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Mathematics

Grade 8: Patterning and Algebra

Planning: Term #

Tracking: Ach. Level

Overall Expectations

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• represent linear growing patterns (where the terms are whole numbers) using graphs, algebraic expressions, and equations;

 

 

 

 

• model linear relationships graphically and algebraically, and solve and verify algebraic equations, using a variety of strategies, including inspection, guess and check, and using a “balance” model.

 

 

 

 

Specific Expectations

 

 

 

 

Patterns and Relationships

 

 

 

 

– represent, through investigation with concrete materials, the general term of a linear pattern, using one or more algebraic expressions (e.g., “Using toothpicks, I noticed that 1 square needs 4 toothpicks, 2 connected squares need 7 toothpicks, and 3 connected squares need 10 toothpicks. I think that for n connected squares I will need 4 + 3(n – 1) toothpicks, because the number of toothpicks keeps going up by 3 and I started with 4 toothpicks. Or, if I think of starting with 1 toothpick and adding 3 toothpicks at a time, the pattern can be represented as 1 + 3n.”);

 

 

 

 

– represent linear patterns graphically (i.e., make a table of values that shows the term number and the term, and plot the coordinates on a graph), using a variety of tools (e.g., graph paper, calculators, dynamic statistical software);

 

 

 

 

– determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation (Sample problem: Given the graph that represents the pattern 1, 3, 5, 7,…, find the 10th term. Given the algebraic equation that represents the pattern, t = 2n – 1, find the 100th term.).

 

 

 

 

Variables, Expressions and Equations

 

 

 

 

– describe different ways in which algebra can be used in real-life situations (e.g., the value of $5 bills and toonies placed in a envelope for fund raising can be represented by the equation v = 5f + 2t);

 

 

 

 

– model linear relationships using tables of values, graphs, and equations (e.g., the sequence 2, 3, 4, 5, 6,… can be represented by the equation t = n + 1, where n represents the term number and t represents the term), through investigation using a variety of tools (e.g., algebra tiles, pattern blocks, connecting cubes, base ten materials) (Sample problem: Leah put $350 in a bank certificate that pays 4% simple interest each year. Make a table of values to show how much the bank certificate is worth after five years, using base ten materials to help you. Represent the relationship using an equation.);

 

 

 

 

– translate statements describing mathematical relationships into algebraic expressions and equations (e.g., for a collection of triangles, the total number of sides is equal to three times the number of triangles or s = 3n);

 

 

 

 

– evaluate algebraic expressions with up to three terms, by substituting fractions, decimals, and integers for the variables (e.g., evaluate 3x + 4y = 2z, where x = 1/2, y = 0.6, and z = –1);

 

 

 

 

– make connections between solving equations and determining the term number in a pattern, using the general term (e.g., for the pattern with the general term 2n + 1, solving the equation 2n + 1 = 17 tells you the term number when the term is 17);

 

 

 

 

– solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a “balance” model (Sample problem: What is the value of the variable in the equation 30x – 5 = 10?).15 by using guess and check. First I tried 6 for x. Since I knew that 6 plus 7 equals 13 and 13, is less than 15, then I knew that x must be greater than 6.”).

 

 

 

 

Student Name:

 

 

 

 

 Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.