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

Lesson 8.4Write and Represent Inequalities

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write inequalities to represent real-world situations.

Why This Matters Detective Navarro is narrowing down suspects. A witness says the suspect is at least 18 years old. The detective writes the inequality a ≥ 18, where a is the suspect's age. How does this help eliminate suspects?

RememberWrite and Represent Inequalities

Writing & Representing Inequalities. Formula: < (less) | > (greater) | ≤ (at most / ≤) | ≥ (at least / ≥) An inequality compares two amounts using <, >, ≤, or ≥. I use one when many values are allowed, not just one. I pick a variable and match the words to the right symbol.

  1. 'At least', 'minimum', 'no less than' translate to ≥ (greater than or equal to).
  2. 'At most', 'maximum', 'no more than' translate to ≤ (less than or equal to).
  3. 'More than' is >; 'Fewer than' / 'Less than' is <

Words: Inequality (Desigualdad)Greater than (Mayor que)Less than (Menor que)At least / At most (Al menos / A lo más)Variable (Variable)

  1. 1Circle the letter of the best answer. Show how you know.

    Solve: 6x = 42

    1. Ax = 7
    2. Bx = 36
    3. Cx = 48
    4. Dx = 252
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Solve: n / 3 = 8

    1. An = 3
    2. Bn = 5
    3. Cn = 11
    4. Dn = 24
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    Solve: 9m = 63

    1. Am = 7
    2. Bm = 54
    3. Cm = 72
    4. Dm = 567
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A detective knows the getaway car was traveling at most 65 miles per hour on the highway. The inequality s ≤ 65 represents the car's speed s. Which speed is NOT possible for the getaway car?

    1. A45 mph
    2. B60 mph
    3. C65 mph
    4. D70 mph
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  5. 5Circle the letter of the best answer. Show how you know.

    A detective knows the getaway car was traveling at most 65 miles per hour on the highway. The inequality s ≤ 65 represents the car's speed s. Does s ≤ 65 include 65 itself?

    1. ANo — it must be strictly less
    2. BYes — the 'or equal to' part includes 65
    3. COnly if the car stops
    4. DOnly on a highway
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A detective knows the getaway car was traveling at most 65 miles per hour on the highway. The inequality s ≤ 65 represents the car's speed s. Which inequality means 'at most 65'?

    1. As ≤ 65
    2. Bs < 65
    3. Cs ≥ 65
    4. Ds > 65
    Show your work

Explain your thinkingHow do the words 'at least' and 'at most' change the inequality symbol compared to 'more than' and 'fewer than'?

Sentence starter 'At least' uses ≥ instead of > because it means the value ___ be equal to the number, while 'more than' means it must be ___.

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 8.4Write and Represent Inequalities

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write inequalities to represent real-world situations.

Why This Matters Detective Navarro is narrowing down suspects. A witness says the suspect is at least 18 years old. The detective writes the inequality a ≥ 18, where a is the suspect's age. How does this help eliminate suspects?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Each case clue describes a boundary. Drag every scenario into the inequality symbol it matches.

    Groups: > (greater than) < (less than) ≥ (greater than or equal to) ≤ (less than or equal to)
    • The getaway driver was going more than 70 mph
    • More than 6 fingerprints were on the safe
    • The ransom note was written under 3 minutes ago
    • Fewer than 9 cars left the parking lot
    • At least 30 dollars in coins was stolen
    • No fewer than 4 witnesses saw the suspect
    • At most 14 footprints were found in the mud
    • No more than 7 keys can open the vault
  2. 2Write the letter of the matching item on each line.

    Match each detective clue phrase to its inequality symbol.

    1. at least
    2. at most
    3. more than
    4. fewer than
    5. no more than
    • A≥
    • B≤
    • C>
    • D<
    • E≤
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A clue says the suspect carried at least 12 stolen gems. Which inequality shows the number g of gems?

    1. Ag ≥ 12
    2. Bg > 12
    3. Cg ≤ 12
    4. Dg < 12
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A witness reports that fewer than 5 people entered the building. Which inequality shows the number n of people?

    1. An < 5
    2. Bn ≤ 5
    3. Cn > 5
    4. Dn ≥ 5
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Which inequality represents: 'A number n is at least 14'?

    1. An ≥ 14
    2. Bn > 14
    3. Cn ≤ 14
    4. Dn < 14
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — Catch the Symbol Mix-Up

    1. 1ClueThe suspect is at least 12 years on the force, where y is the years.
    2. 2Find the key phrase'At least 12' means 12 is allowed and anything larger.
    3. 3Write the inequalityy > 12

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow do the words 'at least' and 'at most' change the inequality symbol compared to 'more than' and 'fewer than'?

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