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.). 




Student Name: 




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