Math Activity
Adding and Subtracting Positive and Negative Numbers
Combining Like Terms
Skills Practiced:
Perform addition and subtraction of rational numbers
Simplifying algebraic expressions
Materials Needed:
-Operations mat
-Different colored chips or squares
Time Needed:
60 minutes
Procedures:
-Introduce idea of positive and negative numbers. Ask students if they have seen negative numbers in real life. If so, what situations?
-Talk about opposites with students. The idea of adding 1 then subtracting 1, what happens? Or multiplying by 5 then dividing by 5, what happens? If need be, model and illustrate this idea on board. (important so that students understand that one positive and one negative zeroes out)
-After that, hand out mats and positive green squares and negative red squares.
-Model a problem on the board. Draw 4 red squares and 2 green squares. Show them that there are 4 negatives, so together, that makes -4. And the same for the green squares. Then, model combining one pos and one neg and zeroing them out (erasing them or setting them to the side). Once you have paired up all the opposites, count what’s left over. That’s your answer. In this case, there would be 2 red negative squares left over.
-Now, convert that model into numbers with the students. 2 + -4 = -2
-Now give the students a problem on the board. For example, -3 + 7. Have students model the scenario with their colored squares. Then have them pair up the opposites (one pos & one neg) and count what’s left over. Have them tell you the answer, then write it on the board.
-Do a few more where you get a positive answer and then do a few where you get a negative answer.
-Then, have students come up with a rule as to what is happening in the different situations. With enough examples and a little prodding, they should be able to tell you the integer rules for adding integers.
-Then, introduce the idea of letters in math. How sometimes they represent things. For example, a waiter at a restaurant might write your order of 2 large cheese pizzas as 2 L CP or something like that. (faster to write)
-Then introduce pizza squares and do a few of the same type of examples as above.
-Then introduce the sandwich squares. Have students do some examples with the pizzas and sandwiches together. Remind them that you have to keep the pizzas and sandwiches separated when combining and counting (since they are not the same thing)
-Then introduce the positive and negative “ones” squares as well as the pizzas and sandwiches. Have students see that there are three different types of squares (ones, sandwiches, and pizzas). None of the different squares can be combined. They can only go with their opposite ones.
Finally, make sure students are practicing modeling the scenario that you put on the board. Then writing down numerically and algebraically what is being modeled and what the result is.
Examples:
Modeled below is 4 + -3 or -3 + 4.
One positive and one negative zero each other out, then count remaining squares.
Result is +1
So 4 + -3 = +1 or -3 + 4 = 1
After introducing variables and letters in mathematics, you could model the situation below
2S + -5S or -5S + 2S
After you pair up and zero out the opposites, you count what’s left over
Results in -3S
So 2S + -5S = - 3S or -5S + 2S = -3S
Now, with pizzas which will be Ps
3P + -3P
Results in 0
3P + -3P = 0 or -3P + 3P = 0
Now combining pizzas and sandwiches. Remind students that pizzas and sandwiches are different and cannot be combined.
3P + 2S -2P -6S
3P + 2S -2P -6S = 1P -4S or P – 4S
If it helps the students, you can tell them to rearrange the terms to put “like” things next to each other.
So 3P + 2S -2P -6S would become 3P – 2P + 2S - 6S
Finally, you can add numbers, pizzas (Ps), and sandwiches (Ss) together to make a bigger more complex problem