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Shapes and perimeters

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CONTENTS

ITEM TYPE NUMBER
Working with shapes and perimeters Workout 32 slides
Shapes and perimeters Library 10 questions
Once you have registered, you can work through the slides one by one. The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account. blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.

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SAMPLE FROM THE WORKOUT

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SLIDE 1 - EXPLANATION

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SLIDE 2 - QUESTION 1

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.1]

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SOLUTION

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DEPENDENCIES

166: Sums
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168: Shapes and perimeters
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170: Measurement and areas

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CONCEPTS

ITEM
 LEV.
Perimeter, boundary 350.1
Perimeter of a square 350.1
Perimeters of shapes made from squares 350.2
Rectangle 350.4
Perimeters of rectangles 350.4
Length 350.6
Width 350.6
Length and width of a square are equal 350.6
Length and width of a rectangle 350.6
Statments of form ALL x are y 350.7
Heuristic: use of diagrams 350.8
Arrangement (implicit possibility of arrangement) 350.9
Circle 351.1
Division of a circle 351.1
Half 351.1
Quarter as half of a half 351.1
Rotation 351.3
Half turn about a centre 351.3
Quarter-turn about a centre 351.3
Rotational symmetry (implicit) 351.4
Rotational assymetry 351.4
Sequential visual reasoning (implicit) 351.5
Mirror image, reflection 352.0
Plane of reflection (implicit) 352.0
Line of reflection 352.0
Identity of shapes (implicit congruency) 352.3
Congruent shapes, congruency 352.4
Geometric puzzle - arrangements 352.6
Connected shape or arrangement 353.1

RAW CONTENT OF THE WORKOUT

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Areas and perimeters SLIDE 1 Each square has side 1 cm Perimeter is another word for the boundary or all the edges of any shape. The perimeter of this square is 4 cm. The perimeter of this shape is 10 cm, which you find by counting. SLIDE 2 Find the perimeters SLIDE 3 SLIDE 4 Find the perimeters SLIDE 5 SLIDE 4 B Find the perimeters SLIDE 5 B ? 18 in ? 26 in ? 32 in ? 18 in SLIDE 6 The following shape is a rectangle A square is a rectangle where the length and width are the same SLIDE 7 ? A rectangle has a length of 24 cm and a width of 8 cm. What is its perimeter? ? A square has side 9 cm. What is its perimeter? ? The width of a rectangle is 7 cm and the perimeter is 34 cm. What is the length of the rectangle? ? “All squares are rectangles, but not all rectangles are squares.” Is this statement true or false? SLIDE 8 ? In problems of this kind, it often helps to make a diagram. ? ? Subtract twice the width The length is half of this, so 10 cm ? “All squares are rectangles, but not all rectangles are squares.” This statement is true. A square is a special kind of rectangle. SLIDE 7 B ? A rectangle has a length of 24 in and a width of 8 in. What is its perimeter? ? A square has side 9 in. What is its perimeter? ? The width of a rectangle is 7 in and the perimeter is 34 in. What is the length of the rectangle? ? “All squares are rectangles, but not all rectangles are squares.” Is this statement true or false? SLIDE 8 B ? In problems of this kind, it often helps to make a diagram. ? ? Subtract twice the width The length is half of this, so 10 in ? “All squares are rectangles, but not all rectangles are squares.” This statement is true. A square is a special kind of rectangle. SLIDE 9 There are two different arrangements that can be made with three squares that touch and do not overlap. One of these is It has perimeter 8. Find the other arrangement and its perimeter. SLIDE 10 SLIDE 11 Divide this circle into two halves, and then into four quarters. SLIDE 12 SLIDE 13 SLIDE 14 Draw what happens when you rotate this circle through four successive quarter-turns about the centre. SLIDE 15 SLIDE 16 Draw what happens when you rotate this square through four successive quarter-turns about its centre. SLIDE 17 SLIDE 18 Make an L-shape out of three squares. Starting with an L–shape as shown in ? rotate the shape about the centre through one quarter turn of a circle. Shape ? is the result. TASK Rotate the shape again twice through one quarter of a circle and sketch the result. If needed, make the shape out of paper and find out what happens when you turn it about the centre. SLIDE 19 SLIDE 20 A lady once looked herself in a mirror. She saw her reflection. A reflection has a line of reflection. Draw what you get when the following shape is reflected in the line. SLIDE 21 SLIDE 22 Reflect all of these shapes in the dashed line (the line of reflection) SLIDE 23 Pair up each shape in the top row with a shape in the bottom row that is identical to it. SLIDE 24 The identical shapes are coloured in pairs. But we often say that all of these are the same shape. The top row are rotations of the blue shape, and the bottom row are reflections of the shapes in the top row. Any shape obtained by rotation or reflection is the same shape. These shapes are said to be congruent. Any shape that can be rotated, flipped and picked up so that it exactly matches another shape is congruent. SLIDE 25 There are five possible congruent shapes involving four squares. Find all five of them, and their perimeters. SLIDE 26 SLIDE 27 There are twelve possible congruent shapes of five squares. Find all of these and their perimeters. SLIDE 28 SLIDE 29 The first shape has exactly two blank squares. Make seven more shapes with exactly two blank squares. (There are more than seven altogether.) SLIDE 30 SLIDE 31 The first shape has a perimeter of 12. Make 15 more congruent and connected shapes on the grids with a perimeter of 12. Hint: the shapes can have more or less than two blank squares. SLIDE 32 SLIDE 22 A rotation of one quarter of a circle is a rotation through 90 degrees.