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.

• 2nd Class
• Mathematical Explorers: Building Foundations
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the sum of two two-digit numbers by partitioning into tens and units.
2. Apply a mental strategy to add two two-digit numbers without renaming.
3. Demonstrate the addition of two two-digit numbers using a column format.
4. Explain the process of adding tens and units separately to find a total.

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Pairs: Partition and Add Cards, present the problem 43 + 25 and ask students to write down how they partitioned the numbers and the total sum on a mini whiteboard before revealing the answer.

Exit Ticket

During Number Line Relays, give each student a 25 - 34 card and ask them to draw a quick number line showing the starting point, the jump backward, and the final position, including the sign of the answer.

Discussion Prompt

After Multiplication Arrays, pose the prompt: 'If you have 5 bags with -3 marbles each, how would you find the total? Explain the steps you would take and why the answer makes sense.'

Extensions & Scaffolding

• Challenge: Create a two-digit addition problem with a sum over 100, partition it on paper, then solve it mentally and write a reflection on which place value helped most.
• Scaffolding: Provide pre-partitioned number cards (e.g., 45 shown as 40 + 5) and a second set of tens and ones blocks for students to build and add.
• Deeper exploration: Ask students to write word problems for their array (e.g., 4 rows of 6 apples) and then solve for the total using both addition and multiplication, comparing the two approaches.

Key Vocabulary

Tens	The digit representing the number of groups of ten in a number. For example, in 34, the 3 represents 3 tens or 30.
Units	The digit representing the individual ones in a number. For example, in 34, the 4 represents 4 units or 4 ones.
Partition	To break a number down into smaller parts, such as breaking a two-digit number into its tens and units.
Column Addition	A method of adding numbers by writing them one below the other, aligning digits by place value (tens under tens, units under units).