Equations with Letter Variables
Strand: Patterns
and Relations (Variables and Equations)
Outcomes: 3 and 4
Strand: Shape and Space
(Measurement)
Outcome: 3
Step 3: Plan for Instruction
Guiding Questions
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
A. Assessing Prior Knowledge and Skills
Before introducing new material, consider ways
to assess and build on students' knowledge and
skills related to counting. For example:
Provide students with centimetre grid paper
and concrete materials such as square tiles.
- Given the equation 24 ÷ n =
4, have the students:
- draw a diagram for the given equation
- create a problem for the given equation
- solve the problem.
- The area of a rectangular dog pen is 24
m2. Have the students:
- draw all the possible
dog pens using only whole numbers for
the length and the width and explain
how they know they have included all
possible dog pens
- identify which rectangular
dog pen would require the least fencing
and explain their thinking.
If a student appears to have difficulty with
these tasks, consider further individual assessment,
such as a structured interview, to determine
the students' level of skill and understanding.
See Sample Structured Interview: Assessing
Prior Knowledge and Skills 
.
B. Choosing Instructional Strategies
Consider the following instructional strategies
for teaching generalizations using variables,
including formulas for finding the perimeter
of polygons, area of rectangles and volume of
rectangular prisms.
- Build on understanding patterns from Grade
5—connecting the concrete, pictorial
and symbolic representations of patterns
and developing rules for patterns.
- Build on understanding measurement (perimeter,
area and volume) from Grade 5—using
patterns and connecting the concrete, pictorial
and symbolic representations to construct
formulas.
- Provide experiences with various models
for patterns and the translations among the
models; i.e., concrete materials, diagrams,
table of values and pattern rules or formulas.
- Encourage students to describe patterns
and rules, orally and in writing, before
using algebraic symbols.
- Provide opportunities to connect the concrete
and pictorial representations to symbolic
representations as well as connecting the
symbolic representations to pictorial and
concrete representations.
- Use real-world contexts in solving problems
using generalizations and formulas.
- Provide a variety of pattern problems using
real-world contexts. Encourage students to
solve the problems in different ways and
explain the process. Also, provide time for
students to share their solutions with others.
Stimulate class discussion to critically
evaluate the various procedures. Emphasize
understanding, flexibility and efficiency
when students select problem-solving strategies.
- Encourage students to draw diagrams to
assist them in visualizing the relationship.
Drawing diagrams will help students to construct
an equation using a variable for the unknown
value and known values.
- Provide pictorial examples of patterns
in which students formulate pattern rules
or formulas.
- In creating a functional relationship
or formula for a given problem, have students
represent and extend the problem in a table,
describe the pattern shown in the table and
use this pattern to write a functional relationship
or a formula in terms of the step number.
Have students use the created formula or
the functional relationship to solve the
problem (Van de Walle and Lovin 2006, pp.
269–270).
C. Choosing Learning Activities
The following learning activities are examples
that could be used to develop student understanding
of the concepts identified in Step 1.
Sample Activities:
Grade 6
