Equations and Inequalities Problem Solving
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
Modeling Real-World Scenarios with Equations & Inequalities. 1. Define the variable and units in the scenario. 2. Look for keywords: 'equals/is' (=) vs 'at least/limit' (≥, ≤, >, <). 3. Write the algebraic model, solve with inverse operations, and check in context
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 / Término | Definition / Definición |
|---|---|
| Equations and Inequalities Problem Solving Resolución de problemas con ecuaciones y desigualdades | Use an equation for one exact value or an inequality for a range of values in a real situation. Usar una ecuación para un valor exacto o una desigualdad para un rango de valores en una situación real. |
| 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. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. A museum has some paintings. After adding 12, they have 45. Which equation models this?
- A p + 12 = 45
- B p − 12 = 45
- C 12p = 45
- D p / 12 = 45
Answer:
2. Write a model, solve, and check reasonableness for each problem.
Complete each empty cell. Show your reasoning below.
| Word Problem | Model | Solution | Reasonable? |
|---|---|---|---|
| Five identical boxes weigh a total of 60 pounds. How much does each box weigh? | |||
| A shelf can hold at most 30 books. There are already 17 books. How many more can be added? | |||
| A baker split 84 cookies equally into bags of 12. How many bags did she use? |
3. A student solved 4n = 52 and got n = 13. Is the answer reasonable if n represents the number of notebooks in a box?
- A No — 13 is too many notebooks
- B No — the answer should be 48
- C Yes — 13 notebooks per box is reasonable
- D Yes — but only if n is a fraction
Answer:
4. Find the Problem-Solving Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: