Mathematics · Grade 6

Active learning ideas

Comparing and Ordering Rational Numbers

Active learning works for this topic because rational numbers live in multiple forms—integers, fractions, and decimals—and students need to see these forms as interchangeable pieces that fit on a single number line. Physical movement and hands-on sorting give every learner a chance to correct misunderstandings in the moment. These activities build the precision and flexibility that paper-and-pencil work alone cannot provide.

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

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 35 min · Whole Class

Floor Number Line: Rational Walk

Mark a number line from -5 to 5 on the floor with tape. Students draw cards with rational numbers, stand at correct positions, and justify choices to the group. Class discusses and adjusts placements collaboratively.

Differentiate between comparing integers and comparing fractions.

Facilitation Tip

During the Floor Number Line activity, stand at the zero mark yourself so students can see how your body aligns with the numbers they place.

What to look for

Provide students with a set of 5 rational numbers including positive and negative integers, fractions, and decimals (e.g., -1.5, 3/4, -2, 0.75, 1/2). Ask them to order the numbers from least to greatest and write one sentence explaining how they determined the order of two specific numbers.

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

Activity 02

• Stations Rotation
• 25 min · Pairs

Pair Sort: Inequality Chains

Provide pairs with cards showing rationals and inequality symbols. They chain numbers like -1.5 < -3/4 = ? > 0.2, testing orders by converting to decimals. Pairs share chains with class for verification.

Construct a number line to accurately order a set of rational numbers.

Facilitation Tip

For the Pair Sort activity, circulate with a clipboard to record which inequality chains students get wrong most often.

What to look for

Present students with two number lines, one accurately ordered and one with errors. Ask: 'Which number line correctly orders the set of rational numbers? Explain your reasoning, referencing the position of zero and the relative distances between numbers.'

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

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Comparison Types

Set up stations: one for integers vs. fractions, one for decimals only, one for mixed signs. Groups complete ordering tasks at each, recording on charts. Rotate every 10 minutes and debrief.

Explain how inequalities are used to describe relationships between rational numbers.

Facilitation Tip

In the Station Rotation activity, place a timer at each station so students practice speed and accuracy under gentle pressure.

What to look for

Write three pairs of rational numbers on the board (e.g., -3/5 and -0.5, 7/4 and 1.75, -1.2 and -1 1/4). Ask students to write the correct inequality symbol (<, >, or =) between each pair on a mini-whiteboard and hold it up.

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

Activity 04

• Stations Rotation
• 30 min · Pairs

Digital Drag: Number Line Builder

Use online tools where students drag rationals to interactive number lines. They order sets individually first, then compare with partners. Discuss discrepancies and export for class gallery.

Differentiate between comparing integers and comparing fractions.

Facilitation Tip

When using the Digital Drag tool, ask students to verbalize their first move before clicking to surface their reasoning.

What to look for

Provide students with a set of 5 rational numbers including positive and negative integers, fractions, and decimals (e.g., -1.5, 3/4, -2, 0.75, 1/2). Ask them to order the numbers from least to greatest and write one sentence explaining how they determined the order of two specific numbers.

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

A few notes on teaching this unit

Teachers approach this topic by starting with concrete tools before moving to symbols, because students need to see that 0.75 and 3/4 occupy the same spot. Avoid rushing to rules for comparing negatives; instead, let students walk the floor line to feel the direction of inequality. Research suggests that students who physically plot numbers before symbolizing them make fewer sign errors and retain the concept longer. Use frequent quick-checks to uncover lingering confusions before they solidify.

Successful learning looks like students using inequality symbols with confidence, converting between fractions and decimals without prompts, and explaining their reasoning by pointing to positions on a number line. They should be able to justify comparisons with both visual and numeric evidence. Peer conversations should include phrases like 'I see it at this point' or 'After converting, it’s clear that...'.

---

Watch Out for These Misconceptions

• During the Floor Number Line activity, watch for students who assume fractions with larger denominators are bigger.

  After students place 1/5 and 1/2 on the floor line, ask them to convert both to decimals and stand on the new positions before revising their order.

• During the Floor Number Line activity, watch for students who believe negative decimals are larger than positives because of alphabetical order.

  Have students walk to -0.7 and 0.3, then hold a quick pair discussion about where zero sits and which side is 'less'.

• During the Station Rotation activity, watch for students who think more decimal places always mean a larger number.

  At the benchmark station, give students decimal grids to shade 0.12 and 0.9 so they see twelve hundredths versus nine tenths before reordering.

---

Methods used in this brief

• Stations Rotation