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

Counting to 100: Forward and Backward

Investigating how numbers grow and the patterns found in the hundreds chart, practicing counting forwards and backwards.

• ACARA Content Descriptions
• AC9M1N01

About This Topic

The Power of Ten introduces students to the fundamental concept of place value by exploring how we group objects to make counting more efficient. In Year 1, students move beyond counting by ones to seeing ten as a single unit or 'bundle'. This shift is vital for understanding the Australian Curriculum standard AC9M1N02, which focuses on partitioning numbers into tens and ones.

By using concrete materials like MAB blocks, icy pole sticks, or Unifix cubes, students visualize how a digit's position changes its value. This topic is not just about naming places; it is about understanding the economy of our number system. Students grasp this concept faster through structured discussion and peer explanation where they have to 'prove' their groupings to a partner.

Key Questions

1. Explain how knowing the pattern of 1 to 10 helps us count to 100.
2. Differentiate the process of counting backwards versus forwards.
3. Analyze the significance of zero in our counting system.

Learning Objectives

• Identify the pattern of counting by tens on a hundreds chart.
• Compare the process of counting forwards and backwards from a given number up to 100.
• Demonstrate counting forwards and backwards by ones and tens to 100.
• Explain how the sequence of numbers 1-10 informs counting to 100.

Before You Start

Counting to 20: Forward and Backward

Why: Students need a foundational understanding of counting sequences and number order before extending to 100.

Number Recognition (1-20)

Why: Accurate recognition of numbers is essential for correctly identifying and sequencing them during counting activities.

Key Vocabulary

Hundreds Chart	A chart with numbers from 1 to 100 arranged in rows and columns, showing number patterns.
Forward Counting	Counting numbers in increasing order, moving from smaller numbers to larger numbers.
Backward Counting	Counting numbers in decreasing order, moving from larger numbers to smaller numbers.
Pattern	A repeating or predictable sequence of numbers or objects.

Watch Out for These Misconceptions

Common Misconception

Thinking the '2' in 25 just means two items.

What to Teach Instead

Students often see digits as independent labels. Use 'Ten-Frames' and physical bundling to show that the '2' represents two whole groups of ten. Peer checking where one student counts the bundles and the other counts the ones helps surface this error.

Common Misconception

Writing 205 for twenty-five.

What to Teach Instead

This happens when students write exactly what they hear (20 and 5). Use place value mats with clear columns to show that the tens and ones sit side-by-side, and use 'expanded' cards that physically overlap to show how 20 and 5 become 25.

Active Learning Ideas

Inquiry Circle: The Great Bundle Race

Give small groups a large bucket of loose items like buttons or sticks. Students must work together to find the fastest way to count them by making groups of ten and then counting the 'leftovers' as ones.

20 min·Small Groups

Role Play: The Place Value Shop

One student acts as the 'Tens Banker' and another as the 'Ones Clerk'. Students must 'buy' numbers by trading ten single units for one ten-rod, simulating the regrouping process in a social setting.

30 min·Pairs

Gallery Walk: Number Representations

Groups create different visual models of the same number (e.g., 24) using blocks, drawings, and tally marks. Students walk around the room to compare how 'two tens and four ones' looks in different formats.

25 min·Whole Class

Real-World Connections

• Calendar use: When looking at a calendar, children count forward to find a future date or backward to find a past date. This helps them understand sequences of days.
• Board games: Many board games require players to count spaces forward along a track. Some games also involve moving backward due to specific game rules or cards.

Assessment Ideas

Exit Ticket

Give each student a hundreds chart. Ask them to circle all the numbers they say when counting backward from 50 to 30. Then, ask them to draw a star next to the number 77.

Quick Check

Ask students to stand and count forward by ones to 20. Then, ask them to sit and count backward by ones from 20 to 1. Observe student participation and accuracy.

Discussion Prompt

Pose the question: 'How does knowing how to count to 10 help you count all the way to 100?' Facilitate a class discussion, encouraging students to share their strategies and observations about number patterns.

Frequently Asked Questions

What are the best materials for teaching place value?

Proportional materials are best for Year 1. This includes things students can actually bundle, like straws or icy pole sticks, because they can see the ten individual ones inside the bundle. Once they understand this, move to MAB blocks where the ten is pre-made.

How do I explain the difference between a digit and a number?

Explain that digits are like letters and numbers are like words. We only have ten digits (0-9), and we use them in different places to make all the numbers in the world. Using a 'digit house' visual can help clarify this.

When should we start using the terms 'tens' and 'ones'?

Start as soon as students are comfortable counting to 20. Use the language while physically grouping objects so the words are immediately linked to the action of making a group of ten.

What are the best hands-on strategies for teaching place value?

The most effective strategies involve 'composing' and 'decomposing' numbers. Active learning missions like 'The Place Value Shop' or 'The Great Bundle Race' require students to physically manipulate the groups. This tactile experience, combined with the need to explain their counting strategy to a peer, ensures they understand that the position of a digit determines its actual quantity.