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Overview
Overview
Algorithms for addition and subtraction are in the Ontario curriculum expectation for the first time in grade 3.
This is because introducing students to efficient algorithms too early has been shown to reduce their understanding of the steps, and therefore lead to more errors with those algorithms.
Alternative & Standard Algorithms for Addition
The following shows a progression of strategies that can be used moving through Grade 1 and into Grade 2. In Grade 3, students who are familiar and proficient with these strategies can be moved on towards the standard North American algorithm.
This first version uses the expanded form of the numbers, which makes the place value of the addends explicit.
This is the partial sums algorithm, where the sums for the ones and tens are shown separately, then added together.
Students often start by adding the tens first, so this is a natural next step.
This next step shows the same strategy, but with the ones added first, which moves students close to the standard North American algorithm.
Partial Sums Strategy
Addition with regrouping on Brainingcamp.mp4Standard North American Addition Algorithm
Alternative & Standard Algorithms for Subtraction
Subtraction using expanded form
Modelling standard subtraction algorithm with base 10 materials.
Base 10 materials are not the preferred manipulative for students just starting out with subtraction. See the video below (In the "Supporting students" section for a different idea.
45 – 27
45 – 27
Teacher think aloud: “I don’t have enough ones - I only have 5, and I need to subtract 7.
“I’m going to decompose (regroup or borrow) one group of ten so that I have 10 more 1’s.”
“Now I can subtract 2 tens and 7 ones. My answer is 18.”
Standard North American Subtraction Algorithm
Subtraction with regrouping on Brainingcamp.mp4Supporting Students with Algorithms
Supporting Students with Algorithms
It is important, when students are starting out using standard algorithms that connections are made with the alternative algorithms they have been using.
Using concrete manipulatives or other visual representations so that they understand the steps they are taking is also key to develop understanding.
Subtraction with regrouping - 10 frames.movReport abuse