Apply Two-Variable Relationships to Solve Problems

6.AT.11 · Unit 9 · Lesson 4

Name   Period

Objectives / Objetivos

Content Objective: I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem.

Language Objective: I can justify a recommendation using the words equation, solution, and at least.

Key Idea / Idea clave

Analyzing & Applying Two-Variable Relationships. 1. Connect the four representations: Scenario, Table, Graph, and Equation. 2. Substitute given values into the equation to make predictions and solve problems. 3. Interpret coordinates and rate of change in the real-world context

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
solution
solución		A value of the variable that makes an equation true.
Un valor de la variable que hace que una ecuación sea verdadera.
substitute
sustituir		To replace a variable with a number so you can compute.
Reemplazar una variable con un número para poder calcular.
at least
al menos		That amount or more — the smallest amount that still works.
Esa cantidad o más — la cantidad mínima que todavía funciona.
predict
predecir		To make a reasonable guess about a future amount using information you already have.
Hacer una estimación razonable sobre una cantidad futura usando la información que ya tienes.
justify
justificar		To explain WHY an answer or recommendation makes sense, using the mathematics.
Explicar POR QUÉ una respuesta o recomendación tiene sentido, usando las matemáticas.
Equation
Ecuación		A math sentence with an equals sign showing two amounts are the same.
Un enunciado matemático con un signo igual que muestra que dos cantidades son iguales.

Practice Preview / Vista previa de práctica

Read each task. Show your work in the spaces provided and explain how you know.

1. The assembly line produces 2.5 cars per hour. How many cars does it produce in one 8-hour shift?

  1. A 10.5 cars
  2. B 16 cars
  3. C 20 cars
  4. D 25 cars

Answer:

2. The order requires 1,000 cars. Using 2.5h = 1,000, how many hours will the plant need?

  1. A 40 hours
  2. B 400 hours
  3. C 997.5 hours
  4. D 2,500 hours

Answer:

3. The plant needs 400 hours to fill the order. Running 24 hours a day, about how many days is that?

  1. A 4 days
  2. B About 17 days
  3. C 50 days
  4. D 400 days

Answer:

4. Suppose the variable s counts 8-hour SHIFTS instead of hours. Which equation gives the cars produced?

  1. A c = 2.5s
  2. B c = 8s
  3. C c = 10.5s
  4. D c = 20s

Answer:

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: