Fabric measures

Fabric measures

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out costs of materials involving decimals.

Do NOT use a calculator for this question. You must show your working in the boxes below.
 
Heta, Jason, and Aroha are buying fabric to decorate their flat.
 
a)
Heta is buying some fabric for a tablecloth.
If the fabric costs $3.20 per metre, show how to work out how much 2.1 metres of fabric will cost him.
 

Show how you worked this out.

 

 

Total cost = $__________
 
b)
 
Aroha is buying 3.4 metres of curtain cloth at a cost of $5.70 per metre.
Show how to work out how much this will cost her.
 

Show how you worked this out.

 

 

Total cost = $__________
 
c)
 
Jason is buying some cloth for a wall hanging. It costs $6.45 to buy 1.5 metres of green cloth. 
Show how much it costs for 1 metre of this cloth.
 

Show how you worked this out.

 

 

Total cost = $__________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
decimals, multiplication, division
Description of task: 
Students perform decimal multiplication and division involving the cost of material, without the use of a calculator.
Curriculum Links: 
Key competencies
This resource involves recording the strategies students use to solve decimal multiplication and division problems. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y10 (03/2004)
a) 6.72 with full working, e.g., any 1 of:

  • vertical algorithm with intermediate working shown;
  • separately breaks down the product using "place value partitioning",
    e.g., 3.2 × 2 + 0.1 × 3.2 = 6.4 + 0.32 or
    2.1 × 3 + 0.2 × 2.1 = 6.3 + 0.42 or
    2 × 3 + 2 × 0.2 + 0.1 × 3 + 0.1 × 0.2 = 6 + 0.4 + 0.3 + 0.02;
  • other reasonable working with the correct answer.

Reasonable working but small computational errors.

 moderate
 

 

 

moderate
b) 19.38 with full working, e.g., any 1 of:

  • vertical algorithm with intermediate working shown;
  • separately breaks down the product using place value partitioning,
    e.g., 5.7 × 3 + 0.4 × 5.7 = 17.10 + 2.28 or
    3.4 × 5 + 0.7 × 3.4 = 17.00 + 2.38 or
    3 × 5 + 3 × 0.7 + 0.4 × 5 + 0.4 × 0.7 = 15 + 2.1 + 2 + 0.28;
  • other reasonable working with the correct answer.

Reasonable working but small computational errors.

 difficult
 

 

 

moderate
c) 4.30 with full working, e.g., any 1 of:  

  • division algorithm with intermediate working shown; sees 1.5 as 3/2 so (6.45 ÷ 3) × 2 or (6.45 × 2) ÷ 3 or subtracts ;
  • 1/3
  • other reasonable working with the correct answer.

Reasonable working but small computational errors.

 difficult

 

 

difficult
Results based on a trial of 169 students at Year 10 in March 2004 

NOTES:

  • Accept 6.70 in a) and 19.35 or 19.40 in b) if the exact answer is given in the working.
  • Do not accept working such as 5.70 × 3 = 17.10, 17.10 + 2.28 = 19.38 unless they show where the 2.28 is derived from.
  • Do not give marks to the vertical or division algorithm, or to equations such as 3.2 × 2.1 = 6.72, if no intermediate working is shown (unless the student can subsequently describe their method).
Diagnostic and formative information: 

 

Common error

 Likely calculation Likely misconception
a)
b)		 672, 67.2, etc.
1938, 193.8, etc.		   Ignores or displaces decimal point.
a)
b)		 9.6, 10.5, etc.
39.90, 40.80, etc.
e.g.

 

   3.2
×2.1
  3.2
  6.4
  9.6
Does not displace second subtotal in multiplication.
a)

b)

 6.3
6.4
17
17.1		 2.1 × 3
3.2 × 2
3.4 × 5
5.7 × 3		 Ignores the decimal point in one of the numbers.
c) 9.675 6.45 × 1.5 Multiplies instead of dividing.

Common Strategies

  • The two common strategies for a) and b) were either using vertical algorithms or using a place value partitioning strategy described in the scoring guide. About 25% of the students attempted to use vertical algorithms, and about 20% attempted place value partitioning. Most of the students using vertical algorithms obtained a correct answer, compared with fewer than half of the students using place value partitioning.
  • The most common strategy for part c) was to recognise that 1.5 equals , and then cut the $6.45 into thirds (about 25% of students did this, and most were successful). Only a few students tried the division using pencil-and-paper algorithm (about 5%). Very few other methods were attempted.
  • A number of students (around 10%) wrote down the relevant equation or algorithm to solve the problems, but showed no evidence of being able to do them without a calculator.

 

Links to the Numeracy project
  • Teaching Multiplication and Division (p.37, 2004).  Both are Ministry of Education publications.