# Solve Problems Using Expressions, Equations, and Inequalities

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Solve Problems Using Expressions, Equations, and Inequalities
Common Core: Engage New York

Properties of Inequalities
Lesson 12- Standard 7.EE.B.4 Properties of Inequalities

What does 7.EE.B.4 cover? Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Date Title Page 1/27/14 FOCUS 7- Inequalities Engage NY- Lesson 12 Fresh Left

Focus 7 - Learning Goal Students will be able to extend their knowledge of equations to include solving and graphing inequalities on a number line. Students will be able to solve real world problems involving equations and inequalities.

Today, my learning target is to…
Justify the properties of inequalities that are denoted by < (less than), ≤ (less than or equal), > (greater than), and ≥ (greater than or equal).

How much prior knowledge do you have regarding that goal?
MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.

Teacher Directed Opening Exercise (10 mins)
Materials Needed: Copies of the sprints for each student Directions: Students complete a two round sprint exercise where they practice their knowledge of solving linear equations in the form 𝑝𝑥 + 𝑞 = 𝑟 and 𝑝(𝑥+𝑞)=𝑟. Provide one minute for each round of the sprint. Follow the established protocol for a sprint exercise. Be sure to provide any answers not completed by the students.

Teacher Directed Example (22 mins)
What do the follow vocabulary terms mean? Preserves the inequality symbol: Preserves the inequality symbol: means the inequality symbol stays the same. Reverses the inequality symbol: Reverses the inequality symbol: means the inequality symbol switches less than with greater than and less than or equal to with greater than or equal to.

Example 1- Station Rotations Math Practices: MP2 & MP4
Materials Needed: Copies of Rotation Charts (#1-4), cut-out cubes in the Teachers’ materials or SMART Notebook computerized interactive dice (see next slide for directions). Directions: Split students into 4 groups. Discuss the directions to the Opening Exercise: px+q=r and p(x+q)=r. There are four stations. Provide each station with two cubes containing integers. At each station, students are to do the following, recording their results in their student materials or math notebooks: (an examples is provided for each student.) Roll each die, recording the numbers under the first and third columns. Students are to write an inequality symbol that makes the statement true. Repeat this four times to complete the four rows in a table. Perform the operation indicated at the station (adding or subtracting a number, writing opposites, multiplying or dividing by a number), writing a new inequality statement. Determine if the inequality symbol is preserved or reversed when the operation is performed.

How to use SMART Notebook Computerized Interactive Dice
Open SMART Notebook (you don’t need a SMART Board) Click on the picture frame icon on the far left side Search dice Click on Interactive and Multimedia Drag TWO blue “KEYWORD” dice onto the white page Click on the upper left corner of each dice. A column of rows should be present. Enter any integer, fraction, or decimal using opposite signs. Then click on the upper left corner again to “close” the dice. Then click on the center of the dice to “roll” each one. Save the Notebook in your Focus 7 to use again another time! Have fun!!

Station 1 Chart- Add or Subtract a Number to Both Sides of the Inequality

Students Examine the Results from Station 1
Make a statement about what you notice, and justify it with evidence. When a number is added or subtracted to both numbers being compared, the symbol stays the same and the inequality symbol is preserved.

Station 2 Chart- Multiply each term by −1

Students Examine the Results from Station 2
Make a statement about what you notice, and justify it with evidence. When both numbers are multiplied by −𝟏, the symbol changes and the inequality symbol is reversed.

Station 3 Chart- Multiply or Divide Both Sides of the Inequality by a Positive Number

Students Examine the Results from Station 3
Make a statement about what you notice, and justify it with evidence. When a positive number is multiplied or divided to both numbers being compared, the symbol stays the same and the inequality symbol is preserved.

Station 4 Chart

Students Examine the Results from Station 4
Make a statement about what you notice, and justify it with evidence. When a negative number is multiplied or divided to both numbers being compared, the symbol changes and the inequality symbol is reversed.

Class Discussion Summarize the Findings
To summarize, when did the inequality change and when did it stay the same? The inequality reverses when we multiply or divide the expressions on both sides of the inequality by a negative number.

Student Practice Exercise (5 minutes)
Complete the following chart using the given inequality, and determine an operation in which the inequality symbol is preserved and an operation in which the inequality symbol is reversed. Explain why this occurs.

Student Practice Exercise Answers may vary

Student Problem Set (part 1)

Student Problem Set (part 1) Answers

Closing (3 min) What does it mean for an inequality to be preserved? What does it mean for the inequality to be reversed? When does a greater than become a less than?

Student Problem Set (part 2)
If 𝑎 is a negative integer, then which of the number sentences is true? If the number sentence is NOT true, give a reason.

Student Exit Ticket (5 min)- Lesson 12-Properties of Inequalities Part 1

Student Exit Ticket (5 min)- Lesson 12-Properties of Inequalities Part 2

Exit Ticket - Lesson 12 Solution Properties of Inequalities Part 1

Exit Ticket - Lesson 12 Solution Properties of Inequalities Part 2

Today, I achieved my learning target by…
Justifying the properties of inequalities that are denoted by: < (less than) ≤ (less than or equal) > (greater than) ≥ (greater than or equal)

How much prior knowledge do you have regarding that goal?
MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.

The End of Lesson 12 Properties of Inequalities 