Equations with Letter Variables
Strand: Patterns
and Relations (Variables and Equations)
Outcomes: 3 and 4
Strand: Shape and Space
(Measurement)
Outcome: 3
Step 5: Follow-up on Assessment
Guiding Questions
- What conclusions can be made from assessment information?
- How effective have instructional approaches been?
- What are the next steps in instruction?
A. Addressing Gaps in Learning
- Build on students' understanding of patterns,
area, perimeter and volume from previous grades.
- Use everyday contexts so students understand
the purpose of the equations and formulas
and are motivated to complete the tasks.
- Encourage students to use manipulatives
to represent various patterns and then draw
corresponding diagrams along with charts.
For example, use square tiles to create arrays
to show area and develop the area formula, A = L × W.
Another example is to use centicubes to construct
rectangular prisms to show how the length
and width are used make one layer and the
height is used to show the number of layers,
thereby laying the foundation for the volume
formula, V = L × W × H or V =
area of the base × the height.
- Have students explain their thinking and
provide scaffolding to overcome any misconceptions
or misunderstandings.
- Use numbers in the patterns that can be
translated readily into diagrams. Then larger
numbers can be used as the formula is applied.
- Explain that there are two types of pattern
rules or relationships: a rule that describes
how a pattern changes from one step to another
step (recursive relationship); a rule that
explains what you do to the step number to
get the value of the pattern for that step
(functional relationship). Emphasize that
the rule connecting the step number to the
number of elements in that step is used to
find how many elements are in any given step
number such as the one‑hundredth step.
Provide examples of each type of rule for
a given pattern.
- In creating functional relationships for
a given pattern, have students explain the
recursive relationship among the numbers in
the individual rows in the table of values
and use this relationship in establishing
the functional relationship that relates the
two rows or columns of numbers in a table
of values.
- Emphasize the importance of drawing diagrams
and/or creating a table of values when representing
a problem with an equation. Provide scaffolding
in labelling the table of values, if necessary.
- Reinforce that variables stand for what
changes in a pattern while constants stand
for what remains the same in the pattern.
- Reinforce understanding of patterns by integrating
patterns in every strand and emphasize the
power of patterns in mathematics.
- Encourage students to bring examples from
newspapers and magazines that apply patterns,
perimeter, area and volume.
B. Reinforcing and Extending Learning
Strategies for Reinforcing and Extending Learning 
Grade 6
