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2-Digit Mental Mathematics

Strand: Number
Outcomes: 6 and 7

Curriculum Focus

This sample targets the following changes to the curriculum:

• The general outcome for number in the revised program of studies states simply that the goal of this entire strand is to "develop number sense." The number strand is no longer divided into "number concepts" and "number operations." Number sense includes, for example, the ability to partition numbers and the ability to reason multiplicatively. These abilities apply to both numbers and operations.
• In the previous program of studies, general outcomes at each grade level specified magnitudes of numbers and particular operations, implying that number sense develops in a linear fashion. A more current understanding of student's mathematical development is that number sense deepens over time. Students' understanding of even 1-digit numbers is not fully developed until they are able to think of numbers abstractly (as quantities that do not necessarily refer to specific objects or as progressions on a scale).
• There were no specific outcomes in the previous program of studies regarding learning and teaching mental mathematics strategies. Mental mathematics strategies were referred to as possible methods for solving addition or subtraction, and students were required to justify the choice of these strategies. However, the strategies themselves were not taught. Very few students invent the most efficient mental mathematics strategies (strategies involving compensation) without the help of structured teaching, and most students benefit from discussion of strategies involving place value splitting or using doubles. Subtraction is significantly more difficult for many students compared to addition. Teaching students how to think of subtraction as addition not only helps them with subtraction, it builds understanding of part–whole relationships.
• The inclusion of mental mathematics strategies for 2-digit numbers in the Grade 3 curriculum recognizes the importance of the ability to add and subtract "in the moment," without supportive technology (either paper and pencil or calculator), in daily life and in the workplace. Efficient mental mathematics strategies greatly reduce the difficulty of these calculations.

2-Digit Mental Mathematics addresses the following outcomes from the Program of Studies:

Strand:

Number

Specific Outcome:

6. Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as: adding from left to right. taking one addend to the nearest multiple of ten and then compensating using doubles. 7. Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as: taking the subtrahend to the nearest multiple of ten and then compensating thinking of addition using doubles.

What is a Planning Guide?

Planning Guides are a tool for teachers to use in designing instruction and assessment that focuses on developing and deepening students' understanding of mathematical concepts. This tool is based on the process outlined in Understanding by Design, by Grant Wiggins and Jay McTighe.

The following steps will help you through the Planning Guide:

• Step 1: Identify Outcomes to Address
• Step 2: Determine Evidence of Student Learning
• Step 3: Plan for Instruction
• Step 4: Assess Student Learning
• Step 5: Follow-up on Assessment

See Bibliography for reference information.