The units and parts method

• “in the ratio 3 : 4”

  A ratio, so nothing has a value yet. Draw 3 units and 4 units rather than writing numbers you do not have.

• “$\frac{2}{3}$ of the buttons”

  The denominator picks the unit count. Thirds means three units, and one of them is the thing worth finding.

• “4 times as many stickers as”

  The smaller amount is 1 unit and the bigger one is 4 of the same units. Count the units, then find one.

• “each of them used 160”

  One value pinned to two different unit counts. This is the line that sizes a unit, and it is usually near the end.

• “How many buttons were there in the jar at first”

  You will scale back up to a whole at the end, so keep track of how many units the whole is worth.

Unit

One equal piece of a bar, worth the same everywhere it is drawn.

1 unit

The line that pins a piece to a real number. Every answer comes from it.

Parts

A second, different-sized piece, so it is never added to the units.

Scale up

Multiply 1 unit by the number of units the question asks about.

All of these still draw as bars. What changes is what the units are counting, and that decision comes before any arithmetic.

• The bar model →

  Does the question already give real amounts? Then write the numbers straight into the bars. Counting units is for when nothing has a value yet.

• Constant total and constant difference →

  Does a ratio change partway through? Then the question is which thing stayed fixed, and that picks the method before you draw anything.

• Branching →

  Does a second fraction apply to what is left over rather than the whole? Then split the remainder first and count units afterwards.

• Units and parts, the before-and-after version →

  Some tuition notes use "units" for a ratio before a change and "parts" for the same ratio after it, for the same reason we do here. If your child's worksheet does that, that page is the one you want.

Real questions from the years it is taught. Try one together, then tap to check.