1.2.1 Calculator Activities

Now that you see how the calculator works, you are ready to investigate some number puzzles and patterns.

Activity symbolActivity: 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?

Hint symbol

Discussion

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?

Solution symbol

Answer

139 multiplication 11 multiplication 91 equals 139139 and 501 multiplication 11 multiplication 91 equals 501501.

Multiplying by 11 and then by 91 seems to give you a number with the original three digits repeated.

Pencast symbolThere’s further explanation of this concept in the following pencast (click on “View document”).

View document [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

Activity symbol Activity: Following Up on Your Discovery

Think about why this works.

Hint symbol

Discussion

What is 11 multiplied by 91? How does a multiplication by this combined product create an answer?

Solution symbol

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.

Pencast

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 symbolActivity: All at Elevens

Type the following calculations with the calculator and write out the answers in your notebook:

  • one multiplication one
  • 11 multiplication 11
  • 111 multiplication 111
  • 1111 multiplication 1111

Can you predict the answer for 11111 multiplication 11111? And for 111111 multiplication 111111? Check it on the calculator.

Hint symbol

Discussion

Look at the pattern the digits in each answer create. In the next two problems you have five and six 1s respectively.

Solution symbol

Answer

  • one multiplication one equals one
  • 11 multiplication 11 equals 121
  • 111 multiplication 111 equals 12321
  • 1111 multiplication 1111 equals 1234321
  • 11111 multiplication 11111 equals 123454321
  • 111111 multiplication 111111 equals 12345654321

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.

Calculator screen showing 111,111 times 111,111 equals 12345654321

Activity symbolActivity: Another Number Pattern

Here’s another number pattern to try.

one multiplication eight plus one

12 multiplication eight plus two

123 multiplication eight plus three

1234 multiplication eight plus four

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?

Hint symbol

Discussion

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?

Solution symbol

Answer

one multiplication eight plus one equals nine

12 multiplication eight plus two equals 98

123 multiplication eight plus three equals 987

1234 multiplication eight plus four equals 9876

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 12345 multiplication eight plus five equals 98765. 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.

Calculator symbol The calculator can be accessed on the left-hand side bar under Toolkit.

1.2 Getting to Know the Calculator

1.2.2 More Calculator Activities