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This page sets out the method for pictograms in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Pictograms topic page.
When you see a pictogram with a key, count whole symbols first, then deal with the parts.
When you see 'draw a bar chart for this data', set up the axes before drawing any bars.
A pictogram is useless until you know what one symbol stands for.
The key might be 2, 5 or 10. It is not always 1.
If one symbol is 4 books, three symbols are 3 × 4 books.
Count the symbols, then multiply by the key.
Half a symbol is worth half the key.
If a symbol is 10, half a symbol is 5.
A longer row is larger only when every row uses the same key.
Do not compare two pictograms that use different keys until you convert them.
Divide the total by the key to see how many symbols to draw.
20 books with a key of 4 needs 5 symbols.
A bar chart uses height. A pictogram uses repeated symbols.
Both need a scale, and both start from zero.
The key is easy to skip because it is written in small type. It is still the part that gives every symbol its value. One circle can stand for 2 items, 5 items or 10 items. If you assume it stands for 1, every total that follows is too small. Write the key down before you touch a row.
A fair pictogram uses one key for the whole diagram. The key does not change from row to row. If two separate charts use different keys, the longer row is not automatically the larger amount. Turn both charts into numbers, then compare the numbers.
Method: 1. Find the key before you count any symbols. 2. Write down what one whole symbol stands for. 3. Use that same value on every row of the chart. 4. If two charts use different keys, convert both before you compare them.
A total uses every row. Turn each row into an amount, including any half symbol, and then add the amounts. Adding the symbols first is safe only when every row is made of whole symbols and they share a key. A half symbol left out of that plan gets forgotten.
A comparison is a subtraction. How many more means the larger amount minus the smaller amount. Find both amounts with the key, then subtract. Subtracting the number of symbols, and forgetting to multiply the difference by the key, gives a difference that is too small.
Method: 1. Convert every row into an amount with the key. 2. Add the amounts when the question asks for a total. 3. Subtract the amounts when the question asks how many more. 4. Compare row lengths only when both rows share one key.
Some exam questions give you a row of symbols and its total, then ask you to complete the key. If 4 symbols stand for 32 cakes, one symbol stands for 32 ÷ 4 = 8 cakes. Always use a row that has only whole symbols to find the key, because a half symbol makes the division harder and easier to get wrong.
Once the key is known, every other row follows from it. To draw a row for 44 cakes with a key of 8, work out 44 ÷ 8 = 5.5, so draw 5 whole symbols and 1 half symbol. A good key gives whole or half symbols for every row. If your key gives awkward answers such as 3.7 symbols, you have probably divided by the wrong row.
Method: 1. Find a row with a total and a whole number of symbols. 2. Divide the total by the number of symbols to get the value of one symbol. 3. Write the key: one symbol represents that value. 4. For each other row, divide the total by the key and draw whole symbols, then a half symbol if there is a remainder of half.
Tip: A pictogram with no key cannot be read. Always write the key first, then do the other rows.
A half symbol is half of the key value and a quarter symbol is a quarter of it. With a key of 12 players, a half symbol means 6 players and a quarter symbol means 3. Write the value of each fraction symbol next to the key before you start, so you are not working it out in your head while you add up a long row.
A row with 6 whole symbols and 1 half symbol is 6.5 symbols. Multiply: 6.5 × 12 = 78. A common slip is to count the half symbol as a whole one and write 7 symbols, or to add 1 to the total instead of half the key. Check by adding whole symbols and fraction symbols separately: 6 × 12 = 72 and 72 + 6 = 78.
Method: 1. Write the value of one whole symbol, then half and quarter beside it. 2. Multiply the whole symbols by the key. 3. Add the value of the half or quarter symbol. 4. Write the total with its unit, such as 78 players.
Tip: When a key makes half symbols awkward, check that the key is a number you can halve easily.
Exam questions often give clues instead of numbers: "twice as many on Saturday as on Friday", "15 fewer on Sunday than on Saturday" or "the total for all four rows was 84". Turn each clue into a number of items first, and only then change the number into symbols. Doing the symbols in your head and the clues at once is where marks go astray.
When a total is given, add the rows you know and subtract from the total to find the last row. If the known rows come to 62 and the total is 84, the last row is 84 - 62 = 22. With a key of 4 that is 22 ÷ 4 = 5.5 symbols. Finish by adding every row, including the new one, to check that you reach the total.
Method: 1. List the rows as numbers of items, not symbols. 2. Use each clue to find the missing numbers, one clue at a time. 3. Divide each number of items by the key to get the number of symbols. 4. Add all the rows and check you reach the total in the question.
"How many more", "difference" and "how many fewer" all mean subtract, and "total", "altogether" and "in all" mean add. Work out the number of items in each row first, then compare. Do not compare the numbers of symbols unless the key is the same for both rows. If both rows share one key, the difference in symbols times the key gives the difference in items.
Bar charts need the same care with the scale. Look at the vertical axis and find how much one small square is worth. If the labels go 0, 20, 40, 60 with 4 equal squares between labels, each square is worth 20 ÷ 4 = 5. A bar that reaches 3 squares above the 40 line is at 40 + 15 = 55, not 43. A bar ending between two lines needs the midpoint of those two numbers.
Method: 1. Find the value of one square or one symbol before you read anything. 2. Read each bar or row as a number of items. 3. Subtract to compare, or add to find a total. 4. Give the answer with its unit, such as 15 cups or 55 visitors.
Tip: Dividing the gap between two labelled lines by the number of squares is the fastest way to find the scale.
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