Mathematical Explorers: Building Number and Space · 3rd Class

Active learning ideas

Addition and Subtraction of Integers

Active learning works for integer addition and subtraction because these operations rely on spatial reasoning and concrete modeling. Students need to see and feel the difference between positive and negative movement, which physical activities like number lines and elevators provide. Movement-based tasks build lasting intuition that paper-and-pencil drills alone cannot.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.5
• NCCA: Junior Cycle - Number - N.6

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

Activity 01

• Collaborative Problem-Solving
• 30 min · Pairs

Number Line Walk: Integer Moves

Mark a large floor number line from -10 to 10. Pairs take turns calling problems like 4 + (-3) or -2 - (-5); the other walks from start to solution and states the result. Switch roles after five problems, then discuss patterns observed.

Explain how adding a negative number is similar to subtracting a positive number.

Facilitation Tip

During the Number Line Walk, have students take turns calling out moves aloud while the whole class follows along with their fingers on their own number lines to build shared accountability.

What to look for

Present students with the equation -7 + 3 = ?. Ask them to solve it using a number line, drawing their steps. Then, ask them to write one sentence explaining their answer.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 25 min · Whole Class

Temperature Tracker: Daily Changes

Whole class records morning temperature as starting integer. Add simulated changes like +2 or -4 throughout lesson using a shared chart. Students predict endpoints before updating, then verify with number lines.

Analyze the effect of adding or subtracting zero from an integer.

Facilitation Tip

For the Temperature Tracker, assign each pair a city to track for a week, then ask them to present their data using addition and subtraction of integers to show change.

What to look for

Pose the question: 'Is adding -5 the same as subtracting 5?' Have students discuss in pairs, using examples and number lines to justify their reasoning. Ask them to share their conclusions with the class.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 35 min · Small Groups

Elevator Challenge: Floor Operations

Small groups use mini number lines as elevators. Draw cards with problems like start at 3, +(-2), -1; move token and record sequence. Groups share one real-world elevator story matching their path.

Design a real-world scenario that requires the addition or subtraction of integers.

Facilitation Tip

In the Elevator Challenge, require each group to record their token moves on a whiteboard equation so you can see their reasoning before they announce the final floor.

What to look for

Give each student a scenario: 'A submarine is at a depth of 50 meters. It ascends 20 meters.' Ask them to write the integer addition or subtraction problem that represents this situation and calculate the final depth.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 20 min · Pairs

Zero Effect Relay: Sign Rules

Pairs line up; teacher calls integer plus zero variant like 5 + 0 or -3 - 0. First student computes and tags partner who verifies on personal number line. Rotate problems to cover all rules.

Explain how adding a negative number is similar to subtracting a positive number.

Facilitation Tip

During the Zero Effect Relay, time the race and have students reflect afterward on why zero never changes the starting value in their equations.

What to look for

Present students with the equation -7 + 3 = ?. Ask them to solve it using a number line, drawing their steps. Then, ask them to write one sentence explaining their answer.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach integer operations by pairing abstract symbols with physical movement first, then connect to real-world contexts like temperature or finance. Avoid teaching rules like 'two negatives make a positive' as a standalone chant. Instead, let students discover the pattern through repeated, guided trials with number lines or tokens. Research shows that students who generate their own rules through movement retain understanding longer than those given rules to memorize.

At the end of these activities, students should confidently explain integer operations using movement, signs, and real contexts. They should model equations with number lines or tokens, justify their steps aloud, and correct peers’ misapplications of sign rules. Success looks like students debating solutions in groups and adjusting their models based on feedback.

---

Watch Out for These Misconceptions

• During Number Line Walk, watch for students who assume adding a negative always makes the result smaller than any starting number.

  Pause the walk and ask the student to model -3 + (-2) on the line. Have them explain why the result is more negative, and ask the class to compare this to -3 + 2 to highlight the difference in direction.

• During Elevator Challenge, listen for groups that claim subtracting a negative always makes the result negative.

  Ask the group to act out -2 - (-3) using tokens, then have them discuss why the floor moves up to +1. Require them to explain their path to another group before they record the answer.

• During Zero Effect Relay, notice students who think adding or subtracting zero changes the starting number.

  Have the student race to confirm that zero tokens do not move the marker. Ask them to explain why zero leaves the position unchanged, and have peers verify with their own relays.

---

Methods used in this brief

• Collaborative Problem-Solving