Fractions
Representations
Prior Knowledge
Misconceptions
Links to other areas
Rules and Applications
Language
Simplifying
Numerator
Denominator
Equivalence
Mixed Numbers
LCM and HCF
a/b is 'a over b'
Number of parts the whole is divided into
Whole number and fraction
Partitioning
Correspondence
Part-part
Part-whole
Dealing with one quantity
Dealing with two quantities
Visual approach
Bar model
Number line to compare size
Addition
Multiplication
Unit bar
Common denominator
Irreducible
Fractions in their lowest form - no common factors
Conceptual Understanding
Understanding how fractions relate to division
Comparing and ordering fractions
with common denominators
with different denominators
Addition #
Subtraction #
Division #
Equivalent fractions
Multiplication
1) Find common denominator
2) Add tops, keep bottoms the same
Stick, Swap, Flip
2) Subtract tops, keep bottoms the same
Multiply the tops and the bottoms
Multiply/divide top and bottom of fraction by the same number
Multiplicative Factor
Algebra
Decimals
Percentages
Measurements
Ratio and Proportion
Other Subjects
Science
Business Studies
Economics
Integers 'x=x/x'
Confusion with mixed numbers
Larger denominator means larger/smaller fractions
Contextual division - must have whole number and remainder as answer
When adding, add tops then bottoms
Needs understanding of need for common denominator
Use 1/2+1/2=2/4 to demonstrate error
2 and 1/3 is the same as 2/3?
When multiplying - may treat whole and fraction separately #
Numerator and denominator treated separately
When adding fractions equalling more than 1, the denominator becomes the total number of pieces?
When adding/subtracting fractions, convert to improper fractions, jumping to same denominator
Flipping the wrong fraction for division
Multiplying - might check denominator is the same
Equivalence/simplifying - look for number pattern rather than multiplicative factor/ratio
When finding common denominator, leaving the numerator unchanged #
When ordering, sorting by either numerator or denominator
Dividing visual shapes into unequal parts
Half/double
Hidden operators
Idea of sharing
Negative Numbers
Comparing size and value
The Four Operations
Addition
Subtraction
Multiplication
Division
With whole numbers #