I can model and solve real-world problems using equations and inequalities.Puedo representar y resolver problemas de la vida real usando ecuaciones y desigualdades.
MissionMisión · Case FilesExpedientes · night shiftturno de noche
Follow the numbers to the truth.Sigue los números hasta la verdad.
The case went cold, and the last files are smudged and out of order. Rebuild each model from the clues, decide between an equation and an inequality, and check every answer against the story.
El caso se enfrió, y los últimos expedientes están borrosos y desordenados. Reconstruye cada modelo con las pistas, decide entre una ecuación y una desigualdad, y comprueba cada respuesta con la historia.
Word bankBanco de palabras 4 words4 palabrasmodel, constraint, reasonableness, …modelar, restricción, razonabilidad, …
- modelmodelar
- To show a real-life situation with an equation or an inequality.Mostrar una situación de la vida real con una ecuación o una desigualdad.
- constraintrestricción
- A limit in a problem that tells what values are allowed.Un límite en un problema que dice qué valores se permiten.
- reasonablenessrazonabilidad
- Checking whether an answer makes sense in the story.Comprobar si una respuesta tiene sentido en la historia.
- inequalitydesigualdad
- A math sentence that compares two sides with <, >, ≤ or ≥.Una oración matemática que compara dos lados con <, >, ≤ o ≥.
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 Problem-Solving Error
- Create two word problems about the same situation: one that requires an equation and one that requires an inequality. Solve both and explain why the models are different.
- A reward r was split equally among 5 detectives, and each detective got $40. Which model fits, and what was the reward?
- r ÷ 5 ≥ 40, so r ≥ 200
- 5r = 40, so r = 8
- r ÷ 5 = 40, so r = 200
- r − 5 = 40, so r = 45
- The evidence locker holds at most 30 boxes, and 17 boxes are inside. Let b be the number of boxes that can still be added. Which model and solution are correct?
- 17 + b ≤ 30, so b ≤ 13
- 17 + b = 30, so b = 13
- 17 + b ≤ 30, so b ≤ 47
- 17 + b < 30, so b < 13
- Seven identical keys weigh 3.5 pounds in all. Let k be the weight of one key in pounds, so 7k = 3.5. How many pounds does one key weigh?
- Each row is a case model. Solve it. Type the solution, or for the inequality the boundary number.
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 clue by the model it needs: an equation for one exact value, or an inequality for a limit or a range.
- Plan a class event with a fixed budget. Write an inequality for it, solve it, and find the greatest whole-number answer. Explain why your answer must be a whole number, and why the answer is not just the number your division gives.
- 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.
- Rhea models 'The elevator takes no more than 8 people'.
- Sione models 'A prize was split equally among 3 winners, and each got $25'.
- Carmen solves 7c = 3.5 for the weight c of one clue card, in ounces.
- Leo and Pilar both model 'Eight more than a number is at least 20' as n + 8 ≥ 20. Leo says n ≥ 12. Pilar says n = 12. Who is right?
- Pilar, because solving always gives one number.
- Leo: solutions are 12 and greater.
- Both, because both found the boundary 12.
- Neither, because the answer should be n ≤ 12.
- What is the best next move?
- Use the greatest whole number that fits.
- Round up and say 17 panels fit.
- Report p = 16 2/3 as the answer.
- Change ≤ to = and say exactly 16 panels are needed.
- 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.
- Which situation needs an inequality instead of an equation?
- The clue weighs exactly 9 grams.
- The vault code has exactly 6 digits.
- The reward was split equally, $40 each.
- The suspect is at least 30 years old.
- Idris visited n sites on a case. After 9 of them were closed, 14 were left open. The model is n − 9 = 14. How many sites did he visit?
- Noelle wants to spend less than $45 on 5 flashlights that each cost f dollars. Which inequality shows her goal?
- 5f ≤ 45
- f + 5 < 45
- 5f < 45
- 5f > 45
- Dmitri solves 6w = 3.6 for the weight w of one clue, in pounds, and gets w = 21.6. Why should he doubt his answer?
- Because a weight cannot be a decimal.
- Six clues at 21.6 lb would exceed 3.6 lb.
- Because he should have added 6 to 3.6.
- Because 21.6 is a multiple of 3.6.
- Amani has $30 for bus tickets that cost $4 each. The inequality 4t ≤ 30 shows how many tickets t she can buy. What is the greatest whole number of tickets she can buy?
- Write two short mystery problems of your own. One needs an equation, and one needs an inequality. Model each, solve each, and say whether your answer makes sense.
- 1 fresh problem with new numbers each time (interactive only).