Embedded Files
We will spend 15 minutes to complete the activity in this section.
What are they?
What are they?
Red and yellow coloured discs that are used to represent/model integers.
For the sake of the following activities, the red disc will represent a negative integer and the yellow disc will represent a positive integer.
Where/how are they used?
Where/how are they used?
Two-colour counters are a great manipulative as they allow students to sort, group, add and subtract. They are a useful tool to demonstrate basic math operations.
How do they support working memory needs?
How do they support working memory needs?
What's nice about the two-colour counters is the fact that they are two colours. This provides a visual to students when working with positive and negative values. Students are also able to model basic numeracy operations and move the discs around. This can help students with working memory issues in that students do not have to try to remember values in their head once numeracy statements are modeled. This especially helps students when working on word problems. Using manipulatives helps to reduce the cognitive load so that students can focus on the math at hand.
Your Task: Adding/Subtracting integers with two-colour counters.
Your Task: Adding/Subtracting integers with two-colour counters.
Part 1: Representing Integers
Part 1: Representing Integers
Using the two-colour counters, (or the two-colour counter virtual manipulative on the link provided) represent the following integers:
Note: on the virtual manipulative site, you click the drop down arrow beside 'manipulatives' and scroll down until you see 'Two-Color' Counters
- Represent a value of +2 with your coloured counters
- Represent a value of -3 with your coloured counters
- Represent a value of 0 with your coloured counters
Reflection:
Reflection:
Turn to the person beside you and discuss each representation.
How did you represent the value of 0? Was there more than one way to represent this?
Click here to see solutions.
Zero pairs: two numbers whose sum is zero ie. +1 and -1.
Zero pairs are often useful in addition and subtraction problems with positive and negative integers. Based on the idea that adding zero pairs to problems will have no affect on the final answer of the problem.
ex. 5 + 4 + (+1 - 1) gives you the same answer as 5 + 4.
Part 2: Adding & Subtracting Integers using Two-Colour Counters
Part 2: Adding & Subtracting Integers using Two-Colour Counters
For the following activity, keep the concept of zero pairs in mind.
Adding integers:
To add integers using two-colour counters, model the first number, model the second number and then combine the integer values. You can think of this as...I'm starting with 3 positive (yellow) discs and I'm adding 4 negative (red) discs. Then simplify.
Ex. 3 + -4
Now you try!
Use two colour counters for:
- -3 + -2
- -2 + 5
Find solutions here.
Subtracting integers:
The idea of subtraction with coloured counters is a bit more abstract. Keep in mind, you cannot take something away that isn't actually there to take away!
Ex. 4 - (-2)
Start with 4 positive (yellow) discs.
The subtraction sign is telling me to now take away 2 negative (red) discs (which I do not have...)
So in order to do this, I need to add 2 negative (red) discs to my pile. However, to maintain a balance, I must also add 2 positive (yellow) discs (this adds 2 zero pairs to my pile).
I can now take away the 2 negative (red discs). The discs that are left are my final answer.
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At the end of this task, share your thoughts here!
At the end of this task, share your thoughts here!
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