Geometry, Measurement & Data
Understanding Data: Graphs and Probability
Grade 1 · Grade 2 · Grade 3
- ✓By the end of this lesson students will be able to identify and interpret data presented in pictographs and bar graphs.
- ✓By the end of this lesson students will be able to create simple pictographs and bar graphs to represent data.
- ✓By the end of this lesson students will be able to collect and organize data using tally marks.
- ✓By the end of this lesson students will be able to use probability language (e.g., 'certain', 'impossible', 'likely', 'unlikely', 'equally likely') to describe the likelihood of events.
Key concepts
Data is information we collect about something. For example, we can collect data about our favourite colours, the number of sunny days, or how many pets our friends have.
Tally marks are a quick way to count things. We draw a line for each item we count. When we get to five, we draw a line across the first four lines to make a group of five. This helps us count faster!
A pictograph is a graph that uses pictures to show data. Each picture stands for a certain number of things. Pictographs always have a title and a key to tell us what each picture means.
A bar graph is a graph that uses bars (rectangles) to show data. The longer or taller the bar, the more of that item there is. Bar graphs also have a title and labels for what each bar represents and the numbers they show.
Probability language uses words to describe how likely something is to happen.
If something is 'certain', it means it *will definitely* happen. There is no doubt.
If something is 'impossible', it means it *cannot* happen. There is no way it will happen.
If something is 'likely', it means it *probably will* happen. There is a good chance.
If something is 'unlikely', it means it *probably will not* happen. There is a small chance.
If two things are 'equally likely', it means they have the *same chance* of happening.
Key facts to remember
- 1Data is information we collect.
- 2Tally marks are a quick way to count, using groups of five.
- 3Pictographs use pictures to show data, and bar graphs use bars.
- 4All graphs need a title and labels so we know what they are showing.
- 5A pictograph must have a key to explain what each picture means.
- 6Probability words help us describe how likely something is to happen.
- 7'Certain' means it will happen, 'impossible' means it won't.
- 8'Likely' means it probably will happen, 'unlikely' means it probably won't.
Worked examples
Example 1
Our class voted for their favourite colours. Here are the results:\nRed: |||| ||\nBlue: |||| ||||\nGreen: |||\nYellow: |||| |\n\n1. How many students chose Red as their favourite colour?\n2. Which colour is liked by the most students?\n3. How many students voted in total?
Answer
1. 7 students chose Red.\n2. Blue is liked by the most students.\n3. 26 students voted in total.
Remember that |||| / means 5!
Example 2
Look at the pictograph below. It shows the number of apples picked by four friends. Each apple picture means 2 apples.\n\n**Apples Picked**\n\n**Friend** | **Number of Apples**\n---|---\nLiam | 🍎 🍎 🍎\nOlivia | 🍎 🍎 🍎 🍎 🍎\nNoah | 🍎 🍎\nEmma | 🍎 🍎 🍎 🍎\n\n1. How many apples did Liam pick?\n2. Who picked the most apples?\n3. How many more apples did Olivia pick than Noah?
Answer
1. Liam picked 6 apples.\n2. Olivia picked the most apples.\n3. Olivia picked 6 more apples than Noah.
Always check the key to know what each picture represents!
Example 3
You have a bag with 5 red marbles, 1 blue marble, and 5 yellow marbles. Describe the likelihood of these events using 'certain', 'impossible', 'likely', 'unlikely', or 'equally likely'.\n\n1. Picking a green marble.\n2. Picking a red marble.\n3. Picking a blue marble.\n4. Picking a red marble or a yellow marble.
Answer
1. Picking a green marble is **impossible** (there are no green marbles).\n2. Picking a red marble is **likely** (5 out of 11 marbles are red, which is a good chance).\n3. Picking a blue marble is **unlikely** (only 1 out of 11 marbles is blue).\n4. Picking a red marble or a yellow marble is **likely** (10 out of 11 marbles are red or yellow). Picking a red marble and picking a yellow marble are **equally likely** (there are 5 of each).
Common mistakes
- ✗Forgetting to give a graph a title or label its parts.
- ✗Not checking the key in a pictograph, leading to incorrect counts.
- ✗Drawing bars of different widths in a bar graph, making it hard to read.
- ✗Confusing 'likely' with 'unlikely' when describing events.
- ✗Not counting all the items when finding a total from tally marks or a graph.
Exam tips
- ★Always read the title and labels of a graph carefully before answering questions.
- ★When interpreting a pictograph, always check the key to know what each picture represents.
- ★When creating a graph, make sure your title is clear, your labels are easy to read, and your bars or pictures are neatly drawn.
- ★When describing probability, think about all the possible things that could happen before choosing your word.
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