PROBLEM SOLVING
1. When you add two numbers together you get a certain answer. For example, if you add
2 and 3 together, you get an answer of 5. Using the same two numbers, subtract the
smaller from the larger number. For example subtract 2 from 3. If the two answers of the
addition and subtraction problems, using the exact same numbers, is the same, that is
called a perfect pair.
Can you find two numbers that are a perfect pair?
If you think it is impossible, explain why.
If you think it is possible, and you have found two numbers that are a perfect pair,
explain why.
Is there more than one perfect pair? How many are there?
PROBLEM SOLVING
Model your understanding using sketches and drawings:
Communicate your understanding using words and sentences:
PROBLEM SOLVING
2. Each shoe below represents a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). They style of shoe
always represents the same digit in all of the number sentences. Examine the number
sentences.
PROBLEM SOLVING
Pair each shoe with a digit. One digit from 0-9 will not be used. Explain your reasoning.
Model your understanding using sketches and drawings:
Communicate your understanding using words and sentences:
PROBLEM SOLVING
3. A perfect trio involves three whole numbers. Using the three numbers, follow the steps
below to see if your three numbers are a perfect trio:
a. Add the first two numbers together
b. Divide the sum by the third number, and record your answer.
c. Using the same three numbers, subtract the second from the first number.
d. Multiply the difference by the third, and record your answer.
If your two recorded answers are the same, you have found a perfect trio.
Can you find three whole numbers that are perfect trios?
If not, how can you show that there are not any perfect trios? Is there a way to prove
there are no perfect trios?
If you can find a perfect trio, is there more than one perfect trio? If so, how many? List
the trio or trios you found. How do you know if you found them all? Describe any special
characteristics of perfect trios. How can you go about finding them? Explain completely.
PROBLEM SOLVING
Model your understanding using sketches and drawings:
Communicate your understanding using words and sentences:
Original activity: http://www.insidemathematics.org/assets/problems-of-themonth/perfect%20pair.pdf