Compare and Order Integers and Rational Numbers
I can compare and order integers using a number line.
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🎯 Content Objective / Objetivo de contenido
I can compare and order integers using a number line.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Why is -3 less than 2, even though 3 looks like a bigger number than 2?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Trivia Game
Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?
Concept Launch
💡 How do you compare and order integers?
To compare integers means to see which one is greater or less. On a number line, numbers get bigger as you go right and smaller as you go left.
Comparing & Ordering Rational Numbers. Formula: Left is Less (<) | Right is Greater (>). 1. Plot or visualize numbers on a horizontal number line. 2. Numbers further to the left are always less than numbers to the right. 3. For negatives: A negative number with a larger absolute value is smaller (-10 < -2)
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Compare and Order Integers Comparar y ordenar enteros |
Use a number line to decide which integers are greater or less and place them in order. Usar una recta numérica para decidir cuáles enteros son mayores o menores y colocarlos en orden. |
−5 < −2 < 0 < 3 | |
| Number line Recta numérica |
A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right. Una recta donde los números se colocan en orden; los números son menores a la izquierda y mayores a la derecha. |
← -3 -2 -1 0 1 2 3 → | |
| Compare Comparar |
To see if a number is bigger, smaller, or equal to another. Ver si un número es mayor, menor o igual que otro. |
-3 < 2 because -3 is farther left on the number line than 2 | |
| Order Ordenar |
To arrange numbers by size, from least to greatest or greatest to least. Acomodar números por tamaño, de menor a mayor o de mayor a menor. |
Least to greatest: -5, -2, 0, 3, 7 (left to right on the number line) | |
| Greater than Mayor que |
The > sign, showing one number is bigger. El signo >, que muestra que un número es mayor. |
4 > -1 because 4 is to the right of -1 on the number line | |
| Less than Menor que |
The < sign, showing one number is smaller. El signo <, que muestra que un número es menor. |
-6 < -2 because -6 is farther left — it is farther from zero |
Which Word Fits?
On a number line, the number farther to the ___ is always less.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Why is -3 less than 2, even though 3 looks like a bigger number than 2?
👂 Listen For
Student explains that -3 is farther left on the number line than 2, and numbers decrease moving left.
Extend: Push students to explain why every negative number is less than every positive number.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Plot each treasure location (depths below sea level and heights above it) on the number line. Then order them from least to greatest.
✍️ Explore Discourse
How does plotting on the number line help you compare and order integers?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
Order these temperatures from coldest to warmest: -8, 3, -1, 5. How does the number line help you put them in order?
👂 Listen For
Student orders -8, -1, 3, 5 and uses left-to-right position on the number line to justify the order.
Extend: Ask students to write a comparison statement using < or > for two of the temperatures and read it aloud.
Practice Check A
Three cities have temperatures of -12°F, -5°F, and 3°F. Which city is warmest?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Which statement is TRUE?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Expression Simplify
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Sort each label into the correct box.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Comparing & Ordering Rational Numbers. Formula: Left is Less (<) | Right is Greater (>). 1. Plot or visualize numbers on a horizontal number line. 2. Numbers further to the left are always less than numbers to the right. 3. For negatives: A negative number with a larger absolute value is smaller (-10 < -2)" — and it works because ___.
Because Compare and Order Integers means ___, but a tricky part is ___, so I have to ___.
A common mistake with Compare and Order Integers is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Number line to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Comparing & Ordering Rational Numbers. Formula: Left is Less (<) | Right is Greater (>). 1. Plot or visualize numbers on a horizontal number line. 2. Numbers further to the left are always less than numbers to the right. 3. For negatives: A negative number with a larger absolute value is smaller (-10 < -2) because ___
Comparing & Ordering Rational Numbers. Formula: Left is Less (<) | Right is Greater (>). 1. Plot or visualize numbers on a horizontal number line. 2. Numbers further to the left are always less than numbers to the right. 3. For negatives: A negative number with a larger absolute value is smaller (-10 < -2) but ___
Comparing & Ordering Rational Numbers. Formula: Left is Less (<) | Right is Greater (>). 1. Plot or visualize numbers on a horizontal number line. 2. Numbers further to the left are always less than numbers to the right. 3. For negatives: A negative number with a larger absolute value is smaller (-10 < -2) so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot each treasure location (depths below sea level and heights above it) on the number line. Then order them from least to greatest.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Which statement is TRUE?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A weather station recorded these temperatures during a winter week: Monday -4°F, Tuesday 2°F, Wednesday -7°F, Thursday -1°F, Friday 5°F. The station needs to report the coldest and warmest days.
✍️ Connection Reasoning
How do you use integer comparison to find the coldest and warmest days?
The coldest day was ___ at ___°F because ___. The warmest day was ___ at ___°F. I ordered them from coldest to warmest by ___.
Turn & Talk — Connect
How does knowing a number's position on the number line tell you whether to use the < or > symbol?
👂 Listen For
Student connects left position to 'less than' and right position to 'greater than', and uses the symbol correctly.
Extend: Push students to generalize a rule for comparing two negative numbers, like -7 and -2.
Summarize: Compare and Order Integers and Rational Numbers
Comparing & Ordering Rational Numbers. Formula: Left is Less (<) | Right is Greater (>). 1. Plot or visualize numbers on a horizontal number line. 2. Numbers further to the left are always less than numbers to the right. 3. For negatives: A negative number with a larger absolute value is smaller (-10 < -2)
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which list shows the integers in order from LEAST to GREATEST?
Bonus Exit Check
Which integer is the LEAST: -3, 5, -8, 2, 0?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Student explains that -3 is farther left on the number line than 2, and numbers decrease moving left.
• Student orders -8, -1, 3, 5 and uses left-to-right position on the number line to justify the order.
• Student connects left position to 'less than' and right position to 'greater than', and uses the symbol correctly.
• Student explains -10 is less than -2 because it is farther left, correcting the 'bigger digits' misconception.
Common mistake: A common mistake in Compare and Order Integers is thinking that a negative number with a bigger digit is the bigger value — for example, believing -15 is greater than -8 because 15 is greater than 8. It's the opposite for negatives: the number farther to the left on the number line (farther from zero) is always the LESSER value, so -15 < -8. Before you submit, check your comparison against the number line, not just the digits.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 3°F — 3°F is the greatest because it is farthest to the right on the number line. The order from coldest to warmest is -12, -5, 3.
✓ Practice 2: -5 < -2 — -5 is farther to the left on the number line than -2, so -5 < -2 is true.
✓ Practice 3: -8 — -8 is farthest to the left on the number line, making it the least (smallest) integer.
✓ Practice 4: 8 — Absolute value is distance from 0, always positive. |−8| = 8.
✓ Exit ticket: -5, -2, 0, 3, 7 — -5 is the smallest (farthest left on the number line), then -2, then 0, then 3, then 7. The correct order from least to greatest is -5, -2, 0, 3, 7.