Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Before, After, and Between Numbers

Active tasks let students physically and visually experience the flow of numbers before, after, and between, which cements place value understanding better than worksheets alone. Moving along a number line or sorting cards turns abstract counting into a lived sequence they can see and correct in real time.

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

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 30 min · Whole Class

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.

What number comes just before or just after a given number?

Facilitation Tip

During Floor Number Line: Hop and Say, position yourself at the zero end so you can see every student’s jump and count aloud together to reinforce the rhythm.

What to look for

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.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Pairs

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.

How can you find the number that comes between two numbers?

Facilitation Tip

For Card Sort: Between Challenge, provide paper clips to group matched trios so students can see the before-middle-after structure physically.

What to look for

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.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Stations Rotation
• 35 min · Small Groups

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.

Can you place numbers correctly on a number line from 0 to 199?

Facilitation Tip

In Station Rotation: Place Value Positions, set a timer for 6 minutes so students move before they lose focus but still complete the task.

What to look for

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.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Think-Pair-Share
• 20 min · Pairs

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.

What number comes just before or just after a given number?

Facilitation Tip

During Partner Relay: Number Line Race, assign roles so one partner runs the card while the other records the next number to keep both engaged.

What to look for

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.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Begin with concrete models like bead strings or place-value charts to show how crossing a ten or hundred changes the sequence. Avoid rushing to abstract symbols; let students verbalize the transition from 99 to 100 while touching each bead. Research shows that pairing verbal counting with physical movement builds stronger number-line images than silent worksheets.

Students will confidently state the number immediately before or after any number from 0 to 199 without hesitation. They will also correctly identify and list one or more numbers that fit between two given numbers, and arrange sets of numbers in ascending order.

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Watch Out for These Misconceptions

• During Card Sort: Between Challenge, watch for students who skip numbers when bridging tens, such as listing only 99, 101 between 98 and 102.

  Have them lay out all the 0–199 cards in order on the floor, then circle the trio 99, 100, 101 to show the missing 100 fits exactly in the middle.

• During Station Rotation: Place Value Positions, watch for students who say the number before 100 is 90.

  Ask them to move the bead counters back one place on the abacus and say the new digit aloud to see that 99 becomes 100, not 90.

• During Floor Number Line: Hop and Say, watch for students who assume only even numbers lie between 150 and 160.

  Have them hop each integer out loud as they land to prove 151, 152, 153, and so on all fit between 150 and 160.

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Methods used in this brief

• Think-Pair-Share
• Stations Rotation