Estimating sums of money
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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.
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 37 + 42 + 28 + 55 to identify whether they use the front-end method. Students who are secure in estimation using front-end as shown in a) should perform at least one of b) or c) to confirm this, and d) which looks at front-end with numbers of a variable length.
- Discuss students' methods. Use the language of estimation in the Computational estimation concept map for each different method.
- Introduce the front-end strategy in addition, i.e., use just the first digit of each number. You may wish to write this down as you discuss it.
Example: Estimate 37 + 42 + 28 + 55.
This is equivalent to 30 + 40 + 20 + 50 = 140 (front-end).
- Students complete the sentence with the word "front-end", and then answer parts b) to d) to assess if they can apply it. Emphasise they are to use the front-end method only (i.e., without trying to adjust the estimate to make it more accurate).
For more information about discussions see Classroom discourse (Mathematics)
Level:
4
Curriculum info:
Key Competencies:
Keywords:
Description of task:
Students estimate an addition problem, share their methods, discuss the front-end method and then do more problems using front-end.
Curriculum Links:
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to whole numbers when estimating addition problems.
Key competencies
This resource involves recording the strategies students use to estimate in multiplication problems. This relates to the Key Competency: Using language, symbols and text.
For more information see https://nzcurriculum.tki.org.nz/Key-competencies.
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 close to 140 and gives a reasonable explanation of their estimation method it. The front-end method would be:
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| b) | 800 and 100 + 300 + 400 = 800 (or equivalent explanation). |
| c) | 11,000 and 2,000 + 5,000 + 4,000 = 11,000 (or equivalent explanation) |
| d) | 7,000 and 4,000 + 3,000 = 7,000 (or equivalent explanation) |
NOTES:
- Other strategies are possible. If they don't use the front-end methods, conference them to see if they can, 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).
- Students may do front-end and compensation to get a closer estimate. Give marks for this. Do not accept the exact answers unless they have first made an estimate using front-end and then adjusted it using compensation sequentially. Highlight this is really computation rather than estimation.
Diagnostic and formative information:
| Common error | Likely calculation | Likely misconception | |
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a) b) c) d) |
162 1,004 12,382 8,756 |
37 + 42 + 28 + 55 143 + 385 + 476 2,836 + 5,192 + 4,354 417 + 4,386 + 97 + 3,856 |
Performs exact calculation rather than estimation. |
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a) b) c) d) |
160 1,000 12,000 8,000 |
40 + 40 + 30 + 50 100 + 400 + 500 3,000 + 5,000 + 4,000 4,000 + 4,000 |
Uses rounding rather than front-end. |
| d) | 7,490 | 400 + 4,000 + 90 + 3,000 | Uses the most significant digit of each number rather than just the highest significant digit. |
Information on front-end estimation
- Front-end always underestimates the true results because all the numbers being added are smaller than the numbers in the original sum. It is, however, easy to learn and to use compensation with.
- Front-end uses just the first, most significant digit of numbers.
Prior knowledge needed
- A firm base of additive basic facts.
- Good place value concepts.
- Understanding that estimation is a quick mental way of getting an answer close to the exact one.
For similar ARB resources about front-end estimation refer to:
- Estimating team scores (front-end with compensation, to give closer estimates by making adjustments using the second most significant figures).
- Estimating stamps (front-end with multiplication problems).
For more information about computational estimation see the Computational estimation concept map.
Links with Numeracy Project.
Using front-end estimation involves at least early additive part-whole (Stage 5) knowledge and strategies (see The Number Framework, Book 1 (2004, p. 10 & 13). Wellington: Ministry of Education).