Lengths, scale and coordinates

Recognise the model, justify the rule and solve independently.

Choose an origin and a positive direction on a number line, and explain why the distance between $a$ and $b$ is $|a-b|$.

Use $c^2=a^2+b^2$ only in a right-angled triangle, after identifying the hypotenuse as the side opposite the right angle.

Write the correspondence between two similar triangles before forming equal ratios of corresponding sides.

Explain why $n$ overlapping objects in a row have $n-1$ joins, and use this to find the total length.