Comparing and Ordering Integers

Active learning helps students internalize the relative positions of integers on the number line, turning abstract symbols into concrete visual and kinesthetic experiences. When students move bodies, cards, or markers, the left-right relationship between numbers becomes intuitive, especially for negative values where larger absolute numbers are actually smaller in value.

• 6th Grade
• Mathematics
• 3 activities
• 20 min–30 min

Learning Objectives

1. Compare the values of two integers using inequality symbols (<, >, =) based on their positions on a number line.
2. Explain the relationship between the position of an integer on a number line and its value, particularly for negative integers.
3. Construct an argument justifying the order of a set of integers, including negative numbers, using number line placement.
4. Evaluate real-world scenarios to order integers, demonstrating understanding of their relative magnitudes in context.

Human Barometer

⏱ 20 min·Whole Class

Whole Class Activity: Live Number Line Ordering

Give each student a card with an integer. Without talking, students arrange themselves on a physical number line marked on the floor, then justify their positions aloud when asked. Include both positive and negative numbers, and place a few negative integers with large absolute values to surface the key comparison misconception.

Prepare & details

Explain how the position on a number line determines the value of an integer.

Facilitation Tip: During the Live Number Line Ordering, have students physically step to their chosen positions and verbalize their reasoning to reinforce the left-right comparison out loud.

Setup: Open space for students to form a line across the room

Materials: Statement cards, End-point labels (Agree/Disagree), Optional: recording sheet

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Argue the Order

Give pairs a specific claim to debate: 'Is -5 less than or greater than -2? Build a number line argument and a real-world argument.' Each pair prepares both types of justification, then shares with the class. This surfaces multiple valid reasoning paths for the same comparison.

Prepare & details

Construct an argument for why -5 is less than -2.

Facilitation Tip: In the Think-Pair-Share, circulate to listen for students who use phrases like 'further left' or 'closer to zero' to guide those who rely only on absolute value.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Human Barometer

⏱ 30 min·Small Groups

Card Sort: Ordering Integers

Provide sets of 10-12 integer cards to each group. Students order them from least to greatest, then write the complete ordering using inequality symbols. A second round adds rational numbers (fractions and decimals) to the same cards so students extend the same logic to non-integers.

Prepare & details

Evaluate real-world scenarios that require ordering negative numbers.

Facilitation Tip: During the Card Sort, watch that students do not sort by digit alone; prompt groups to place cards on a large number line strip to confirm their order before finalizing.

Setup: Open space for students to form a line across the room

Materials: Statement cards, End-point labels (Agree/Disagree), Optional: recording sheet

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Teaching This Topic

Experienced teachers avoid relying solely on rules like 'the bigger the negative number, the smaller it is' because such phrases often confuse students. Instead, teachers anchor instruction in the number line model and use consistent language: 'A number to the left is less than a number to the right.' They also model error correction by reading inequalities aloud both ways ('-3 < 2' and '2 > -3') to build fluency with symbol reversal.

What to Expect

Students will correctly order integers from least to greatest, use inequality symbols with accuracy, and explain their reasoning using number line language. They will also recognize that reversing an inequality statement requires flipping the symbol and be able to justify their choices through discussion or written work.

Watch Out for These Misconceptions

Common Misconception

During Live Number Line Ordering, watch for students who place -8 to the right of -5 because they see 8 as larger than 5.

What to Teach Instead

Have the student step onto the number line and physically compare positions, saying, 'Which side of zero is -8 on? Which side is -5 on? Which number is further left?' Guide them to place the cards accordingly and verbalize, 'Since -8 is further left, it is less than -5.'

Common Misconception

During Think-Pair-Share when rewriting 3 > -1 as something else, watch for students who write -1 > 3 without flipping the symbol.

What to Teach Instead

Prompt students to read both statements aloud: 'Three is greater than negative one' and 'Negative one is less than three.' Ask them to check if both statements are true and verify the symbol matches the meaning.

Assessment Ideas

Exit Ticket

After Live Number Line Ordering, give students a number line from -10 to 10. Ask them to plot -4, 7, -1, and 0, then write a single sentence comparing -4 and 7 using an inequality symbol and explain why that comparison is true.

Quick Check

During Card Sort, present pairs like (-6, -2) and (4, -4). Ask students to place the correct inequality symbol between each pair and briefly explain their choice using the number line positions before sorting the rest of the cards.

Discussion Prompt

After Think-Pair-Share, pose the question: 'Why is -15 considered colder than -8?' Have students discuss in pairs, using the number line and vocabulary like 'less than' and 'further left' to justify their explanations with the whole class.

Extensions & Scaffolding

• Challenge: Provide integers with absolute values beyond the typical range (e.g., -15, 12, -8) and ask students to order them and explain how they compare to zero.
• Scaffolding: Offer a partially completed number line template with some integers missing; students fill in the blanks before inserting their own numbers.
• Deeper exploration: Ask students to create their own 'temperature scenario' using integers and write inequalities to compare them, then swap with a partner to solve.

Key Vocabulary

Integer	A whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, and 5.
Number Line	A visual representation of numbers where each point corresponds to a real number. It is typically drawn as a straight line with arrows at both ends.
Inequality Symbols	Symbols used to compare two numbers or expressions. '<' 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, 3 and -3 are opposite integers.