1.2.1 Calculator Activities
Now that you see how the calculator works, you are ready to investigate some number puzzles and patterns.
Activity: Doubling Up
Enter any three-digit number into the calculator. Multiply that value by 11 and then by 91. What do you notice about the answer? Now try a different three-digit number. Do you think this always works?
Look at your six-digit number output. Then compare to the number that you put in.
Try at least one other number. Does it show the same pattern?
Multiplying by 11 and then by 91 seems to give you a number with the original three digits repeated.
There’s further explanation of this concept in the following pencast (click on “View document”).
Activity: Following Up on Your Discovery
What is 11 multiplied by 91? How does a multiplication by this combined product create an answer?
Multiplying 11 by 91 gives 1001, so multiplying by 11 and then by 91 is the same as multiplying by 1001. Write out 139 × 1001 as a long multiplication, and see if this helps you explain why the trick works. Don’t worry if you’re not comfortable with this just yet: that’s why you’re doing this course! Just accept it as a party trick, and consider showing it to your friends.
If you are interested in having the long multiplication explained have a look at this pencast by clicking on view document below. You will need the volume turned up on your computer and the newest version of Adobe Reader, Adobe X or higher. If you didn’t download this earlier, do so now.
Activity: All at Elevens
Type the following calculations with the calculator and write out the answers in your notebook:
Can you predict the answer for ? And for ? Check it on the calculator.
Look at the pattern the digits in each answer create. In the next two problems you have five and six 1s respectively.
Note: For the last calculation, the answer is too long to fit on the top black screen, but if you look below, the full answer is shown in the white screen. Keep an eye out for this when you have very long calculations or answers.
Activity: Another Number Pattern
Here’s another number pattern to try.
Work out the first two answers in your head and the next two on the calculator, and see if you can spot the pattern. What do you think the next line in the pattern will be?
Try to describe the pattern in the answers. Then go back and look at each calculation in turn. Can you see a pattern in the first number on each line? And a pattern in the last number of the problem? How about a pattern in each answer?
The lines start 1, 12, 123, 1234, so the next line will start 12345. Multiply that number by 8. The number that is added forms a pattern, too: 1, 2, 3, 4 …, so the next line will be the multiplication part +5. The answers form a pattern as well: 9, 98, 987, 9876 …, so the answer to the next line should be 98765.
The next line reads . Check that it’s correct on your calculator.
If you’re feeling brave write down the next line as well and check it with the calculator.
The calculator can be accessed on the left-hand side bar under Toolkit.