Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 6, Lesson 1: Division Expressions with Fractions and Whole Numbers

Standard 6.NOS.1

What students are learning Qué aprenden

Key idea: Dividing by a fraction asks how many of those pieces fit. 3 ÷ 1/4 means: how many quarter-foot pieces fit in 3 feet? Each foot has 4 quarters, so 3 × 4 = 12. Check: 12 quarters make 3 feet.Idea clave: Dividir entre una fracción pregunta cuántas de esas piezas caben. 3 ÷ 1/4 significa: ¿cuántas piezas de un cuarto de pie caben en 3 pies? Cada pie tiene 4 cuartos, así que 3 × 4 = 12. Comprueba: 12 cuartos forman 3 pies.

Words to know Palabras clave

Division of Fractions División de fracciones
Find how many small pieces fit in a big one.
Hallar cuántas partes pequeñas caben en una grande.
Reciprocal Recíproco
A fraction turned upside down.
Una fracción volteada de arriba abajo.
Quotient Cociente
The answer when you divide.
La respuesta de dividir.
Dividend Dividendo
The number you split up.
El número que se reparte en grupos.
Divisor Divisor
The number you divide by.
El número entre el que divides.
Unit fraction Fracción unitaria
A fraction with 1 on top, like 1/4.
Una fracción con 1 arriba, como 1/4.
Multiplicative inverse Inverso multiplicativo
Two numbers that multiply to make 1.
Dos números que al multiplicarse dan 1.
Tape diagram Diagrama de cinta
A bar cut into equal parts to show amounts.
Una barra dividida en partes iguales para mostrar cantidades.

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. I want to cut a 3-foot strip of tape into 1/4-foot pieces, so I write 3 ÷ 1/4. It asks: how many 1/4-foot pieces fit in 3 feet?
  2. Each foot holds 4 quarter-foot pieces, so 3 feet hold 3 × 4 = 12 pieces.
  3. That is why the shortcut works: dividing by 1/4 gives the same answer as multiplying by its reciprocal, 4/1. So 3 ÷ 1/4 = 3/1 × 4/1 = 12. (Some people call this Keep, Change, Flip.)
  4. Check by multiplying: 12 pieces × 1/4 foot = 12/4 = 3 feet. So 3 ÷ 1/4 = 12 pieces.
  5. One more move to know: mixed number → improper fraction: multiply the bottom by the whole number, add the top, keep the same bottom. 3 1/2 → (2 × 3) + 1 = 7 → 7/2.

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!

Match each division expression to its quotient.

5 ÷ 1/2

Check the answer

The answer is: 10

Take-home sheet Hoja para llevar a casa

Lesson 6.1: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 6.1: 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 Interpret Division of Fractions is assuming that dividing always makes the answer smaller. For 4 ÷ 1/3, students reason 'dividing shrinks the number' and compute 4 ÷ 3 ≈ 1.3 instead of asking how many 1/3-foot pieces fit into 4 feet (each whole foot holds 3 thirds, so 4 × 3 = 12). Before you submit, check: if the divisor is a fraction smaller than 1, the quotient must be BIGGER than the dividend, not smaller.

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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