In this lesson, students will learn how to subtract integers. Students will begin by reviewing the rules for adding integers. From there, the relationship between adding and subtracting integers will be revealed to help students make connections with what they already know. Students will then practice with subtracting integers. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students will be able to subtract integers.
The goal of this warm-up is to help students recognize that subtraction is the same as adding the opposite. Give students time to answer the questions. Encourage students to try and find the answer to the expressions as well.
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Students will recognize that both expressions have similar numbers. One on the left has subtraction, while the one on the right has an addition with a negative integer.
Some students will wonder if both have the same value. You should ask them this question if nobody talks about it.
You can have students come up with a real-life situation to represent both of these expressions. For example, `7 – 10` could mean “I had `$7` in my account, and then I withdrew `$10`.” Meanwhile, `7 + (-10)` could mean “I had `$7` in my account, and then there was a `$10` fee.” As the end of this discussion, students are likely to conclude that these answers are equivalent.
Because of how closely related subtracting integers is to adding integers, make the connection known to students!
Subtracting integers can always be rewritten with addition. Once that is done, we apply the rules for adding signed numbers.
Before you ask students to actually simplify expressions with subtraction, you should ask them to practice rewriting the expressions with “add the opposite”.
For the next few examples, allow students some time to try them on their own and then discuss with a classmate to compare their answers. As you go over each problem, ask students to offer explanations and see if they can explain their reasoning.
As students are working, observe the strategies they use to help them subtract integers. You may notice that some students do not have to write the expression as addition to still understand the concept and get to the answer. Students might just recognize the answer is negative and do `85 - 62`. They might also recognize that `85 – 62` is positive, so `62 – 85` must be negative.
With this next example, students should recognize that both of the given values are negative; therefore, they will add the values and keep the negative sign. They may also choose to rewrite as `-15 + (-13)` before recognizing the values can be added.
It is important to be mindful of student misconceptions, such as using the incorrect sign for their answers. It may help to use real-world examples, like owing money to someone for negative values.
By this example, students should be more familiar with subtracting integers. With this example, it is important that students recognize that subtracting a negative results in adding a positive so you should encourage them to rewrite this as `18 + 4`, then to add.
You can use a real-world example to help explain. If you had a wrong charge of `$4` on your account, then when the bank removes the charge, your account balance goes up.
In this last example, students should recognize that it becomes `4 + 7`. Understanding the signs of numbers is essential as students move further along in their math journey, so it is important that students understand the significance of understanding how to subtract integers.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for subtracting integers. Check out the online practice and assign to your students for classwork and/or homework!
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