Mental Math

Activity symbol Activity: All in Your Head

Try working out the following problems in your head using the strategies from the previous activity.

(a) six plus 17

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Discussion

Consider breaking down numbers to make easy addition problems.

For example,equation sequence seven plus 24 equals sum with, 3 , summands one plus six plus 24 equals one plus 30 equals 31. Splitting the numbers up like this means that you can work in tens, which makes them much easier to add up in your head.

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Answer

(a) Here are two different approaches you might try:

multiline equation row 1 six equation left hand side equals right hand side three plus three row 2 17 equation left hand side equals right hand side 10 plus seven row 3 13 plus 10 equals 23

Or, equation sequence six plus 17 equals 17 plus six equals sum with, 3 , summands 17 plus three plus three equals 20 plus three equals 23.

(b) 25 plus 13

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Answer

(b) equation sequence 25 plus 13 equals sum with, 3 , summands 25 plus 10 plus three equals 35 plus three equals 38

(c) 29 plus 19

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Answer

(c) Here, we could say that 29 is one less than 30, and 19 is one less than 20, so 29 plus 19 is two less than 30 + 20, or 50. So, the answer is 48.

Alternatively, you could write equation sequence 29 plus 19 equals 30 minus one plus 20 minus one equals 50 minus two equals 48.

(d) sum with, 5 , summands 12 plus five plus eight plus three plus two

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Answer

(d) equation sequence sum with, 5 , summands 12 plus five plus eight plus three plus two equals open 12 plus eight close plus open sum with, 3 , summands five plus three plus two close equals 20 plus 10 equals 30.

Here instead of spitting the numbers up to help us work in tens we have grouped them together to give us tens.

Pencast symbol Want a little more practice with mental math? Check out this pencast on mental math (Click on “View document”).

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You can practice these mental techniques in lots of different ways, but it is a good idea to start with easier problems and/or situations before you move forward. Get comfortable with the process and never be afraid to make mistakes. That’s how you learn! You might like to practice with your friends and family and see how you get on together.

Addition in the Real World

3.1.2 Subtraction