Lesson 7: Equations and Inequalities Problem Solving6.AT.8

I can…

I can model and solve real-world problems using equations and inequalities.

Key words

• Model — To show a real-life situation with an equation or inequality.
• Equation — A math sentence with an equal sign showing both sides are the same.
• Inequality — A math sentence that compares two sides with <, >, ≤, or ≥.
• Reasonableness — Checking if your answer makes sense.
• Variable — A letter that stands for a number that is unknown or can change.
• Constraint — A limit in a problem that tells what values are allowed.

Steps

1. Clue: 'A total divided equally among 4 people gave each $85.'
2. This has an exact total, so I use an equation. Let t be the total.
3. Divided among 4 to get 85 means t ÷ 4 = 85, so t = 85 × 4 = 340.
4. Check reasonableness: $340 split 4 ways is $85 each. That makes sense!

Try it

A box of donuts has some donuts. After giving away 7, there are fewer than 5 left. Which inequality represents the starting number of donuts d?

Check your answer

d − 7 < 5

Starting with d donuts and giving away 7 leaves fewer than 5: d − 7 < 5. Solve: d < 12. ✓

Sentence starter

I know ___ because ___.

Goal: I can explain my reasoning using the words model, equation, inequality, and reasonableness.