Equality and Inequality

Strand: Patterns and Relations
Outcomes: 4, 5

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

Once students have shown an area of weakness or a gap, address it through intervention. If the problem shows up in written work, move back to the concrete and check whether the student understands at the concrete level. If so, work on connecting it to the symbolic level directly and with the pictorial representation as an intermediary step. If the student can show the process but is unable to satisfactorily explain it, the problem may be language or the student has only memorized what to do. Be sure that the student's lack of explanation has been checked out orally. If the student can explain the process or justify the answer orally, the problem could be with written language and not the mathematics concepts and skills.

Focus on the basic requirements of the two specific outcomes for this section. What is preventing the student from demonstrating the meaning of equality or inequality with manipulatives? If it is the terms, go back to the section on developing understanding of them and do further work. If it is making the pictorial representations, investigate whether it is a misconception that only equalities can be shown or a lack of knowledge of the symbols to put between the diagrams of the sets. Check whether or not the student has seen inequalities represented in diagrams or pictures. If symbols are an issue, have the student transfer concrete inequalities and equalities on the balance pan scale to their pictorial form, since these do not use the symbols. When these symbols are no longer a problem for the student, start to record the equalities or inequalities as equations, using the symbol.

B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

As students master addition and subtraction of numbers to one hundred, present them with more equations to assess as equal or unequal based on relational thinking and have the students share their thinking. As an example, students will learn to recognize that 42–23 will have the same difference as 52–33 or 32–13, even though they may not know or have yet worked out the actual difference between these numbers.
Provide parents with information about the students' work on equalities and inequalities. Include the importance of solving equations with variables in all the possible positions, so that any reinforcement at home includes variety. Parents will especially benefit from understanding that the meaning of the equal sign is "the same as." If parents have been informed of the common misconceptions of an equal sign meaning "the answer is coming" or "do something," they will be better prepared to ensure their children do not maintain such a misconception.