Unit 2 · Standard 6.NS.1
Divide Mixed Numbers
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
2 1/3 means 2 wholes and 1/3 more — picture 2 full circles and 1/3 of another
Mixed Number
A whole number plus a fraction, like 2 1/2.
7/3 is improper because 7 > 3. It equals 2 1/3 as a mixed number.
Improper Fraction
A fraction where the top is bigger than or equal to the bottom, like 7/4.
2 1/3 → multiply 2 × 3 = 6, add 1 → 7/3. Same value, different form.
Convert
To change a number to a new form but keep the same value.
8/6: GCF is 2 → 8÷2 / 6÷2 = 4/3 = 1 1/3
Simplify
To make a fraction smaller using the same parts, like 2/4 = 1/2.
The reciprocal of 3/4 is 4/3. To divide by 3/4, multiply by 4/3.
Reciprocal
A fraction turned upside down. You use it in keep-change-flip.
Key Ideas & Notes
- Agent Chen is mapping a suspect's route.
- The total distance is 3 1/2 miles, and each segment between landmarks is 1/4 mile.
- She needs to know how many segments are on the route to place surveillance cameras at every landmark.
- Convert each mixed number to an improper fraction, then use Keep, Change, Flip to divide.
Think About It
- What is the total distance of the route?
- How long is each segment?
- Will the number of segments be more or less than 3?
My Notes
Guided Examples
Example 1
What is 1 1/2 ÷ 3/4?
Solution: 1 1/2 = 3/2. Then 3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2.
Answer: A. 2
Example 2
Convert 3 2/5 to an improper fraction.
Solution: 3 × 5 = 15, then 15 + 2 = 17. So 3 2/5 = 17/5.
Answer: A. 17/5
Example 3
What is 2 1/4 ÷ 3/4?
Solution: 2 1/4 = 9/4. Then 9/4 ÷ 3/4 = 9/4 × 4/3 = 36/12 = 3.
Answer: A. 3
Write About the Math The Writing Revolution
I can explain my steps using the words mixed number, improper fraction, convert, reciprocal, and simplify.
1. Kernel Sentence subject + verb
Model: Mixed Number is a whole number plus a fraction, like 2 1/2.Número mixto es un número entero más una fracción, como 2 1/2.
Write a kernel sentence about mixed number. Use a subject and a verb.Escribe una oración base sobre número mixto. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Mixed Number matters in mathNúmero mixto importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Mixed Number matters in math because ___.Número mixto importa en matemáticas porque ___.
Mixed Number matters in math, but ___.Número mixto importa en matemáticas, pero ___.
Mixed Number matters in math, so ___.Número mixto importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about mixed number.Di un hecho verdadero sobre mixed number.
Mixed number ___.
Ask a question about mixed number.Haz una pregunta sobre mixed number.
How does ___ ?¿Cómo ___ ?
Show excitement about mixed number.Muestra entusiasmo sobre mixed number.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with mixed number.Dile a un compañero qué hacer con mixed number.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
First I changed ___ into ___.Primero cambié ___ a ___.
Then I ___.Luego ___.
I would use this when ___.Usaría esto cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is 3 1/2 ÷ 1/4?
- 14
- 3 1/8
- 7/8
- 13/4
2. A recipe makes 2 1/4 batches of cookies. Each batch uses 3/4 cup of butter. How many cups of butter are needed in total?
- 3 cups
- 1 1/2 cups
- 2 cups
- 6 cups
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A detective has a rope that is 5 1/4 feet long. She needs to cut it into pieces that are each 3/4 foot for tying evidence tags. How many pieces can she cut? Write the equation, show each step (convert, keep-change-flip, multiply, simplify), and verify your answer.
Sentence starter: First I convert 5 1/4 to ___. Then I use KCF: ___ × ___ = ___. The answer is ___ pieces. I can verify because ___ × 3/4 = 5 1/4.
Reflect — Exit Ticket
What is 2 2/3 ÷ 2/3?
- 4
- 2/3
- 8/3
- 1 7/9
Answer Key & Teacher Guide
- Try It 1: A. 14 — 3 1/2 = 7/2. Then 7/2 ÷ 1/4 = 7/2 × 4/1 = 28/2 = 14.
- Try It 2: A. 3 cups — This is multiplication: 2 1/4 × 3/4 = 9/4 × 3/4 = 27/16. Wait — re-read: we need 2 1/4 batches at 3/4 cup each, but the question for division practice should be: if you have 2 1/4 cups and each batch needs 3/4 cup, how many batches? 2 1/4 ÷ 3/4 = 9/4 × 4/3 = 36/12 = 3.
- Exit Ticket: A. 4 — 2 2/3 = 8/3. Then 8/3 ÷ 2/3 = 8/3 × 3/2 = 24/6 = 4.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Mixed Number is a whole number plus a fraction, like 2 1/2.
- 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).