Missing numbers and rules
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Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
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.
Task administration:
This task can be completed with pen and paper or online (with SOME auto marking).
Level:
3
Curriculum info:
Keywords:
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 34 of the 4 patterns is at curriculum level 3 (Year 6)

Correctly completes and identifies the correct sequential rule for 23 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]:

moderate moderate 
b) 
35, 47, 59, 71, 83, 99 and
explanation or rule:

moderate
moderate

c) 
136, 130, 124, 118, 112, 106, 100 and explanation or rule:

moderate moderate 
d) 
84, 76, 68, 60, 52, 44, and explanation or rule:
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 768, 124118, 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 "restart" 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 rewrote 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.
See the Algebraic patterns concept map for further information about patterns and rules.