Fractions

Representations

Prior Knowledge

Misconceptions

Links to other areas

Rules and Applications

Language

Learning Outcomes # #

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

Two different schemes # #

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 #