I can write a number as a product of its prime factors using a factor tree.Puedo escribir un número como producto de sus factores primos usando un árbol de factores.
MissionMisión · Sound StudioEstudio de sonido · night shiftturno de noche
Mix the track, then check the math.Mezcla la pista y revisa las matemáticas.
It is midnight and the studio is empty, except for one last session. The sync board rejects any recipe that still hides a composite beat, so every loop gets checked twice before the final mix.
Es medianoche y el estudio está vacío, salvo por una última sesión. La consola rechaza cualquier receta que todavía esconda un tiempo compuesto, así que cada ciclo se revisa dos veces antes de la mezcla final.
Word bankBanco de palabras 5 words5 palabrasprime number, composite number, factor tree, …número primo, número compuesto, árbol de factores, …
- prime numbernúmero primo
- A number greater than 1 with exactly two factors: 1 and itself.Un número mayor que 1 con exactamente dos factores: 1 y él mismo.
- composite numbernúmero compuesto
- A number greater than 1 with more than two factors.Un número mayor que 1 con más de dos factores.
- factor treeárbol de factores
- A diagram that splits a number into smaller factors until every branch ends in a prime.Un diagrama que separa un número en factores más pequeños hasta que cada rama termina en un primo.
- prime factorizationfactorización prima
- A number written as a product of primes only, like 12 = 2 × 2 × 3.Un número escrito solo como producto de primos, como 12 = 2 × 2 × 3.
- exponentexponente
- A small raised number that tells how many times the base is used as a factor: 2³ = 2 × 2 × 2.Un número pequeño y elevado que dice cuántas veces se usa la base como factor: 2³ = 2 × 2 × 2.
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 Marcus's Mistake
- Choose 24, 36, or 60. Show two factor trees with different first factor pairs. Finish both trees with prime factors, then explain how you checked that both products equal your chosen number.
- Every loop here is built from the primes 2, 3 and 5. Fill the empty cells. The last column counts every prime factor, repeats included.
- A sample pack's label is smudged. It reads 2² × 3 × ? × 5, and the pack plays 420 beats. The missing number is prime. What is it?
- A mixing preset lasts 2² × 3 × 5² beats. A loop syncs with the preset only if its length divides the preset's beats evenly. Which loop length can sync?
- 8
- 9
- 14
- 50
- Sam uses all 120 drum pads to make a rectangle on a wall. Rows × columns must equal 120. A 4 × 30 and a 30 × 4 rectangle count as one rectangle. A single row of 120 counts. How many different rectangles can Sam build?
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.
- Every number needs a label before it goes on a track. Sort each number into Prime, Composite, or Neither.
- Choose two composite signal periods between 10 and 40 beats. Make a factor tree on paper for each, write both prime factorizations with exponents, and name every prime that the two periods share.
- 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.
- Ruben built a factor tree for 150. Find the step where his thinking first goes wrong.
- Amara factored 200 correctly, then checked her answer. Find the step where the check goes wrong.
- Kenji factored 180 and wrote only the different primes. Find the step where his thinking goes wrong.
- Three producers factored 126. Dev wrote 2 × 63. Mei wrote 2 × 3 × 3 × 7. Priya wrote 2 × 3² × 7. Who has the complete prime factorization of 126?
- Only Mei
- Only Priya
- Mei and Priya
- Dev, Mei and Priya
- What is the best next move?
- List each prime once: 2 × 7.
- Add the primes: 2 + 7 + 7.
- Use 2 × 7².
- Write the repeated 7 as 7 × 2 = 14 and give 2 × 14.
- 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 expression is the complete prime factorization of 168?
- 2³ × 3 × 7
- 2 × 3 × 7
- 2² × 6 × 7
- 2³ × 21
- A loop is 2³ × 3² × 7 beats long. How many beats is that?
- Which of these numbers is prime?
- 49
- 51
- 91
- 89
- Every complete factor tree for 396 ends in the same prime leaves, however it starts. How many leaves does a complete tree for 396 have? Count every leaf, repeats included.
- Ilse says, "Since 102 = 2 × 3 × 17, the number 102 cannot be divided evenly by 9." Is Ilse right?
- No. 3 is a factor of 102, so 9 must be a factor too.
- Yes. 9 = 3 × 3 needs two 3s, and 102 has only one 3.
- Yes. 9 does not appear in 2 × 3 × 17, so it cannot be a factor.
- Not enough information. You must multiply 2 × 3 × 17 out first.
- Create your own problem. Pick a composite number between 100 and 200. Build two factor trees for it, each starting with a different pair of factors. Write the prime factorization with exponents, check it by multiplying, and explain how you know each tree is finished.