Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 6, Lesson 11: Fraction Division Problem Solving

Standard 6.NOS.1

What students are learning Qué aprenden

Key idea: In a word problem, decide what the question asks. 'How many 1/6-gallon tests fit in 2/3 gallon?' is 2/3 ÷ 1/6 = 4. 'Three people share 1/2 pound — how much each?' is 1/2 ÷ 3 = 1/6 pound. Check by multiplying back: 4 × 1/6 = 2/3.Idea clave: En un problema, decide qué pregunta. «¿Cuántas pruebas de 1/6 de galón caben en 2/3 de galón?» es 2/3 ÷ 1/6 = 4. «Tres personas reparten 1/2 libra, ¿cuánto recibe cada una?» es 1/2 ÷ 3 = 1/6 de libra. Comprueba multiplicando: 4 × 1/6 = 2/3.

Words to know Palabras clave

Fraction Division Problem Solving Resolución de problemas de división de fracciones
Divide with fractions to find how many groups or how big.
Dividir con fracciones para hallar cuántos grupos o qué tamaño.
Model Modelo
A picture or math sentence that shows the problem.
Un dibujo o una oración matemática que muestra el problema.
Equation Ecuación
A math sentence with an equal sign.
Una oración matemática con un signo de igual.
Solution Solución
A value that makes the math sentence true.
Un valor que hace verdadera la oración matemática.
Reasonableness Razonabilidad
Checking that an answer makes sense.
Comprobar que una respuesta tiene sentido.
Inverse operations Operaciones inversas
Two actions that undo each other, like × and ÷.
Dos acciones que se deshacen entre sí, como × y ÷.

Sentence starters Frases para empezar

I know ___ because ___.

First, I ___. Then, I ___.

The answer is ___, so ___.

How we did it in class today Cómo lo hicimos hoy en clase

  1. Agent Torres has 2/3 gallon of dust and each test uses 1/6 gallon. I ask: how many tests fit?
  2. The total 2/3 is the dividend. The size of each test 1/6 is the divisor. My equation is 2/3 ÷ 1/6.
  3. In sixths, 2/3 = 4/6, and 4 sixths ÷ 1 sixth = 4. Multiplying by the reciprocal gives the same answer: 2/3 × 6/1 = 12/3 = 4.
  4. So she can run 4 tests. I check by multiplying back: 4 × 1/6 = 4/6 = 2/3. It matches the total, so the answer is reasonable.

Play with today's math Jueguen con las matemáticas

Interactive Lesson Model — This is the exact same interactive tool your student used in class today. Change the numbers and watch what happens!

Modelo interactivo de la lección — Esta es la misma herramienta interactiva que su estudiante usó en clase hoy. ¡Cambie los números y observe qué sucede!

Works on a phone, a tablet, or a computer. Nothing to install, nothing to sign in to.

Try this together Inténtenlo juntos

Pick one question to talk about. You don't need to do them all!

A garden hose is 5/6 of a yard long. Each piece cut from it is 5/12 of a yard. How many pieces can be cut?

  1. 25/72
  2. 2
  3. 10
  4. 5/2
Check the answer

The answer is: 2

Take-home sheet Hoja para llevar a casa

Lesson 6.11: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 6.11: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

If they get stuck... Si se traban...

Watch out for this: A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup — how many servings? The correct setup is total ÷ group size = 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 servings. A student who reverses the setup calculates 1/8 ÷ 3/4 = 1/8 × 4/3 = 4/24 = 1/6, an answer smaller than 1 that can't possibly be a serving count. Before you submit, check: does my answer make sense as a NUMBER OF GROUPS? If the setup gives a fraction less than 1 for a 'how many' question, you likely swapped the dividend and divisor.

Try asking: "Can you show me how you got that? Did we miss a step?"
Pregunte: «¿Puedes mostrarme cómo lo hiciste? ¿Nos saltamos algún paso?» Hablar de las matemáticas en voz alta ayuda mucho.

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