Mathematics · Year 1 · Number Sense and Counting Systems · Term 1

Counting to 20: Forward and Backward

Practicing counting forwards and backwards within 20, focusing on number sequence and recognition.

• ACARA Content Descriptions
• AC9M1N01

About This Topic

This topic focuses on the foundational structures of our number system, specifically how numbers increase and decrease in predictable ways. Students explore the 100s chart to identify visual and numerical repetitions, such as the way the ones digit repeats in every row. Understanding these patterns is essential for mental computation and building a sense of number magnitude as outlined in AC9M1N01.

By connecting these patterns to real-world contexts, such as counting the petals on a flower or the beats in a clap, students begin to see mathematics as a language of order. This unit also introduces the concept of zero as a placeholder and a starting point, which is a critical shift from preschool counting. This topic comes alive when students can physically model the patterns using large-scale floor charts and collaborative movement.

Key Questions

1. Explain the pattern when counting forwards from 1 to 20.
2. Differentiate the process of counting backwards from 20 to 1.
3. Analyze the importance of knowing number order for everyday tasks.

Learning Objectives

• Identify the number that comes immediately before and after a given number up to 20.
• Demonstrate counting forwards from any number up to 20.
• Demonstrate counting backwards from any number up to 20.
• Compare the sequence of numbers when counting forwards versus backwards within 20.

Before You Start

Counting to 10

Why: Students need to be familiar with the number sequence and recognition of numbers up to 10 before extending this skill to 20.

Number Recognition (0-10)

Why: Understanding the visual representation and name of numbers up to 10 is foundational for learning their order and sequence.

Key Vocabulary

Counting forwards	Saying numbers in increasing order, starting from a smaller number and moving to a larger number.
Counting backwards	Saying numbers in decreasing order, starting from a larger number and moving to a smaller number.
Number sequence	The order in which numbers appear, following a specific pattern of increase or decrease.
Digit	A single symbol used to write numbers, such as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Watch Out for These Misconceptions

Common Misconception

Thinking that numbers end at 10 or 100.

What to Teach Instead

Students often view 10 or 100 as a 'wall' rather than a transition point. Use a continuous number roll or a long paper tape where students can see the pattern 1-9 repeating in the next decade to show the infinite nature of numbers.

Common Misconception

Confusing 'teen' numbers like 13 and 31.

What to Teach Instead

This often stems from hearing the 'three' sound first in both. Hands-on modeling with bundles of ten helps students physically feel the difference between one ten and three tens, correcting the error through tactile feedback.

Active Learning Ideas

Stations Rotation: Pattern Detectives

Set up three stations where students find patterns: one with a 100s chart and transparent counters, one with physical base-ten blocks, and one with a digital number line. Students move in small groups to identify what happens to the 'ones' column as they move down the chart.

45 min·Small Groups

Think-Pair-Share: The Mystery of Zero

Show students a sequence of numbers with a missing zero and ask what would happen if zero disappeared from our world. Students discuss in pairs how we would write '10' or '100' without it, then share their theories with the class.

15 min·Pairs

Inquiry Circle: Giant Number Line

Clear a space and have students work together to place number cards from 0 to 100 in the correct order across the room. They must justify where a number like 45 goes by looking at the numbers already placed (44 and 46).

30 min·Whole Class

Real-World Connections

• A sports coach uses counting backwards from 10 to start a race or a drill, ensuring all athletes begin at the same time.
• A librarian might count the number of books on a shelf forwards to check inventory or backwards to organize them for reshelving.
• When playing musical chairs, children count forwards to determine the number of chairs needed and then count backwards as they move around the chairs.

Assessment Ideas

Quick Check

Show students a number line from 1 to 20. Ask: 'What number comes next?' after pointing to a number. Then ask: 'What number comes before?' after pointing to another number. Record correct responses.

Exit Ticket

Give each student a card with a number between 5 and 15. Ask them to write the number that comes directly after it and the number that comes directly before it on the back of the card.

Discussion Prompt

Ask students: 'Imagine you are counting the cars in a parking lot. Would you count forwards or backwards? Why?' Then ask: 'If you were counting down the minutes until recess, would you count forwards or backwards? Explain your choice.'

Frequently Asked Questions

Why is the 100s chart so important in Year 1?

The 100s chart acts as a visual map of our base-ten system. It allows students to see vertical patterns (adding ten) and horizontal patterns (adding one) simultaneously. This spatial representation helps children internalize the structure of numbers before they move into abstract mental arithmetic.

How can I help students who struggle with counting backwards?

Counting backwards requires more cognitive load than counting forwards. Use physical movement, like walking backward on a number line, to link the concept to a physical sensation. Start with small ranges, like 10 to 0, before moving to 20 to 10.

What is the role of zero in Year 1 patterns?

Zero is taught as both a quantity (nothing) and a placeholder. In patterns, it marks the start of a new decade. Helping students see that 10, 20, and 30 all end in zero helps them predict the next 'big' number in a sequence.

How does active learning help students understand number patterns?

Active learning turns abstract sequences into physical experiences. When students use station rotations or collaborative number lines, they aren't just memorizing; they are constructing a mental map. Peer discussion during these activities forces students to verbalize the 'rules' they see, which cements their understanding of the base-ten structure more effectively than a worksheet.