Example 1
A ₹36 lunch, plus a 25% tip. Total?
- 25% = 1/4; 1/4 of 36 = 9.
- 36 + 9 = 45.
- Estimate check: a bit more than 36, under 50 ✓
Answer: ₹45
⚖️ Grade 7 · equations · session 4 of 12 · 60 minutes · ⭐ Plus
Multi-step problems with rational numbers and estimation
Real problems mix whole numbers, fractions, decimals and negatives. Plan the steps, convert to the easiest form, estimate first, then check your answer is reasonable.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up4 min
- Friendly forms9 min
- Planning steps9 min
- Estimate and check9 min
- Activity 17 min
- Activity 27 min
- Activity 35 min
- Quiz6 min
- Set the project4 min
By the end you can
- Convert between fractions, decimals and percents to make a problem easier
- Solve multi-step problems with positive and negative rational numbers
- Estimate first and check the answer is reasonable
- NJSLS-M 7.EE.B.3 (Common Core 7.EE.3)
Before you start
- Operations with fractions, decimals and integers
- Percent of a number
Have ready
- Paper for planning
- A calculator for checking only
Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE
Warm-up · think first
Estimate: 19.8 × 5.1. Then 0.49 of 802.
Show the answer
About 20 × 5 = 100, and about half of 800 = 400. Estimating first tells you if a later answer is silly.
Teacher tip: Ask the class for their estimates before anyone calculates.
Part 1 of 3 · learn, see, practise
Choose the friendliest form
25% = 0.25 = 1/4. Use whichever form makes the step easiest.
Finding 1/4 of 64 is easier than 0.25 × 64; finding 0.1 of 37 is easier than 1/10 of 37.
Negative numbers show change, debt or below zero.
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Answers (for the teacher)
- 0.75
- 9
- 60
- 5.5
- 325
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The rest of this lesson is in Plus
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You have seen the plan, the warm-up and part 1. With Plus you also get:
- Part 2: Plan the steps, with practice at three levels
- Part 3: Estimate and check, with practice at three levels
- Class activity 1: Trip planner
- Class activity 2: Error hunt
- Class activity 3: Weather report
- A 8-question quiz
- After-class project: Class party budget
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Multi-step problems with rational numbers and estimation: questions
What is a multi-step problem?
A word problem that needs more than one calculation, such as a discount followed by tax.
Why estimate first?
An estimate tells you roughly what the answer should be, so you can spot mistakes like a misplaced decimal point.
Which standard is this?
New Jersey 7.EE.B.3 (Common Core 7.EE.3).
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