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.

• Grade 6
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Compare and order sets of integers, including positive numbers, negative numbers, and zero, using a number line.
2. Explain the meaning of inequality symbols (<, >, =) when comparing two integers.
3. Predict the relative order of integers based on their position on a number line without explicit plotting.
4. Represent relationships between integers using inequality statements.
5. Analyze the position of integers on a number line to determine their magnitude relative to zero.

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.

Prepare & details

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'.

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

⏱ 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.

Prepare & details

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.

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·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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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

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

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Floor Number Line, provide a half-page number line with integers -6, 0, and 4. Ask students to: 1. Plot the integers. 2. Write an inequality comparing -6 and 4. 3. Circle the word 'colder' or 'warmer' to describe -6 compared to 4.

Quick Check

During Inequality Match-Up, display a number line with -3, 1, and -1 marked. Ask students to hold up index cards with '<' or '>' to show the relationship between -3 and 1, then between -1 and 0.

Discussion Prompt

After Real-World Integer Hunt, pose: 'Two friends owe money: A owes $12, B owes $5. Who has the higher balance and why?' Facilitate a turn-and-talk where students explain using number line positions and inequality symbols.

Extensions & Scaffolding

• Challenge: Ask students to create a set of five integers that includes both positive and negative numbers. Then, have them write three true inequality statements and three false ones for a partner to correct.
• Scaffolding: Provide a partially labeled number line on paper for students to fill in before sorting integers during Card Sort.
• Deeper: Introduce absolute value as 'distance from zero' after Card Sort, using student-generated examples to explore why -7 and 7 have the same absolute value but are not equal.

Key Vocabulary

Integer	A whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.
Number Line	A visual representation of numbers, typically horizontal, with integers ordered from least to greatest from left to right.
Inequality Symbols	Symbols used to show that two numbers are not equal. '<' means 'less than', '>' means 'greater than', and '=' means 'equal to'.
Opposite Integers	Two integers that are the same distance from zero on the number line but in opposite directions. For example, 5 and -5 are opposite integers.