Using Variables to Write Pattern Rules Goal Use numbers and variables to represent mathematical relationships. 1. a) What stays the same and what changes in the pattern below? b) Describe the pattern rule in words. At-Home Help A variable is a letter or symbol, such as a, b, or x, that represents a number. An algebraic expression is a combination of one or more variables; it may include numbers and operation signs. For example, 2 d 5 is an algebraic expression that could represent two times the figure number plus five. c) Write an algebraic expression that describes the pattern. 2. a) Fill out the table of values for the pattern of circles. Term number 1 2 3 4 5 Term value b) Describe how the number of circles (or term value) is related to the figure number (or term number). c) Write an algebraic expression for the number of circles. 3. Omar says this pattern can be described by the expression 2 (n 1). Tynessa says the pattern can be described by the expression 3 n. a) Explain Omar s reasoning. 80 Variables, Expressions, and Equations Copyright 2017 by Nelson Education Ltd.
b) Explain Tynessa s reasoning. 4. a) Write an algebraic expression for the number of squares you would need to build the figures in this pattern. b) Write an algebraic expression for the number of triangles you would need to build the figures in this pattern. c) Write an algebraic expression for the number of circles you would need to build the figures in this pattern. 5. Look at the following pattern. a) Write an algebraic expression for the number of squares you would need to build the figures in this pattern. b) Write an algebraic expression for the number of triangles you would need to build the figures in this pattern. c) Add the two algebraic expressions together to form an expression for the total number of blocks you would need to build the figures in this pattern. 6. a) Fill out the table of values for the pattern below. Figure number 1 2 3 4 5 10 Number of white squares Number of shaded squares b) Write an algebraic expression for the number of shaded squares in each figure. c) Write an algebraic expression for the total number of squares in each figure. Copyright 2017 by Nelson Education Ltd. Variables, Expressions, and Equations 81
Test Yourself 1. a) Use words to describe the pattern rule for the total number of blocks in each figure below. 3. Each algebraic expression represents a pattern rule. Draw examples that show possible figures for the first three terms of each pattern. a) x 5 b) Write an algebraic expression to describe the pattern rule. b) 2z 2. Use each description to create an algebraic expression for the pattern rule. c) 4p 1 a) The number of blocks triples each time. b) The first figure has four blocks. The number of blocks increases by one each time. c) The first figure has two triangles and one circle. The number of triangles increases by one each time. The number of circles stays the same. d) 3v 2 4. Evaluate each expression for the given variable. a) a 4, where a 5 b) 7b, where b 2 c) 10 c, where c 8 d) 9d 1, where d 1 Copyright 2017 by Nelson Education Ltd. Variables, Expressions, and Equations 89
Study Planner Sunday Monday Tuesday Wednesday Thursday Friday Saturday Study Topic Checklist Factors and Exponents Ratio, Rate, and Percent Data Management Patterns and Relationships 2-D Measurement Addition and Subtraction of Integers 2-D Geometry Variables, Expressions, and Equations Fraction Operations 3-D Geometry Surface Area and Volume Probability Notes Goals Copyright 2017 by Nelson Education Ltd. Study Planner 151
REWARD CONTRACT When you complete a topic in your Nelson Math Workbook, colour in a circle. START My reward will be... Factors and Exponents Ratio, Rate, and Percent Data Management Patterns and Relationships 2-D Measurement Fraction Operations Variables, Expressions, and Equations 2-D Geometry Addition and Subtraction of Integers 3-D Geometry Surface Area and Volume Probability FINISH Name: Date: Parent/Guardian: iv Reward Contract Copyright 2017 by Nelson Education Ltd.