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Do not find the solutions to these equations. Use relational thinking to tell wheter the following
equations are true or false. Circle the correct answer and explain why your answer is true or false in
writing without using the solutions to the equations..
a. 322+8 = 322+7
False. Although 322 is the same on both sides, 7 is one less than 8 so the solution to 322 + 7 will be
one less than 322 + 8
b. 7+8 = 6+9
True. Six is one less than 7 but 9 is one more than 8 so although the parts have changed the
total is still the same. You can think of taking 1 from one part and giving it to the other part, the
total does not change.
c. 11 + 17 = 7 + 21
True. This is kind of like the one from above. 7 is ten less than 17 but 21 is ten more than 11. The
parts are different but the total does not change because you have taken the same amount from
one part and added it to the other part.
d. 26+4 = 20+64
False. When you look at the parts, you can see that 20 is 6 less than 26 but 64 is 60 more than 4. 60
is a lot more than the 6 removed from the 26. The parts have not been changed to keep the total
the same.
Use relational thinking to solve for the missing number in the following equations. Fill in the blank.
Explain how you solved for the missing number by thinking about the relationships between the
numbers, not just finding solutions.
a. 10+9 = N+15
N = 4 because 9 is 6 less than 15 so you must take 6 away from the 10. That would leave 4. The
amount added to one part must be given to the other part for the total to remain the same.
b. 28+2 = N+20
N= 10 because 20 is 8 less than 28 so you have to add 8 to the other part (2). 2+8=10. The amount
taken from one part must be added to the other part for the total to remain the same.
c. 43+5=N+25
N= 23 because 25 is 20 more than 5 so you have to subtract 20 from 43 which leaves 23. The
amount subtracted from one part must be the same amount added to the other part if the total is to
remain the same.
d. 58+10=60+N
N = 8 because 60 is 2 more than 58. Since we added 2 to one part (58), we must subtract 2 from
the other part (10) to keep the total the same.