I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.Puedo hallar el máximo común divisor y el mínimo común múltiplo de dos números, y usar cada uno para resolver un problema real.
MissionMisión · Case FilesExpedientes · night shiftturno de noche
Follow the numbers to the truth.Sigue los números hasta la verdad.
A cold case has reopened after dark. The last files are locked behind number clues, and the wrong tool leaves a false lead. Choose factors or multiples carefully, then prove each answer by checking it.
Un caso sin resolver se reabrió al caer la noche. Los últimos expedientes están bajo llave con pistas numéricas y la herramienta equivocada deja una pista falsa. Elige con cuidado entre factores y múltiplos y luego comprueba cada respuesta.
Word bankBanco de palabras 5 words5 palabrasfactor, multiple, common factor, …factor, múltiplo, factor común, …
- factorfactor
- A whole number that divides another number evenly, with no remainder.Un número entero que divide a otro número exactamente, sin residuo.
- multiplemúltiplo
- What you get when you multiply a number by 1, 2, 3, and so on.Lo que obtienes al multiplicar un número por 1, 2, 3, y así sucesivamente.
- common factorfactor común
- A factor that two or more numbers share.Un factor que dos o más números comparten.
- greatest common factor (GCF)máximo común divisor (MCD)
- The largest factor that two or more numbers share.El factor más grande que comparten dos o más números.
- least common multiple (LCM)mínimo común múltiplo (mcm)
- The smallest multiple that two or more numbers share.El múltiplo más pequeño que comparten dos o más números.
Stage 1 of 5Etapa 1 de 5
Start StrongEmpieza fuerte
Each rung is harder than the last, and the numbers change every time.
Cada peldaño es más difícil que el anterior y los números cambian cada vez.
- 6 fresh problems with new numbers each time (interactive only).
Stage 2 of 5Etapa 2 de 5
Stretch Your ThinkingAmplía tu pensamiento
Plan, solve, then check that your answer makes sense.
Planea, resuelve y revisa que tu respuesta tenga sentido.
- Find the error
- Reginald is having hot dogs for 24 guests and wants the same number of hot dogs and buns, with none left over. Hot dogs come in packs of 10 and buns in packs of 8. How many packs of each should he buy, and how many will he have? Explain which tool you used and why.
- Fill in the table
- A detective has 54 fingerprint cards and 72 photo prints. She makes as many identical folders as she can. Each folder has the same number of cards and of prints. Nothing is left over. How many fingerprint cards go in each folder?
- An evidence board is 60 cm long and 45 cm wide. Officer Reyes covers it with identical square stickers, with no gaps, no overlaps, and no stickers cut. She uses the largest square stickers possible. How many stickers does she use?
- The vault code is a whole number with these clues. It is a multiple of 5. It is greater than 10 and less than 30. It has exactly 6 factors. What is the code?
- Eva has 24 red tags and 96 blue tags. She wants identical bundles with the same number of red tags and the same number of blue tags in each bundle, with none left over. What is the greatest number of bundles she can make?
- 12 bundles
- 48 bundles
- 24 bundles
- 96 bundles
Stage 3 of 5Etapa 3 de 5
InvestigateInvestiga
Use the model to test an idea. Then check it.
Usa el modelo para probar una idea. Luego compruébala.
- Sort each number: is it a factor of 24, a multiple of 24, or neither?
- Write your own word problem about two numbers that needs either the GCF or the LCM. List the factors or multiples you used, name the tool, and give the answer with a unit.
- 4 fresh problems with new numbers each time (interactive only).
Stage 4 of 5Etapa 4 de 5
Find and FixEncuentra y corrige
Somebody made a mistake. Find the step and fix it.
Alguien cometió un error. Encuentra el paso y corrígelo.
- Mateo listed the factors of 36 and wrote 1, 2, 3, 4, 6. Tap the step where his work goes wrong.
- Anaya found the greatest common factor of 9 and 15. Tap the step where her thinking goes wrong.
- Night guards walk past the vault: Officer Park every 9 days and Officer Reyes every 12 days. Both are there today. Hana says they will both be there again in 3 days. Tap the step where her thinking goes wrong.
- Jamal says 5 is a multiple of 20, because 5 goes into 20. Lena says 5 is a factor of 20, and 20 is a multiple of 5. Who is right?
- Lena: 5 is a factor of 20; 20 is a multiple of 5.
- Jamal is right: 5 goes into 20, so 5 is a multiple of 20.
- Both are right: factor and multiple mean the same thing.
- Neither is right: 5 does not divide 20 evenly.
- What is the best next move?
- Pick 30, the first number on both lists.
- Pick 5, the biggest factor they share.
- Pick 40, the last number on the first list.
- Pick 150, the product of 10 × 15.
- 1 fresh problem with new numbers each time (interactive only).
Stage 5 of 5Etapa 5 de 5
Prove Your UnderstandingDemuestra tu comprensión
Say how sure you are, solve, then create a problem of your own.
Di qué tan seguro estás, resuelve y luego crea un problema tuyo.
- Which list shows ALL the factors of 28?
- 1, 2, 4, 7, 14, 28
- 1, 2, 4, 7, 14
- 2, 4, 7, 14
- 28, 56, 84, 112
- What is the greatest common factor of 36 and 90?
- Which number is a multiple of 4 AND a factor of 36?
- 9
- 12
- 16
- 24
- Which problem is solved by finding a greatest common factor?
- Two lights blink every 4 seconds and every 6 seconds. When do they blink together next?
- How many 3-person teams can be made from 28 students?
- List the first five numbers you say when you count by 7s.
- The vault keypad accepts only multiples of 7. The code is the 12th multiple of 7. What is the code?
- Create two Case Files problems that use the same two numbers. One problem needs the greatest common factor (splitting into equal groups). The other needs multiples (a repeating pattern). Solve both, and explain how you chose the right tool each time.