Knitting needles

Knitting needles

Auto-markingPencil and paperOnline interactive
Overview
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Connecting to the Curriculum
Marking Student Responses
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Further Resources
This task is about continuing number patterns and finding a rule.
illustration: wool and needles for knitting
The conversion chart below shows the diameters of various size knitting needles and the numbers of the needles in 2 different systems, English and United States. Unfortunately, baby Sarah scribbled over the table, and some of the figures can't be read.
table showing some numbers scribbled over

Question 1Change answer

a)  Fill in the table below to complete the 6 missing entries.
Diameter in mm 2.0 2.4 3.6 4.0
English number 13 12 9 8
U.S. number 0 1 2 5

Question 1Change answer

b) What is the diameter of a U.S. number 7 needle?  mm

Question 2Change answer

c)  What is the English number of a needle with diameter 5.6 mm?

Question 3Change answer

d)  Complete the following statement to show the rule for converting from the English number to the U.S. number.
The rule is:  – English number = U.S. number
Task administration: 
This task is completed with pencil and paper or online with auto-marking.
Copyright: 
Image: George Hodan | Public domain pictures | Public domain
Level:
4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
number patterns, functional rules, linear equations
Description of task: 
Students identify and write in missing entries from a conversion table, answer questions interpreting the table, and state the rule for conversion.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y8 (11/2004)

a)
Diameter in mm 2.0 2.4 2.8 3.2 3.6 4.0
English number 13 12 11 10 9 8
U.S. number 0 1 2 3 4 5

easy
(for all 6 entries correct)

b)

4.8

easy

c)

4

moderate

d)

13

difficult

Results are based on a trial set of 225 students.

Next steps: 
Extension
Find a rule to convert from U.S. number to diameter in mm. You may wish to start like this:

"Multiply the U.S. number by __________ and then __________."

 
Extension answer
The rule as suggested is "Multiply the U.S. number by 0.4, and then add 2" [0.4x + 2].
Another variant would be "Divide the U.S. number by 5, add 1, and then multiply by 2" [2(x/5 + 1)].