Foundations of Mathematical Thinking · Senior Infants · Counting and Number Sense · Autumn Term

Counting On and Counting Back

Understanding percentages as fractions and decimals, and calculating percentages of quantities.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.9

About This Topic

Counting on and counting back build essential number sequence fluency for Senior Infants. Children start from any number, such as 5, and count on three more to reach 8, or count back from 10 to 1. These practices answer key questions like 'What number comes next from 7?' and develop confidence with numbers to 20. Regular practice strengthens forward and backward recitation, a core part of the NCCA Counting and Number Sense unit.

This topic connects directly to early addition and subtraction precursors. Visualizing a mental number line emerges as children jump from one number to another, fostering part-whole thinking. In the Foundations of Mathematical Thinking strand, it supports oral counting goals and prepares for written numerals. Concrete tools like fingers or counters make the sequence tangible before abstract jumps.

Active learning benefits this topic greatly because young children thrive on movement and repetition. Games with full-body number lines, partner counting chains, or songs with gestures create joyful contexts for practice. These approaches reduce anxiety, encourage peer support, and embed skills through multi-sensory engagement, leading to lasting number sense.

Key Questions

1. Start at 5 and count on 3 more , what number did you reach?
2. Can you count back from 10 to 1?
3. If I am at number 7, what number comes next?

Learning Objectives

• Demonstrate counting on from a given number up to 20.
• Identify the number that comes immediately after a given number up to 20.
• Recite numbers in descending order from 20 down to 1.
• Calculate the result of counting back a specified number of steps from a given number up to 20.

Before You Start

Rote Counting to 20

Why: Students need to be able to recite numbers in order before they can count on or count back from a specific number.

Number Recognition (0-20)

Why: Recognizing the numerals helps students connect the spoken number to its written form during counting activities.

Key Vocabulary

Count on	To say the next number in a sequence after a starting number. For example, starting at 5 and counting on 3 more means saying 6, 7, 8.
Count back	To say the previous number in a sequence before a starting number. For example, counting back from 7 means saying 6, 5, 4.
Next number	The number that immediately follows another number in the counting sequence. If you are at 9, the next number is 10.
Number sequence	A list of numbers in a specific order, either increasing (counting on) or decreasing (counting back).

Watch Out for These Misconceptions

Common Misconception

Counting on always starts from 1.

What to Teach Instead

Children often default to rote forward counting from the beginning. Use a floor number line where they physically start midway and hop forward, helping them see the sequence as flexible. Peer teaching in pairs reinforces correct starts through shared demonstration.

Common Misconception

Counting back means skipping numbers.

What to Teach Instead

Rushing leads to gaps, like from 10 to 7 directly. Manipulatives such as bead strings allow slow, tactile slides backward, building accuracy. Group relays add fun accountability, as teams check each other's counts aloud.

Common Misconception

Direction changes confuse the sequence.

What to Teach Instead

Some mix up on and back paths. Bidirectional number line walks clarify flow both ways. Whole-class chants with gestures solidify orientation through repetition and visual cues.

Active Learning Ideas

Floor Number Line: Hop and Count

Tape a number line from 0 to 20 on the floor. Call out a starting number and direction, such as 'Start at 6, count on 4.' Children hop along the line while chanting numbers. Extend by having them lead for peers.

30 min·Whole Class

Partner Finger Chains: Count On/Back

Pairs face each other and hold up fingers to show a starting number, like 7. One partner says 'count on 3,' and both extend fingers while counting aloud together. Switch roles after five rounds.

20 min·Pairs

Bead String Relay: Group Counts

Provide bead strings or knotted ropes marked 1-20. Small groups start at a called number and slide beads while counting on or back as a team. First group to reach the target wins a point.

25 min·Small Groups

Song Circle: Counting Back Chant

Sit in a circle and sing adapted songs like 'Ten Little Ducks' for counting back. Pass a soft toy around as children count down together, removing one 'duck' each verse. Discuss the final number reached.

15 min·Whole Class

Real-World Connections

• Children in a kindergarten class might count on to see how many children are present after a few more arrive, or count back the number of snacks left on a plate.
• A librarian might count on to find the next available book on a shelf or count back to find a specific book number in a series.

Assessment Ideas

Quick Check

Ask individual students to start at a number like 8 and count on 4 more. Observe if they can correctly state the final number. Then, ask them to count back from 12 by 3. Note their accuracy in both forward and backward counting.

Exit Ticket

Provide students with a card showing a number, for example, 'Start at 6'. Ask them to write the number that comes next. On another card, show 'Count back from 10'. Ask them to write the number that comes before 10.

Discussion Prompt

Pose a scenario: 'Imagine we have 7 blocks, and we add 3 more. How many blocks do we have now?' Encourage students to explain their counting on strategy. Then ask, 'If we had 15 toys and put 5 away, how many are left?' Listen for their counting back process.

Frequently Asked Questions

How can active learning help teach counting on and back?

Active learning engages Senior Infants kinesthetically, turning abstract sequences into physical experiences. Floor number lines for hopping, partner finger counts, and song circles with gestures build fluency through movement and collaboration. These methods reduce errors from rote memory alone, boost retention via multi-sensory input, and foster confidence as children lead activities. Over time, skills transfer to mental counting for addition foundations.

What are effective activities for counting back in senior infants?

Use songs like 'Ten Green Bottles' in a circle, passing objects while counting down. Bead strings in small groups let children slide back tactilely. Floor number lines for backward hops make direction concrete. These 15-30 minute activities, repeated daily, embed the skill joyfully and address NCCA oral counting goals.

Common mistakes when teaching counting on?

Pupils often restart from 1 or skip numbers. Address with visual aids like marked ropes or fingers held up from the start point. Partner chains ensure verbal checks, while group relays add motivation. Short, frequent sessions prevent overload and build accuracy progressively to 20.

How does counting on link to addition in early years?

Counting on mirrors addition by bridging from a start number, like 5 + 3 as '5, 6, 7, 8.' Concrete tools like counters or body hops connect counting to quantity. In NCCA strands, this fluency supports mental strategies before formal symbols, easing transition to Junior Infants operations.