≥ 14 by first subtracting 8 from both sides of theinequality. [SAB, question 5] Then, play panels 2 and 3. Ask students to try a differentapproach 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 5and 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 6Students practice using algebraic operations to solve inequalities in one variable.

Have student pairs practice what they’ve learned by completing the problems in their activitybooks. [SAB, question 8]After students complete the problems, select one or two inequalities and ask one or two pairsof students present their solutions for those inequalities to the class. Address any questionsand misconceptions that arise in the discussions that follow.



Discuss question 2 as a class. Ask students to share some of their responses. This will help


2 of 3 8/8/2014 11:05 AM

students develop their mathematical communication skills. Students should realize that thetables 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 = -1.5. Thus, the inequality will be truefor values of x < -1.5.

CONSOLIDATION ACTIVITY (25 minutes)Students build their understanding of using algebraic properties to solve inequalities by looking forerrors in another student's solutions. Students will also use their whiteboards to write inequalitiesfor 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 onJacob'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 ofthe question prompts listed above.To debrief question 2, ask a few students to share their inequalities and solutions.


Online page 9

Homework 15.4Students continue to practice solving linear inequalities using algebraic operations. Studentsare also asked to verbalize a solution method and confront some common misconceptionsabout solving linear inequalities.Staying Sharp 15.4The main concepts and skills in these problems are:

Sketching a horizontal line through a given point and writing an equation for the line1.Sketching a vertical line through two given points and writing an equation for the line2.Computing the rates of change of two linear functions from their x-y tables3.Identifying that there are no common coordinates in the x-y tables for parallel lines4.Writing an equation for a line from its graph, with slope triangles given5.Finding the y-coordinate of a point on a line given an x-coordinate and the line’s graph6.


3 of 3 8/8/2014 11:05 AM



Lesson materials


Student Activity BookLesson 15.5 “Inequalities in the plane”Computer lab

Lesson preview

Suggestedtime

Activity Goals

10 min OpenerUse inequalities to describe coordinates of points on acoordinate plane

25 min Core activity Determine solution regions


35 min Online assessmentAssess your understanding of key ideas and skills of thistopic



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 thedescriptions. For each point, you might ask:

Are there other compound inequalities that could describe that point?What inequalities?

Online page 2


1 of 3 8/8/2014 11:05 AM


CORE ACTIVITY (25 minutes)Students investigate how to graph linear inequalities in the plane through the context of a problemsituation.

Online pages 3-4Students are introduced to the problem situation. They work with their partners to complete theactivity 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 completethe 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 5-11Students are formally introduced to the concept of an inequality in two variables. Then theremainder 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 asingle 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 tocome 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 linearinequality in two variables.Page 11: Use this page to show how the graphical solution looks in the context of the problemsituation. 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 togive too much away. Students will be coming back to this problem.]

Online page 12Students complete a puzzle to reinforce the learning in this Exploring.

Have students complete the puzzle in their activity books. [SAB, question 8] Then invitestudents up one at a time to match the inequalities with the correct graph.


Online page 13


2 of 3 8/8/2014 11:05 AM

Students process the homework due today: Homework 15.4 and Staying Sharp 15.4.

You may want to review a few of the problems from question 1. Asking students to verbalizetheir problem solving strategy, as in question 2, helps build communication skills andconceptual understanding.

ONLINE ASSESSMENT (35 minutes)

Online pages 14

Students complete the online Guided assessment in the online services for this topic. You will needto reserve a computer lab for this activity. Completion of the items in the Guided assessment willprovide you and your students with formative assessment data related to student understanding ofthe 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 yourclass, and then view the assignment report.


Online page 15

Homework 15.5Students will practice writing and graphing linear inequalities in two variables.Staying Sharp 15.5The main concepts and skills in these problems are:

Solving a two-step inequality in one variable1.Writing an equation for a line from its slope and a point, then finding another point on it2.Interpreting the point of intersection of two lines in the context of the situation3.Identifying lines as parallel from their equations4.Graphing a line from its y-intercept and slope using slope triangles5.Writing an equation for a line from its y-intercept and slope and/or its graph6.


3 of 3 8/8/2014 11:05 AM



Lesson materials


Student Activity BookLesson 15.6 “Compound inequalities in the plane”Assessment reports

Lesson preview

Suggestedtime

Activity Goals

10 min OpenerBuild intuition for graphing compound inequalities inthe plane

30 min Core activity Graph compound inequalities in the plane


25 min Review online assessmentAnalyze and learn from performance on the onlineassessment



Lesson activities

OPENER (10 minutes)Students build intuition for graphing compound inequalities in the plane by graphing compoundinequalities on a number line. Students will connect their understanding of “or” statements, asused in compound inequalities in one variable, to the use of “or” statements when graphingcompound inequalities in the plane.

