Mathematics · 6th Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.6.NS.C.7a
• CCSS.Math.Content.6.NS.C.7b

• 20–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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.

What to look for

Provide students with a number line from -10 to 10. Ask them to plot the integers -7, 3, -1, and 0. Then, ask them to write one sentence comparing -7 and 3 using an inequality symbol.

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

Activity 02

• 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.

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.

What to look for

Present students with pairs of integers, such as (-4, -9) and (5, -5). Ask them to write the correct inequality symbol (<, >, or =) between each pair and explain their reasoning using the number line concept.

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

Activity 03

• 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.

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.

What to look for

Pose the question: 'Why is -10 considered colder than -2?' Have students discuss in pairs, using the number line and vocabulary like 'less than' and 'greater than' to support their explanations.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.'

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

  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.

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Methods used in this brief

• Human Barometer
• Think-Pair-Share