Lesson 1 of 8 · Grades 3 to 5
Collecting data and tally charts
Data is information you collect. A tally chart is a quick way to record it while you count, one mark at a time, in groups of five.
What is data?
Data is information you collect. A class might ask, "What is your favourite fruit?" and write down every answer. The answers are the data. Once the data is written down, you can count it, compare it and answer questions with it.
Collecting data sounds easy, but there is one catch: if you lose count halfway through, the answers do not mean very much. A tally chart solves that problem. It lets you record each item the moment you hear it, so you never have to remember a number in your head.
One mark for each answer
A tally mark is a short upright line. You make one mark for each item. When someone says apple, you make a mark in the apple row. When someone says grape, you make a mark in the grape row. The answer and the mark happen together, which is why tally charts are so reliable.
Here is a tally chart from a class vote. Each row is one fruit, and the marks in the row show how many children chose it.
Show the data as a table
| Choice | Count |
|---|---|
| Apple | 7 |
| Banana | 5 |
| Cherry | 4 |
| Grape | 9 |
Groups of five
Counting one mark at a time is slow, and long rows of marks are hard to read. So every fifth mark is drawn across the four marks before it. Four upright strokes and one diagonal stroke make one finished group, and a group always means exactly five.
In the chart above, apple has one full group and two single strokes, so 5 + 2 = 7 children chose apple. Grape also has one full group, plus four single strokes, so 5 + 4 = 9 children chose grape. Cherry has no full group at all, just four single strokes, so 4 children chose cherry.
A second vote
Tally charts are not only for food. A class can tally favourite colours in the same way. Read this chart row by row and say each count out loud.
Show the data as a table
| Choice | Count |
|---|---|
| Red | 6 |
| Blue | 8 |
| Green | 3 |
Blue has the most marks, so blue is the most popular colour in this vote. Green has the fewest, with only three. A tally chart makes that comparison easy, because the rows sit next to each other and you can see the lengths.
Reading a tally back
To read any tally, first count the full groups and multiply by five. Then count the single strokes and add them. One full group and four singles is 5 + 4 = 9. Three full groups and two singles is 15 + 2 = 17.
To write a count as a tally, do the opposite. For 12, take out two full groups of five (10 marks) and write two single strokes for the 2 left over. For 8, take out one full group and write three singles.
Worked example
A class votes for its favourite pet. Dog has 3 full groups of five and 2 single strokes. Cat has 2 full groups of five and 4 single strokes. How many more votes did dog get?
Step 1: read the dog tally. Three full groups are 3 × 5 = 15, and 15 + 2 = 17 votes.
Step 2: read the cat tally. Two full groups are 2 × 5 = 10, and 10 + 4 = 14 votes.
Step 3: compare the two counts with subtraction. 17 - 14 = 3.
Step 4: check by adding the difference to the smaller count. 14 + 3 = 17, which is the dog total.
Answer: 3 more votes for the dog.
Watch out for this
The diagonal stroke is part of the group, not an extra mark. Four upright strokes and one diagonal stroke are exactly five marks. Also count the leftovers after the last full group: 15 marks with two singles is 17, not 15 and not 18.
Remember
- One mark stands for one item.
- Every group of five is four upright strokes and one diagonal stroke.
- To read a tally, multiply the full groups by five and add the singles.
- To write a count, make as many full groups as you can and leave the rest as singles.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
-
A tally has 3 full groups of five and 4 single strokes. How many marks is that?
Show answer
19. Each full group is 5, so 3 × 5 = 15, and 15 + 4 = 19.
-
The tally for Blue has 2 full groups of five and 2 single strokes. How many votes is that?
Show answer
12. 2 × 5 = 10, and 10 + 2 = 12.
-
A tally shows 8 marks. How many full groups of five are in it?
Show answer
1 full group, with 3 single strokes left over. 8 ÷ 5 = 1 remainder 3.
-
The tally for Pears has one full group and 3 single strokes. How many pears were counted?
Show answer
8. One full group is 5, and 5 + 3 = 8.
-
A class votes for a pet. Dog has 2 groups and 4 more, cat has 1 group and 4 more, and fish has 1 group and 1 more. How many votes were there in total?
Show answer
29. Dog is 14, cat is 9 and fish is 6. 14 + 9 + 6 = 29.
Puzzle · Tally riddle
Puzzle time
Maya counts the strawberries she picked. Her tally has 3 full groups of five and 2 single strokes. How many strawberries are in the tally?
Show a hint
Each full group is worth 5. Multiply the number of full groups by 5 first, then add the single strokes.
Show the answer
Answer: 17. Three full groups are 3 × 5 = 15 marks, and 15 + 2 = 17 marks. Maya picked 17 strawberries.