Online page 1

Students graph the compound inequality on a number line and predict what the graph lookslike in the plane. [SAB, questions 1-3] In debriefing, discuss the connection between numberline graphs and coordinate plane graphs. Ask:


1 of 3 8/8/2014 11:05 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 tothink 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 canfinish debriefing then.

Online page 2


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 howto graph “or” statements in the coordinate plane. [SAB, question 1]Page 4: Before showing the animation depicting the graphing of the “and” statement, givestudents 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 studentsto verify their solutions.



Discuss question 5 as a class. Ask students to translate their answers to parts a through c intoequations 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 makesense in the context of the problem. (For example, it does not make sense to buy negativeboxes 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 theitems the class did well on and those the class did not do well on. Instruct students to writethe 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 discussthese 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 notperform well. Be prepared to project particular questions (perhaps two questions) from the


2 of 3 8/8/2014 11:05 AM

Guided assessment. Next, allow students several minutes to work with their partners to re-dothese problems in their activity books, and then discuss as a class.Share with students their individual score reports. Tell students they should take some timeoutside of class to revisit problems from the Guided assessment, in particular those for whichthey did not get the correct answers.


Online page 8

Homework 15.6This lesson’s homework helps students prepare for the end-of-unit assessment. Students willalso be taking the online More practice in the topic Solving linear inequalities. Students willneed to bring their Student Activity Books home and will also need online access in order tocomplete Parts I and II of the homework. Remind students where and when they can getonline access in school or in the community.Staying Sharp 15.6The main concepts and skills in these problems are:

Finding solutions of inequalities in one variable and understanding a common sign error1.Writing an equation for a line from two points2.Completing a three-column input-output table for two linear function rules3.Explaining the use of an input-output table to find and check an intersection point4.Graphing a line from a point and its slope using slope triangles5.Writing an equation for a line from a point and its slope and/or its graph6.


3 of 3 8/8/2014 11:05 AM



Lesson materials


Student Activity BookLesson 15.7 “Checking for understanding”Unit 5 end-of-unit assessmentCard sort - Graphing compound inequalities (live link)

Lesson preview

Suggestedtime

Activity Goals

10 min OpenerReview linear inequality concepts prior to taking the endof unit assessment


50 min End-of-unit assessmentDemonstrate your understanding of importantmathematical skills and concepts from the unit

10 min Consolidation activityGraph compound inequalities by completing a card sortactivity


Reflect on the day's lesson and understand tonight'shomework 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, questions1-3] In debriefing, find out which methods students used to solve the inequality and ask themto describe how they used a particular method to arrive at the solution.

Online page 2


1 of 3 8/8/2014 11:06 AM




Ask students if they recorded any questions or challenges they encountered as theycompleted 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 tocomplete the assessment.Students who finish the assessment early can work on the next activity in their StudentActivity Book.

CONSOLIDATION ACTIVITY (10 minutes)

In this activity, students work with their partners to match various compound inequalities to theircoordinate plane graphs. For this activity, you will need to download the master for the cards fromthe Lesson materials section. Print one set of cards for each pair of students. You may want to cutthe cards in advance to save class time. Students will also reflect on their performance and effortthis 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 planesolution. 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 activitysheet. Have them reflect on their performance and effort over the course of this unit andwrite a goal they have for themselves for the next unit of study. [SAB, question 2] Ifnecessary, use Lesson 8.3 to remind students of what a SMART goal is and what enabling goalsare. Students will have an opportunity to revise their goal when they receive feedback ontheir end-of-unit assessment in the next topic.

WRAP UP AND INTRODUCE HOMEWORK (5 minutes)Online page 6

Homework 15.7Students practice graphing compound inequalities in the plane.Staying Sharp 15.7The main concepts and skills in these problems are:

Writing an equation for a line from its slope and a point1.Identifying points that are on a line from their coordinates, given the equation of theline

2.

Graphing lines from their algebraic rules and identifying their point of intersection3.Identifying a point of intersection of two linear functions by completing x-y tables4.


2 of 3 8/8/2014 11:06 AM

Graphing lines from their algebraic rules using slope triangles5.Identifying the quadrant of the point of intersection of two lines6.


3 of 3 8/8/2014 11:06 AM

advice for instruction | 15. solving linear inequalities...

Documents