Lesson 8.48.4 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can write inequalities to represent real-world situations — one step at a time, with support.
Why This Matters This is your support small group for Lesson 8.4. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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.
- Key words: “at most.” Is 8 allowed? Yes.
- “At most” means less than or equal to: r ≤ 8.
- 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." Write an inequality for the number of items.
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
Lesson 8.48.4 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can write inequalities to represent real-world situations — one step at a time, with support.
Why This Matters This is your support small group for Lesson 8.4. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.
-
1Complete each step, then write the final answer.
Height Can ride? 54 in. ? Is exactly 54 inches allowed? Clue: "Riders must be at least 54 inches tall." Write an inequality for a rider's height h.
- 1What does "at least 54" mean?
- 2Can a rider be exactly 54 inches tall? Which symbol do we use?
- 3Write the inequality.
Final answer: -
2Complete each step, then write the final answer.
Weight Allowed? 15 lb ? Is exactly 15 pounds allowed? Clue: "A backpack can weigh at most 15 pounds." Write an inequality for the weight w.
- 1What does "at most 15" mean?
- 2Can the backpack weigh exactly 15 pounds?
- 3Which symbol do we use?
- 4Write the inequality.
Final answer: -
3Complete each step, then write the final answer.
The temperature is less than 30 degrees. Which symbol goes in the box: t ☐ 30?
Show your workHint "Less than 30" does not include 30.
Final answer: -
4Complete each step, then write the final answer.
A theater holds no more than 250 people. Which symbol goes in the box: p ☐ 250?
Show your workHint "No more than 250" means the number cannot go over 250. Can exactly 250 people come in?
Final answer: -
5Complete each step, then write the final answer.
Yuzuki wants to earn more than $60 to buy a game. Write an inequality for her earnings e. Which symbol goes in the box: e ☐ 60?
Show your workHint "More than 60" means greater than 60. Is 60 itself included?
Final answer: -
6Complete each step, then write the final answer.
A team needs at least 10 players. Tom writes s > 10. Is he right? Which symbol should go in the box: s ☐ 10?
Show your workHint Can the team play with exactly 10 players? Does > include 10?
Final answer:
Explain your thinkingWhy does "at least 10" use ≥, but "more than 10" uses >? Talk about the number 10.
Sentence starter "At least" ___ the number, so I use ___. · "More than" does not include ___, so I use ___.