Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.9

Lesson 8.5Understand Inequalities and Their Solutions

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can graph the solutions of an inequality on a number line.

Why This Matters Detective Okafor is building a timeline. The suspect was seen at the scene no earlier than 2:00 PM, meaning the arrival time t satisfies t ≥ 2. She needs to plot this on a timeline to share with her team. How should she mark the number line?

RememberUnderstand Inequalities and Their Solutions

Graphing Inequalities on the Number Line Graphing an inequality shows every value that makes it true. I draw a circle at the boundary number and shade the side that works. The circle tells me if the boundary is included.

Draw the boundary circle at the given constant number.
Open Circle (○) for < or > (boundary value is not included in solution set).
Closed Circle (●) for ≤ or ≥ (boundary value is included). Shade right for >, left for <

Words: Number line (Recta numérica)Open circle (Círculo abierto)Closed circle (Círculo cerrado)Solution set (Conjunto solución)Inequality (Desigualdad)

1Circle the letter of the best answer. Show how you know.
Which inequality represents: 'You must be at least 48 inches tall to ride'?
1. Ah > 48
2. Bh ≥ 48
3. Ch < 48
4. Dh ≤ 48
Show your work
2Circle the letter of the best answer. Show how you know.
Which inequality represents: 'A store can hold no more than 75 people'?
1. Ap < 75
2. Bp ≥ 75
3. Cp ≤ 75
4. Dp > 75
Show your work
3Circle the letter of the best answer. Show how you know.
Which inequality represents: 'The speed limit is more than 25 mph'?
1. As ≥ 25
2. Bs < 25
3. Cs > 25
4. Ds = 25
Show your work
4Circle the letter of the best answer. Show how you know.
Which inequality represents: 'The temperature is less than 40 degrees'?
1. At > 40
2. Bt ≤ 40
3. Ct < 40
4. Dt = 40
Show your work
5Circle the letter of the best answer. Show how you know.
A detective determines that fewer than 12 people were at the scene. The inequality p < 12 represents the number of people p. She graphs this with an open circle at 12 and shading to the left. Why did the detective use an open circle at 12?
1. ABecause 12 is negative
2. BBecause the shading goes left
3. CBecause 12 is not a whole number
4. DBecause p < 12 does not include 12 itself
Show your work
6Circle the letter of the best answer. Show how you know.
A detective determines that fewer than 12 people were at the scene. The inequality p < 12 represents the number of people p. She graphs this with an open circle at 12 and shading to the left. Which number is a solution to p < 12?
1. A11
2. B12
3. C13
4. D15
Show your work

Explain your thinkingHow do you decide between an open circle and a closed circle when graphing?

Sentence starter I use a ___ circle when the symbol is ___ because the boundary value ___ part of the solution.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.9

Lesson 8.5Understand Inequalities and Their Solutions

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can graph the solutions of an inequality on a number line.

Part 1Understand the ideamodels and meaning

1Write the name of the correct group on each line.
Detective Okafor is filing clues. Sort each inequality by the circle its graph uses.

Groups: Open circle (boundary NOT included) Closed circle (boundary IS included)
- c > 20
- t < 11
- w ≥ 14
- m ≤ 2
2Write the letter of the matching item on each line.
Match each clue inequality to the correct graph in the case file.
1. n > 13
2. n ≤ 16
3. n ≥ 20
4. n < 17
- AOpen circle at 13, shaded right
- BClosed circle at 16, shaded left
- CClosed circle at 20, shaded right
- DOpen circle at 17, shaded left

Part 2Apply itreal-world problems

3Circle the letter of the best answer. Show how you know.
A detective determines that fewer than 12 people were at the scene. The inequality p < 12 represents the number of people p. She graphs this with an open circle at 12 and shading to the left. How would the graph change if 12 or fewer people were at the scene?
1. AThe shading would flip to the right
2. BNothing would change
3. CThe circle would be closed (filled in) at 12
4. DThe circle would move to 11
Show your work
4Circle the letter of the best answer. Show how you know.
Clue: the witness ran more than 15 feet, so d > 15. On the number line, what do you draw?
1. AOpen circle at 15, shade right
2. BClosed circle at 15, shade right
3. COpen circle at 15, shade left
4. DClosed circle at 15, shade left
Show your work
5Circle the letter of the best answer. Show how you know.
Clue: the getaway car held at most 4 suspects, so s ≤ 4. How is this graphed?
1. AClosed circle at 4, shade left
2. BOpen circle at 4, shade left
3. CClosed circle at 4, shade right
4. DOpen circle at 4, shade right
Show your work

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Level 2 Extension — Crack the Graphing Mistake
1. 1Clue inequalityk > 19 (the loot weighed more than 19 pounds)
2. 2Circle typeClosed circle at 19
3. 3Shade directionShade right
4. 4Final graphClosed circle at 19, shaded right
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingHow do you decide between an open circle and a closed circle when graphing?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help