Mathematics
Grade 7: Patterning and Algebra 
Planning: Term # Tracking: Ach. Level 

Overall Expectations 
1 
2 
3 
4 
•
represent linear growing patterns (where the terms are whole numbers) using
concrete materials, graphs, and algebraic expressions; 




•
model reallife linear relationships graphically and algebraically, and solve
simple algebraic equations using a variety of strategies, including
inspection and guess and check. 




Specific Expectations 




Patterns and Relationships





–
represent linear growing patterns, using a variety of tools (e.g., concrete
materials, paper and pencil, calculators, spreadsheets) and strategies (e.g.,
make a table of values using the term number and the term; plot the
coordinates on a graph; write a pattern rule using words); 




–
make predictions about linear growing patterns, through investigation with
concrete materials (Sample problem: Investigate the surface area of towers
made from a single column of connecting cubes, and predict the surface area
of a tower that is 50 cubes high. Explain your reasoning.); 




–
develop and represent the general term of a linear growing pattern, using
algebraic expressions involving one operation (e.g., the general term for the
sequence 4, 5, 6, 7, … can be written algebraically as n + 3, where n
represents the term number; the general term for the sequence 5, 10, 15, 20,
… can be written algebraically as 5n, where n represents the term number); 




–
compare pattern rules that generate a pattern 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 at 1 and add 2 to
each term to get the next term”) with pattern rules that use the term number
to describe the general term (e.g., for 1, 3, 5, 7, 9, …, the pattern rule is
“double the term number and subtract 1”, which can be written algebraically
as 2 x n – 1) (Sample problem: For the pattern 1, 3, 5, 7, 9,…, investigate and
compare different ways of finding the 50th term.). 




Variables, Expressions and Equations





–
model reallife 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 reallife 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.”). 




Student Name: 




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