Mathematics · Year 2 · The Power of Place Value · Autumn Term

Counting in Steps: 2s, 5s, and 10s

Practicing counting forwards and backwards in multiples of 2, 5, and 10 from any number.

• National Curriculum Attainment Targets
• KS1: Mathematics - Number and Place Value

About This Topic

Developing a mental number line is a key aspect of mathematical fluency in Year 2. This topic involves students estimating the position of numbers on scales and understanding the intervals between them. By looking at partially labeled number lines, children learn to use 'benchmark' numbers like 0, 50, and 100 to orient themselves. This skill is vital for rounding and for understanding the relative magnitude of numbers within the National Curriculum framework.

Students also explore counting in steps of 2, 3, 5, and 10, noticing how the tens or ones digits change predictably. This pattern-seeking behavior is essential for early multiplication and division. Students grasp this concept faster through structured discussion and peer explanation, where they have to justify why a number belongs in a specific spot.

Key Questions

1. Predict the next number in a sequence when counting in steps of 2, 5, or 10.
2. Differentiate between counting forwards and backwards in equal steps.
3. Explain how counting in steps helps us find patterns in numbers.

Learning Objectives

• Calculate the next number in a sequence when counting forwards or backwards in steps of 2, 5, or 10.
• Identify and explain the pattern when counting forwards and backwards in equal steps of 2, 5, or 10.
• Differentiate between counting forwards and backwards in steps of 2, 5, or 10 from a given starting number.
• Predict missing numbers in a sequence based on counting in steps of 2, 5, or 10.

Before You Start

Counting to 100

Why: Students need a solid foundation in counting to at least 100 to build upon with larger steps.

Number Recognition and Ordering

Why: Identifying and ordering numbers is essential for understanding sequences and the concept of moving forwards or backwards on a number line.

Key Vocabulary

Counting forwards	Moving along a number line in the direction of increasing numbers, adding a consistent amount each time.
Counting backwards	Moving along a number line in the direction of decreasing numbers, subtracting a consistent amount each time.
Steps of 2	Counting by adding or subtracting two each time, often used for even numbers.
Steps of 5	Counting by adding or subtracting five each time, often resulting in numbers ending in 0 or 5.
Steps of 10	Counting by adding or subtracting ten each time, which changes the tens digit predictably.

Watch Out for These Misconceptions

Common Misconception

Counting the lines instead of the jumps/intervals.

What to Teach Instead

This leads to being 'off by one' errors. Use physical jumping on a floor number line to show that we are measuring the space between the marks, not the marks themselves.

Common Misconception

Believing the middle of any number line is always 5.

What to Teach Instead

Students often over-generalize the 0-10 scale. Using different start and end points in gallery walks helps them see that the midpoint depends on the total range.

Active Learning Ideas

Human Number Line Simulation

Give students cards with different numbers. Without talking, they must arrange themselves in order along a physical line on the floor, then explain their position relative to their neighbors.

20 min·Whole Class

Think-Pair-Share: The Mystery Scale

Show a number line with only 0 and 100 marked. Point to a spot and ask students to think of the number, pair up to compare estimates, and share their reasoning with the group.

15 min·Pairs

Inquiry Circle: Pattern Hunters

Groups are given a 100-square and a set of colored counters. They must mark out jumps of 3 or 5 and describe the visual patterns they see forming on the grid.

25 min·Small Groups

Real-World Connections

• Shopkeepers often count items in bundles of 10 or 2 when stocking shelves or preparing orders, making counting in tens a practical skill for inventory management.
• When counting pairs of shoes or socks, children naturally count in steps of 2. This helps them quickly determine the total number of individual items.
• Giving out sweets or small toys in groups of 5 or 10 to a class of children uses counting in steps to ensure fairness and speed.

Assessment Ideas

Quick Check

Present students with a number line showing only 0, 10, 20, and 40. Ask: 'What number comes next after 20 if we are counting in tens?' Then ask: 'What number comes before 40 if we are counting in tens?'

Exit Ticket

Give each student a card with a starting number (e.g., 15) and an instruction (e.g., 'Count forwards in steps of 5 three times'). Students write the sequence they generated and the final number.

Discussion Prompt

Pose the question: 'Imagine you have 30 stickers and you give away 5 stickers every day. How many days will it take to give them all away?' Encourage students to explain their counting strategy, whether forwards or backwards, in steps of 5.

Frequently Asked Questions

How do number lines help with mental maths?

They provide a visual scaffold for 'jumping' forward or backward. A strong mental number line allows students to visualize the distance between numbers, which is the basis for finding the difference in subtraction.

What are the best hands-on strategies for teaching number lines?

Using washing lines with numbered pegs is a classic, effective strategy. It allows students to physically slide numbers along to adjust their positions. Collaborative tasks where students have to place 'mystery numbers' on a blank line encourage them to use logic and estimation rather than just counting.

Why does my child struggle with counting in 3s?

Counting in 3s is harder because it doesn't follow the clear visual patterns of 5s or 10s on a 100-square. It requires more practice with physical grouping and repeated addition.

What is an 'unmarked' number line?

It is a line with a start and end point but no intervals in between. It is used to develop estimation skills and a sense of relative size.