Lesson Plan -- Math 097 Grade Level:

9-10 Title: Section 1.7

Author: Kyle Linford

Enduring Understanding:

Students will gain an understanding of single variable inequalities through connections with their previous understanding of inequalities and the process for solving equations.

Objectives:

SWBAT:

Solve for a variable in an inequality

Apply the additive and multiplicative properties when solving inequalities

Change the inequality sign when multiplying both sides by a negative number

Utilize the distributive property to simplify terms in an inequality

Utilize techniques for solving equations (clearing fractions, decimals, etc.) to solve an inequality

Combine like terms

Content Standard(s): CCSS.MATH.CONTENT.6.EE.B.5—Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes and equation or inequality true. CCSS.MATH.CONTENT.6.EE.B.8—Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. CCSS.MATH.CONTENT.6.NS.C.7.A—Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

Resources: Miller, Julie, O’Neil, and Hyde. MTH 097 and MTH 169. McGraw Hill, n.d. Print.

Vocabulary: Inequality Less than, greater than, greater than or equal to, less than or equal to

Materials: Two Sided Scale Weights

Assessment Strategies FORMATIVE: Solving in class inequality problems SUMMATIVE: Completing the exit ticket and the independent practice

Differentiation: Ability:

Reviewing the topics of interval notation and inequalities helps struggling learners refresh their memories, draw connections to prior knowledge, and limit the amount of prerequisite knowledge.

Offering separate worksheets for different skill levels helps struggling learners take more time, while more advanced learners can more to more challenging topics.

Working in groups helps struggling learners get more input on how to view the problem and offers them a resource for asking questions.

Allowing students to work with others on the independent practice to answer questions allows for struggling learners to have better support with the content.

Having students work at their own pace helps struggling learners take their time with problems.

Providing an answer key helps all students check their work and analyze where they made mistakes.

Making connections helps all learners build their connected thinking about the topic and refer back to prior knowledge.

Intelligences:

The class discussions and teacher commentary in the Build section and the Checking for Understanding help auditory learners.

The scale activity allows for visual learners and kinesthetic learners to observe how the quantities in an inequality are not the same.

The scale activity allows for visual learners and kinesthetic to better interpret how the additive property is utilized.

The use of the number line and board work to show the multiplicative property helps visual learners.

Having students work in groups helps interpersonal learners share and develop their ideas for how to solve problems.

Allowing students to work with others on the independent practice helps interpersonal learners share and develop their ideas for how to solve problems.

Allowing students the opportunity to work alone on the independent practice helps intrapersonal learners focus individually on their work

Instructional Activities & Strategies

ANTICIPATORY SET: (5 minutes)

Bell Work: When students walk into the classroom, they will be instructed to follow the task designated on the board. The task will be for them to complete a warm up activity where they graph inequalities on a number line and write the solution sets in interval notation.

The instructor will launch the lesson by introducing the topic of linear inequalities and provide a rationale

on the need to understand and study inequalities with real-world examples of where they can occur.

Launch:

So far, we have explored how to work with equations. We had situations were two quantities were equal

to one another. However, this is not always the case. Sometimes we work with quantities that are not

equal to one another, such as how one job pays less than another, how a car has great gas mileage on

highway travel than in city travel, how certain energy drinks have more caffeine in them than others, or

how certain businesses like Netflix have videos that stream less than or greater than average streaming

rates. In any situation like these, we want to explore and understand the relationship between these

unequal quantities.

The instructor will remind students of inequalities and connect the concept of inequalities to the balance

concept of the previous equality topic.

Ask: When we worked with equations before, we said that we had a balanced scale. What do we have

with an inequality? How does our scale look now?

Students will be guided to explaining how the inequality suggests an imbalanced scale where one quantity

is greater than the other. Taking this idea, the instructor will present students with a problem that

requires the use of the additive property of inequalities to be solved. Using a balance scale, the instructor

will place a metal washer in one of the cups with 3 metal nuts and 5 metal nuts in the other. Students will

observe that the scale is imbalance: one side has more weight than the other.

Ask: What would happen if I were to put two more nuts in each of the cups?

Students will be guided to observing that the scale will still be imbalanced in the same orientation. The

instructor will then have students hypothesize what would happen if they removed 3 nuts from both sides

to get the washer by itself. To build students’ critical thinking, the instructor will then have students

record in their notes how they think this demonstration relates to inequalities and how it connects with

something they have explored in the past. The class will then share a few of their ideas.

BUILD: (15 minutes)

Input:

The instructor will define the additive property of inequality for students and connect it with the additive

property of equality that students have seen before. The instructor will then have students graph the

solution set to the inequality on a number line and check their work using the test point method.

Ask: Do you think our other properties when solving equations are the same for inequalities?

The instructor will then inform students of the multiplicative property of inequalities, while highlighting

the need to reverse the inequality sign when multiplying by a negative multiple. When students are

presented with a negative value, they will check their work with the test point method and observe that it

does not work unless they change the orientation of the sign.

Ask: Why does the sign change?

The instructor will demonstrate why the sign must change when multiplying by a negative multiple by

using the inequality 5 < 10 and multiplying both sides by -1. It is important to specify that while one

quantity was larger and farther away from zero than the other, the negative multiple makes that number

a negative value, still farther from zero than the other quantity. This means that the value is now smaller

than the other. Using a number line to show these values’ distances from zero will be necessary.

