Counting On with Even and Odd Numbers 1-20

Have you ever witnessed that magical moment when a child’s face lights up with understanding? When they suddenly see a pattern that was hidden just moments before? Right now, your little mathematician is standing at the threshold of one of their first great number adventures – discovering the secret patterns hidden within numbers 1 to 20.

These aren’t just ordinary numbers – they’re the building blocks of mathematical confidence. And tucked within this special collection lies one of mathematics’ most beautiful secrets: the dance between even numbers (the perfect pair-makers) and odd numbers (the ones with an extra friend).

We’re about to share something extraordinary with you: the “counting on” strategy. Think of it as your child’s mathematical superpower – a way to explore numbers that transforms them from passive observers into active number detectives. This isn’t about memorising lists or chanting rules; it’s about empowering young minds to make their own discoveries.

Join us on this number exploration journey. You’ll discover proven teaching strategies, engaging activities that make learning irresistible, and our exclusive “Number Explorer’s Toolkit” – everything you need to guide your child’s mathematical adventure. Let’s unlock the magic of numbers together!

Understanding Counting On

Before children can become confident number detectives, they need to master the fundamental skill that transforms how they interact with numbers. Counting on is more than just a technique – it’s the bridge between knowing number names and truly understanding their mathematical relationships. This powerful strategy forms the foundation for all future arithmetic learning and opens the door to pattern discovery.

What Makes Counting On Different from Rote Counting

Counting on represents a significant cognitive leap from simple number recitation. When children can “count on,” they demonstrate flexible number understanding by starting from any given number rather than always beginning at one.

Rote Counting Example: Child sees 7 objects, counts “1, 2, 3, 4, 5, 6, 7”

Counting On Example: Child sees 5 objects, adds 2 more, says “Five… six, seven”

This fundamental shift shows children understand numbers as quantities with relationships, not just sequential names. For numbers 1-20, this skill becomes the foundation for addition, subtraction, and pattern recognition.

Building Sequential Number Understanding

The counting on strategy develops number flexibility through progressive steps:

Stage 1: Forward Counting On Starting from any number between 1-10, children count forward by 1, 2, or 3. For example:

• Start at 8, count on 2: “Eight… nine, ten”
• Start at 12, count on 3: “Twelve… thirteen, fourteen, fifteen”

Stage 2: Backward Counting On Children learn to count backwards from numbers 1-20:

• Start at 15, count back 2: “Fifteen… fourteen, thirteen”
• Start at 7, count back 3: “Seven… six, five, four”

Stage 3: Skip Counting Patterns Using counting on to identify number patterns:

• Count on by 2s from 0: “Zero… two, four, six, eight, ten…”
• Count on by 2s from 1: “One… three, five, seven, nine…”

Why Counting On Reveals Even and Odd Patterns

When children count on systematically through numbers 1-20, they naturally discover the alternating pattern of even and odd numbers. This discovery-based approach creates lasting understanding because children arrive at conclusions through their own investigation.

Discovery Process:

1. Child starts with 2 objects, arranges in pairs perfectly
2. Counts on 1 more to get 3, discovers the extra object
3. Counts on 1 more to get 4, arranges in pairs again
4. Pattern emerges: pair-no pair-pair-no pair

This organic discovery process builds mathematical confidence and problem-solving skills simultaneously.

Even and Odd Foundations

Once children have mastered counting on, they’re ready to discover one of mathematics’ most elegant patterns. Even and odd numbers aren’t just arbitrary categories – they represent a fundamental mathematical relationship that children can explore and understand through hands-on investigation. This foundation in number patterns builds logical thinking skills that extend far beyond basic arithmetic.

Understanding Even Numbers Through Pairing

Even numbers between 1-20 are the ultimate team players – they always work perfectly in pairs! When your little explorer uses counting on to reach an even number, they’ll discover something wonderful: every single object can find a partner.

The Even Number Family (1-20): 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Visual Pairing Magic:

Number 6: (. .) (. .) (. .) = Three perfect pairs!

Number 12: (. .) (. .) (. .) (. .) (. .) (. .) = Six perfect pairs!

Number 20: (. .) (. .) (. .) (. .) (. .) (. .) (. .) (. .) (. .) (. .) = Ten perfect pairs!

Discovery Insight: When children count on to collect an even number of objects, they experience the satisfaction of perfect pairing – no object is left alone!

Recognising Odd Numbers Through Remainders

Odd numbers are the friendly rebels of the number world – they always have one extra friend who doesn’t have a pair! When young mathematicians count on to odd numbers, they make an exciting discovery through hands-on exploration.

The Odd Number Adventure Squad (1-20): 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Visual Remainder Discovery:

Number 7: (. .) (. .) (. .) . = Three pairs plus one extra!

Number 13: (. .) (. .) (. .) (. .) (. .) (. .) . = Six pairs plus one extra!

Number 19: (. .) (. .) (. .) (. .) (. .) (. .) (. .) (. .) (. .) . = Nine pairs plus one extra!

Discovery Insight: Children learn that odd numbers always have one object that can’t find a partner – and that’s perfectly fine! This “extra one” becomes their special identifying feature.

The Last Digit Pattern Recognition

Once children understand even and odd concepts through counting on and pairing, they can learn the efficient “last digit” recognition method for numbers 10-20:

Even Last Digits: 0, 2, 4, 6, 8

• 10 (ends in 0) = Even
• 12 (ends in 2) = Even
• 14 (ends in 4) = Even

Odd Last Digits: 1, 3, 5, 7, 9

• 11 (ends in 1) = Odd
• 13 (ends in 3) = Odd
• 15 (ends in 5) = Odd

This pattern recognition accelerates identification whilst reinforcing the underlying mathematical concepts discovered through counting on.

Let’s Go on Number Adventures!

Now that your little explorer understands the magic of counting on, it’s time for some hands-on adventures! Each activity is designed to turn mathematical discovery into an exciting journey of exploration.

Adventure 1: The Counting On Investigation Station

Mission: Become a number detective and solve the even/odd mystery!

Explorer’s Equipment: 20 identical treasures (buttons, counters, blocks), number cards 1-20, investigation journal

The Adventure Begins:

1. Your young detective selects a mystery number card
2. Uses counting on skills to collect exactly that many treasures
3. Attempts the “Pairing Challenge” – can all treasures find partners?
4. Records discovery: “Number ___ is ___ because ___”
5. Selects new mystery number and repeats investigation

Counting On Discovery Element: Instead of counting from 1 each time, children practice starting from different numbers. If they have 8 objects and want 12, they count on: “Eight… nine, ten, eleven, twelve!” This reinforces that counting on is a powerful mathematical tool.

Learning Victory: Children develop systematic investigation skills whilst building confidence with numbers 1-20

Adventure 2: Even Steven & Odd Todd’s Number Line Journey

Meet Our Number Heroes:

• Even Steven loves landing on numbers that make perfect pairs
• Odd Todd enjoys numbers with one extra friend

Quest Equipment: Floor number line 1-20, character markers, adventure instruction cards

The Journey Rules:

1. Explorers start at different positions on the magical number line
2. Draw an adventure card: “Count on 3 spaces” or “Count back 2 spaces”
3. Move character marker using counting on strategy
4. Declare: “I landed on ___, which belongs to ___ because ___”
5. Demonstrate reasoning using pairing magic

Counting On Discovery Element: Children experience counting on as movement and direction, not just adding objects. They physically feel the “counting on 3” as three forward steps, making the concept kinesthetic and memorable.

Extension Quests:

• “Help Even Steven visit three even numbers in a row”
• “Guide Odd Todd to odd numbers using only counting on by 2s”
• “Create your own adventure cards with different counting on challenges”

Adventure 3: Building Block Tower Challenge

The Great Tower Mystery: Can you split your tower into two equal smaller towers?

Building Materials: Colourful building blocks, tower investigation sheet, measuring rulers

Construction Process:

1. Young architect selects target number between 1-20
2. Uses counting on to collect precise number of blocks
3. Builds magnificent single tower
4. The Big Test: Can the tower split into two identical smaller towers?
5. Records discovery: successful split (even) or one block remains (odd)

Counting On Discovery Element:
By counting on each block to build their tower (“I have seven blocks, counting on three more makes ten blocks total”), children physically experience how counting on reveals the final quantity that they then test for even/odd properties.

Mathematical Magic: Links even/odd understanding to early division concepts whilst demonstrating that odd numbers are “even plus one”

Adventure 4: Skip Counting Pattern Detective

The Case: Uncover the secret patterns hidden in numbers 1-20!

Detective Tools: Number line, coloured pencils, pattern investigation notebook

Investigation Process:

1. Even Team Investigation: Start at 0, count on by 2s: “Zero… two, four, six, eight…”
2. Colour these numbers blue on number line – they form the “Even Explorer Team”
3. Odd Team Investigation: Start at 1, count on by 2s: “One… three, five, seven, nine…”
4. Colour these numbers orange – they become the “Odd Detective Squad”
5. Pattern Discovery: Compare the two teams and predict future members

Counting On Discovery Element: Skip counting by 2s is advanced counting on! Children learn that “counting on by 2” from any starting point reveals either all even numbers or all odd numbers, depending on where they begin.

Advanced Detective Work:

• “Which team would 22 join? Use counting on to investigate!”
• “Start at 30 and count on by 2s – even or odd pattern?”
• “Create counting on patterns using different numbers”

Adventure 5: The Pairing Palace Challenge

Royal Mission: Help the Number Royalty organise their kingdoms!

Palace Equipment: Your Number Explorer’s Toolkit, small objects for pairing, royal recording scrolls

The Royal Process:

1. Select a visiting number (use toolkit number cards)
2. Use counting on to gather royal subjects (objects) for that number
3. The Royal Test: Can all subjects pair up for the royal dance?
4. Kingdom Assignment:
   • Perfect pairs → Even Steven’s “Pair-Perfect Palace”
   • One extra subject → Odd Todd’s “Extra Friend Forest”
5. Record the royal decision with reasoning

Counting On Discovery Element: Children use counting on to collect exact quantities, then immediately apply their counting on knowledge to test the even/odd property. This connects counting accuracy with pattern recognition.

Royal Extensions:

• “Royal Predictions: If 15 goes to Extra Friend Forest, where will 17 go?”
• “Kingdom Tours: Use counting on to visit five Even Palace residents”
• “Royal Mathematics: Are there more Even Palace or Extra Friend Forest residents between 1-20?”

Curriculum Integration Methods

Mathematical learning becomes most meaningful when it connects naturally with other subjects and real-world applications. The counting on approach to even and odd numbers provides rich opportunities for cross-curricular learning whilst meeting key educational objectives. These integration strategies help children see mathematics as part of their everyday world rather than an isolated subject.

Key Stage 1 Mathematics Alignment

The counting on approach for even and odd numbers directly supports multiple KS1 mathematical objectives:

Number and Place Value:

• Count to and across 100, forwards and backwards
• Identify and represent numbers using objects and pictorial representations
• Use the language of: equal to, more than, less than (fewer), most, least

Addition and Subtraction:

• Add and subtract one-digit and two-digit numbers to 20
• Solve one-step problems involving addition and subtraction

Cross-Curricular Learning Opportunities

English Language Development:

• Mathematical vocabulary: even, odd, pair, remainder, pattern, sequence
• Descriptive language: “I notice that…” “This shows…” “The pattern continues…”
• Comparative language: same, different, more, fewer

Science Connections:

• Pattern recognition in nature (petals, leaves, symmetry)
• Classification and sorting skills
• Systematic observation and recording

Art and Design:

• Creating visual patterns using even and odd groupings
• Symmetrical designs reflecting even number pairs
• Asymmetrical compositions showing odd number remainders

Assessment Integration Strategies

Formative Assessment Through Counting On:

• Observe counting accuracy when children count on from different starting points
• Note strategy preferences (concrete materials vs mental counting)
• Document pattern recognition development
• Record vocabulary usage in mathematical explanations

Summative Assessment Applications:

• Number identification speed tests using counting on strategies
• Problem-solving tasks requiring even/odd classification
• Pattern completion challenges
• Real-world application scenarios

As Michelle Connolly, Founder of LearningMole, notes: “When children discover mathematical patterns through their own investigation rather than memorisation, they develop the critical thinking skills that serve them throughout their educational journey.”

Home Learning Extension Activities

Family Involvement Strategies:

• Household object sorting (cutlery, toys, books) by even/odd quantities
• Cooking mathematics: dividing ingredients into even portions
• Garden counting: flowers, vegetables, garden tools
• Shopping applications: counting items in pairs

Technology Integration: LearningMole’s educational video resources provide visual demonstrations of counting on techniques, allowing children to see mathematical concepts in action. These curriculum-aligned materials support both classroom instruction and home learning with consistent methodology.

Supporting Every Young Explorer

Every child’s mathematical journey is unique. Here’s how to recognise progress and provide support that meets each little explorer where they are.

Key Milestones for Number Explorers (Ages 5-7)

Beginning Explorers:

• Counts objects accurately to 20
• Can start counting from numbers other than 1
• Shows understanding that numbers represent quantities
• Beginning to use counting on for simple additions

Developing Adventurers:

• Uses counting on confidently for addition within 10
• Recognises some even/odd patterns through hands-on investigation
• Can arrange objects in pairs with minimal guidance
• Explains thinking using mathematical language

Confident Mathematicians:

• Counts on expertly from any number 1-20
• Identifies even/odd numbers using multiple strategies
• Explains mathematical reasoning clearly
• Applies patterns to predict beyond practiced range
• Uses counting on flexibly in problem-solving

Quick Assessment Questions

Counting On Mastery Check:

1. “Show me how to count on from 8 to reach 13.”
2. “If you start at 15 and count on 4 more, where do you land?”
3. “I have 6 stickers. If I count on 3 more, how many do I have?”

Even/Odd Understanding Check:

1. “How can you tell if 16 is even without counting from 1?”
2. “If 11 is odd, what can you tell me about 13? Why?”
3. “Show me why 18 makes perfect pairs using your toolkit.”

Supporting Different Learning Adventures

Visual Learners thrive with:

• Colourful number lines and sorting mats from your toolkit
• Pairing demonstrations using shapes and symbols
• LearningMole’s visual learning videos
• Pattern charts showing numerical relationships

Kinesthetic Explorers love:

• Physical object manipulation and counting games
• Movement-based number line activities
• Building and construction challenges
• Hands-on sorting adventures

Auditory Adventurers enjoy:

• Counting songs and mathematical rhymes
• Verbal explanations of discovered patterns
• Discussion-based learning sessions
• Audio-supported counting on practice

Supporting Struggling Explorers

For Counting Challenges:

• Start with a smaller number range (1-10)
• Use one-to-one correspondence activities
• Provide physical counting supports
• Break counting on into smaller, manageable steps

For Pattern Recognition Difficulties:

• Increase visual supports using toolkit materials
• Use consistent mathematical language
• Provide additional guided practice with concrete objects
• Connect to familiar real-world examples and situations

As Michelle Connolly, Founder of LearningMole, observes: “When children discover mathematical patterns through their own investigation rather than memorisation, they develop the critical thinking skills that serve them throughout their educational journey.

Extending Adventures at Home

Family Mathematical Moments:

• Sort household objects by even/odd quantities during chores
• Use counting on during cooking: “We have 8 biscuits, count on 4 more makes 12!”
• Garden mathematics: counting flowers, vegetables, garden tools in pairs
• Shopping adventures: “We need 15 apples – count on from the 7 we have!”

Digital Learning Support: LearningMole’s educational video library provides visual demonstrations of counting on techniques, allowing children to see mathematical concepts in action. These curriculum-aligned resources maintain consistent methodology between classroom and home learning environments.

Your Next Mathematical Adventure Awaits

Every mathematical journey begins with a single number, and you’ve just equipped your young explorer with one of the most powerful tools in their mathematical toolkit: the ability to count on with confidence and discover patterns independently.

Remember that magical moment we mentioned at the beginning? That spark of understanding when a child suddenly sees the pattern hidden within numbers? You’ve just provided the pathway to countless such moments. Through counting on, your little mathematician hasn’t just learned about even and odd numbers – they’ve learned how to be mathematical detectives, investigators, and independent thinkers.

What Your Explorer Has Discovered:

• Numbers are quantities with relationships, not just names in a sequence
• Mathematical patterns can be discovered through investigation, not just memorisation
• Counting on is a flexible tool for addition, pattern recognition, and problem-solving
• Even and odd numbers follow predictable, logical patterns
• Mathematics is an adventure, not a chore

The Adventure Continues: With this strong foundation in counting on and number patterns, your child is ready for:

• Advanced addition and subtraction strategies
• Multiplication as repeated addition using skip counting
• Exploring patterns in larger numbers beyond 20
• Problem-solving with confidence and systematic thinking

LearningMole’s Continued Support: This adventure is just the beginning. LearningMole’s comprehensive educational resources provide ongoing support for mathematical development, ensuring every child has access to high-quality, engaging learning experiences that build confidence and competence.

The path from counting to mathematical mastery starts here, with solid understanding and genuine excitement for discovery. Through the counting on approach, you’ve given your child something invaluable: the knowledge that they can figure things out for themselves. Ready for the next adventure? Your mathematical explorer certainly is!