Comparing fractions becomes muddled when one drawing is a large rectangle and the other is a tiny circle. Before asking which fraction is larger, agree what counts as one whole. Two identical paper strips make that agreement visible without bringing food or unequal slices into the example.
Make two genuinely equal wholes
Cut two strips from the same sheet with matching length and width. Place one on top of the other to check them, then label each complete strip one whole. Ask the child what would change if you trimmed the end off just one strip.
The IES mathematics practice guide recommends using representations and clear mathematical language to develop understanding. The strip activity in this article is an original worked example of those general principles, not a published intervention or a test of attainment. [1]
Fold before naming the fraction
Fold the first strip into two equal parts and the second into four equal parts. Unfold both. Check the sections rather than accepting any two or four pieces as halves or quarters. Equal parts are essential to the meaning of these fraction names.
Shade one part of each strip. On the first, one of two equal parts is shaded: one half. On the second, one of four equal parts is shaded: one quarter. Line up the left edges and compare the shaded lengths. With these equal wholes, the half covers more of the strip.
Write 1/2 and 1/4 beside the drawings only after the child can identify the whole and its equal parts. Ask what the bottom number describes. Here it tells how many equal parts make one whole, rather than how many pieces are shaded.
Build an equivalent fraction
Shade a second quarter on the four-part strip. Now two quarters cover the same length as one half on the other strip. Record 2/4 = 1/2. Keep the strips aligned so that the equation describes something visible.
If the child says two must be more than one, point to what each count is counting. Two quarter-parts and one half-part can cover the same amount because the pieces have different sizes. You are comparing amounts of the same whole, not just the written top numbers.
Try three quarters next. The shaded amount now extends beyond the half but does not fill the whole. Ask the child to explain that position in words before introducing further fraction rules.
Deliberately change the whole
Draw a third strip that is twice as long as the original strips, with the same width. Divide it into four equal parts and shade one quarter. That quarter can match the shaded half of an original strip. The fraction names differ because the wholes differ.
This is not a contradiction of the earlier comparison. In the first comparison, the wholes were equal. In the second, they were not. Write a short note under the drawings identifying which whole each fraction belongs to.
Avoid turning this into a trick question. Let the child measure, overlap and explain. The useful discovery is that identifying the whole is part of the problem, rather than a detail the adult is entitled to hide.
Use the school’s representation next
Compare this paper work with the school’s model, which may use bars, shapes or a number line. Ask the child to locate one whole and show how it is divided. Keep the terminology consistent with the class wherever possible.
If the child can fold the strips but cannot explain the symbols, return to the model rather than add more written comparisons. If the folds themselves are frustrating, provide accurately divided strips so the discussion stays about fractions rather than fine-motor precision.
References
Sources for the cited guidance and reported material. Worked examples and practical tools are original to Zolls.
- Institute of Education Sciences. Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades.