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.
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 examplewriting an inequality for a constraint
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A club trip requires each member to save at least $45. Write an inequality for the amounts that work.
- Name the variable: let s = the dollars a member saves.
- Find the key phrase: 'at least' means the amount can equal 45 or be more.
- That phrase matches the symbol ≥, so write s ≥ 45.
- Test values: 45 works and 52 works, but 39 falls below the limit.
Answer: s ≥ 45, so any amount of 45 dollars or more is a solution.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A team must win at least 7 games to reach the playoffs. Write an inequality for the wins.
- Name the variable: let w = .
- The phrase 'at least' means w can be equal to or it.
- Write the inequality: w 7
- Test: is 6 a solution? Is 11 a solution?
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 outA 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 — this wrongly excludes 18 itself, even though 'at least 18' means 18 counts as a match. The same error happens in reverse with 'at most': for 'the getaway bag holds at most 12 items,' students write n < 12 instead of n ≤ 12. Always ask: does the key phrase include the number ('at least,' 'at most,' 'no more than,' 'no fewer than' → use ≥ or ≤) or exclude it ('more than,' 'fewer than' → use > or <)?
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.
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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 ___.