Estimating and Solving Word Problems
Check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context. Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts.
Read this first
Estimate first. Then work it out. If the two are far apart, check your work.
An estimate of 40 sits close to the exact answer of 38.
Words you need
- Estimate
- A close answer, worked out quickly.
- Reasonable
- An answer that makes sense.
- Model
- Turning a word problem into maths.
Worked example
e.g. Four tickets cost $9.50 each. Estimate, then work out the exact cost.
- Round 10 to estimate.
- 4 lots of 40. That is the estimate.
- Now work it out exactly. 4 x 38.
- 40. The answer is reasonable.
Write the number sentence before you calculate. It keeps you on track.
Practice
The pictures fade as you go. By the last few you are on your own.
1Estimate 6 x $4.90.with a picture
AnswerAbout $30.
2You estimate 294. What went wrong?with a picture
AnswerThe answer is far too big. Check the working.
3Estimate 198 + 203.with a hint
Need a hint?
Round both to the nearest hundred.
AnswerAbout 400.
4Three friends share $60 equally. Write a number sentence.with a hint
Need a hint?
Sharing means divide.
Answer60 / 3 = 20. Each gets $20.
5Estimate 51 x 4.on your own
AnswerAbout 200.
6A book costs $12.95. Estimate the cost of 5.on your own
AnswerAbout $65.
7Why estimate before you calculate?on your own
AnswerSo you can spot a silly answer straight away.
Think about it
1
Can an estimate be wrong?
One good answerNo. It is meant to be close, not exact.
2
What should you do if the exact answer is far from the estimate?
One good answerCheck the working. One of them is wrong.
Common mistakes
Estimating after you finish.
Do it first. Then it can catch a mistake.
Rounding both numbers up every time.
Round to the nearest, so the estimate stays close.