Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

Representing Data with Pictograms

Active learning works for this topic because students need to test their understanding of how symbols represent quantities in real time. When they move from interpreting to constructing, they experience firsthand how the key shapes the data's meaning and clarity.

• NCCA Curriculum Specifications
• NCCA: Primary - Data
• NCCA: Primary - Reasoning

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 30 min · Pairs

Pair Survey: Favourite Fruits Pictogram

Pairs survey 10 classmates on favourite fruits using tally marks. Agree on a key, such as one apple icon for two votes, then draw the pictogram. Pairs share and interpret each other's work with the class.

How does a pictogram show information?

Facilitation Tip

During the Pair Survey: Favourite Fruits Pictogram, circulate to ensure pairs agree on a key before tallying, as this prevents later revisions.

What to look for

Provide students with a pictogram showing class pets. Ask: 'If one dog symbol represents 2 pets, how many cats are there if there are 3 cat symbols?' and 'What is the total number of pets shown?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 40 min · Small Groups

Small Group: Playground Games Pictogram

Small groups observe and tally playground activities for one recess. Create a pictogram with a key of one ball icon for three turns. Display on class board and discuss totals.

What does the key on a pictogram tell you?

Facilitation Tip

In the Small Group: Playground Games Pictogram, assign roles like recorder, tally keeper, and symbol drawer to keep everyone engaged.

What to look for

Give students a list of 10 favourite colours from 5 students. Ask them to create a pictogram to represent this data, including a clear key. They should also write one sentence explaining their key.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 35 min · Whole Class

Whole Class: Weather Pictogram Challenge

Class brainstorms a weekly weather survey. Volunteers collect data daily. Together, construct a large pictogram using a key of one cloud for two rainy days, then predict next week's weather.

Can you draw a pictogram to show your class's favourite colours?

Facilitation Tip

For the Whole Class: Weather Pictogram Challenge, display student drafts anonymously to discuss readability before finalizing the key.

What to look for

Present two pictograms showing the same data but with different keys. Ask students: 'How does the key change how easy or difficult it is to read the pictogram? Which pictogram do you think is better and why?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 25 min · Individual

Individual: Snack Time Pictogram

Each student tallies their week's snacks from a list. Draw a personal pictogram with a key of one biscuit for two items. Share in a class gallery walk to spot patterns.

How does a pictogram show information?

Facilitation Tip

With the Individual: Snack Time Pictogram, provide graph paper to help students space symbols evenly and avoid overlapping.

What to look for

Provide students with a pictogram showing class pets. Ask: 'If one dog symbol represents 2 pets, how many cats are there if there are 3 cat symbols?' and 'What is the total number of pets shown?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teachers approach this topic by starting with concrete examples students can touch and count, then moving to abstract representation. Use physical objects like counters or toys to model the key before transitioning to drawn symbols. Avoid rushing to digital tools, as the act of drawing and spacing symbols builds spatial reasoning. Research shows students grasp proportional reasoning better when they manipulate and visualize partial symbols, so build in opportunities for halves and thirds early.

Successful learning looks like students confidently creating and interpreting pictograms with accurate keys, where each symbol's value is correctly applied in totals. They should explain their choices and adjust based on peer feedback, showing they understand the purpose of the key.

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Watch Out for These Misconceptions

• During Pair Survey: Favourite Fruits Pictogram, watch for students assuming each fruit symbol represents one piece of fruit.

  Have pairs test their key by counting their actual tally and checking if the total matches the symbol count. If not, prompt them to adjust the key until it aligns, using their recorded data as evidence.

• During Small Group: Playground Games Pictogram, watch for students ignoring half symbols or rounding them to whole numbers.

  Assign a recount task where groups must defend their totals by pointing to the exact half symbols and calculating their proportional value based on the key.

• During Whole Class: Weather Pictogram Challenge, watch for students omitting the key entirely or assuming it’s understood.

  Require each group to present their pictogram without announcing the key first. Classmates must deduce the key from the symbols and totals, then the presenting group confirms or corrects their understanding.

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Methods used in this brief

• Gallery Walk