Estimating people
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Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using a way of estimating that you have discussed with your teacher.
Ali wants a quick estimate of the number of people in a crowd.
Make an estimate of about how many people there are and explain how you did it in the box.
Task administration:
This task can be completed with pencil and paper or online.
This assessment activity is designed to be carried out with a group of students or a whole class. A suggested lesson sequence:
- Give the students the problem of estimating 8,682 - 6,824 to identify whether they use the rounding one number method.
- Discuss students' methods. Use the language of estimation in the Computational estimation concept map for each different method.
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Introduce the rounding one number method in subtraction. This is done by changing just the smaller number to the nearest 10, 100, etc., using rounding. A final compensation can be made by adjusting the estimate by the approximate amount that the smaller number is rounded by. You may wish to write this example down as you discuss it.
Example: Estimate 8,682 - 6,824
8,682 - 6,824 ~ 8,682 - 7,000 = 1,682 (changing one number using rounding)
1,682 is too small by about 200 because 6,824 is rounded up by about 200 - Students complete the sentence with "rounding one number", and then answer parts b) to d) to assess if they can apply it. Emphasise they are to use the rounding one number method only.
For more information about discussions click on Classroom discourse (Mathematics)
Copyright:
Image: Dreamstime
Level:
4
Curriculum info:
Key Competencies:
Keywords:
Description of task:
Students estimate a subtraction problem, share their methods, discuss the rounding one number method, and then do more problems by rounding one number.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.Answers/responses:
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a)
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Makes a reasonable estimate between 2,000 and 3,000 and gives a reasonable explanation of their method of estimating it.
The rounding one number method is: 1,682 because it is 8,682 - 7,000
Final compensation may also be used, e.g., 1,682 is about 200 too small, so the answer is about 1,882
Many other acceptable estimation methods are possible.
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b)
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3,364
because you just take off 2,000
or
equivalent answer and explanation showing the method.
Final compensation may also be used (e.g., 3,364 - 200 = 3,164).
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c)
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2,281
because you just take off 5,000
or
equivalent answer and explanation showing the method.
Final compensation may also be used (e.g., 2,281 + 100 = 2,381).
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d)
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14,807
because you just take off 40,000
or
equivalent answer and explanation showing the method.
Final compensation may also be used (e.g., 14,807 + 300 = 15,107).
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NOTE:
- Do not accept an exact answer unless students have first made an estimate and then adjusted it using successive compensations.
- Students may use front-end rather than rounding which will not be as accurate. Give marks for this.
- Other strategies are possible. If students don't use the rounding one number method, conference them to see if they can use it, even if they prefer other strategies.
- Students may use a combination of estimation and computation (i.e., computations that they cannot easily do in their heads and may need to write down).
Diagnostic and formative information:
| Common error | Likely calculation | Likely misconception | |
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a) b) c) d) |
1,858 3,177 2,418 15,092 |
8,682 - 6,824 5,364 - 2,187 7,281 - 4,863 54,807 - 39,715 |
Performs exact calculation rather than estimation. |
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a) b) c) d) |
2,000 3,000 2,000 10,000 |
9 000 - 7 000 5 000 - 2 000 7 000 - 5 000 50 000 - 40 000 |
Uses rounding on both numbers |
Information on rounding one number for estimation
- This resource assesses whether students can use the estimation strategy known as rounding one number method in subtraction situations. This is where only one number is changed, either by rounding or front-end methods. The rounding method is just as easy, but more accurate than front-end.
- The research literature refers to estimation that changes numbers to more suitable ones as reformulation.
- Final compensation (i.e., updating the estimate to a more accurate one) is very easy to do with this method by either taking off or adding on the approximate amount that the second number was changed by. If both numbers are changed by rounding or front-end methods, then compensation becomes much harder.
- Rounding one number is particularly useful for subtraction, or for adding just two amounts.
Prior knowledge needed
- A firm base of additive basic facts.
- Good place value concepts.
- A knowledge of the rounding method.
For similar ARB resources involving rounding in estimation refer to: Estimating farm animals (rounding with addition) and Estimating bags and boxes (rounding with multiplication)
For more information about computational estimation see the Computational estimation concept map.
Links with Numeracy Project
Using rounding one number as an estimation method for subtraction involves at least early additive part-whole (Stage 5) knowledge and strategies. (see Book 1: The Number Framework (2004, p. 10 & 13). Wellington: Ministry of Education).
Using rounding one number as an estimation method for subtraction involves at least early additive part-whole (Stage 5) knowledge and strategies. (see Book 1: The Number Framework (2004, p. 10 & 13). Wellington: Ministry of Education).