I can use integers to represent quantities in everyday life, explain what 0 means in each situation, and name the opposite of an integer on the number line.Puedo usar números enteros para representar cantidades de la vida diaria, explicar qué significa 0 en cada situación y nombrar el opuesto de un entero en la recta numérica.
MissionMisión · Harbor WorksPuerto de trabajo · night shiftturno de noche
Keep the port running.Mantén el puerto en marcha.
Night shift at the port: the tide table, the crane log and the sonar readings have all been mixed together. Sort out which side of 0 each reading belongs to before the morning ships arrive.
Turno de noche en el puerto: la tabla de mareas, el registro de la grúa y las lecturas del sónar se han mezclado. Averigua de qué lado del 0 va cada lectura antes de que lleguen los barcos de la mañana.
Word bankBanco de palabras 5 words5 palabrasinteger, opposite, negative number, …número entero, opuesto, número negativo, …
- integernúmero entero
- A counting number, its opposite, or 0.Un número para contar, su opuesto o el 0.
- oppositeopuesto
- A number the same distance from 0 as another number, but on the other side of 0.Un número a la misma distancia del 0 que otro número, pero del otro lado del 0.
- negative numbernúmero negativo
- A number less than 0, written with a − sign. It is to the left of 0.Un número menor que 0, escrito con signo −. Está a la izquierda del 0.
- positive numbernúmero positivo
- A number greater than 0. It is to the right of 0.Un número mayor que 0. Está a la derecha del 0.
- number linerecta numérica
- A line where numbers are placed in order, smaller on the left and greater on the right.Una recta donde los números se colocan en orden, los menores a la izquierda y los mayores a la derecha.
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.
- At 6 a.m. in Reykjavik the temperature was −12°C. At 2 p.m. it was the opposite of the 6 a.m. temperature, and at 11 p.m. it was the opposite of the 2 p.m. temperature. What were the temperatures at 2 p.m. and 11 p.m.?
- −12°C and 12°C
- 0°C and 12°C
- 12°C and −12°C
- 12°C and 24°C
- A football team starts at the line of scrimmage, which is 0. During one series they had a 10-yard loss, a 4-yard gain, a 3-yard loss, and a 21-yard gain. Where does the series leave them?
- 8 yards past the line of scrimmage
- 12 yards past the line of scrimmage
- 18 yards past the line of scrimmage
- 38 yards past the line of scrimmage
- Describe two different real-world situations that use negative integers. For each one, tell exactly what 0 means in that situation, write one negative integer it could produce, and explain what the opposite of that integer would mean in the same situation.
- A tide gauge reads −8 at low tide. At high tide, the reading is the opposite of the low-tide reading. Six hours later, it flips to the opposite again. Then it flips once more. What is the final reading?
- The dock is level 0. Write an integer for each report, then write its opposite. Fill in every empty cell.
- The harbor chart sets 0 at the water surface. The number line shows a diver at −12 meters and a crane hook at 12 meters. Which statement is true?
- They are equal, because both are 12 meters from the surface.
- Opposites: 12 m from the surface, on opposite sides.
- Both are above the surface, because 12 is in both numbers.
- The diver is higher, because the − sign means above 0.
- A crane lifts a container to 8 meters above the dock, shown on the number line. Then it lowers the container to the opposite position. How many meters does the container travel in the second move?
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.
- Harbor logs use 0 for the starting level. Sort each report by the kind of integer it needs.
- Make an expedition profile with five integers, some above and some below sea level. Label 0, choose one pair of opposites, and explain what each sign means in your story.
- 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.
- A diver is 9 meters below the water surface, which is 0. Rosa wrote the integer for the diver. Find the step where her work goes wrong.
- Hugo wants the opposite of the opposite of −4. Find the step where his reasoning goes wrong.
- Mara places the opposite of −3 on a number line. Find the step where her thinking goes wrong.
- Rin says, "The opposite of any number is a positive number." Leo says, "A number and its opposite are the same distance from 0." Sol says, "The opposite of 0 is 0." Who is right?
- Rin and Leo
- Rin only
- Leo and Sol
- All three
- What is the best next move?
- Stop here, because −(−9) = 9 is the answer.
- Take the opposite of 9 to finish the last sign.
- Add the two results: 9 + 9 = 18.
- Drop all the signs and write 9.
- 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.
- A freighter's anchor rests 23 meters below the water surface, which is 0. Which integer shows the anchor's position?
- −23
- 23
- −32
- 0
- What is the opposite of −48?
- −48
- 48
- −84
- 0
- How many units apart are 15 and its opposite on a number line?
- Which point on the number line is the opposite of point B?
- Point A
- Point B
- Point C
- Point D
- Dock level is 0. A tide gauge reads −4 at low tide, and the high-tide reading is its opposite. What does the high-tide reading show?
- The water is 4 meters below dock level
- The water is exactly at dock level
- The water is 8 meters above dock level
- The water is 4 meters above dock level
- Create your own harbor problem. Choose a situation with a starting level of 0. Write one negative integer and one positive integer from it, say what each one means, and give the opposite of each. Explain what 0 means in your situation.