explain who is correct and WHY; adapt corrdct method

Question

Tylishia says that she can calculate 324-198 by adding 2 to both numbers and calculating 326-200.

Marcus says that she could get the correct answer by subtracting 2 from 324 and adding 2 to 198 and calculate 322-200 instead.

 

a) explain who is correct and WHY. do not just indicate which answer is numerically correct; use representation ( a picture or number line) to help you explain why the correct argument makes sense.

 

b) adapt the correct method ( from part 1) to 183-49 and explain why this method makes sense for this problem

Answer 1

Maggie, when we subtract, we are finding how far apart two numbers are. If I were to start two steps closer and end two steps past, I've still gone the same distance.

 

If, however, I start two steps closer and stop short two steps, I've cut off some distance.

 

For 183 - 49, what if we add one to both? 184 - 50 is easier to do in my head than 183 - 49.

 

I hope this makes sense!

Answer 2

Picture a partial number line:

 

|- - - - - ... - - - - - | - - - - - - - - - | - - - - ...

0                         198                 324

 

|- - - - - ... - - -  - - - | - - - - - - - - - | - - - - ...

0                            200                  326

 

 

|- - - - - ... - - - -  - - | - - - - -  - | - - - - ...
0                           200             322

 

 

 324 - 198 = 324 - 198 + 0

                = 324 - 198 + (2 - 2)

                = 324 - 198 + 2 - 2

                = 324 + 2 - 198 - 2

                = (324 + 2) - (198 + 2)        [note: Marcus made error here]

                = 326  -  200

 

183-49

   49 is close to 50, so let's add 1 to both numbers, because the difference will be the same.

      184 - 50 = 134