Estimating food numbers
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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 assessment activity is designed to be carried out with a group of students or a whole class. A suggested lesson sequence:
- Introduce the interval strategy in multiplication.
- Get a first estimate that is smaller than the actual answer by using just the first (most significant) digit in each number (Front-end estimation).
- Get another estimate that is bigger than the actual answer by rounding-up each number to the next biggest 10, 100, 1 000, etc.
Example. Estimate 138 × 3.
A first estimate is at least 100 × 3 = 300 (front-end).
A second estimate is that it is no more than 200 × 3 = 600 (rounding-up).
- Get the students to complete the sentence at the top of their worksheet with "interval". Emphasise they are to use this method when they do parts a) and b).
Level:
4
Curriculum info:
Key Competencies:
Keywords:
Description of task:
Students discuss making an interval estimate in multiplication problems (i.e., getting a lower and an upper limit for the actual answer using the front-end and rounding-up estimation methods). They then use this method on two problems.
Curriculum Links:
This resource can help to identify students' ability to apply multiplicative strategies flexibly to whole numbers when estimating multiplication 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:
a) |
i) 2 400 or 2 600 ii) Any 1 of:
iii) 2 800 |
1 mark (for both i) & ii) correct) 1 mark (for both iii) & iv) correct) |
b) |
i) 800 or 900 ii) Any 1 of:
iii) 1 500 |
1 mark (for both i) & ii) correct) 1 mark (for both iii) & iv) correct) |
Total | 4 marks |
Diagnostic and formative information:
Common error | Likely calculation | Likely misconception | |
a) i) b) i) |
2 712 1 058 |
678 × 4 23 × 46 |
Performs exact calculation rather than estimation. |
Information on interval estimation
- Front-end always underestimates the true results because both the numbers being multiplied are smaller than the numbers in the original product. Front-end is where just the most significant digit of a number is used in the estimation.
- Rounding-up always overestimates the true results because both the numbers being multiplied are bigger than the numbers in the original product. Rounding-up takes each number to the next biggest 10, 100, 1 000, etc.
- The interval method recognises that the answer lies somewhere between these two extremes.
Prior knowledge required
- A firm base of multiplicative basic facts.
- Good place value concepts.
- Understanding that estimation is a quick mental way of getting an answer close to the exact one.
For more information on estimation, click on Computational estimation concept map.
Links with Numeracy Project
Using interval estimation with multiplication involves advanced additive/early multiplicative part-whole (Stage 6) knowledge and strategies (see The Number Framework, Book 1 (2004, p. 10 & 14). Wellington: Ministry of Education).
Other ARB resources
For similar resources about estimation with multiplication refer to:
- Estimating stamps (front-end in multiplication).
- Estimating bags and boxes (rounding in multiplication).
- Estimating sweets II
- Estimating lots
- Estimating sweets and buses
- Estimate these
- Estimate the menu
- Estimate these II
- Estimating cards, money and pinecones
- Who is estimating? Multiplication
- Estimating bags and boxes
- Estimating sweets
- Estimating in sport
- Ula lole
- Estimating multiplication
- How I estimate: Multiplication