Foundations of Mathematical Thinking · Senior Infants · Sorting and Collecting Information · Spring Term

Making Simple Graphs and Charts

Constructing and interpreting bar charts and line plots to display discrete and continuous data.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Statistics and Probability - SP.2

About This Topic

Representing Information involves taking data collected from the real world and displaying it in a way that is easy to understand. In Senior Infants, this usually means creating concrete graphs (using the actual objects) or simple pictograms. The NCCA curriculum focuses on the ability to 'read' these displays to answer questions like 'Which is the most popular?' or 'How many more people like apples than pears?'

This topic bridges the gap between counting and data analysis. It helps children see that math can be used to tell a story about their class or their environment. By creating their own representations, students learn that data is just a collection of individual answers organized to show a bigger picture. This topic is most successful when the data is personally meaningful to the students, such as their favorite Irish snacks or how they travel to school.

Key Questions

1. Can you colour in a square for each person who likes apples?
2. Which food got the most votes , how do you know from our chart?
3. How many more children like bananas than oranges?

Learning Objectives

• Construct a simple bar chart to represent collected data, assigning one square per data point.
• Compare quantities represented in a bar chart to identify the most and least frequent categories.
• Calculate the difference between two quantities shown in a bar chart to answer 'how many more' questions.
• Interpret a line plot to identify the mode (most frequent data point) in a set of discrete data.

Before You Start

Counting and Cardinality

Why: Students must be able to accurately count objects to collect and represent data.

Sorting and Classifying

Why: The ability to sort objects into distinct groups is fundamental to creating categories for graphs.

Key Vocabulary

Bar Chart	A graph that uses rectangular bars to show and compare quantities. Each bar represents a category, and its height shows the amount.
Line Plot	A graph that uses Xs or other symbols above a number line to show how often each value occurs in a data set.
Category	A group or class into which data is sorted, such as types of fruit or favourite colours.
Frequency	How often something occurs in a data set. In a bar chart, this is often shown by the height of the bar.

Watch Out for These Misconceptions

Common Misconception

Not lining up objects or pictures from a common baseline.

What to Teach Instead

Use a grid or a 'starting line' on the floor. If one column starts higher than another, the 'taller' column might not actually have more items. Physically aligning the items helps students see why a fair start is necessary for a graph to be accurate.

Common Misconception

Thinking that the size of the picture represents the value, rather than the number of pictures.

What to Teach Instead

Use uniform-sized stickers or blocks for all categories. If students use a giant picture for '1 elephant' and a tiny picture for '3 mice,' they will be confused. Using identical blocks for every 'vote' makes the numerical relationship clear.

Active Learning Ideas

Inquiry Circle: The Human Bar Graph

Ask a question like 'What is your favorite fruit?' Students stand in lines (columns) based on their choice. They then look at the lines to see which is the longest and shortest, discussing what this tells them about the class's favorites.

20 min·Whole Class

Stations Rotation: Data Collectors

Set up stations where students collect data (e.g., counting the number of blue vs. red cars in a picture, or sorting a bag of colored bears). At each station, they must represent their count by stacking blocks or placing stickers on a simple grid.

30 min·Small Groups

Think-Pair-Share: Reading the Chart

Show a simple pictogram of 'Our Pets.' Pairs are given a specific question (e.g., 'How many more dogs are there than cats?') to solve together using the chart, then they explain their counting strategy to the class.

15 min·Pairs

Real-World Connections

• Librarians create charts to track which books are borrowed most often, helping them decide which new books to purchase for the library.
• Supermarket managers use sales data to create charts showing which products sell best, informing decisions about stocking shelves and running promotions.
• Weather reporters use simple charts and graphs to show daily temperature changes or rainfall amounts, helping people plan their activities.

Assessment Ideas

Quick Check

Provide students with a collection of small objects (e.g., buttons of different colours). Ask them to sort the objects into groups and then create a bar chart by drawing one square for each object in its corresponding category. Observe if they correctly assign one square per object and group by category.

Discussion Prompt

Display a pre-made bar chart showing the results of a class survey (e.g., favourite playground equipment). Ask students: 'Which piece of equipment got the most votes? How can you tell from the chart?' and 'How many more children chose the slide than the swings? How did you figure that out?'

Exit Ticket

Give each student a small worksheet with a simple line plot showing the number of pets owned by different children. Ask them to write down: 'What is the most common number of pets a child in this group has?' and 'How many children have exactly two pets?'

Frequently Asked Questions

What is a concrete graph?

A concrete graph uses the actual objects being counted. For example, if you are graphing favorite shoes, the children would put their actual shoes in rows on the floor. This is the most basic form of graphing and is perfect for Senior Infants because it is 100% real.

How do pictograms differ from bar graphs?

A pictogram uses pictures or symbols to represent data (like a picture of an apple for each child who likes apples). A bar graph uses solid bars. In Senior Infants, we usually stick to pictograms or block graphs because they are easier for children to relate back to the individual items they counted.

What kind of questions can I ask about a graph?

Focus on comparison and total: 'Which has the most?', 'Which has the least?', 'Are any the same?', 'How many are there altogether?', and 'How many more are in this group than that group?'

How can active learning help students understand representing information?

Active learning makes data collection a social event. When students create a 'Human Bar Graph,' they are the data. This physical involvement makes the abstract concept of a 'column' or 'most' very concrete. By working in groups to build block graphs, they have to agree on where each block goes, which surfaces misconceptions about baselines and spacing much faster than individual work.