Mathematics
Grade 7
15 min
Add and subtract integers using counters
Add and subtract integers using counters
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and represent positive and negative integers using physical or visual counters.
Explain the concept of a 'zero pair' and its role in integer operations.
Accurately add any two integers using a counter model.
Accurately subtract any two integers using a counter model, including cases requiring the addition of zero pairs.
Solve simple real-world problems involving addition and subtraction of integers by modeling with counters.
Articulate the steps involved in adding and subtracting integers using counters to a peer.
Ever wonder how to keep track of your money when you owe some and have some? 💰 Or how to calculate temperature changes when it drops below zero? 🌡️
In this lesson, you'll learn a fun and visual way to add and subtract p...
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Key Concepts & Vocabulary
TermDefinitionExample
IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, 5.The numbers -2, 0, and 7 are all integers.
Positive IntegerAn integer greater than zero. These are usually represented with a '+' sign or no sign at all.In the number +5, 5 is a positive integer. We can also just write 5.
Negative IntegerAn integer less than zero. These are always represented with a '-' sign.In the number -3, -3 is a negative integer.
Counter (for Integers)A small object or visual representation used to model integers. Typically, one color represents positive integers and another color represents negative integers.We might use yellow counters for positive numbers and red counters for negative numbers.
Positive Count...
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Core Formulas
Representing Integers with Counters
Use positive counters for positive integers and negative counters for negative integers.
To start any operation, first set up the counters that represent the initial integer(s) in the problem.
Adding Integers with Counters
To add integers, combine all the counters representing each integer. Then, identify and remove any zero pairs. The remaining counters represent the sum.
This rule applies whether you are adding integers with the same sign or different signs. Zero pairs always cancel out.
Subtracting Integers with Counters (Direct Removal)
To subtract an integer, start with the counters for the first number and physically remove the counters that represent the second number.
This works directly when you have enough of the correct...
5 more steps in this tutorial
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Challenging
A counter model for a subtraction problem has 3 positive counters and 5 negative counters on the mat AFTER adding the necessary zero pairs but BEFORE removing any counters. If the final answer to the problem is +8, what was the original subtraction problem?
A.3 - 5
B.8 - 5
C.3 - (-5)
D.-5 - (-3)
Challenging
Consider the problems A = (2 - 5) and B = (-1 - 2). Both result in -3. How do their counter models fundamentally differ in the first step?
A.Model A starts with positive counters, while model B starts with negative counters, but both require adding 2 zero pairs.
B.Model A requires adding zero pairs to remove positive counters, while model B starts with enough negative counters to add more negative counters.
C.Model A requires adding 3 zero pairs to remove 5 positive counters, while model B requires adding 2 zero pairs to remove 2 positive counters.
D.Model A and B are modeled identically because they have the same answer.
Challenging
After performing an integer operation with counters, you are left with 4 negative counters. If the operation was ADDITION and you started with 7 positive counters, what was the other number in the problem?
A.+3
B.-3
C.+11
D.-11
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