Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 6, Lesson 13: Prime Factorization

Standard 6.NOS.4

What students are learning Qué aprenden

Key idea: A prime number can only be divided evenly by 1 and itself, like 2, 3, 5, and 7. Prime factorization means breaking a number into primes that multiply to make it. Keep splitting until every number is prime: 40 = 2 × 2 × 2 × 5.Idea clave: Un número primo solo se puede dividir exactamente entre 1 y entre sí mismo, como 2, 3, 5 y 7. Descomponer en factores primos es separar un número en primos que se multiplican para formarlo. Sigue dividiendo hasta que todos los números sean primos: 40 = 2 × 2 × 2 × 5.

Words to know Palabras clave

Prime Factorization Factorización prima
A number written as a product of primes.
Un número escrito como producto de números primos.
Prime number Número primo
A number over 1 that only splits by 1 and itself.
Un número mayor que 1 que solo se divide entre 1 y sí mismo.
Composite number Número compuesto
A number over 1 that is not prime.
Un número mayor que 1 que no es primo.
Factor Factor
A number that goes into a number with none left.
Un número que divide a otro sin que sobre nada.
Factor tree Árbol de factores
A picture that splits a number down to prime numbers.
Un dibujo que separa un número hasta sus números primos.
Exponent Exponente
A small raised number. It counts the times a number is used.
Un número pequeño arriba. Cuenta las veces que se usa un número.

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 the prime factorization of 60. I start by splitting it: 60 = 6 × 10.
  2. 6 is not prime, so I break it: 6 = 2 × 3. Both 2 and 3 are prime, so I stop those branches.
  3. 10 is not prime, so I break it: 10 = 2 × 5. Both 2 and 5 are prime, so I stop.
  4. Now every factor is prime: 60 = 2 × 2 × 3 × 5.
  5. Using exponents, I write it as 2² × 3 × 5. I check: 2 × 2 × 3 × 5 = 60. Correct.

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 number to its prime factorization.

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Check the answer

The answer is: 2 × 2 × 3

Take-home sheet Hoja para llevar a casa

Lesson 6.13: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 6.13: 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 Prime Factorization is stopping the factor tree too soon — leaving a composite number like 4, 6, 8, or 9 in the final answer instead of continuing to split it. For example, writing 20 = 4 × 5 as the prime factorization (4 is composite) instead of finishing with 20 = 2 × 2 × 5. Before you submit, check every number in your final answer: if any factor can still be broken into smaller factors, the tree isn't finished yet.

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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