Mathematics
Grade 8: 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
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 reallife 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 onevariable 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.