Write Inequalities
I can write inequalities to represent real-world situations.
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🎯 Content Objective / Objetivo de contenido
I can write inequalities to represent real-world situations.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
A witness says the suspect is 'at least 18 years old,' written as a ≥ 18. Why does the detective use an inequality here instead of an equation like a = 18?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Case File: The Suspect Constraints
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?
Concept Launch
💡 How do I write an inequality from words?
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.
'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Inequality Desigualdad |
A math sentence that compares two sides with <, >, ≤, or ≥. Una oración matemática que compara dos lados con <, >, ≤ o ≥. |
x > 5 means x can be 6, 7, 8, ... — any number greater than 5 | |
| Greater than Mayor que |
The > sign, showing one number is bigger. El signo >, que muestra que un número es mayor. |
8 > 3 — eight is larger than three | |
| Less than Menor que |
The < sign, showing one number is smaller. El signo <, que muestra que un número es menor. |
2 < 7 — two is smaller than seven | |
| At least / At most Al menos / A lo más |
'At least' means ≥. 'At most' means ≤. 'Al menos' significa ≥. 'Como máximo' significa ≤. |
'At least 10 players' → p ≥ 10 (could be 10, 11, 12, ...); 'At most 5 tries' → t ≤ 5 (could be 5, 4, 3, ...) | |
| Variable Variable |
A letter that stands for an unknown number. Una letra que representa un número desconocido. |
In x > 5, the letter x stands for any number greater than 5. | |
| No more than No más de |
A phrase meaning less than or equal to (≤). Una frase que significa menor o igual que (≤). |
"No more than 8 people" means people ≤ 8. |
Which Word Fits?
A math sentence comparing values with <, >, ≤, or ≥ is an ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
A witness says the suspect is 'at least 18 years old,' written as a ≥ 18. Why does the detective use an inequality here instead of an equation like a = 18?
👂 Listen For
Students explain that 'at least 18' allows many values (18 and up), so an inequality with ≥ captures it while an equation would force one value.
Extend: How would the meaning change if the clue used a > 18 instead of a ≥ 18? Justify whether an 18-year-old still fits.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Match each phrase to the correct inequality symbol. Drag each phrase card into the matching symbol category.
✍️ Explore Discourse
How do the words 'at least' and 'at most' change the inequality symbol compared to 'more than' and 'fewer than'?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How do the phrases 'at least' and 'at most' change which inequality symbol you choose compared to 'more than' and 'fewer than'?
👂 Listen For
Students match 'at least' to ≥ and 'at most' to ≤ (include the value), and 'more than'/'fewer than' to > and < (exclude the value).
Extend: Compare 'no more than 8 exits' with 'fewer than 8 exits.' Could 8 exits be allowed in each case? Justify.
Practice Check A
A parking garage charges if your stay is more than 2 hours. Which inequality represents times t that are charged?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Which inequality represents: 'The temperature is less than 40 degrees'?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Expression Simplify
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Sort each inequality into whether x = 10 is a solution.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <." — and it works because ___.
Because Inequality means ___, but a tricky part is ___, so I have to ___.
A common mistake with Inequality is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Greater than to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <. because ___
'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <. but ___
'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Match each phrase to the correct inequality symbol. Drag each phrase card into the matching symbol category.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Which inequality represents: 'The temperature is less than 40 degrees'?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
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.
✍️ Connection Reasoning
What speeds are possible for the getaway car? How did the phrase 'at most' help you write the inequality?
The car's speed could be ___ or ___ because 'at most 65' means the speed is ___ 65.
Turn & Talk — Connect
Where do you see inequalities in real life, such as age limits or speed limits?
👂 Listen For
Students give a real example (ride height, speed limit, ticket age) and write an inequality with the correct symbol for a range of values.
Extend: Critique: 'A speed limit of 25 mph means you must drive exactly 25.' Write the correct inequality and explain the real rule.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which inequality represents: 'A number n is at least 14'?
Bonus Exit Check
Which inequality represents: 'You must be at least 48 inches tall to ride'?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students explain that 'at least 18' allows many values (18 and up), so an inequality with ≥ captures it while an equation would force one value.
• Students match 'at least' to ≥ and 'at most' to ≤ (include the value), and 'more than'/'fewer than' to > and < (exclude the value).
• Students give a real example (ride height, speed limit, ticket age) and write an inequality with the correct symbol for a range of values.
• Listen for students naming a specific strategy tied to 6.EE.8 — not just "I picked a symbol." They should explain matching the key phrase (at least, at most, more than, fewer than) to the correct inequality symbol.
Common mistake: A common mistake in Write Inequalities is skipping the key idea: "'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: t > 2 — 'More than 2 hours' means strictly greater than: t > 2. Exactly 2 hours is not charged.
✓ Practice 2: t < 40 — 'Less than' means <, so the inequality is t < 40.
✓ Practice 3: h ≥ 48 — 'At least' means greater than or equal to, so h ≥ 48.
✓ Practice 4: p ≤ 75 — 'No more than' means less than or equal to, so p ≤ 75.
✓ Exit ticket: n ≥ 14 — 'At least 14' means 14 or greater, so n ≥ 14.