Counting in Multiples of 50 and 100

Counting in multiples of 50 and 100 requires students to visualize number patterns and understand place value. Active learning strategies like station rotations and collaborative investigations allow students to physically manipulate numbers and discuss patterns, making abstract concepts more concrete.

• Year 3
• Mathematics
• 3 activities
• 15 min–45 min

Learning Objectives

1. Calculate the next three numbers in a sequence when counting forwards or backwards in multiples of 50.
2. Compare the steps taken when counting in 100s to counting in 1s, identifying similarities in place value progression.
3. Explain how counting in multiples of 50 and 100 aids in estimating and understanding the magnitude of larger numbers.
4. Identify the pattern when counting forwards and backwards in multiples of 100 up to 1000.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: The Place Value Factory

Set up three stations: one for building numbers with base ten blocks, one for drawing part-whole models, and one for 'secret code' challenges using expanded form. Students rotate in small groups to represent the same three digit number in three different ways.

Prepare & details

Predict the next three numbers in a sequence counting in 50s.

Facilitation Tip: During The Place Value Factory, ensure students are actively discussing their observations about how base ten blocks represent different values at each station.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: The Zero Hero

Show students a number like 407 and ask what would happen if the zero disappeared. Pairs discuss why the zero is necessary and then present their 'defence of zero' to the class using place value counters.

Prepare & details

Analyze how counting in 100s is similar to counting in 1s.

Facilitation Tip: During The Zero Hero, encourage pairs to use base ten blocks or drawings to visually represent the numbers before and after the zero is removed, reinforcing the concept of place value.

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

Inquiry Circle

⏱ 30 min·Small Groups

Inquiry Circle: Number Scavenger Hunt

Provide groups with digit cards 0-9. Challenge them to find the largest, smallest, and closest number to 500 they can make, explaining their reasoning to another group using the language of hundreds, tens, and ones.

Prepare & details

Explain why counting in 50s helps us understand larger numbers.

Facilitation Tip: During the Number Scavenger Hunt, prompt groups to explain their reasoning for selecting specific numbers based on the challenge, ensuring they articulate the role of place value.

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

Teaching This Topic

Focus on the multiplicative nature of the place value system, moving beyond rote memorization. Use concrete manipulatives and visual aids to help students grasp that a digit's value depends on its position. Encourage students to verbalize their thinking, using precise mathematical language like 'hundreds,' 'tens,' and 'multiples.'

What to Expect

Students will be able to fluently count forwards and backwards in multiples of 50 and 100. They will demonstrate an understanding of how the value of a digit changes based on its place in a number, and confidently partition three-digit numbers.

Watch Out for These Misconceptions

Common Misconception

During The Place Value Factory, watch for students who write numbers like 'one hundred and five' as 1005.

What to Teach Instead

Redirect students to use the base ten blocks at the station to physically build 105, showing only one hundred block and five unit blocks, contrasting this with the many blocks needed to represent 1005.

Common Misconception

During The Zero Hero, watch for students who believe that the digit with the highest face value is always the largest number.

What to Teach Instead

Ask students to use the number cards from The Zero Hero activity to build numbers like 92 and 112, then have them compare these using base ten blocks to demonstrate that the number of hundreds (place value) is more significant than the face value of the digit.

Assessment Ideas

Exit Ticket

After The Zero Hero, provide students with a number like 507 and ask them to write what the number would be if the zero disappeared, and explain why.

Quick Check

During The Place Value Factory, observe students' interactions at the number building station to see if they correctly represent numbers based on place value.

Discussion Prompt

During The Zero Hero, pose the question: 'What happens to the value of a number if a zero is removed from the tens place, like going from 407 to 47?' Encourage students to explain their reasoning using place value language.

Extensions & Scaffolding

• Challenge: Ask students to create their own number sequences involving multiples of 50 and 100, including both increasing and decreasing patterns.
• Scaffolding: Provide students with partially completed number lines or charts that highlight multiples of 50 and 100 for reference.
• Deeper Exploration: Have students explore how counting in multiples of 50 and 100 relates to real-world scenarios like saving money or measuring distances.

Key Vocabulary

Multiple	A number that can be divided by another number without a remainder. For example, 150 is a multiple of 50.
Sequence	A set of numbers that follow a specific pattern or rule, such as counting in steps.
Place Value	The value of a digit based on its position within a number, such as the hundreds, tens, or ones place.
Hundred	The number 100, representing one group of ten tens, or ten groups of ten ones.
Fifty	The number 50, representing half of one hundred.