I can use the commutative, associative, and identity properties to rewrite expressions.Puedo usar las propiedades conmutativa, asociativa y de identidad para reescribir expresiones.
MissionMisión · Corner KitchenCocina de la esquina · night shiftturno de noche
Cook up the right answer.Cocina la respuesta correcta.
After closing, the head chef hands you the secret menu: price formulas that must stay equivalent no matter how you shuffle them. Test every swap, regroup, and combine, and expose the one that changes the dish.
Después del cierre, la jefa de cocina te entrega el menú secreto: fórmulas de precios que deben seguir siendo equivalentes sin importar cómo las cambies de lugar. Prueba cada cambio de orden, agrupación y combinación, y descubre el que cambia el plato.
Word bankBanco de palabras 5 words5 palabrascommutative property, associative property, identity property, …propiedad conmutativa, propiedad asociativa, propiedad de identidad, …
- commutative propertypropiedad conmutativa
- You can change the order of numbers when adding or multiplying and get the same answer.Puedes cambiar el orden de los números al sumar o multiplicar y obtener la misma respuesta.
- associative propertypropiedad asociativa
- You can change the grouping of numbers when adding or multiplying and get the same answer.Puedes cambiar la agrupación de los números al sumar o multiplicar y obtener la misma respuesta.
- identity propertypropiedad de identidad
- Adding 0 or multiplying by 1 keeps the same value.Sumar 0 o multiplicar por 1 mantiene el mismo valor.
- equivalent expressionsexpresiones equivalentes
- Expressions that have the same value for every value of the variable.Expresiones que tienen el mismo valor para todo valor de la variable.
- propertypropiedad
- A rule that is always true for the numbers it covers.Una regla que siempre es verdadera para los números que cubre.
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 Property Error
- Explain why the commutative property works for addition and multiplication but NOT for subtraction and division. Give a specific number example for each operation to prove your point.
- Fill in the table
- Two cooks add up the weight of a tray. Cook A writes 14 + n + 6 and Cook B writes n + 20, where n is the weight of the sauce. Which statement is correct?
- They are not equivalent, because one has three terms and the other has two.
- They are not equivalent, because the 6 moved to a different place.
- They are equivalent only when n = 0.
- They are equivalent: reorder the terms, then add 14 + 6 = 20.
- A catering quote is 9 + 4n + 11 + 2n dollars for n trays. Rewrite it with fewer terms, then find the quote for 5 trays.
- A bag has 12 kg of flour and the kitchen uses 5 kg. Trainee Imani writes 5 − 12 for the flour left because "the order shouldn't matter." What is true?
- 12 − 5 = 7 kg is left, but 5 − 12 cannot be done: order matters.
- The two give the same answer, because they use the same numbers.
- Order matters for division, but never matters for subtraction.
- She is right, because you can swap the numbers in any operation.
- A cook lists the cost of n burgers as n + n + n + n + 6. Which equivalent expression is the simplest?
- 10n
- 4n + 6
- n⁴ + 6
- 6n + 4
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 pair: are the two expressions equivalent for every value of n?
- Pick three whole numbers from 1 to 25 where two of them multiply to a friendly number like 10 or 100. Use the model to reorder and regroup them, and write all three lines. Name the property you used each time. Then write one product that shows the Identity Property.
- 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.
- Chef Dev says 24 ÷ n can be rewritten as n ÷ 24. Tap the step where his reasoning goes wrong.
- Nia looked at 3 × (n × 4) = 3 × (4 × n) and labeled it. Tap the step where her reasoning goes wrong.
- Mo wants a simpler way to write n + n + n + 4. Tap the step where his work goes wrong.
- Ana says 7 × 1 = 7 shows the identity property. Ben says 7 × 0 = 0 shows the identity property too, because zero is special. Who is right?
- Only Ben: multiplying by 0 is the identity.
- Both are right: any property that uses 0 or 1 is an identity property.
- Only Ana: multiplying by 1 keeps the number the same.
- Neither, because the identity property is only for adding.
- What is the best next move?
- Replace n × 1 with 1, because anything times 1 is 1.
- Remove ×1 and +0; neither changes the value.
- Move the parentheses to make n × (1 + 0) + 7.
- Replace 0 + 7 with 0, because adding 0 gives 0.
- 2 fresh problems 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 property is shown by 3 × (n × 5) = (3 × n) × 5?
- Commutative property of multiplication
- Identity property of multiplication
- Associative property of multiplication
- Use properties to regroup 5 × 37 × 20 so the mental math is easy. What is the product?
- Which expression is equivalent to 7 + 3n + 8 + n?
- 4n + 15
- 3n + 15
- 19n
- 15n + 4
- Which statement is FALSE?
- n + 9 = 9 + n for every n
- n ÷ 4 = 4 ÷ n for every n
- n × 8 = 8 × n for every n
- (n + 2) + 6 = n + (2 + 6) for every n
- Evaluate 1 × n + 0 + n × 1 when n = 12.
- Create your own expression with a variable and at least three terms. Rewrite it two different ways and name the property you used each time. Then give one example of a swap that would NOT work, using division.