Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Operations with Integers

Active learning lets students physically manipulate numbers and move through space, which builds lasting intuition for integer operations. Partitioning numbers into tens and ones, jumping on number lines, and arranging counters into arrays turn abstract rules into visible, tactile logic that sticks beyond worksheets.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1.2

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

Activity 01

• Stations Rotation
• 25 min · Pairs

Pairs: Partition and Add Cards

Provide cards showing two-digit numbers split into tens and ones. Pairs match pairs like 30+20 and 4+5 to form full additions without renaming, then write the sum in columns. Switch partners to check work and share mental tricks.

How do you add two-digit numbers by adding tens and units separately?

Facilitation Tip

During Pairs: Partition and Add Cards, circulate and ask each pair to explain how they split 48 into 40 and 8 before adding 23 split into 20 and 3.

What to look for

Present students with the addition problem 43 + 25. Ask them to write down how they would partition the numbers (e.g., 40 + 3 + 20 + 5) and then calculate the total sum.

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

Activity 02

• Stations Rotation
• 35 min · Small Groups

Small Groups: Number Line Relays

Mark a floor number line from -10 to 100. Groups take turns jumping to solve additions or subtractions, like start at 34, add 25. Record jumps on mini whiteboards and discuss paths as a group.

What strategy can you use to add numbers like 34 + 25 in your head?

Facilitation Tip

During Number Line Relays, remind teams to announce the jump size and direction before they leap so peers can check for accuracy.

What to look for

Give each student a card with a different two-digit addition problem, such as 51 + 36. Ask them to solve it using column addition on the back of the card and then circle the number that represents the total number of tens in their answer.

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

Activity 03

• Stations Rotation
• 30 min · Whole Class

Whole Class: Multiplication Arrays

Project grid paper. Class chorally counts arrays for 3x4 as repeated addition, then draws own arrays for facts up to 5x5. Pairs verify each other's work before sharing with class.

Can you set out an addition sum in columns and find the correct answer?

Facilitation Tip

During Multiplication Arrays, ask groups to point to the number of rows and the number in each row before writing the equation.

What to look for

Ask students: 'Imagine you have 24 marbles and your friend gives you 35 more. How could you figure out the total number of marbles quickly in your head? Explain the steps you would take.'

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

Activity 04

• Stations Rotation
• 20 min · Individual

Individual: Division Sharing Mats

Give counters and mats divided into groups. Students share 12 counters into 3 groups, recording as 12 ÷ 3 = 4. Extend to drawings for remainders, then self-check with inverse multiplication.

How do you add two-digit numbers by adding tens and units separately?

Facilitation Tip

During Division Sharing Mats, prompt students to say how many items each person gets and how many are left over before writing the quotient.

What to look for

Present students with the addition problem 43 + 25. Ask them to write down how they would partition the numbers (e.g., 40 + 3 + 20 + 5) and then calculate the total sum.

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

A few notes on teaching this unit

Teachers introduce each operation with a short demonstration using base-ten blocks or counters, then immediately hand the materials to students for guided practice. Avoid rushing to the algorithm; instead, insist on verbalizing place value or direction before writing symbols. Research shows that students who construct meaning through movement and discussion retain sign rules and regrouping better than those who memorize steps from a slide.

Students will confidently explain why place value matters in addition, interpret subtraction as movement on a line, see multiplication as repeated groups, and model division as fair sharing. They will describe their steps aloud and connect concrete materials to written equations without guessing the sign of the answer.

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Watch Out for These Misconceptions

• During Pairs: Partition and Add Cards, watch for students who add the tens digits first and then add the ones digits to the original tens total, producing an incorrect sum.

  Hand each pair two sets of base-ten blocks to build both numbers separately. Ask them to combine the ones first, count if they reach ten or more, and then combine the tens, narrating each step aloud before recording the sum.

• During Number Line Relays, watch for students who assume subtracting a larger number always yields a positive result because they only move right on the line.

  When a team lands on a negative value, pause the relay and ask, 'What does this negative position mean in our scenario?' Have them tell a short story about owing marbles or losing points to anchor the direction of movement.

• During Multiplication Arrays, watch for students who conclude that multiplying two negative numbers gives a negative because they only see the sign of one factor.

  Have groups build an array for 3 x (-2) by repeatedly adding groups of negative counters and observing the running total. Then ask them to build (-2) x 3 by flipping the direction of addition, leading them to see why two negatives produce a positive.

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Methods used in this brief

• Stations Rotation