Published over 1 year ago by Ann Baker

This DOES IT MATTER tackles some very **common misconceptions** about fractions and common error patterns that often go unnoticed. Many of the fraction misconceptions arise because students are often presented with mundane 'shade the fraction' activities in which the fractions are already drawn.

Download your copy here if needed: Does It Matter-Fractions1

Presenting 'already drawn' fraction practice masks students' lack of fundamental understandings, as this DOES IT MATTER may reveal when you share it with your students.

**These misunderstandings include**:

- Not understanding that fractions are about equal parts, 3 of the examples given here have one part of four parts shaded but the parts are not all equal.
- 3 of the examples accurately show quarters but not in the same shape or orientation that they are usually presented
- The middle example, top row, has a quarter shaded but only 3 pieces (a half and 2 quarters) are drawn so some students will say that a quarter has not been shaded, or they might say a third has been shaded. Some students will visualize the horizontal line extended and 'see' the quarters.
- The bottom left rectangle has 2 eighths shaded, some students may have understanding of equivalence, some may visually join the 2 shaded shapes and 'see' that it is the same as a quarter and some will say it is not a quarter.

We suggest that you have copies of this slide available for the students, so that, after discussion (and we hope some debate) they can test, prove or disprove their assertions.

Allow time for think, pair, share prior to students being given the opportunity to cut up the pieces.

Explain to the students that their job is to take turns to state their thinking, one shape at a time. They should listen to their partner and say

- “I agree because..."
- “I disagree because...... and that this process should be like a game of tennis, bouncing the 'ball' back and forth.

They can then share with another partner before cutting up the shape to match the points made in the discussion.

**Reflection**

Stimulate further discussion by asking the students the following questions:

- “How did this activity challenge your thinking about quarters?”
- “Why do you think some real quarters and some not real quarters were included?”
- “Which of the examples was the trickiest for you? Why was that do you think?”
- “What are some of the things we now know we need to consider when we interpret fraction diagrams?”
- “Are there any questions, struggles or successes that we can all share and learn from, from today's activity?”

**Follow Up**

Use the next Does it Matter silde to explore how you shade 3/8.

Ideally you'd do this on another day, paying attention to which of the 'misconceptions' that were uncovered during the earlier 'Does it Matter how you shade a quarter' activity. Each of the potential pitfalls are illustrated here too, and you'll discover if the misconceptions have been successfully cleared up.

Download a copy for your use here: Does It Matter-Fractions2

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