Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 4, Lesson 5: Determine the Whole Given the Part and Percent

Standard 6.AT.4

What students are learning Qué aprenden

Key idea: If $42 is 60% of a price, the full price is $70. The full amount represents 100%.Idea clave: Si $42 representa el 60% de un precio, el precio total es $70. La cantidad total representa el 100%.

Words to know Palabras clave

Determine the Whole Given the Part and Percent Hallar el total dados la parte y el porcentaje
Use a part and its percent to find the whole.
Usar una parte y su porcentaje para hallar el total.
Part Parte
A piece of the whole.
Una pieza del total.
Whole Total
The full amount. It is always 100%.
La cantidad completa. Siempre es 100%.
Double number line Recta numérica doble
Two number lines side by side. Marks that line up go together.
Dos rectas numéricas juntas. Las marcas que coinciden van juntas.
Equation Ecuación
A math sentence with an equal sign.
Una oración matemática con un signo de igual.
Percent Porcentaje
A number out of 100, shown with the % sign.
Un número de cada 100, con el signo %.
Inverse operation Operación inversa
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. Akela paid $42 for a sweater on sale, and that was 60% of the original price. The $42 is the part; the original price is the whole, which is 100%.
  2. I put the matching values in a ratio table: 60% pairs with $42. I want a friendly 10% row, so I divide both values by 6: 10% pairs with $7.
  3. To reach the whole, I multiply both values in the 10% row by 10: 100% pairs with $70. The original price is $70, which is larger than the sale price.
  4. I can check the table with an equation: 0.6 × v = 42, so v = 42 ÷ 0.6 = 70. The equation describes the same part-to-whole relationship.

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 bike's sale price is $36, which is 40% of the original price. What was the original price?

  1. $14.40, because 0.4 × 36 = 14.40
  2. $40, because the percent is 40
  3. $76, because 36 + 40 = 76
  4. $90, because 36 ÷ 0.4 = 90
Check the answer

The answer is: $90, because 36 ÷ 0.4 = 90

Take-home sheet Hoja para llevar a casa

Lesson 4.5: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 4.5: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

Try at home Para hacer en casa

Make up a mystery whole: imagine a student finished 12 math problems, and that was 40% of their homework. Write the equation 0.40 × w = 12. Divide 12 by 0.40 to reveal the total number of problems, then check by calculating 40% of your answer.

Inventen un entero misterioso: imaginen que un estudiante completó 12 problemas de matemáticas, que representan el 40% de su tarea. Escriban la ecuación 0.40 × w = 12. Dividan 12 entre 0.40 para descubrir el número total de problemas y luego comprueben calculando el 40% de su respuesta.

Talk about it:

When the whole is missing, why do we divide by the decimal percent instead of multiplying?

Cuando falta el total, ¿por qué dividimos entre el porcentaje decimal en vez de multiplicar?

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

Watch out for this: Multiplying the part by the percent instead of dividing. Multiplying gives a smaller number, but the whole must always be bigger than the part.
Atención: Multiplicar la parte por el porcentaje en vez de dividir. Multiplicar da un número menor, pero el total siempre debe ser mayor que la parte.

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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