Unit 9 · Standard 6.NS.6
Rational Numbers on the Number Line
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
1/2 = 0.5, -3/4 = -0.75, 6 = 6/1 — all rational numbers
Rational number
Any number you can write as a fraction. This includes fractions, decimals, and integers.
3/4 means 3 out of 4 equal parts — like 3 slices of a pizza cut into 4
Fraction
A number that shows part of a whole, like 3/4.
0.5 = 1/2 (halfway between 0 and 1 on the number line)
Decimal
A number with a dot, like 0.5, that shows a part less than one.
A line with marks at -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2
Number line
A straight line with numbers spaced out evenly.
1/2 = 0.5 = 2/4 — all name the same point on the number line
Equivalent
Having the same value, just written a different way.
..., -3, -2, -1, 0, 1, 2, 3, ...
Integer
Whole numbers and their opposites, like -2, -1, 0, 1, 2.
Key Ideas & Notes
- Captain Vega's advanced treasure map uses precise coordinates — not just whole numbers!
- One clue says the treasure is at -2.5 on the map (halfway between -2 and -3).
- Another clue points to 3/4 of the way from 0 to 1.
- A third clue leads to -1 1/2.
- Plot each rational number at its precise location on the number line.
Think About It
- Where would -2.5 fall on a number line between -3 and -2?
- How is plotting 3/4 different from plotting a whole number?
- Can a negative number be a fraction or decimal?
My Notes
Guided Examples
Example 1
Which point is located between -1 and -2 on the number line?
Solution: -1.5 is between -1 and -2 because it is 0.5 units to the left of -1 (or 0.5 units to the right of -2).
Answer: B. -1.5
Example 2
Which fraction is equivalent to 0.25?
Solution: 0.25 means 25 hundredths = 25/100 = 1/4.
Answer: A. 1/4
Example 3
Where is -3/4 located on the number line?
Solution: -3/4 = -0.75, which is between 0 and -1. It is 3/4 of the way from 0 toward -1.
Answer: A. Between 0 and -1
Write About the Math The Writing Revolution
I can explain my reasoning using the words rational number, fraction, decimal, and number line.
1. Kernel Sentence subject + verb
Model: Rational number is any number you can write as a fraction. This includes fractions, decimals, and integers.Número racional es cualquier número que puedes escribir como fracción. Incluye fracciones, decimales y enteros.
Write a kernel sentence about rational number. Use a subject and a verb.Escribe una oración base sobre número racional. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Rational number matters in mathNúmero racional importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Rational number matters in math because ___.Número racional importa en matemáticas porque ___.
Rational number matters in math, but ___.Número racional importa en matemáticas, pero ___.
Rational number matters in math, so ___.Número racional importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about rational number.Di un hecho verdadero sobre rational number.
Rational number ___.
Ask a question about rational number.Haz una pregunta sobre rational number.
How does ___ ?¿Cómo ___ ?
Show excitement about rational number.Muestra entusiasmo sobre rational number.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with rational number.Dile a un compañero qué hacer con rational number.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I placed ___ between ___ and ___.Coloqué ___ entre ___ y ___.
I knew because ___.Lo supe porque ___.
I see this when ___.Veo esto cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Where is -3/4 located on the number line?
- Between 0 and -1
- Between -3 and -4
- Between -1 and -2
- Between 0 and 1
2. Which rational number is closest to 0 on the number line?
- -1/4
- 0.5
- -2
- 1.75
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Name three different rational numbers between -1 and 0. Write each as both a fraction and a decimal. Explain how you know they are between -1 and 0.
Sentence starter: Three rational numbers between -1 and 0 are: ___ = ___, ___ = ___, and ___ = ___. I know they are between -1 and 0 because ___.
Reflect — Exit Ticket
Which rational number is located between -2 and -3 on the number line?
- -1.5
- -2.75
- -3.5
- 2.5
Answer Key & Teacher Guide
- Try It 1: A. Between 0 and -1 — -3/4 = -0.75, which is between 0 and -1. It is 3/4 of the way from 0 toward -1.
- Try It 2: A. -1/4 — |-1/4| = 0.25, |0.5| = 0.5, |-2| = 2, |1.75| = 1.75. Since 0.25 is the smallest absolute value, -1/4 is closest to zero.
- Exit Ticket: B. -2.75 — -2.75 is between -2 and -3 because it is 0.75 units to the left of -2. -1.5 is between -1 and -2, and -3.5 is between -3 and -4.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Rational number is any number you can write as a fraction. This includes fractions, decimals, and integers.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).