Mathematical Explorers: Building Foundations · 2nd Class · Counting and Place Value to 199 · Autumn Term

Before, After, and Between Numbers

Finding the highest common factor (HCF) and lowest common multiple (LCM) of two or more numbers using prime factorisation.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1.5

About This Topic

Before, after, and between numbers form a core skill in 2nd Class counting and place value up to 199. Students learn to identify the number immediately before or after any given number on the line from 0 to 199. They also find one or more numbers between two others and place sets of numbers in correct order. These tasks strengthen sequential understanding and prepare for addition, subtraction, and data handling.

This topic aligns with NCCA Primary Mathematics strands on number, fostering spatial awareness of quantity through the number line. Students practice mental strategies like counting on or back by ones or tens, which builds fluency and confidence. It connects to real-life contexts such as ordering birthdays, house numbers, or scores in games, making maths relevant.

Active learning shines here because physical movement and games turn abstract sequencing into concrete experiences. When students hop on floor number lines or race to place cards correctly, they internalize positions kinesthetically. Collaborative challenges reveal errors quickly, while peer teaching reinforces correct reasoning.

Key Questions

1. What number comes just before or just after a given number?
2. How can you find the number that comes between two numbers?
3. Can you place numbers correctly on a number line from 0 to 199?

Learning Objectives

• Identify the number immediately preceding a given number within the range of 0 to 199.
• Determine the number immediately succeeding a given number within the range of 0 to 199.
• Calculate the number that falls between two given numbers on a number line up to 199.
• Arrange a set of three numbers in sequential order on a number line from 0 to 199.

Before You Start

Counting to 100

Why: Students need a solid foundation in counting sequentially to understand the concept of 'before' and 'after'.

Number Recognition to 100

Why: Identifying specific numbers is crucial for locating them on a number line and determining their neighbors.

Key Vocabulary

Before	The number that comes immediately earlier on the number line. For example, 45 comes before 46.
After	The number that comes immediately later on the number line. For example, 72 comes after 71.
Between	A number that is greater than one number and less than another number. For example, 101 is between 100 and 102.
Number Line	A visual representation of numbers in order, extending infinitely in both directions. For this topic, we focus on the segment from 0 to 199.

Watch Out for These Misconceptions

Common Misconception

Numbers between 98 and 102 are only 99, 100, 101.

What to Teach Instead

Students overlook carrying over tens; between 98 and 102 includes 99, 100, 101. Hands-on number line walks show the full sequence visually. Pair discussions help peers spot gaps in counting.

Common Misconception

The number before 100 is 90.

What to Teach Instead

This skips from tens to ones place value confusion. Manipulating bead strings or abacus models clarifies place transitions. Group games with error-sharing build correction through trial.

Common Misconception

Between 150 and 160 means only even numbers.

What to Teach Instead

Assumes patterns without checking sequence. Collaborative card placement on lines reveals all integers fit. Active sorting reinforces inclusive counting rules.

Active Learning Ideas

Floor Number Line: Hop and Say

Mark a number line from 0 to 199 on the floor with tape and cards. Call out a number; students hop to it, then state the one before and after. Extend by asking for a number between two called numbers. Rotate leaders for calls.

30 min·Whole Class

Card Sort: Between Challenge

Provide cards with numbers 0-199. In pairs, draw two cards and find all numbers between them on a personal number line strip. Discuss and record three examples. Share one with the class.

25 min·Pairs

Stations Rotation: Place Value Positions

Set three stations: before/after spinner game, between number puzzles, and ordering mixed cards up to 199. Groups rotate every 7 minutes, recording answers on mini-whiteboards for quick checks.

35 min·Small Groups

Partner Relay: Number Line Race

Pairs line up at 0 end of a long number line. First student hops to a called number, says before/after, tags partner who finds between from there. First pair to 199 wins.

20 min·Pairs

Real-World Connections

• Bus drivers use sequential numbering to plan their routes and identify stops. They need to know which stop comes before and after a specific location to manage their schedule efficiently.
• Librarians organize books using Dewey Decimal or Library of Congress systems, which are numerical. Understanding the order of numbers helps them locate specific books and reshelve them correctly.
• Construction workers often number houses on a street sequentially. They need to identify which house number comes before or after a given address when delivering materials or performing services.

Assessment Ideas

Quick Check

Present students with a card showing a number (e.g., 135). Ask them to write down the number that comes immediately before and the number that comes immediately after on a small whiteboard. Circulate to check responses.

Exit Ticket

Give each student a slip of paper with two numbers, like 88 and 90. Ask them to write the number that comes between them. Then, provide another pair, like 140 and 141, and ask them to write the number that comes after. Collect these as students leave.

Discussion Prompt

Draw a number line from 150 to 160 on the board. Ask students: 'If I place the number 154 here, which number is before it? Which number is after it? Can you name two numbers that are between 150 and 160?' Encourage them to explain their reasoning.

Frequently Asked Questions

How do you teach before, after, and between numbers up to 199?

Start with concrete tools like floor number lines and hundred charts. Use daily warm-ups calling numbers for students to identify positions. Progress to mental challenges and games that mix skills, ensuring practice across ones and tens.

What activities work best for number line skills in 2nd Class?

Kinesthetic games like hopping on floor lines or relay races engage movement learners. Card sorts and station rotations allow differentiated practice. These build fluency while keeping energy high in short bursts.

How can active learning help students master before, after, and between numbers?

Active methods like physical number lines and partner relays make positions memorable through body movement and quick feedback. Students correct errors in real time during games, boosting retention over worksheets. Collaboration uncovers misconceptions as peers explain reasoning, aligning with NCCA emphasis on exploratory maths.

Common mistakes with numbers between 0 and 199?

Errors often stem from place value slips, like confusing 99 before 100 as 90. Address with visuals and talk time. Regular low-stakes games normalize mistakes, turning them into learning moments without pressure.