Multiplication Investigation

You will need to be able to:

• perform the basic spreadsheet skills

Language used:

Introductory Investigation

• Set your spreadsheet up the same way as the one pictured below.

• Select A1.
• Use the arrow keys to move from A1 to C1.

  1. What is shown in the left hand section of the formula bar?

  2. What is shown in the right hand section of the formula bar?

  3. Why does cell C1 show the number 11 rather than what you typed?

  4. How would you normally write the formula in cell C1?

• Change the number in A1 to 2 and note what happens in C1.
• Vary the number in A1 from 3 to 9 and note what happens in C1.

5. Describe any pattern you notice as you change the number in A1.

6. Use this pattern to write down how you would predict the value in C1, when given a value in A1.

Spreadsheet Skills

We can use the spreadsheet to show patterns more clearly if we keep as much information on the screen as we can.

• Select B1.
• mouse pointer to the bottom right hand corner of the cell and stop when it changes from a white cross to a small dark cross.
• Drag the corner down to cell B9.

Dragging is completed by moving the mouse while holding down the mouse button. This should generate a column of 11s.

• Select C1.
• Copy this cell down to C9 in the same way as above, by dragging.
• Select C2, then using the arrow keys move down column

7. What happens to the cell references in the formulas in each of the cells in this column?

• Click on cell A2.
• Type =A1+1 into this cell.
• Copy this cell down to A9 as you did before, by dragging.

This should generate a list of the natural numbers from 1 to 9 in column A and the results of the formula in column C should now be displayed.

• Select A2 and again use the arrows to move down the column, noting the changes in cell references.
• Highlight the cell range A8:C9.
  Do this by selecting A8 then dragging to C9. The entire cell range should be highlighted.
• Copy this entire region down to C30 by dragging from the bottom right hand corner of the region.

Further Investigations

The counting numbers should be continued in column A, column B should be all 11s and column C should list the results of the multiplication.

8. Where does your pattern, described in questions 5 and 6 fail to hold?

9. Is there a new pattern after this point?

10. Describe this new pattern.

11. Once you have discovered this pattern, find out where it holds and where it doesn’t.

12. Continue to investigate these patterns further.

Further Spreadsheet Skills

• Type 1 into cell D1 and 2 into cell D2.
• Highlight both cells D1 and D2.
• Drag the bottom right hand corner down to cell D20.

13. Describe what happens?

This is a shortcut method and can be used to generate sequences of numbers.

• Type 2 into cell D1 and 4 into cell D2.
• Highlight D1:D2.
• Drag down to cell D20.

14. What set of numbers does this generate?
15. What other patterns can you achieve by trying other values in cells D1:D2? Try to generate the odd numbers, the three times table, the eight times table, the integers from -10 to 10.

You should now know how to:

• copy down

  formulas

  numbers

  regions (groups of cells)

• generate number patterns using a formula

  natural numbers

  even numbers

  integers

• generate the same number patterns using a shortcut method
• name and describe the functions of the various parts of the formula bar.

Spreadsheet Summary:

• Write a definition of each of the skills listed in the shaded box above. Describe in your own words how you would perform those skills.

Expert Investigations

1. Work through the same process as in Part C, but replace the 11 with 111. Note the patterns that emerge.

2. Again, using the spreadsheet replace 111 with 1111 and note any patterns which emerge this time.

3. Try changing the numbers to 101 and 1001?