Why technology?
Spreadsheets and graphing tools do repetitive calculations instantly, draw accurate graphs, and let you explore "what if?" questions. They don’t replace understanding, but they extend what you can investigate.
Spreadsheet basics
A spreadsheet (Google Sheets, Excel, Numbers) is a grid of cells. Columns are letters, rows are numbers, so each cell has a cell reference like B3.
| A | B | C | |
|---|---|---|---|
| 1 | Item | Price | Qty |
| 2 | Pens | 1.50 | 4 |
| 3 | Paper | 6.25 | 2 |
Formulas
A formula starts with =.
| Formula | Does |
|---|---|
| =B2*C2 | multiplies price by quantity |
| =SUM(D2:D10) | adds a range |
| =AVERAGE(B2:B20) | mean |
| =MEDIAN(B2:B20) | median |
| =MAX(B2:B20), =MIN(…) | largest, smallest |
| =ROUND(B2, 2) | rounds to 2 decimals |
| =B2*(1+$F$1) | applies a rate stored in F1 |
Fill down
Write a formula once, then fill down (drag the corner) to copy it. References adjust automatically: =B2*C2 becomes =B3*C3 in the next row.
Absolute references
To keep a reference fixed, use $: $F$1 is an absolute reference. It’s useful for a tax rate or interest rate stored in one cell.
Example: compound interest table
| Year | Balance |
|---|---|
| 0 | 1000 |
| 1 | =B2*(1+$E$1) |
| 2 | fill down… |
With E1 = 0.05, the column shows $1,050, $1,102.50, $1,157.63 …
Charts
Select data and insert a chart: bar, line, circle or scatter. Add a title and axis labels. Scatter plots can show a trendline with its equation.
Graphing technology
Tools like Desmos, GeoGebra and graphing calculators draw functions instantly.
- Type y = 2x + 3 to see a line.
- Use sliders: y = mx + b with sliders for m and b shows how each changes the graph.
- Find intersections, zeros and maximums by clicking.
- Plot data and fit lines or curves (regression).
Exploring with technology
Example: Which rectangle with perimeter 40 m has the largest area?
Spreadsheet: width in column A (1 to 19), length =20−A2, area =A2*B2. The table shows the maximum at width 10: a 10 m × 10 m square, area 100 m².
Being a smart user
- Estimate first so you can spot errors.
- Check that formulas reference the right cells.
- Watch rounding: format cells to sensible decimal places.
- Know the maths behind the output.
Worked examples
Example 1: Formula to add C2 to C15? =SUM(C2:C15).
Example 2: You copy =A2*$B$1 down one row. What does it become? =A3*$B$1.
Example 3: In Desmos, how could you find where y = x² and y = x + 2 meet? Graph both and click the intersection points: (−1, 1) and (2, 4).
Common mistakes
- Forgetting the = sign (the cell shows text instead of calculating).
- Not using $ for fixed values, so copied formulas break.
- Trusting output blindly.
Try it yourself
- Write a formula for the mean of B2 to B31.
- A tax rate is in cell H1. Write a formula for the total in row 2 (price in B2).
- What will =A5*2 become if filled down one row?
- Name one advantage of sliders in graphing software.
Answers: 1) =AVERAGE(B2:B31) 2) =B2*(1+$H$1) 3) =A6*2 4) You can see instantly how changing a parameter changes the graph.
Quick recap
- A spreadsheet uses cell references and formulas to calculate.
- Fill down copies formulas; absolute references ($) stay fixed.
- Graphing technology draws and analyzes graphs quickly.