Grades 2 to 3 - Number (Number Operations)

The sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will use a variety of strategies to apply a basic operation (+,-, x,÷) to whole numbers and use these operations in solving problems.

It is expected that students will:

demonstrate and describe the processes of addition and subtraction of whole numbers up to 1000 with and without regrouping, using manipulatives, diagrams, and symbols
explore and demonstrate the processes of multiplication and division up to 50, using manipulatives, diagrams, and symbols
recall addition and subtraction facts up to 18 and multiplication facts up to 25

It is expected that students will choose, use, and defend the appropriate calculation strategy or technology to solve problems.

It is expected that students will:

calculate and justify the methods they used to find sums, differences, products, and quotients using estimation strategies, mental math techniques, manipulatives, algorithms, and calculators
verify their solutions to problems by using inverse operations, estimation, and calculators

To view the prescribed learning outcomes for Number (Number Operations) in other grades click on an icon below.

SUGGESTED INSTRUCTIONAL STRATEGIES

Students develop an understanding of the basic operations by doing meaningful tasks. In addition to developing proficiency with the mechanics of the operations, they need to develop skills that extend beyond computational facility. These skills include analysing complex problem-solving situations, knowing when to select operations, and analysing the reasonableness of the solution. Students also need to be able to determine whether an exact or approximate answer is required and which method is the most appropriate in any given situation. Problem-solving contexts motivate students to develop computational skills that they can apply in new situations.

Have students act out multiplication situations using classroom activities. For example, have some children act out the following situation to arrive at the answer: If students are working in groups of two, and there are four groups of two, and each student needs a calculator, how many calculators do they need? On the chalkboard, introduce multiplication as repeated addition. Show this as 2 + 2 + 2 + 2= 8 and then
4 x 2 = 8.
Construct sets of objects to demonstrate multiplication situations.
Have children experience real sharing opportunities as readiness for division (e.g., twelve carrot sticks for three children). Then have children divide objects from a random number of objects.
Encourage students to make estimations of computations and then check the closeness of their estimates to the correct answer with calculators or with the work of other students.

SUGGESTED ASSESSMENT STRATEGIES

Throughout the day, children make choices about how and when to use numbers and number operations. They exhibit their skills and understanding as they work and play, as well as when they are prompted to focus on mathematical tasks. As teachers present problem situations to students, they can assess students' ability to choose the appropriate operations as well as their ability to carry them out. Students who voluntarily introduce numbers into other activities are generally confident of their developing skills.

Observe

As students demonstrate ways of answering multiplication questions, watch for evidence that they are able to show multiplication as repeated addition or grouping. Note which students use mathematical terms voluntarily and correctly in their explanations.
Compare students' estimations to their calculations. Are they close?

Question

Ask students to describe situations both inside and outside of school in which they use various number operations and technology. For example:
- Tell me about a time when subtracting helped you do something?
- When does your mother use multiplication at home or in her job? How does she go about it? Try to find out and tell us.
- List the ways in which people we have been learning about (e.g., the Inuit, community helpers) might need to use division (or another number operation).

Collect

Ask students to keep dated collections of their work that include number operations. Ask them to choose examples from their portfolio that will show that they understand number operations.