Mathematics

Grade 5: Patterning and Algebra	Planning: Term # Tracking: Ach. Level
Overall Expectations	1	2	3	4
• determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations;
• demonstrate, through investigation, an understanding of the use of variables in equations.
Specific Expectations
Patterns and Relationships
– create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets);
– build a model to represent a number pattern presented in a table of values that shows the term number and the term;
– make a table of values for a pattern that is generated by adding or subtracting a number (i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, …) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term);
– make predictions related to growing and shrinking geometric and numeric patterns (Sample problem: Create growing L’s using tiles. The first L has 3 tiles, the second L has 5 tiles, the third L has 7 tiles, and so on. Predict the number of tiles you would need to build the 10th L in the pattern.);
– extend and create repeating patterns that result from translations, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).
Variables, Expressions and Equations
– demonstrate, through investigation, an understanding of variables as changing quantities, given equations with letters or other symbols that describe relationships involving simple rates (e.g., the equations C = 3 x n and 3 x n = C both represent the relationship between the total cost (C), in dollars, and the number of sandwiches purchased (n), when each sandwich costs $3);
– demonstrate, through investigation, an understanding of variables as unknown quantities represented by a letter or other symbol (e.g., 12 = 5 + [1] or 12 = 5 + s can be used to represent the following situation: “I have 12 stamps altogether and 5 of them are from Canada. How many are from other countries?”);
– determine the missing number in equations involving addition, subtraction, multiplication, or division and one- or two digit numbers, 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: What is the missing number in the equation 8 = 88 ÷ [1]?)
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Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.