Foundations of Mathematical Thinking · 1st Class · Counting and Numbers to 100 · Autumn Term

Showing Numbers in Different Ways

Explore various ways to represent rational numbers, including fractions, decimals, and percentages, and their interconversions.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.1
• NCCA: Junior Cycle - Strand 3: Number - N.1.2

About This Topic

Patterns in the Hundred Square introduces students to the visual geography of numbers. In 1st Class, the hundred square is not just a chart but a map that reveals how our number system repeats and grows. Students learn to navigate this grid, discovering that moving down a row adds ten, while moving across a row adds one. This exploration is a key part of the NCCA Algebra strand, as it focuses on identifying and extending patterns.

Mastering the hundred square builds the mental agility needed for 'adding on' and 'taking away' without relying on fingers. It helps students visualize the relationship between numbers, such as why 24 and 34 are vertically aligned. This topic comes alive when students can physically model the patterns, using transparent counters or 'window' tools to isolate specific sequences and explain the rules they discover to their peers.

Key Questions

1. What are different ways you can show a number, such as with objects, drawings, or words?
2. How can you show the number 15 using pictures and on a number line?
3. Can you match a group of objects to the correct number?

Learning Objectives

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

Before You Start

Counting and Cardinality to 20

Why: Students need to be able to count reliably to understand what a number represents.

Recognizing Numerals to 20

Why: Students must be able to identify numerals before they can represent them in different ways.

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.

Watch Out for These Misconceptions

Common Misconception

Thinking that moving 'down' means adding one.

What to Teach Instead

Students often carry over the left-to-right counting rule to vertical movement. Use a physical 'jump' activity on a floor grid to show that one step down covers ten individual squares. Peer-led 'directions' games help reinforce that vertical moves are 'tens' moves.

Common Misconception

Getting lost at the end of a row (e.g., not knowing what follows 20).

What to Teach Instead

The 'wrap around' concept can be tricky. Use a hundred square that can be rolled into a cylinder to show how 10 connects to 11. Hands-on modeling with a number line that folds into a square helps bridge this gap.

Active Learning Ideas

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').

25 min·Small Groups

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.

20 min·Whole Class

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.

15 min·Pairs

Real-World Connections

• Shopkeepers use different ways to show prices, such as the numeral '$15', the word 'fifteen dollars', or by showing 15 items in a display.
• Construction workers might count materials using bundles of 10 and then individual items, showing a quantity like 15 in different groupings.

Assessment Ideas

Exit Ticket

Give each student a card with a number (e.g., 12). Ask them to draw a picture showing that many objects, write the number in word form, and place the number on a small number line segment from 10 to 20.

Quick Check

Display a collection of 8 counters on the board. Ask students to hold up fingers to show the numeral for that quantity. Then, ask them to write the word form on a mini-whiteboard.

Discussion Prompt

Present two different representations of the same number, one with objects and one with a drawing. Ask students: 'How are these the same? How are they different? Which way do you prefer for showing the number 10 and why?'

Frequently Asked Questions

Why use a hundred square instead of just a number line?

A number line is linear, but a hundred square highlights the base-ten structure. It shows the recurring patterns in the units place and the steady increase in the tens place. The NCCA curriculum uses it to prepare children for mental addition of two-digit numbers.

How can active learning help students understand the hundred square?

Active learning turns the square into a puzzle or a map. Instead of looking at a static chart, students engage in simulations where they move physically or use 'window' tools to hide and reveal numbers. This active exploration encourages them to look for rules and relationships rather than just memorizing positions.

What are 'number square puzzles'?

These are fragments of a hundred square (e.g., a T-shape or a cross) with only one number filled in. Students must use their knowledge of the grid's patterns to fill in the rest. They are excellent for developing spatial-numerical reasoning in small groups.

At what age should children master the hundred square?

In 1st Class (ages 6-7), the focus is on numbers up to 100. By the end of the year, students should be able to identify patterns, find 'one more/less' and 'ten more/less' easily. It remains a vital tool through 2nd Class for more complex operations.