Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 6, Lesson 7: Find Factors and Multiples

Standard 6.NOS.4

What students are learning Qué aprenden

Key idea: A factor divides a number evenly: 4 is a factor of 12. A multiple is what you get when you skip-count: 12, 24, 36 are multiples of 12. Use the greatest common factor to split things into equal groups, and the least common multiple to find when two repeating events happen together.Idea clave: Un factor divide a un número exactamente: 4 es factor de 12. Un múltiplo es lo que obtienes al contar de salto en salto: 12, 24, 36 son múltiplos de 12. Usa el máximo común divisor para repartir en grupos iguales, y el mínimo común múltiplo para saber cuándo dos sucesos que se repiten coinciden.

Words to know Palabras clave

Find Factors and Multiples Hallar factores y múltiplos
List the factors and multiples, then see what two numbers share.
Hacer la lista de factores y múltiplos y ver qué comparten dos números.
Factor Factor
A number that goes into a number with none left.
Un número que divide a otro sin que sobre nada.
Multiple Múltiplo
A number you land on when you count by it.
Un número al que llegas al contar de a saltos con otro.
Greatest common factor (GCF) Máximo común divisor (MCD)
The biggest number that goes into both.
El número más grande que divide a ambos.
Least common multiple (LCM) Mínimo común múltiplo (mcm)
The smallest number both numbers count up to.
El número más pequeño al que llegan ambos al contar.
Factor pair Par de factores
Two numbers that give the number as a product.
Dos números cuyo producto es ese número.
Prime factorization Factorización prima
A number written as a product of primes.
Un número escrito como producto de números primos.
Common factor Factor común
A number that divides two numbers with none left over.
Un número que divide a dos números sin que sobre nada.
Greatest common factor Máximo común divisor
The biggest number that goes into both.
El número más grande que divide a ambos.
Least common multiple Mínimo común múltiplo
The smallest number both numbers count up to.
El número más pequeño al que llegan ambos al contar.

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. The store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of each, with nothing left over — so the number of packs has to be a factor of BOTH quantities.
  2. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Listing them in order is what makes the comparison easy.
  3. The numbers in both lists are the common factors: 1, 2, 3, 4, 6, and 12.
  4. The greatest of those is 12, so the GCF of 48 and 36 is 12. The manager can make 12 combo packs — each holding 48 ÷ 12 = 4 pencils and 36 ÷ 12 = 3 notebooks.

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!

At home, the dog gets a bath every 4 weeks and the cat gets its medicine every 6 weeks, and both happen this week. When will they next happen in the same week?

  1. Week 2, the greatest common factor of 4 and 6
  2. Week 12, the least common multiple of 4 and 6
  3. Week 10, because 4 + 6 = 10
  4. Week 24, because 4 × 6 = 24
Check the answer

The answer is: Week 12, the least common multiple of 4 and 6

Take-home sheet Hoja para llevar a casa

Lesson 6.7: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 6.7: 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 is reaching for the wrong tool: listing FACTORS for a problem about repeating cycles. Ayasha's classes repeat every 6 and 8 weeks, so the weeks they land on are multiples — answering with the GCF of 2 claims a class that meets every 8 weeks happens in week 2. Use the size of the answer as a check: a GCF is never larger than the smaller number, and an LCM is never smaller than the larger one.

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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