Estimate these II

Estimate these II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about making sensible estimates for some number problems.

In each box below clearly show how you worked out your best estimate. Estimate; do not do an exact calculation.

 

a) Card A: Estimate the total cost of 1 first aid kit, 1 store tent, and 1 torch. 

 

     
 
My estimate is: ____________________
 
b) 
 
Card B: Estimate the total cost of 40 tins of tomatoes and 20 loaves of bread.  
 

     
 
My estimate is: ____________________
 
c) 
 
Card C: Estimate the total cost of 3 utensil sets, 8 batteries, 2 water bottles, and 5 gas cookers.
 

     
 
My estimate is: ____________________
 
d)
 
Card D: Estimate how much it cost each of the 9 people for the kayaking lesson, assuming they all paid the same amount. Estimate, do not do an exact calculation.
 

     
 
My estimate is: ____________________
 
e)
 
Card E: Energy bars come in boxes of 48. Each bar costs $2.05. Estimate how much each person pays if the cost is equally shared between 18 people.
 

     
 
My estimate is: ____________________
 
 
 
 
Card A
Estimate the total cost of hiring the hall, the lights, and 100 seats for one night.

Hall - $96.25 per night
 
 
Lights - $71.66 per night
Card B
Estimate the total cost of 12 plastic swords.
Sword - $24.50 each
 Card C
Estimate the total cost of 17 umbrellas.
Umbrella - $9.60 each
 
Card D
Estimate the total cost of 2 metres of silk, 5 metres of cotton, and 9 metres of elastic.
Silk - $9.95 per metre
 Cotton - $4.25 per metre
 Elastic - $2.80 per metre
Card E
If the total costs for the show are $512, then estimate the number of tickets that will need to be sold to cover costs if each ticket costs $4.80.
Ticket - $4.80 each
Task administration: 
This task is completed with pencil and paper, and other equipment.
 
Equipment:
Task cards (A to E); Student worksheet
  • This task assesses students' ability to use an accurate method of estimation to calculate costs.
  • Assessments can be carried out with one student at a time or with a group/class of students using an OHP. If done 'one-on-one', the student may respond orally to how they got their estimate, rather than writing down an explanation of their estimation method on the Student Workcard provided.
  • Before starting, it is important to emphasise to the student/s that this is an estimation task, and therefore they will be assessed on their method of estimation rather than their ability to calculate the correct answer. It will become apparent in their workings/explanations if they are making exact calculations, rather than estimating.
  • The teacher is to read out the following instructions:


In this activity you are going to be estimating the cost of various things that are needed for the school production at Pipinui School.
You must clearly show each step in working out your best estimate on the work card provided. You will be assessed on how you got your estimate, rather than calculating the correct answer. You will not be able to use calculators.

a) Show the student/s Card A and say;
Write down your estimate of the total cost of hiring the hall, the lights, and the seats for one night. Clearly show (or explain) what you did to get your estimate.
b) Show the student/s Card B and say;
Write down your estimate of the total cost of 12 plastic swords. Clearly show (or explain) what you did to get your estimate.
c) Show the student/s Card C and say;
Write down your estimate of the total cost of 17 umbrellas. Clearly show (or explain) what you did to get your estimate.
d) Show the student/s Card D and say;
Write down your estimate of the total cost of material if 2 metres of silk, 5 metres of cotton, and 9 metres of elastic are needed. Clearly show (or explain) what you did to get your estimate.
e) Show the student/s Card E and say;
If the total costs for the show are $512, write down your estimate of the number of $4.80 tickets that will need to be sold to cover these costs. Clearly show (or explain) what you did to get your estimate.

Level:
3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, addition, multiplication, money
Description of task: 
This practical task involves students making estimates of sets of items and demonstrating their method(s) of estimation.
Curriculum Links: 
This resource can help to identify students' ability to apply additive and simple multiplicative ideas flexibly to combine or partition whole numbers to make sensible estimates for addition and multiplication problems.
Key competencies
This resource involves recording the strategies students use to solve addition and multiplication problems. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, sets 6-7
Multiplicative thinking, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

2 marks
or
 
 
 
1 mark

 a)

*Satisfactory estimate given based on an acceptable method of
estimation. (The exact calculation is $205.86).
E.g., estimate of $210.00; the sum of rounding the hall hire cost up to
$100, rounding the light hire cost down to $70, and rounding the seat hire
cost up to $40.
Acceptable method but 1 error made, including: a rounding error, ** or a calculation error.
2 marks
or
 
 
1 mark		 b)

*Satisfactory estimate given based on an acceptable method of
estimation. (The exact calculation is $294.00).
E.g., estimate of $250, rounding down the number of students to 10, and
rounding up the cost of the swords to $25 and multiplying.
Acceptable method but 1 error made, including: a rounding error, ** or a calculation error.

2 marks
or
 
 
1 mark

 c)

*Satisfactory estimate given based on an acceptable method of
estimation. (The exact calculation is $163.20).
E.g., estimate of $170, rounding up the cost of the umbrellas to $10, and
multiplying.
Acceptable method but 1 error made, including: a rounding error, ** or a calculation error.

2 marks
or
 
 
 
 
1 mark

 d)

**Satisfactory estimate given based on an acceptable method of
estimation.(The exact calculation is $66.35).
E.g., estimate of $70, rounding the cost of the silk to $10 and multiplying
by 2, rounding the cost of the cotton to $4 and multiplying by 5, and
rounding the cost of the elastic to $3 and the amount needed to 10 metres,
and taking the sum of these.
Acceptable method but 1 error made, including: a rounding error, ** or a calculation error.

2 marks
or
 
 
1 mark

 e)

**Satisfactory estimate given based on an acceptable method of
estimation. (The exact calculation is 106.67 rounded to 107 tickets).
E.g., estimate of 100, rounding the costs for the show to $500 and
rounding the ticket price to $5 and dividing these.
Acceptable method but 1 error made, including: a rounding error, ** or a calculation error.
 

NOTE:

*Final estimates will vary due to variations in estimation methods used. You should be looking for a logical and sensible method of estimation. No marks to be awarded for exact calculations.

**A rounding error could include instances when a student has rounded up or down inappropriately, e.g., rounding $9.95 to $9.00 rather than $10.00 or rounding 12 to 20 rather than 10.