Showing Numbers in Different Ways

Active learning works especially well for this topic because students need to physically interact with the hundred square to internalize the relationship between tens and ones. Movement and collaboration help turn abstract connections into concrete understanding, making patterns visible in real time rather than memorized from a static chart.

• 1st Class
• Foundations of Mathematical Thinking
• 3 activities
• 15 min–25 min

Learning Objectives

1. Identify different representations of numbers up to 100, including numerals, words, and pictorial models.
2. Compare and contrast pictorial representations of numbers with their corresponding numeral form.
3. Demonstrate the number 15 using a variety of concrete materials and drawings.
4. Explain how a number line visually represents the order and magnitude of numbers.
5. Match a collection of objects to its numeral and word representation.

Inquiry Circle

⏱ 25 min·Small Groups

Inquiry Circle: Hundred Square Detectives

Give small groups a hundred square with several numbers missing or 'stolen' by a character. Students must use the surrounding numbers to deduce what is missing and explain the rule they used (e.g., 'I looked at the number above and added ten').

Prepare & details

What are different ways you can show a number, such as with objects, drawings, or words?

Facilitation Tip: During Hundred Square Detectives, assign clear roles so every student participates in the investigation, such as 'reader,' 'pointer,' and 'recorder.'

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

Simulation Game

⏱ 20 min·Whole Class

Simulation Game: Human Number Grid

Create a large grid on the floor using masking tape. Students act as 'numbers' and move according to instructions like 'add ten' (jump forward one row) or 'subtract one' (step left). This physical movement helps internalize the grid's logic.

Prepare & details

How can you show the number 15 using pictures and on a number line?

Facilitation Tip: In the Human Number Grid, stand back and observe which students naturally lead others, then gently guide those who hesitate to take steps forward.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Pattern Hunters

Ask students to find all the numbers that end in '5' on the square. They color them in, discuss with a partner what they notice about the shape they made (a vertical line), and share why they think that pattern happens.

Prepare & details

Can you match a group of objects to the correct number?

Facilitation Tip: For Pattern Hunters, pause after the pair discussion to ask one student to explain their partner’s idea before sharing their own.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Teaching This Topic

Teachers should model the grid’s structure by walking through it themselves while narrating each move aloud. Avoid rushing through transitions; pause at the end of each row to emphasize the jump back to the next ten. Research shows that pausing to ask, 'What changed here?' after moving down or across strengthens pattern recognition. Keep language consistent: always say 'ten more' for a downward move and 'one more' for a rightward move.

What to Expect

By the end of these activities, students should confidently explain how to move from one number to another on the hundred square, describe the value of each step, and represent the same number in multiple ways. They should also begin to verbalize the rules of the number system as they move through the grid.

Watch Out for These Misconceptions

Common Misconception

During Hundred Square Detectives, watch for students who move down the grid one square at a time instead of counting ten at once. Redirect by having them trace a full row with their finger while saying, 'One row down means ten more.'

What to Teach Instead

During Human Number Grid, notice students who count each step downward as one. Stop the activity and ask the student to stand on the starting number, take one big step down, and count aloud how many squares they passed.

Common Misconception

During Hundred Square Detectives, watch for students who assume 20 is followed by 21 without noticing the row break. Ask them to roll the hundred square into a cylinder and point to where 10 connects to 11.

What to Teach Instead

During Human Number Grid, if a student hesitates after 19 or 29, have them step onto the next square and say the number aloud while the class echoes, reinforcing the pattern of returning to the next ten.

Assessment Ideas

Exit Ticket

After Hundred Square Detectives, give each student a card with a number (e.g., 34). Ask them to mark it on a mini hundred square, write the word form, and circle the digit in the tens place.

Quick Check

During Human Number Grid, as students step on numbers, ask the class to show on fingers how many tens are in the number they are standing on.

Discussion Prompt

After Pattern Hunters, present two different representations of the same number, one with objects and one with a drawing. Ask: 'How are these the same? How are they different? Which way helps you see the tens and ones most clearly?'

Extensions & Scaffolding

• Challenge early finishers in Hundred Square Detectives to find and explain a pattern that skips two squares at a time.
• Scaffolding for students struggling in the Human Number Grid: provide a small number line strip they can hold while stepping to see the count as they move.
• Deeper exploration: After Pattern Hunters, ask students to create their own hundred-square puzzle with missing numbers for peers to solve.

Key Vocabulary

Numeral	A symbol or number, such as 1, 2, or 3, used to represent a quantity.
Word Form	Writing a number using words, such as 'fifteen' for the number 15.
Pictorial Representation	Showing a number using pictures or drawings, like drawing 15 stars.
Number Line	A straight line with numbers placed at intervals, used to show numerical order and relationships.
Quantity	The amount or number of something.