Relating Shape, Area, and Perimeter

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Relating Linear Dimensions Relating Shape, Area, and Area and Perimeter

Goal Relate the area of a rectangle to its length and width. Goal Investigate how changes in shape affect area and perimeter.

1. What is the area of each rectangle? 1. At-Home Help At-Home Help 4 cm Area is measured by finding out Shapes can have the same area a) a) area: 2 cm how many square units are but different perimeters. needed to cover the surface. The area of a rectangle is related perimeter: b) to its side lengths. 5 cm 3 cm 4 cm 4 cm b) area: 3 cm 5 cm area ϭ 4 cm ϫ 5 cm ϭ 20 square centimetres c) perimeter ϭ 4 cm ϩ 5 cm ϩ area ϭ 3 cm ϫ 5 cm perimeter: 4 cm ϩ 5 cm 4 cm ϭ 15 square centimetres ϭ 18 cm

5 cm 2 cm The shapes have the same . 10 cm 2. Complete the table. area ϭ 10 cm ϫ 2 cm Rectangle Width Length Area 2. ϭ 20 square centimetres area: A 3 cm 2 cm a) perimeter ϭ 10 cm ϩ 2 cm ϩ 10 cm ϩ 2 cm B 7 cm 14 square centimetres ϭ 24 cm C 4 cm 6 cm Shapes can also have the same perimeter: perimeter but different areas. D 7 cm 49 square centimetres

3. What is the length of the other side? b) area: a) b) perimeter:

8 cm 10 cm area ϭ 32 square centimetres The shapes have the same . area ϭ 20 square centimetres

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Solve Problems Using Test Yourself Page 1 Organized Lists

Goal Use an organized list to solve area problems. Circle the correct answer. 1. You want to estimate the area of the top surface of a desk. 1. How many different rectangles could you At-Home Help Which item would you use? make with an area of 24 square tiles? An organized list allows you to A. a piece of string C. an envelope What are they? record information in a clear and organized way. B. a measuring cup D. a balance scale Vanessa has 35 cents. She has 2. What is the area of this shape to 2 of these 3 types of coins— the nearest whole square centimetre? quarters, dimes, and nickels. How many combinations of coins E. 18 square centimetres might she have? F. 20 square centimetres 2. Sara chooses 3 numbers for the combination 25 10 5 of her new bike lock. She uses 1, 4, and 7. 110 G. 14 square centimetres She can use each number only once. 102 H. 16 square centimetres What are the possible combinations? 031 023 015 There are 5 possible combinations. 3. Which of the following would not be measured using square centimetres? A. a schoolyard C. a photograph B. a placemat D. a piece of note paper

4. Which measurement would be the most reasonable estimate 3. Ben goes to the grocery store for his mom. He spends less than $5. for the area of your kitchen floor? He buys at least one of each of the following items. E. between 1 square metre and 3 square metres • apples at 50¢ each • bread at $1.60 a loaf F. between 10 square metres and 20 square metres • crackers at $1.25 a package G. between 30 square metres and 40 square metres Find all the combinations of what he might have bought. H. between 40 square metres and 50 square metres

5. What is the area of this rectangle? A. 24 cm

B. 24 square centimetres 4 cm C. 10 cm

D. 20 square centimetres 6 cm

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Test Yourself Page 2 Exploring Multiplication

Circle the correct answer. Goal Solve multiplication problems using models.

6. What is the length of the other side? 3 cm 1. Circle the letter of the problem that can be At-Home Help E. 6 cm solved using multiplication. Multiplication involves groups of F. 15 cm I A. Rey read 22 pages on Monday, 29 pages the same size. G. 6 square centimetres area ϭ 18 square centimetres on Tuesday, and 27 pages on Thursday. 4 ϫ 28 is 4 groups of 28 objects. How many pages did he read altogether? 28 groups of 4 has the same H. 9 square centimetres product. B. Natalie read on Monday, Tuesday, and 7. Which of these measurements is the same for the 2 rectangles? Thursday. She read 31 pages each day. A. length How many pages did she read altogether? C. Paulette read 96 pages in total on Monday, Tuesday, and Thursday. B. width 3 cm How many pages did she read each day? C. perimeter D. Chantal read 37 pages on Monday. Vinh read 29 pages on Monday. 8 cm 7 cm D. area How many more pages did Chantal read than Vinh?

Explain how you know this problem can be solved using multiplication.

4 cm 8. Which is true for the shape shown? E. area ϭ 14 square centimetres perimeter ϭ 8 centimetres F. area ϭ 8 square centimetres 2. Solve the problem in Question 1 using multiplication. perimeter ϭ 14 centimetres G. area ϭ 8 centimetres perimeter ϭ 14 square centimetres H. area ϭ 8 square centimetres 3. Circle the letter that shows base ten blocks being used to model perimeter ϭ 8 centimetres multiplication. A. B. 9. How many different rectangles can be made using exactly 28 square tiles placed side by side? A. 4 B. 5 C. 3 D. 8 Explain how you know that the base ten blocks are being used to model multiplication. 10. Each of the digits 3, 5, and 6 is used only once to make a new number. How many different numbers can be made? E. 5 F. 3 G. 8 H. 6

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Patterns with Multiple Attributes

REWARD CONTRACT Describe, extend, and create patterns that Goal change in many ways. My reward will be �� When you complete a 1. a) Complete the pattern. At-Home Help topic in your Nelson Math Patterns made with shapes Workbook, colour in a ** ** can be b) Describe it. • described by the shapes and circle� colours and how they change •represented with a letter model For example, START c) Write a letter model for it.

A black square is followed by a Addition and Measuring Length and white triangle and then a white Patterns in Subtraction 2. a) Complete the pattern. Mathematics Data Time square. Then the shapes repeat. Numeration Management A – B – C – A – B – C – A – B – C b) Describe it. Multiplication and Division Facts Dividing Greater Multiplying Numbers Greater Numbers Area and Grids 2-D Geometry 3-D Geometry and 3-D Measurement c) Write a letter model for it.

Patterns and Fractions and 3. Write a letter model for the pattern. Motion in Decimals NIS Probability Geometry FI H

Name: Date: 4. Create a pattern with at least 2 shapes and 2 colours.

Parent/Guardian:

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