March 23, 2009
Algebra: Ontario Curriculm
– model real-life relationships involving constant rates where the initial
condition starts at 0 (e.g., speed, heart rate, billing rate), through
investigation using tables of values and graphs (Sample problem: Create a
table of values and graph the relationship between distance and time for a car
travelling at a constant speed of 40 km/h. At that speed, how far would the
car travel in 3.5 h? How many hours would it take to travel 220 km?);
– model real-life relationships involving constant rates (e.g., speed, heart
rate, billing rate), using algebraic equations with variables to represent the
changing quantities in the relationship (e.g., the equation p = 4t represents
the relationship between the total number of people that can be seated (p) and
the number of tables (t), given that each table can seat 4 people [4 people
per table is the constant rate]);
– translate phrases describing simple mathematical relationships into
algebraic expressions (e.g., one more than three times a number can be written
algebraically as 1 + 3x or 3x + 1), using concrete materials (e.g., algebra
tiles, pattern blocks, counters);
– evaluate algebraic expressions by substituting natural numbers for the
variables;
– make connections between evaluating algebraic expressions and determining
the term in a pattern using the general term (e.g., for 3, 5, 7, 9, …, the
general term is the algebraic expression 2n + 1; evaluating this expression
when n = 12 tells you that the 12th term is 2(12) + 1, which equals 25);
– solve linear equations of the form ax = c or c = ax and ax + b = c or
variations such as b + ax = c and c = bx + a (where a, b, and c are natural
numbers) by modelling with concrete materials, by inspection, or by guess and
check, with and without the aid of a calculator (e.g., I solved x + 7 =
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.”).
