### Annabella Wood29 June 2006

Problems to explore ...

 1) 156 2) 578 3) 396 4) 274 5) 537 6) 1154 +   39 + 102 + 851 + 154 + 623 + 3296

Here's what I would do. I would add 3 to the top line, and subtract 3 from the bottom line. That leaves me with 540 + 620. That gives me 1160. Is the result the same as if you worked the problem in other ways?

Let's work through #6 together. What number could we use to make #6 an easier addition problem? ____

Do you add or subtract it from the top line? ____________

Do you add or subtract it from the bottom line? __________

What is our new addition problem? _________ + _________ = _____________.

Does the result come out the same if we solve the problem in other ways? If so, we're doing great.
Now let's look at #3. Can you make this a simpler problem by adding and subtracting? _______

Why not? _________

Could we make it easier by using a round number? ____

Is problem #3 similar to #1? ______ If so, in what way? ______

What would you suggest doing to solve this problem? (There is more than one correct answer to this question, of course.) _____

Go ahead and explore #4 on your own... Did you need to use the original numbers? _______________

Can you write down two different ways you can change the numbers so that it is easier to solve than the original?

1) __________________ + ___________________ = __________________

2) __________________ + ___________________ = __________________

How many ways can you do this problem? ______________

Congratulations!

Now, put down your pencils, and let's think a little bit about what you've discovered, in arithmetic and ...

 Playing with Arithmetic Index Page 1 Page 2 Page 3

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