Mathematics

Grade 6: Patterning and Algebra	Planning: Term # Tracking: Ach. Level
Overall Expectations	1	2	3	4
• describe and represent relationships in growing and shrinking patterns (where the terms are whole numbers), and investigate repeating patterns involving rotations;
• use variables in simple algebraic expressions and equations to describe relationships.
Specific Expectations
Patterns and Relationships
– identify geometric patterns, through investigation using concrete materials or drawings, and represent them numerically;
– make tables of values, for growing patterns given pattern rules, in words (e.g., start with 3, then double each term and add 1 to get the next term), then list the ordered pairs (with the first coordinate representing the term number and the second coordinate representing the term) and plot the points in the first quadrant, using a variety of tools (e.g., graph paper, calculators, dynamic statistical software);
– determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph (Sample problem: For the pattern rule “start with 1 and add 3 to each term to get the next term”, use graphing to find the term number when the term is 19.);
– describe pattern rules (in words) that generate patterns by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term (e.g., for 1, 3, 5, 7, 9, …, the pattern rule is “start with 1 and add 2 to each term to get the next term”), then distinguish such pattern rules from pattern rules, given in words, that describe the general term by referring to the term number (e.g., for 2, 4, 6, 8, …, the pattern rule for the general term is “double the term number”);
– determine a term, given its term number, by extending growing and shrinking patterns that are generated by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term (Sample problem: For the pattern 5000, 4750, 4500, 4250, 4000, 3750, …, find the 15th term. Explain your reasoning.);
– extend and create repeating patterns that result from rotations, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, geoboards, dot paper).
Variables, Expressions and Equations
– demonstrate an understanding of different ways in which variables are used (e.g., variable as an unknown quantity; variable as a changing quantity);
– identify, through investigation, the quantities in an equation that vary and those that remain constant (e.g., in the formula for the area of a triangle, A = (b x h)/2 , the number 2 is a constant, whereas b and h can vary and may change the value of A);
– solve problems that use two or three symbols or letters as variables to represent different unknown quantities (Sample problem: If n + l = 15 and n + l + s = 19, what value does the s represent?);
– determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: Use the method of your choice to determine the value of the variable in the equation 2 x n + 3 = 11. Is there more than one possible solution? Explain your reasoning.).
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Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.