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Name__________________________________________
Date____________
UNDERSTANDING SUBTRACTING INTEGERS USING VIRTUAL COLOR CHIPS
Objective:
to use an online applet to subtract integers. to be able to state and understand the rule for subtracting integers to apply the rule for subtracting integers without using the applet.
Directions: 1. On the www.google.com search line, type NLVM. 2. Click Click on the first first link. link. 3. Click on the box in the matrix where “ 6 – 8” meets Number & Operations. 4. Scroll down and choose “ Color Chips – Subtracting”. 5. Consider that problem that appears. Follow the prompts to represent this subtraction problem using the virtual color chips. Red is negative, and black is positive . 6. As you follow the prompts to represent the problem, try to understand how the action you are performing represents the math process of subtracting integers. 7. Type your your answer answer into into the box box and check check your your answer. answer. 8. After completing the first problem, scroll to the bottom of the box, and click “ User”. 9. Type in the number “ 4” and “-5” as terms in the subtraction subtraction problem. Follow the prompts. 10. Write the answer: 4 – (-5) (-5) = _____ _____ Solve the following problems using the applet. Be looking for a rule to help you subtract integers.
-1 – (4) = _____
-2 – (-6) = _____
3 – (8)= _____
-6 – (-4) = _____
THINKING CAREFULLY ABOUT THE PROCESS OF SUBTRACTING INTEGERS USING THE APPLET MODEL…
r eferring to the applet. Solve -3 – (2) using the applet. Answer each prompt below while referring To use the applet to solve this problem, first you would represent -3 with: _______________________ After hitting “Continue”, you will be instructed instru cted to add two zero pairs to the th e workspace. Now, the workspace consists consists of how many of each color chips? chips? _______red & _______black _______black The next prompt tells you to ____________________________________ _________________________________________________ __________________________ _______________ __ Removing the 2 positive chips represents the subtraction process in the problem -3 – (+2) Do not simplify the remaining chips yet. Notice that your workspace consists of the original _____ red tiles, and _____ more red tiles. So the original original subtraction problem went from looking like this: -3 – (+2) to this: -3 + (-2) (-2) Notice that the original problem -3 – (+2) and the altered problem -3 + (-2) look similar. What changes were made from the original original problem of -3 – (+2) to become -3 + (-2)? The subtraction sign was changed to a(n) ________________________ a(n) ________________________ sign. sign. The sign of the second number was changed from (+2) to _________.
continued other side Most textbooks teach the following Rule for Subtracting Integers: “Add the Opposite ”. Let’s think about why this rule makes sense. Consider each of the following following problems. As discussed on the previous side, each each problem will be turned into an addition problem by following the applet prompts. Before solving each problem, first write the addition problem that each subtraction problem will become. Then solve the problem. Check your answer by using the the applet. The first problem has been done for you.
-1 – (4) = _____
-2 – (-6) = _____
becomes…
becomes…
-1 + (-4) answer:
-5 -
3 – (+8)= _____
-6 – (-4) = _____
becomes…
____ + ____
becomes…
____ + ____
answer: _____
____ + ____
answer: _____
answer: _____
Application: Subtracting integers by applying the Rule: To Subtract Integers, Add the Opposite.
1)
Show the addition problem that each problem becomes.
The first three problems have been done for you.
You may only use a calculator to check answers, check answers, not to solve problems. -10 – (-3) -10 + (+3) =
