Mathematics · Year 3 · Place Value and the Power of Three Digits · Autumn Term

Counting in Multiples of 50 and 100

Students practice counting forwards and backwards in multiples of 50 and 100, identifying patterns and predicting next numbers.

• National Curriculum Attainment Targets
• KS2: Mathematics - Number and Place Value

About This Topic

This topic is the cornerstone of Year 3 mathematics, moving students beyond simple two digit numbers into the realm of hundreds. It focuses on the multiplicative nature of our base ten system, where each column to the left is ten times greater than the one before. Students learn to partition numbers like 342 into 300, 40, and 2, which is essential for later work with formal calculation methods. Understanding that a '3' can represent 3, 30, or 300 depending on its position is a significant conceptual leap at this stage.

In the UK National Curriculum, this aligns with the requirement to read, write, and compare numbers up to 1000. It also introduces the vital role of zero as a placeholder, ensuring students understand why 105 is different from 15. This topic particularly benefits from hands-on, student-centered approaches where children can physically manipulate base ten blocks to see how ten 'tens' literally form one 'hundred' block.

Key Questions

1. Predict the next three numbers in a sequence counting in 50s.
2. Analyze how counting in 100s is similar to counting in 1s.
3. Explain why counting in 50s helps us understand larger numbers.

Learning Objectives

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

Before You Start

Counting in 1s, 2s, 5s, and 10s

Why: Students need a solid foundation in counting by various small increments before extending this to larger multiples like 50 and 100.

Numbers up to 1000

Why: Familiarity with the range of numbers up to 1000 is necessary to place the multiples of 50 and 100 within this context.

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.

Watch Out for These Misconceptions

Common Misconception

Students may write 'one hundred and five' as 1005.

What to Teach Instead

This happens when children write exactly what they hear. Use place value columns and physical counters to show that 1005 actually has one thousand, and that the 'hundred' part of 105 only needs a 1 in the hundreds column.

Common Misconception

Believing that the digit with the highest face value is always the largest.

What to Teach Instead

A student might think 92 is larger than 112 because 9 is bigger than 1. Peer discussion comparing physical stacks of base ten blocks helps students see that the number of columns (the place) matters more than the digit itself.

Active Learning Ideas

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.

45 min·Small Groups

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.

15 min·Pairs

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.

30 min·Small Groups

Real-World Connections

• Supermarket pricing often uses multiples of 50p or £1 for items, like multipacks of crisps or larger bottles of juice, helping shoppers quickly estimate total costs.
• Train timetables for longer journeys might show departure times in increments of 50 minutes or 100 minutes between services, allowing passengers to predict when the next train will arrive.
• Measuring distances in kilometers on road signs often involves numbers that are multiples of 100, giving drivers a sense of scale for longer trips.

Assessment Ideas

Exit Ticket

Provide students with a card showing the start of a sequence, e.g., '200, 300, 400, __, __, __'. Ask them to write the next three numbers counting in 100s. Then, give them another sequence, e.g., '750, 700, 650, __, __, __', and ask for the next three numbers counting backwards in 50s.

Quick Check

Display a number line from 0 to 1000 on the board. Ask students to come up and place a marker on the number line for every multiple of 50. Then, ask them to place another marker for every multiple of 100, discussing the patterns they observe.

Discussion Prompt

Pose the question: 'Imagine you are saving money and add £50 to your piggy bank every week. How would you figure out how much you have after 10 weeks? How is this similar to counting in 1s?' Encourage students to explain their strategies and use vocabulary like 'multiple' and 'sequence'.

Frequently Asked Questions

How can active learning help students understand place value?

Active learning allows students to move from concrete to abstract thinking. By physically exchanging ten 'tens' rods for one 'hundred' flat in a simulation or game, students internalise the scaling nature of base ten. This hands-on experience provides a mental anchor that makes abstract written columns much easier to navigate later.

Why is partitioning important in Year 3?

Partitioning is the ability to break numbers into parts. It is the foundation for mental and written addition and subtraction. If a child can partition 456 into 400, 50, and 6, they can eventually handle complex calculations by dealing with each part separately.

What is the difference between place and value?

Place refers to the position of a digit (e.g., the tens column), while value refers to how much that digit is worth (e.g., 5 in the tens column has a value of 50). Using place value headings consistently helps clarify this.

How do I support a child struggling with three digit numbers?

Focus on 'making' the numbers using physical resources like arrow cards or base ten blocks. Seeing the 300, 40, and 2 physically overlap to create 342 helps them understand that the digits are 'hiding' their full values.