The whole comes first. A fraction only makes sense when you know what one whole represents.
Represent a fraction as equal parts, a number on a line and a division.
Three quarters of a small bottle and three quarters of a large bottle describe the same proportion, but different volumes. When comparing amounts, keep the whole and its units consistent. A diagram must show equal-sized parts, not just the right number of regions.
Predict a result, change a value, and use the diagram to explain your reasoning.
Predict before changing a value. Every whole in a bar diagram uses the same size. The models use non-negative amounts up to two wholes per input.
In 3/5, one whole contains five equal fifths and you count three of them. The numerator counts; the denominator names the unit. More parts in the whole means each part is smaller. Five fifths make one whole.
The number 3/4 is the point three quarter-steps from zero. It is also 3 ÷ 4: sharing three identical whole items equally among four people gives each person three quarters of one item. A fraction can be zero, equal to one or greater than one.
If 3 of 12 counters are blue, the fraction blue is 3/12 = 1/4. The denominator counts all counters, not only the counters of the other colour. To find 3/4 of 12 counters, split 12 into four equal groups and take three groups: 9 counters.
Work out the next step before opening the explanation.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Count the pieces used and the equal pieces in one original ribbon.
3/8
The numerator is 3 pieces; 8 pieces make the original whole.
The whole set is all 24 students. Simplify the fraction.
6/24 = 1/4
Six of 24 students is one of four equal-sized groups.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
This round saves on this device. It is practice, not a school mark.
A bottle marked 3/4 full tells you a proportion. Its capacity tells you the actual volume. Both pieces of information matter.