Model:

To demonstrate both of these properties, the instructor will work through examples that utilize both of

these properties individually: 𝑥 − 2 < 4, 𝑥

2< 4, and −2𝑥 > 4.

Check for Understanding:

To check for student understanding, the instructor will have the class answer the questions as a whole.

Additionally, the instructor will utilize quick, formative feedback by question students about their comfort

level with this topic by indicating with a thumb up, down, or in the middle when the topic has been

explained.

GUIDED PRACTICE: (20 minutes)

To demonstrate understanding, the class will practice solving the problems 𝑥+1

2−

𝑥−2

3> 2. First, the

instructor will have the class connect this problem to similar work they have done with equations and

hypothesize some properties or procedures they might use to solve the inequality. The instructor will

then have the class share their ideas and determine the necessary steps for solving the problem. The

instructor will make sure to utilize the clearing fractions method of multiplying both sides of the inequality

by a common multiple of the denominators, 6.

Ask: Is there any other way I could have solved this problem?

Students will be guided to observing that they could have solved the problem by making a common

denominator and combining the rational expressions.

To check for student understanding, the class will practice solving linear inequalities for 5-7 minutes,

while the instructor monitors their work and provides help. The class will then spend 5 minutes reviewing

their work as a class and analyzing any mistakes they made.

INDEPENDENT PRACTICE: (10 minutes)

The class will practice their understanding of the additive and multiplicative properties of inequality by

working on practice problems and asking the instructor questions.

CLOSING: (12 minutes)

The instructor will close the lesson by having students record connections with the work they have done

in previous sections and describe what the main idea of this lesson was or why it was important. Students

will first record their answers in their notes and then share a few with the class. The instructor will

remind students of past topics.

Students will then be presented with an exit ticket where they are to solve a linear inequality and write

the solution set in interval notation.

Note:

Name: _________________________

Unit 2, Section 1.7 – Linear Inequalities in One Variable

Thinking Column: How are inequalities similar to things we have worked with before? Did we ever have infinitely many solutions when working with equations? When?

Notes: Vocabulary

Linear Inequality of One Variable:

Additive Property of Inequality:

Multiplicative Property of Inequality:

Test Point Method:

I. Characteristics of Inequalities a. Anatomy of Inequalities

b. Solution Sets Inequalities generally have ___________________________ solutions.

Can we assume that since we can multiply, we can also divide?

Writing Solution Sets: 1. 2. 3.

II. Properties of Inequalities a. Additive Property

Ex: 𝑥 − 2 < 4

b. Multiplicative Property

Ex: 𝑥

2< 4

Ex: −2𝑥 > 4

What are some methods for solving this problem? How are compound inequalities related to unions and intersections?

Combining Properties:

𝑥 + 1

2−

𝑥 − 2

3> 2

III. Compound Inequality Definition: a. Intersection Set-Up

𝑎 < 𝑥 𝑎𝑛𝑑 𝑥 < 𝑏

𝑎 < 𝑥 < 𝑏

b. Union Set-Up

𝑎 < 𝑥 𝑜𝑟 𝑏 > 𝑥

c. Solving 1. 2. 3.

Practice Problems:

−6 ≤ 2𝑥 − 5 < 1

8 >𝑡 + 4

−2> −5

2

5(2𝑥 − 1) > 10

−3𝑦 − 5 > 4 𝑜𝑟 4 − 𝑦 ≤ 6

IV. Applications

a. Kayla received grades of 87%, 82%, 96%, and 79%

on her last four algebra tests. To graduate with honors, she needs at least a B in the course. Is it possible for Kayla to earn an A in the course if an A requires an average of 90% or more?

b. The amound of money A in a savings account is shown by the equation A = P + Prt. If an investor deposits $5000 at 6.5% simple interest, the account will grow according to the formula A = 5000 + 5000(0.065)t. How many years will it take for the investment to exceed $10,000?

c. For a day in July, the temperatures in Austin, Texas,

ranged from 20˚C to 29˚C. The formula relating Celsius temperatures to Fahrenheit temperatures

is given by 𝐶 =5

9(𝐹 − 32). Convert the inequality

20° ≤ 𝐶 ≤ 29° to an equivalent inequality using Fahrenheit temperatures.

Main Idea/Purpose: Connections:

Name: _________________________

Unit 2, Section 1.7 Warm-Up

Task: On your own, graph the following inequalities and write their solution sets in interval notation. When finished, turn your warm-up upside down.

1. 𝑥 > 2

2. 𝑥 ≤ 0

3. 𝑥 ≤ 9

4. −5 < 𝑥 ≤ 0

5. −1 ≤ 𝑥 < 15

Name: _________________________

Unit 2, Section 1.7 Practice Problems

Task: Solve each of the following linear inequalities. Then graph their solutions and check your answers using the test point method. Write your answer in interval notation.

1. 4𝑧 + 2 < 22

2. 8𝑤 − 2 ≤ 13

3. 2

5(2𝑥 − 1) > 10

4. −5𝑥 + 7 < 22

5. 3𝑘−2

−5≤ 4

Name: _________________________

Unit 2, Section 1.7 Exit Ticket

Task: On your own, solve the following linear inequalities, graph their solutions, and write their solution sets in interval notation. When finished, turn in your exit ticket.

1. 3𝑦 + 11 > 5

2. −3

2𝑦 > −

21

16

3. 3 − 4(𝑦 + 2) ≤ 6 + 4(2𝑦 + 1)