Fractions, ratios and percentages

Recognise the model, justify the rule and solve independently.

Name the whole that a fraction refers to, and notice when that whole changes.

Represent a ratio $a:b$ as $ak$ and $bk$ with one common unit $k$, and find $k$ from the given information.

Apply successive percentage changes by multiplying factors such as $1+p/100$, rather than adding the percentages.

Find a combined mean from the total sum and the total count, and explain why group means cannot simply be averaged when the groups differ in size.