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Model: $5(\mathrm{3}).$
Interpret the expression.  $5\left(\mathrm{3}\right)$ means $5$ take away $\mathrm{3}$ . 
Model the first number. Start with 5 positives.  
Take away the second number, so take away 3 negatives.  
But there are no negatives to take away.
Add neutral pairs until you have 3 negatives. 

Then take away 3 negatives.  
Count the number of counters that are left.  
The difference of $5$ and $\mathrm{3}$ is $8$ .  $5\left(\mathrm{3}\right)=8$ 
Model each subtraction.
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$82$
This means $8$ take away $2$ .  
Start with 8 positives.  
Take away 2 positives.  
How many are left?  $6$ 
$82=6$ 
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$\mathrm{5}4$
This means $\mathrm{5}$ take away $4$ .  
Start with 5 negatives.  
You need to take away 4 positives.  
Add 4 neutral pairs to get 4 positives.  
Take away 4 positives.  
How many are left?  
$\mathrm{9}$  
$\mathrm{5}4=\mathrm{9}$ 
ⓒ  
$6\left(\mathrm{6}\right)$
This means $6$ take away $\mathrm{6}$ .  
Start with 6 positives.  
Add 6 neutrals to get 6 negatives to take away.  
Remove 6 negatives.  
How many are left?  
$12$  
$6\left(\mathrm{6}\right)=12$ 
ⓓ  
$\mathrm{8}\left(\mathrm{3}\right)$
This means $\mathrm{8}$ take away $\mathrm{3}$ .  
Start with 8 negatives.  
Take away 3 negatives.  
How many are left?  
$\mathrm{5}$  
$\mathrm{8}\left(\mathrm{3}\right)=\mathrm{5}$ 
Model each subtraction.
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Model each subtraction.
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Model each subtraction expression:
ⓐ
We start with 2 positives. 

We need to take away 8 positives, but we have only 2.  
Add neutral pairs until there are 8 positives to take away.  
Then take away eight positives.  
Find the number of counters that are left.
There are 6 negatives. 

$28=\mathrm{6}$ 
ⓑ
We start with 3 negatives. 

We need to take away 8 negatives, but we have only 3.  
Add neutral pairs until there are 8 negatives to take away.  
Then take away the 8 negatives.  
Find the number of counters that are left.
There are 5 positives. 

$\mathrm{3}\left(\mathrm{8}\right)=5$ 
Model each subtraction expression.
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4
Model each subtraction expression.
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3
Do you see a pattern? Are you ready to subtract integers without counters? Let’s do two more subtractions. We’ll think about how we would model these with counters, but we won’t actually use the counters.
While we may not always use the counters, especially when we work with large numbers, practicing with them first gave us a concrete way to apply the concept, so that we can visualize and remember how to do the subtraction without the counters.
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