Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Pictograms and Block Graphs

Active learning works for pictograms and block graphs because young children learn best when they create, move, and discuss together. Handling physical materials helps them connect abstract numbers to real objects, making data tangible and memorable. When students build graphs with their hands, they internalize concepts like alignment and scale without rote memorization.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.1.3
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.1.4

• 15–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 20 min · Whole Class

Inquiry Circle: Sticky Note Graph

The teacher draws a large grid on the board. Each student writes their name on a sticky note and places it in the column for their favorite school subject. The class then discusses the results, focusing on which column is the 'winner' and why.

What does each picture or block in a graph stand for?

Facilitation Tip

During the Sticky Note Graph activity, circulate with a ruler to ensure students align their sticky notes flush against the baseline and to each other.

What to look for

Provide students with a simple pictogram of class pets (e.g., 1 dog symbol = 1 pet). Ask them to answer: 'How many children have a cat?' and 'Which pet is the most popular?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Graph Makers

Stations include: 'The Fruit Graph' (using plastic fruit to build a 3D pictogram), 'The Weather Watch' (drawing symbols for a week's weather data), and 'Graph Detectives' (answering questions about a pre-made pictogram).

How can you read a block graph to find out which group has the most?

Facilitation Tip

When setting up Graph Makers stations, provide example graphs with errors for students to correct before creating their own.

What to look for

Display a block graph showing students' favourite fruits. Ask students to point to the fruit with the most votes and the fruit with the fewest votes. Then, ask: 'How many more students like apples than bananas?'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: What's the Story?

Show a pictogram without a title or labels. In pairs, students must 'invent' what the graph might be about based on the pictures and the totals. They share their ideas, which highlights why titles and labels are essential for clarity.

Can you draw a block graph to show your classmates' favourite colours?

Facilitation Tip

For the Think-Pair-Share activity, give pairs one minute of quiet thinking time before discussion to ensure all students contribute.

What to look for

Present a scenario: 'We collected data on how many times each student in our class visited the playground this week. If we make a block graph, what should the blocks represent? What title should we give our graph?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach pictograms by starting with concrete objects, like counting shoes or crayons, before moving to symbols. Always model the 'bottom-up' rule and use real-world examples, like lining up blocks to show votes for class snack choices. Avoid abstract explanations of scale—instead, let students discover uneven graphs during peer review. Research shows that young learners grasp one-to-one correspondence best when they physically place each unit, so hands-on building is essential.

Successful learning looks like students who can construct a graph with equal-sized units, read the tallest column to find the most popular choice, and explain their graph to a partner. They should also identify where graphs are incorrect, such as uneven starting points or mismatched sizes. Confidence in discussing data shows true mastery of visual literacy.

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Watch Out for These Misconceptions

• During the Collaborative Investigation: Sticky Note Graph activity, watch for students drawing pictures of different sizes in the same graph.

  Provide identical sticky notes and a ruler to ensure every unit is the same size. After building the graph, have students swap with a partner and use a sticky note to 'test' whether each column is equal in height.

• During the Station Rotation: Graph Makers activity, watch for students starting their columns at different heights.

  Tape a thick baseline on each table and demonstrate how to stack blocks or sticky notes starting from that line. Ask students to place their finger at the bottom of each column to check alignment before finalizing their graph.

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Methods used in this brief

• Inquiry Circle
• Stations Rotation
• Think-Pair-Share