This activity sheet engages students in using algebra tiles or colored disks to discover the rules for subtraction of signed integers.
First, students develop the rules using the color tiles to help them visualize the operation of subtraction. When students try to remove the chips, they are modeling the operation of subtraction. To be able to subtract discs from what is on the table it is necessary to add some zero pairs to the table. Zero pairs do not change the value of what is on the table. Each problem clearly states what must be removed and what must it be removed from.
The students are instructed to study six experiments:
1. Removing fewer yellow chips from more yellow chips
2. Removing fewer red chips from more red chips
3. Removing more yellow chips from fewer yellow chips
4. Removing more red chips from fewer red chips
5. Removing more red chips from fewer yellow chips
6. Removing more yellow chips from fewer red chips
Students observe patterns in their answers. They understand that experiment 1 will have an answer that is yellow chips, experiment 2 will have an answer that is red chips. This is true because what each problem started with and what was being removed. They notice that experiment 3 had answers that were yellow chips and that experiment 4 had answers that were red chips. This was true because zero pairs were needed to complete the subtraction. Then experiment 5 had answers that were yellow chips and experiment 6 had answer that were red chips. Again these answers were controlled by the zero pairs that were used to complete the subtraction.
After studying these results of the six experiments students begin to generalize what they saw happening. Students change problems from chips to negative and positive numbers. When the problem says remove three yellow from five yellow chips student visualize they are solving the problem (+5) - (+3). They visualize the answer is two yellow or +2. Similar visualization takes place when the are removing two red chips from one yellow chip. They realize they are solving the problem (+1) - (-2). They realize they will need to add two zero pairs to the table to complete the subtraction , so the answer will be three yellow discs or +3.
Extension problems have students extend the rules to decimals and fractions. The emphasis is on determining the sign of the answer based upon what numbers they are given.
Comment from a buyer:
• Thank you!
• Awesome resource!
• Looking forward to using this!
• Also, another good way to show the process with manipulatives.
• Thanks for making my work easier!!
• Love practicing with manipulatives