Simplify Algebraic Expressions Challenge

Grade 6 Math · Unit 6 Challenge Studio (6.AT.7) · Lesson 6-15
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I can simplify algebraic expressions by combining like terms.Puedo simplificar expresiones algebraicas combinando términos semejantes.

MissionMisión · Summit TrailSendero a la cumbre · night shiftturno de noche

Every checkpoint gets you higher.Cada punto de control te lleva más alto.

Fog rolls over the upper ridge and the trail map is covered in long packing lists. Shorten every list without losing a single item, or the crew will reach camp short on supplies.

La niebla cae sobre la cresta y el mapa del sendero está lleno de listas de equipo muy largas. Acorta cada lista sin perder ni un solo artículo, o el grupo llegará al campamento sin provisiones.

Word bankBanco de palabras 5 words5 palabrasterm, like terms, coefficient, …término, términos semejantes, coeficiente, …
termtérmino
A number, a variable, or a product of them. Terms are separated by + or − signs.Un número, una variable o un producto de ellos. Los términos se separan con signos + o −.
like termstérminos semejantes
Terms with the same variable raised to the same exponent, like 2x and 5x.Términos con la misma variable elevada al mismo exponente, como 2x y 5x.
coefficientcoeficiente
The number in front of a variable. In 9x, the coefficient is 9; in x, it is 1.El número que está delante de una variable. En 9x, el coeficiente es 9; en x, es 1.
constantconstante
A term with no variable, like the 8 in 3x + 8. Its value never changes.Un término sin variable, como el 8 en 3x + 8. Su valor nunca cambia.
simplifysimplificar
To rewrite an expression in a shorter form that always has the same value.Reescribir una expresión de forma más corta que siempre tiene el mismo valor.

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.

  1. 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.

  1. Find the Simplification Error
  2. Three students simplified 4x + 3 + 2x + 5 + x differently. Student A got 7x + 8. Student B got 7x² + 8. Student C got 6x + 9. Who is correct? Explain the mistakes the other two students made.
  3. Fill in the table
  4. The trail crew writes each supply list as an expression. For every list, combine the x-terms, combine the constants, then find the value when x = 3. Fill in the empty cells.
  5. Three trail sections have lengths 3x + 4, 2x + 7 and x + 1 kilometers, where x is the number of switchbacks on the trail. The sections are walked end to end. How long is the whole trail when x = 2?
  6. A tape diagram shows four parts of a checkpoint pack: 2x pounds of water, 5 pounds of snacks, 3x pounds of water and 4 pounds of snacks. Which expression is the simplest form of the whole pack's weight?
    • 5x + 9
    • 14x
    • 5x² + 9
    • 6x + 9
  7. A hiking leader packs 3 kits that each weigh (x + 2) pounds. She also carries 4x pounds of tents. The total weight is 3(x + 2) + 4x. When this is simplified to ax + b, what is a + b?

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.

  1. Simplify each expression in your head or on paper, then sort it by what it becomes.
  2. Write your own expression with at least four terms that can be simplified. Simplify it by combining like terms, then check the original and the simplified expression at two values of x.
  3. 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.

  1. Hana simplified 5n + 8 + 3n. Find the step where her work first goes wrong.
  2. Diego simplified 9p + p + 2. Find the step where his work first goes wrong.
  3. Kofi simplified 12k + 9 − 4k − 5. Find the step where his work first goes wrong.
  4. Three hikers simplified 11a + 8 − 6a. Lena wrote 5a + 8. Omar wrote 17a + 8. Suri wrote 5a − 8. Who simplified correctly?
    • Omar
    • Suri
    • None of them
    • Lena
  5. What is the best next move?
    • Combine 9p − 5p and −4 + 10, keeping each sign with its term.
    • Combine 9p + 5p and 4 + 10.
    • Work left to right: 9p − 4 = 5p, then 5p − 5p.
    • Say it cannot be simplified, because it has minus signs.
  6. 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.

  1. Which pair of terms can be combined into one term?
    • 7p and 7
    • 5m and m
    • 3x² and 3x
    • 4a and 4b
  2. Which expression is the simplest form of 14x + 12 − 6x − 9?
    • 20x + 3
    • 8x + 21
    • 8x − 3
    • 8x + 3
  3. The trail crew's load is 3m + 8 + 4m + 2 kilograms, where m is the number of tents. What is the load when m = 5?
  4. Which expression is equivalent to 2(x + 4) + 3x?
    • 5x + 8
    • 5x + 4
    • 13x
    • 6x + 8
  5. Which expression simplifies to 9x + 5?
    • 6x + 3x + 5x
    • 9 + 5x
    • 4x + 5 + 5x
    • 4x + 5 + 5
  6. Create your own problem. Write a trail packing list as an expression with at least four terms: two x-terms, two constants, and one subtraction. Simplify it, check it by finding the value of both expressions when x = 2, and explain which terms you combined and why.
  7. 1 fresh problem with new numbers each time (interactive only).