Missing numbers and rules

Missing numbers and rules

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Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
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Further Resources
This task is about identifying missing numbers and the rule for a growing number pattern.

For each set of numbers

1) write the three missing numbers,

2) write the rule for the number pattern.

Question 1Change answer

Write the 3 missing numbers in this pattern:  9,  15,  21, ,

Write the rule for the pattern 

Question 1Change answer

Write the 3 missing numbers in this pattern: 35, 47, , 71, ,

Write the rule for the pattern 

Question 1Change answer

Write the 3 missing numbers in this pattern: , 130, 124, 118, , , 100

Write the rule for the pattern 

Question 1Change answer

Write the 3 missing numbers in this pattern:  84, 76, 68, 

Write the rule for the pattern 

Task administration: 
This task can be completed with pen and paper or online (with SOME auto marking).
Level:
3
Description of task: 
Students identify missing numbers and the rule for a growing number pattern.
Curriculum Links: 
Links to National Standards (Patterns and relationships Level 3)
This resource can be used to provide one source of evidence of students' understanding of equations for linear relationships (Year 8) or representing relationships (Year 7) for Number and Algebra.
  • Correctly completes the 4 patterns and identifies a generalised functional algebraic expression for the patterns (e.g., written as linear equation) above curriculum level 3 
  • Correctly completes and identifies the correct sequential rule for 3-4 of the 4 patterns is at curriculum level 3 (Year 6) 
  • Correctly completes and identifies the correct sequential rule for 2-3 of the 4 patterns is early curriculum level 3 (Year 5) 
  • Correctly completes and identifies the correct sequential rule for 1 of the 4 patterns is below curriculum level 3 (< Year 5) 
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: 
    Y6 (10/2013)
a) 9, 15, 21, 27, 33, 39 and 
explanation or rule [moderate]:

  • plus 6
  • adding six each time
  • counting up in six/skip counting by 6s
moderate
moderate
 
b)
35, 47, 59, 71, 83, 99 and 
explanation or rule:
  • plus 12
  • adding 12 each time
  • counting up in 12/skip counting by 12s
moderate
moderate
c) 136, 130, 124, 118, 112, 106, 100 and
explanation or rule:

  • subtract/minus/takeaway 6
  • taking away 6 each time
  • counting back in 6s/skip counting backward by 6s

moderate
moderate
 
d) 84, 76, 68, 60, 52, 44, and
explanation or rule:

  • subtract/minus/takeaway 8
  • taking away 8 each time
  • counting back in 8s/skip counting backward by 8s
Note: Question d) was more difficult recombine because it involved recombining and compensation to subtract the 8 multiple times - this leaves more room for simplesubtraction errors and may make it harder to recognise the pattern (and therefore rule).
difficult
difficult
Diagnostic and formative information: 
  Common error Likely misconception
a)-d) 6,12,6,8 Doesn't indicate whether the rule is involves adding or subtracting the number. 
 
a)
 
b) 
examples:
12, 18, 24
59, 71 63, 75
68, 75, 83, 91*
Starts the pattern again/ignores the current pattern
Students work out the rule for the pattern but then apply the rule starting from a new starting point 
 
*Error also involes taking the pattern in the wrong direction (adds instead of subtracts)
a)-d)
 
Addition/subtraction error (recombination)
There were a range of addition/subtraction errors made by students. These questions about patterns do require students to add/subtract a number of times.
Next steps: 
For students who did not specific the whether the rule is involves adding or subtracting the number. In most cases this is simply an omission and can be recitifed by asking the student whether it the pattern involves adding or subtracting.
 
For students who made addition or subtraction error they could ensure that their basic facts are sufficiently developed to aid them work out problems like 76-8, 124-118, etc. Once students are confident with single operations they could explore adding and subtracting with multiple numbers, e,g., resources Adding sweets (L2) and Saving for a pet involve adding multiple numbers. In addition, students could explore applying a rule on a range of numbers: Machine rules (L2) and Number machines II (L3).
 
Students who "re-start" the pattern need to check back on their work and explain how the whole pattern goes and expaplin how the rule works for this whole pattern not just a bit of it. This understanding that the general rule should be consistent for the whole pattern is a key understanding in all exercises about patterns and rules. 
 
Some students also wrote the re-wrote pattern instead of the rule. These students may need to explore creating their own simple patterns (with a rule) and using rules (Machine rules (L2)) to help them differentiate between the pattern and the rule, and before they can start to find the general rule in a pattern.