Estimating facts
Progression Tags:
Number Facts progression, 4th Step
The purpose of the activity
In this activity, the learners learn to apply their basic multiplication facts to problems involving multiples of tens, hundreds, thousands, etc. They learn that facility with these new number facts is central to making efficient estimations.
The teaching points
- There are three types of estimations in maths. (This activity focuses on computational estimation.)
- Estimating measurements, for example, the length of a table.
- Estimating quantities, for example, the number of people watching a basketball game.
- Computational estimates, for example, estimating the answer to $24.95 x 18.
- A computational estimate involves finding an approximation to a calculation that you either cannot work out exactly or you do not need to work out exactly.
- An estimate is not a guess because an estimate involves using a strategy to find a good approximation to a calculation.
- Computational estimates involve using easier-to-handle numbers. For example, a computational estimate for 4,124 x 19 is 4,000 x 20. These easier-to-handle numbers are most often multiples of 10.
- Estimation strategies build on mental strategies where the largest value of a number is considered first.
- Discuss with the learners situations where computational estimations are used in everyday life (for example, comparing values in supermarket purchases, estimating the annual cost of power, estimating the cost of a proposed holiday, determining the reasonableness of a calculator computation).
- A consideration of the context of the problem is important when making sense of a computational estimate. For example, if the estimate involves the amount of concrete needed to cover a driveway, which of the following is reasonable: 0.5 m3, 5 m3, 50 m3?
Resources
- Calculators.
The guided teaching and learning sequence
1. Write the following numbers on the board and ask the learners to find the one that is the best estimate of the number of days that a 10-yearold has lived.
- 350 days
- 3,500 days
- 35,000 days
- 350,000 days.
2. Discuss with the learners the reasoning they used to estimate 3,500 days.
“Why did you select 3,500?” (350 x 10 = 3,500)
3. Check that the learners understand how to multiply a number by 10. Encourage them to explain the meaning as “multiplying by tens” rather than stating the rule “add a 0”. While “add a 0” gives the correct answer, it doesn’t convey a conceptual meaning unless it is linked to an explanation like “add a 0 in the ones place as there are no ones in the answer”. For example:
- 3 x 10 is 3 tens or 30
- 25 x 10 is 25 tens or 250
- 455 x 10 is 455 tens or 4,550.
4. If the learners seem unsure, pose several more problems where they multiple numbers by 10.
5. Ask: “What computation would you use to estimate how many days a 20-year-old has lived?”
6. Tell the learners to choose a computational estimate they could calculate quickly in their heads (without pen and paper or a calculator).
7. List the suggestions one at a time on the board. With each suggestion, ask the learner to state whether they think that the estimate would be ‘over’ or ‘under’ the answer.
8. After each suggestion, ask the learners to do the calculation in their heads. Ask for a volunteer to share how they worked out their answer.
“How did you work out 300 x 20?” (I thought of it as 20 lots of 3 hundred, which is 60 hundreds or 6,000.)
9. Repeat with other calculation estimates, for example:
- 350 x 20 = 7,000 (I thought of it as 700 x 10, which is 700 tens or 7,000)
- 400 x 20 = 8000 (I thought of it as 20 lots of 4 hundreds, which is 80 hundreds or 8,000)
- 3,500 x 2 = 7,000 (I thought of it as 2 lots of 3 thousand 5 hundreds, which is 7 thousands).
10. Discuss the estimates with the learners, encouraging them to see that the estimates will generally fall in a range around the exact answer.
11. Write 5,700 on the board. Have the learners work in pairs to write down computations that have 5,700 as the answer and that could be worked out mentally. Suggest they try to find a calculation for each of the number operations (multiplication, division, subtraction and addition).
12. Share ideas, asking the learners to explain how they worked out each problem mentally. For example:
- 57 x 100 (57 hundreds)
- 570 x 10 (570 tens)
- 57,000 ÷ 10 (There are 5,700 tens in 57,000)
- 5,000 + 700 (5 thousands and 7 hundreds)
- 6,000 – 300 (60 hundreds take away 3 hundreds is 57 hundreds).
Follow-up activity
Ask the learners to work in pairs to find the missing factors or products in the following chart.
When they have completed the given problems, ask the learners to take turns posing similar problems for a partner to solve.
Downloads
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