Making sense of fractions

Transcription

1 6 Making sense of fractions 6 Making sense of fractions This session is designed to enable learners to: address common misconceptions about dividing shapes into fractions (for example quarters are not created by simply dividing a shape into four parts they must be equal parts); identify fractions of a given shape. and reflect on and discuss these processes. Biscuits, or lump of plasticine or dough. For each pair or small group of learners, you will need: Card set A Fraction dominoes; Card set B True or false?; And possibly: Card set C Shapes for cutting up; scissors; large sheet of paper for making a poster; glue stick; tracing paper; squared paper.

2 Show the group an object that does not easily divide exactly into two equal pieces, for example a biscuit or lump of plasticine. Ask for a volunteer to break it into halves. Ask the group whether they agree that the object has been cut/broken into halves. Discuss their reasons. Repeat the activity for thirds and quarters. Discussion should focus on how many pieces each fraction produces and that each piece should be the same size. Ask learners to work in pairs. Give each pair a copy of Card set A Fraction dominoes (two pages). Note that each domino is made up of one part-shaded shape (on the left) and one fraction (on the right). Ask learners to arrange the dominoes in a chain so that each part-shaded shape is next to the fraction it represents. If learners finish early, they could make and add some dominoes of their own, using the blanks. Next, give each pair of learners Card set B True or false? (two pages). Explain to learners that they have to choose a few cards and, for each of these, decide whether it is true or false and justify their decision. Explain that some cards are more difficult than others so if, having considered a card, they are not sure of the answer, they can put it back and try another one. They can justify their True or false? decisions orally or in writing or, in some cases, by cutting up a card. It may be helpful to have some tracing paper and there are spare copies of the diagrams on Card set C for cutting up. Learners could stick their chosen cards on a large sheet of paper and write their justifications, to make a poster. Learners can attempt as many cards as they wish.

3 Answers and justifications can be discussed in the whole group, with learners commenting on other learners justifications. In discussion, learners may realise that two fractions are equivalent. This would create an opportunity to use the shapes to consider equivalent fractions if it seems appropriate. Give learners some squared paper and ask them to draw some 5 5 squares. Ask them to shade squares to show 3 (or any other fraction) shaded in as many different ways 5 as they can. The activity can be repeated using other sizes of square, or rectangles. A True Fraction of a number. 6 8 and 3 are equivalent. B True Fraction of an area. Folding or cutting quickly reveals that the square contains two equal triangles. C True Fraction of an area. One out of four equal shapes is shaded D True Fraction of an area. Dividing the larger isosceles triangle into two right-angled triangles shows that four out of eight triangles are shaded. E False Fraction of an area. The shape is divided into four pieces but these are not equal. In fact, 1 of the area of the rectangle is shaded. 8 F True Fraction of an area. If we subdivide each small square into two, we can see that eight out of twelve are shaded: G False Fraction of an area. By subdividing the large square into 20 small squares we can see that 12 are shaded, so the area shaded is 3 5. H False Fraction as a comparison of areas. The small shape is only 2 of the area of the large shape. 3

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5 Card set A Fraction dominoes {page 1 of 2)

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7 Card set A Fraction dominoes (page 2 of 2)

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9 Card set B True or false? (page 1 of 2) A 3 of the faces are smiling. B The small shape is 1 of the larger one. 2 C 1 of the shape is shaded. D 1 2 of the square is shaded.

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11 Card set B True or false? (page 2 of 2) E 1 of the square has been shaded. F 2 3 of the shape has been shaded. G 1 2 of the shape has been shaded. H The small shape is 3 of the large one.

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13 Card set C Shapes for cutting up