 Grade 4 Download Print Version
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Strand: Number
Outcome: 3

## Step 1: Identify Outcomes to Address

### Guiding Questions

• What do I want my students to learn?
• What can my students currently understand and do?
• What do I want my students to understand and be able to do, based on the Big Ideas and specific outcomes in the program of studies? See Sequence of Outcomes from the Program of Studies

Strand: Number  Specific Outcomes 8. Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context. 9. Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2- and 3-digit numerals), concretely, pictorially and symbolically, by: using personal strategies for adding and subtracting with and without the support of manipulatives creating and solving problems in context that involve addition and subtraction of numbers.

 Specific Outcomes 3. Demonstrate an understanding of addition of numbers with answers to 10 000 and their corresponding subtractions (limited to 3‑ and 4-digit numerals) by: using personal strategies for adding and subtracting estimating sums and differences solving problems involving addition and subtraction.

 Specific Outcomes 2. Use estimation strategies, including: front-end rounding compensation compatible numbers in problem-solving contexts.

### Big Ideas

Principles and Standards for School Mathematics states that computational fluency is a balance between conceptual understanding and computational proficiency (NCTM 2000). Conceptual understanding requires flexibility in thinking about the structure of numbers (base ten system), the relationship among numbers and the connections between addition and subtraction. The ability to generate equivalent representations of the same number provides a foundation for using personal strategies to add and subtract, recognizing that for some problems either operation may be used. Computational proficiency includes both efficiency and accuracy. Personal strategies must be compared and evaluated to derive methods that are efficient as well as accurate.

Understanding the operations of addition and subtraction and the connections between them is crucial. John Van de Walle states, "Addition names the whole in terms of the parts, and subtraction names a missing part" (2001, p. 107). Only addition is used in finding the whole when given the parts; however, either addition or subtraction may be used in finding a missing part when given the whole and the other part(s). He goes on to say that addition and subtraction problems include three main types:

• problems involving change—changing a number by adding to it or taking from it
• part–part–whole problems—considering two static quantities either separately or combined
• comparison problems—determining how much two numbers differ in size.

Recognizing which numbers in a problem refer to a part or to a whole helps the students see the inverse relationship between addition and subtraction and understand their properties (Willis et al. 2006). By using a variety of problems, the students will construct their own meaning for the inverse relationship between addition and subtraction and for the following properties: 