Here is a constructed example of a lower-KS2 fraction difficulty: a child says 1/6 is bigger than 1/3 because 6 is bigger than 3. The denominator is the number below the line; it tells us how many equal parts make the whole.
Draw two equal-length bars. Divide one into three equal parts and the other into six. One third covers the same length as two sixths, so 1/3 is greater than 1/6. The comparison works because the two wholes are the same size. A useful explanation is: “More equal pieces in the same whole means each piece is smaller.”
Next, find 2/3 of 18: share 18 counters into three equal groups of 6, then take two groups, giving 12. Once that idea is secure, try 3/4 of 20: four equal groups of 5, then three groups, giving 15. Look for an explanation of the groups as well as the answer.
For an upper-KS2 connection, compare 3/4 of 20 with 75% of 20. Since 75% means 75/100, which is 3/4, both give 15. The useful step is explaining why the two forms represent the same amount.
Use school feedback to choose the next task
Suppose schoolwork shows correct whole-number addition but repeated fraction errors. The first question is whether the child understands what the denominator represents. These illustrative checks can make the tuition brief more precise.
Adding fractions in lower KS2. For 2/7 + 3/7, a child might add both numbers and write 5/14. Draw one strip divided into seven equal parts. Shade two parts, then three different parts: five of the seven parts are now shaded, so the answer is 5/7. The denominator, the bottom number, stays seven because the size of each part has not changed. Same-denominator addition within one whole is part of England’s Year 3 programme.
For a follow-up, try 6/7 − 2/7. Cross out two of six shaded sevenths to leave 4/7. A useful sign of understanding is explaining why the answer still counts sevenths, without copying the first calculation.
Revisiting decimals in upper KS2. A child may say 0.35 is larger than 0.4 because 35 is larger than 4. Write 0.4 as 0.40: forty hundredths is more than thirty-five hundredths, so 0.4 > 0.35. This consolidates decimal place value developed in Year 4; later work extends the range of numbers. The next step depends on whether the child can explain the comparison, not just select the correct symbol.
Agree which difficulty to address first. For example, ask for a new same-denominator fraction task after teaching and check that the child can explain why the denominator stays unchanged.