Mathematics · Grade 6

Active learning ideas

Comparing and Ordering Integers

Active learning works for comparing and ordering integers because students need to physically and visually engage with the abstract concept of negative and positive quantities. Movement and hands-on tasks help correct misconceptions about number line positions and symbol usage. These activities build spatial reasoning and symbolic fluency simultaneously.

• Ontario Curriculum Expectations
• 6.NS.C.7.A
• 6.NS.C.7.B

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 35 min · Whole Class

Floor Number Line: Human Plotting

Mark a number line on the floor with tape from -20 to 20. Call out integers for students to stand on, then ask pairs to compare their positions and state inequalities aloud. Have them predict where the next number goes before placing it. End with students creating their own sets for classmates.

Construct a number line to accurately order a set of integers.

Facilitation Tip

During Floor Number Line, walk beside students and ask them to explain why their integer belongs where they placed it, listening for vocabulary like 'to the left' or 'closer to zero'.

What to look for

Provide students with three integers, such as -8, 5, and -2. Ask them to: 1. Plot these integers on a provided number line. 2. Write an inequality statement comparing the smallest and largest integers. 3. Explain in one sentence why -8 is less than 5.

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

Activity 02

• Stations Rotation
• 25 min · Small Groups

Card Sort: Ordering Challenge

Distribute cards with integers like -8, 0, 5, -3. In small groups, students arrange cards on desks from least to greatest, justifying with number line sketches. Switch sets midway and time them for friendly competition. Discuss any errors as a class.

Explain how inequalities are used to describe relationships between integers.

Facilitation Tip

During Card Sort, circulate and ask struggling pairs to start with zero and build outward, using quiet think time before sorting aloud.

What to look for

Display a number line with several integers marked. Ask students to hold up fingers to indicate the position of a given integer (e.g., 'Show me where -3 goes'). Then, present two integers and ask students to write '<' or '>' on a mini-whiteboard to show their relationship.

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

Activity 03

• Stations Rotation
• 30 min · Pairs

Inequality Match-Up: Pairs Game

Prepare cards with integers and inequality statements, such as -4 ___ 2. Pairs draw cards, match true statements, and explain using horizontal number lines drawn on paper. Incorrect matches go back; first to 10 wins. Rotate partners halfway.

Predict the outcome of comparing two integers based on their position on a number line.

Facilitation Tip

During Inequality Match-Up, listen for explanations that include 'farther left means smaller' and gently correct any comparisons that ignore direction.

What to look for

Pose the question: 'Imagine you are comparing the scores of two video game players. Player A has a score of -15, and Player B has a score of -7. Who is winning and why? How does the number line help you explain this?' Facilitate a class discussion where students use the vocabulary and number line concepts.

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

Activity 04

• Stations Rotation
• 40 min · Individual

Real-World Integer Hunt: Individual Scavenger

Students list 10 real-world integers, like golf scores or elevations, then order them on personal number lines. Share in small groups, comparing lists and debating inequalities. Compile class examples on a shared board.

Construct a number line to accurately order a set of integers.

What to look for

Provide students with three integers, such as -8, 5, and -2. Ask them to: 1. Plot these integers on a provided number line. 2. Write an inequality statement comparing the smallest and largest integers. 3. Explain in one sentence why -8 is less than 5.

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

A few notes on teaching this unit

Experienced teachers approach this topic by emphasizing spatial reasoning over rote rules. They avoid teaching 'bigger numbers are always bigger' because that fails with negatives. Instead, they model the number line as a tool for comparison and encourage students to verbalize their thinking while moving or sorting. Research shows that students who explain their reasoning during these activities retain concepts longer.

Successful learning looks like students accurately plotting integers on a number line, using inequality symbols correctly, and explaining their reasoning with reference to position and direction. Partners should challenge each other’s reasoning during collaborative tasks. By the end of the activities, students should confidently compare any two integers and order sets of three or more.

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Watch Out for These Misconceptions

• During Floor Number Line, watch for students who place -5 to the right of 3 because they think the negative sign makes it 'bigger'.

  Ask them to stand at -5 and 3 on the floor line and feel the temperature analogy (colder at -5) or discuss bank balances (owing more is worse). Have peers point out that -5 is farther from zero on the left side.

• During Floor Number Line, watch for students who group zero with the negatives because they see the zero as 'nothing'.

  Have them stand on zero and ask if it feels like a debt or a credit. Prompt a discussion where students explain that zero is neutral, neither positive nor negative, by comparing it to freezing and boiling points on a temperature line.

• During Card Sort, watch for students who order -7, -2, -9 as -7, -2, -9 because they compare the digits without direction.

  Ask them to plot the numbers on a number line drawn on their desks. Then, prompt them to explain why -9 is the smallest by pointing to its position farthest left and comparing distances from zero.

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Methods used in this brief

• Stations Rotation