Lesson: Subtract Integers Using Models (Counters/Numberline)

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Lesson Objective

Subtract integers using counters and models

Lesson Plan




·         6NSO.C9 Know integer subtraction is the inverse of integer addition; use the number line to model addition and subtraction of integers and add and subtract integers


Key Points

Subtract integers using counters and models

·         To subtract a positive number on the number line, move left

·         To subtract a negative number on the number line, move right

·         A negative and positive unit together equal one (a black counter and white counter together equal one)



Directions:  Use counters or a number line to solve the following subtraction problems.

1.      8 – 7

2.      3 – 9

3.      -7 – (9) 


The number line below shows the number sentence:  -4 + 6 = 2   Write a subtraction number sentence for the same number line.




Warm Up: (5 mins)

·         Review addition of positive and negative integers  

§  16 + -8

§  -1 + 7

§  3 + 8

§  4 + -10

§  -5 + -9

§  -2 + 9


Opening: (5 mins)

·         Today we are going to explore subtract with positive and negative integers

·         Usually when we think of subtraction, we think about taking away

·         Today when we think of subtraction, I want us to add thinking about doing the opposite of addition. 

·         We can use this line of thinking because subtraction and addition are inverse operations – they are the opposite of one another.

Intro/Direct Instruction: (10 mins)

·         Model with students using the number line to subtract integers 

·         Tell students that the first number tells us where to start on the number.  The operation and the second number tell us what direction to go in.  

·         Walk through an example --- when adding -2 to a number we would move 2 units to the left  -- however since we are subtracting negative 2 we need to move two units to the right 

·         Explain that when we subtract a positive we move the LEFT 

·         When we subtract a negative we move the RIGHT

·         Walk students through using counters to subtract.  Remind them that subtraction in some cases is a way to describe taking away.  Show a model with two positive numbers (9 – 5) in this case you are taking away five from nine

·         However, sometimes it is not this easy.  Let’s look at the following example:

·         Otis earned $5 babysitting.  He owes Latoya $7. 

·         To set up this problem, we will start with the 5 dollars Otis has – we represent that with 5 white counters.  Now we need to take away $7 or 7 white tiles.  However, we only have the five white counters so it’s not possible to take away 7.  In order for us to take away 7 white counters, we need to add 2 more white counters.  In order to add the two white counters we have to add 2 black counters.  We can do this because a white counter and a black counter together equal 0.  Now we can take away seven white counters and we are left with two black counters – meaning our final answer is two black counters or two negatives (-2)

Guided Practice: (10mins)

·         Allow students to practice with number lines and with counter examples – walking them through each step?

·         For number line problems:

o    Ask: where do we start

o    Which way are we going to move?

o    How many spaces are we going to move?

·         For counters:

o    What does my starting board look like? (How many counters, what color)

o    How many are we taking away?

o    Do we have enough? (Yes – take them away and solve; No – next question)

o    How many more do I need in order to take that amount away?

o    What counters do I need to add to the board (you have to add the same number of white as black or vice versa)


Independent Practice: (15 mins)

·         Students complete worksheet – teacher circulates to monitor understanding/practice – or pull a small group of students who struggled during the guided practice



·         Exit Ticket

·         Describe to your neighbor – how do you subtract with a number line?  Switch – how do you subtract with counters  






Lesson Resources

Notes Subtract Integers with Models   Notes
Notes 6 Subtract With Models  
Notes 6 Subtract With Models  
Exit Ticket Subtract Integers models  


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