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Wrong number

$A group of shapes consisting of three stars and five squares. Question asking for the fraction of the group that are stars. Student answer is 3/5, which is incorrect.$

When working with fractions of collections, students using the double-count strategy can lose sight of the whole and interpret a part-whole situation as a ratio.

$A circle divided by vertical diameter. One half divided in half again. Question asking for fractions seen. Student answer is thirds, which is incorrect.$

Students who automatically use the double-count strategy can be easily fooled by tasks such as this. Even though they know there should be equal parts, they are too focussed on counting parts to visualise the missing dividing lines.

$Five fraction cards, from left to right 1/2, 1/3, 1/4, 1/6, 1/8. Question asking to order from smallest to largest. Student response incorrect.$

When a fraction is perceived as consisting of two whole numbers, it is easy to forget about the relative size of the parts and just focus on the size of the numbers.

$Question asking ‘Which fraction is larger 7/8 or 5/6? Explain’. Student answer incorrect, ‘They are the same because both have just one more to make a whole’.$

A sense of the relative size of fractions can be lacking in students who persist in seeing the numerator and denominator as separate counts.