I can show that two expressions are equivalent by simplifying and combining like terms.Puedo mostrar que dos expresiones son equivalentes simplificando y combinando términos semejantes.
MissionMisión · Pixel ArcadeArcade de píxeles · night shiftturno de noche
Clear every level.Supera todos los niveles.
After closing, the arcade unlocks a secret Bonus Round full of formulas that look alike but score differently. Find the counterexample that exposes each fake, and prove the real matches by simplifying.
Después del cierre, el arcade abre una Ronda Bonus secreta llena de fórmulas que se parecen pero puntúan distinto. Encuentra el contraejemplo que delata cada falsa y demuestra con una simplificación las que sí son equivalentes.
Word bankBanco de palabras 5 words5 palabrasequivalent expressions, like terms, simplify, …expresiones equivalentes, términos semejantes, simplificar, …
- equivalent expressionsexpresiones equivalentes
- Expressions that have the same value for every value of the variable, even if they look different.Expresiones que tienen el mismo valor para todo valor de la variable, aunque se vean diferentes.
- like termstérminos semejantes
- Terms with the same letter to the same power, like 2n and 5n.Términos con la misma letra elevada a la misma potencia, como 2n y 5n.
- simplifysimplificar
- To rewrite an expression in a shorter form that has the same value.Reescribir una expresión en una forma más corta que tiene el mismo valor.
- combinecombinar
- To add or subtract like terms to make one term.Sumar o restar términos semejantes para formar un solo término.
- counterexamplecontraejemplo
- One test value that shows two expressions are not equivalent.Un valor de prueba que muestra que dos expresiones no son equivalentes.
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 Simplification Error
- A student says 2x + 3 and 5x are equivalent because both equal 5 when x = 1. Is the student correct? Explain why testing one value is not enough to prove equivalence, and find a value of x where they give different results.
- Fill in the table
- Game designers claim that 4n and n + 6 give the same score. The table shows what each formula gives for four values of n. Which statement is correct?
- They are equivalent, because both formulas give 8 when n = 2.
- No: at n = 3, 4n = 12 but n + 6 = 9.
- They are not equivalent, because 4n and n + 6 look different.
- You cannot tell unless every value of n is tested.
- In the Pixel Arcade, Game A scores 5n + 2 + 3n − 1 points when you collect n coins. Game B scores ?n + 1 points. For the two games to always give the same score, what number belongs in the blank?
- Four players compared their score formulas in pairs. Exactly one pair is equivalent. Which pair is it?
- 7n − 3 and 3 − 7n
- 4(n + 2) and 4n + 2
- 9n + 1 and 10n
- 5 + 2n + 6 and 2n + 11
- Two bonus formulas are 2(n + 3) + n and 3n + 6. Find the score each formula gives for the value of n in each row.
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 expression: is it equivalent to 3n + 12, or not?
- Write a short game story for an expression like 4x + 2x + 5. Combine the like terms to write an equivalent expression, then check both expressions at two different values of x.
- 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.
- Zara simplified 7m + 4 − 3m − 1 and got 4m + 5. Tap the step where her work goes wrong.
- Ravi rewrote 5(2n + 3) as 10n + 3. Tap the step where his work goes wrong.
- Lena wants to know whether 7n + 4 and 3n + 4 are equivalent. She tested one easy number. Tap the step where her reasoning goes wrong.
- Dara says 4n + 3n = 7n². Emil says 4n + 3n = 7n. Who is right?
- Emil: add coefficients; keep n.
- Dara is right: when you combine like terms, the powers add up too.
- Both are right: 7n and 7n² are two ways to write the same value.
- Neither is right: 4n and 3n are not like terms, so they cannot be combined.
- What is the best next move?
- Agree with Lin, because both give 9.
- Substitute x = 1 again to double-check.
- Add 3x + 6 to make 9x.
- Try a different x in both expressions.
- 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 expression is equivalent to 9 + 5n + 2 + n?
- 5n + 11
- 14n
- 6n + 11
- 11n + 6
- Which expression is NOT equivalent to 4 + n + 9?
- n + 13
- 13 + n
- 9 + n + 4
- 13n
- Rewrite 4(3n + 5) in the form 12n + c. What number is c?
- Which expression is equivalent to 2(n + 5) + 3n?
- 5n + 10
- 5n + 5
- 8n + 10
- 10n
- Marcus rewrote 6 + (2n + 5) as (6 + 2n) + 5. Which property did he use?
- Commutative property
- Associative property
- Distributive property
- Identity property
- Create your own pair of equivalent expressions. At least one of them must have parentheses or three or more terms. Show they are equivalent in TWO ways: by simplifying and by testing a value. Then write a pair that only LOOKS equivalent and give a counterexample.