Equality and Inequality
Strand: Patterns and Relations
Outcomes: 4, 5
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 equalities and inequalities. In Grade 1, students were introduced to equality as balance and inequality as imbalance. They will have used the equal sign with sums or differences on either the left or right of the sign. With numbers from zero to twenty, they should have recorded different representations of the same quantity as equalities, such as 3 + 6 = 5 + 4. Some examples of ways to assess student retention and comprehension of these Grade 1 outcomes are as follows.
Can students:
- tell you what the equal sign means?
- understand and solve equations in which the sum or difference is on the left of the equal symbol with the same proficiency as those with the sum or difference on the right?
- tell you how a balance pan scale works? Are they clear about the relative position of the pans when items on both sides are equal? Do they understand that when one side is higher than the other, the items there must have a lesser value or lighter weight than those on the lower side?
- record other names for a given number?
- understand equalities with different representations for the same number on each side of the equal symbol?
- prove equality and inequality using a balance?
- determine if two given concrete sets are equal or unequal, and explain the process used?
If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview, to determine the student’s level of skill and understanding.
Sample Structured Interview: Assessing Prior Knowledge and Skills 
B. Choosing Instructional Strategies
Consider the following general strategies for teaching the basic concepts of equality and inequality.
- Begin with concrete materials such as a balance scale and manipulatives. Interlocking cubes demonstrate this well, since each number can be represented by a different cube colour. This makes the combinations on each side of the scale still obvious even after the addends have been joined and the multi-coloured sticks from each pan compared by standing them beside one another.
- Draw comparisons to other things in the students' experiences or the world in general that work the same way and reinforce the sense making in mathematics. For example, compare the way the equal symbol is made into the "not equal" symbol to the way that signs show no parking, no littering, no biking or no smoking. It then makes sense to students that drawing a diagonal line through a sign means the inverse of what was originally communicated. Likewise, students understand the tilting of a balance pan scale more easily if they have had the opportunity to use a see-saw and know that the heavier person may sit on the ground and hold the lighter person aloft.
- Allow sufficient time for students to grasp and internalize these concepts. It may take an average student thirty to forty exposures before they own a concept. Having a balance pan scale in the room once and demonstrating how it works will not be enough. Some students will require more opportunities to experiment with the balance pan scale to gain an understanding of how equalities and inequalities affect the tilt or balance of the scale. Reinforce daily that the equal sign means "is the same as."
- Move from the concrete to the pictorial by showing what was done with the scale in diagrams.
- Take the next connecting step and add the symbolic representations to the concrete actions and the illustrations.
- Have the students practise translating from one representation to the other. When shown an equality or inequality, can they draw a diagram that illustrates it? Can they demonstrate what it means with a balance pan scale? Given the illustration, can they provide a concrete and symbolic representation?
C. Choosing Learning Activities
Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.
Grade 2
