Equations and Inequalities Problem Solving

6.AT.8 · Unit 7 · Lesson 7

Name   Period

Objectives / Objetivos

Content Objective: I can model and solve real-world problems using equations and inequalities.

Language Objective: I can explain my reasoning using the words model, equation, inequality, and reasonableness.

Key Idea / Idea clave

'Equals' or 'exactly' points to an equation (=); 'at least, at most, more than, fewer than' points to an inequality.

I Notice / Observo

  • Which clue leads to an equation and which leads to an inequality?
  • What operation does 'divided equally among 4' suggest?

I Wonder / Me pregunto

  • How do you decide when to use an equation versus an inequality?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Model
Modelar		To show a real-life situation with an equation or inequality.
Mostrar una situación real con una ecuación o desigualdad.
Equation
Ecuación		A math sentence with an equal sign showing both sides are the same.
Una oración matemática con un signo igual que muestra que ambos lados son iguales.
Inequality
Desigualdad		A math sentence that compares two sides with <, >, ≤, or ≥.
Una oración matemática que compara dos lados con <, >, ≤ o ≥.
Reasonableness
Razonabilidad		Checking if your answer makes sense.
Revisar si tu respuesta tiene sentido.
Variable
Variable		A letter that stands for a number that is unknown or can change.
Una letra que representa un número desconocido o que puede cambiar.
Constraint
Restricción		A limit in a problem that tells what values are allowed.
Un límite en un problema que indica qué valores se permiten.

Practice Preview / Vista previa de práctica

  1. A museum has some paintings. After adding 12, they have 45. Which equation models this?
    1. p + 12 = 45
    2. p − 12 = 45
    3. 12p = 45
    4. p / 12 = 45
  2. Write a model, solve, and check reasonableness for each problem.
  3. A student solved 4n = 52 and got n = 13. Is the answer reasonable if n represents the number of notebooks in a box?
    1. Yes — 13 notebooks per box is reasonable
    2. No — 13 is too many notebooks
    3. No — the answer should be 48
    4. Yes — but only if n is a fraction
  4. Find the Problem-Solving Error
    1. Step 1: Problem — A parking lot holds at most 200 cars. There are 134 already. How many more can park?
    2. Step 2: Model — 134 + c = 200
    3. Step 3: Solve — c = 66
    4. Step 4: Answer — Exactly 66 more cars can park.

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

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