Fractions and Parts of a Whole 1/2
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Fractions and Parts of a Whole 1/2
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Each pupil chooses two large sheets and three small sheets.
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Each pupil will have two sheets 15 x 15 cm and three sheets 10 x 10 cm.
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Folding instruction:Fold opposite sides with all sheets and open folds.
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Fold all sheets.
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Activity: As shown place a sheet of each size on your table.
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A discussion question: Is the area of the rectangles formed by folding the sheets half the area of each unfolded sheet? Is this true for each size of a sheet? Explain.
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Answer: With each sheet size the area of the folded rectangle is half the area of the unfolded sheet which has the shape of a square.
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When we say a half it must always be related to the whole which we are using.
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Folding instructions: Fold onto each other the shorter sides of one folded sheet of each size.
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Folding instructions: Open out the two folded sheets to a square shape and mark the folding lines of both sheets with your measuring tool.
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A discussion question: What is the area size of each square that has been marked with lines?
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In each case there are four squares and are congruent. Each marked square is one quarter of the larger square.
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Answer: In each sheet the red square has an area size of one quarter of the larger square. In each sheet there are 4 squares of equal area.
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Answer: Each quarter of the square sheets is written with the fraction
. In every square sheet there are 4 equal area quarters..
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Folding instruction: Fold two small square sheets and one large square sheet on the lines of symmetry as shown.
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A discussion question: Mark on all the sheets the lines of folding using your measuring tool. What is the area size of each rectangle that has been marked with lines? Explain.
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This fold demonstrates congruent rectangular shapes each one a quarter size of the original square sheet. In further lessons we will relate to equal areas but with non congruent shapes.
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Answer 1: Each quarter of the square sheets is written with the fraction
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Answer 2: Each quarter is colored red.
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A discussion question: What is the area size of each marked shape as a part of the square? What unit fraction is used to show the size of the red shape part in each square? Explain.
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The two red shapes are different shapes but each represents a quarter of the square that includes the shape. The two shapes are not of equal area size.
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Answer: Each quarter of the square sheets is written with the fraction
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A discussion question: Do both marked red quadrilaterals have the same area size? Explain.
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Answer: Each quadrilateral represents a quarter of two different squares not having the same area size. The two quarters have different area sizes.
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Folding instruction:Fold the two small square sheets and one large square sheet on opposite parallel sides as shown.
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The pupils must fold the correct sheets.
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A discussion question:Mark on all the sheets the lines of folding using your measuring tool. What is the area size of each rectangle that has been marked with lines? Explain.
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Answer 1: In each square shape there are 8 eighths of equal area size. We can represent this area size with the unit fraction
.
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Answer 2: Each eighth in each sheet is colored red.
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Folding instruction: Using the remaining sheets (one large and one small) fold each vertex to the center of lines of symmetry and open the folds.
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A discussion question:Mark on all the sheets the lines of folding using your measuring tool. What is the area size of each triangle that has been marked with lines? Explain.
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Answer 1: In each square shape there are 8 eighths of equal area size. We can represent this area size with the unit fraction
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Answer 2:Each eighth in each sheet is colored red.
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A discussion question: Do both marked red polygons have the same area size? Explain.
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Answer:Each polygon represents an eighth of two different squares not having the same area size. The two eighths have different area sizes.
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A discussion question: On the sheet 2 triangles are colored blue. What is the area size together of the 2 blue triangles? What is the area size together of the 4 triangles (2 red and 2 blue).
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Answer: The area size together of the two red triangles is
of the area size of the square.
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Final activity: Write your name on the five square sheets and save them for the next lesson.
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The named sheets should be carefully saved for the next lesson.
- Lesson Aims
- Recognizing unit fractions using the area model for parts of a whole.
- Recognizing the form of a unit fraction representing the numerator and denominator.
- Recognizing the concept part of a whole.
- Investigating parts of a whole in relation to squares of different area sizes.
- Lesson Content.
In this lesson 1/2 representing a unit fraction as one part of a whole using squares of different area sizes.
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- Materials
Origami sheets of 2 sizes: 10 x 10 cm, 15 x 15 cm.
