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

Lesson 8.4Write and Represent Inequalities

Start hereWords, worked example, and sentence starters

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?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
InequalitySpanish: Desigualdad A math sentence that compares two sides with <, >, ≤, or ≥. x ≥ 18
Greater thanSpanish: Mayor que The > sign, showing one number is bigger. 8 > 3 — eight is larger than three
Less thanSpanish: Menor que The < sign, showing one number is smaller. 2 < 7 — two is smaller than seven
At least / At mostSpanish: Al menos / A lo más 'At least' means ≥. 'At most' means ≤. 'At least 10 players' → p ≥ 10 (could be 10, 11, 12, ...); 'At most 5 tries' → t ≤ 5 (could be 5, 4, 3, ...)
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. the x in x ≥ 18
No more thanSpanish: No más de A phrase meaning less than or equal to (≤). “No more than 8 people” means people ≤ 8.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A van can carry at most 8 riders. Write an inequality for r, the riders.

  1. Key words: “at most.” Is 8 allowed? Yes.
  2. “At most” means less than or equal to: r ≤ 8.
  3. Test: 8 works, 5 works, 9 does not.

Answer: r ≤ 8

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Clue: 'A bag holds fewer than 10 items.' What does 'fewer than' mean?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The phrase tells me the symbol is .
  • My inequality is because .
  • The value (is / is not) a solution because .
  • This inequality has many solutions because .

Word bank inequalityat leastat mostmore thanless thangreater thansymbolconstraintvariablesolutionboundaryrange

Watch out!A common mistake

A common mistake in Write Inequalities is using a strict symbol (> or <) for a phrase that actually includes the boundary value. For 'the suspect is at least 18 years old,' students often write a > 18 instead of the correct a ≥ 18

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

Lesson 8.4Write and Represent Inequalities

Level 0Most support · every hint printed

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?

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A van can carry at most 8 riders. Write an inequality for r, the riders.

  1. Key words: “at most.” Is 8 allowed? Yes.
  2. “At most” means less than or equal to: r ≤ 8.
  3. Test: 8 works, 5 works, 9 does not.

Answer: r ≤ 8

  1. 1Circle 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
    Steps to try
    1. Find the comparison phrase: 'less than 40 degrees'. Does 40 itself count, or only temperatures below it?
    2. 'Less than' with no 'or equal to' means a strict symbol — no bar underneath — pointing toward the smaller side.
    3. Test a value: is 35 degrees 'less than 40'? Yes — so pick the strict symbol that puts t on the smaller side of 40.
    Show your work
  2. 2Circle 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
    Steps to try
    1. 'At least 48' — ask yourself: can a rider who is EXACTLY 48 inches tall ride? That decides whether 48 is included.
    2. When the boundary value is allowed, you need a symbol with the 'or equal to' bar under it.
    3. Allowed heights are 48, 49, 50, and up. Pick the symbol that includes 48 itself AND points toward bigger numbers.
    Show your work
  3. 3Circle 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
    Steps to try
    1. 'No more than 75' — could the store hold exactly 75 people? Could it hold 76?
    2. 'No more than' allows the boundary but nothing above it — that calls for a symbol with the 'or equal' bar.
    3. Test values: 75 people is fine, 76 is not. Pick the symbol that keeps p at 75 or below.
    Show your work
  4. 4Circle 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
    Steps to try
    1. 'More than 25' — is exactly 25 included, or only speeds above 25?
    2. 'More than' (not 'at least') is strict — no 'or equal' bar under the symbol.
    3. Test: 26 works, but 25 itself does not. Pick the strict symbol that puts s above 25.
    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