Compare and Order Integers and Rational Numbers Challenge

Grade 6 Math · Unit 7 Challenge Studio (6.NOS.8) · Lesson 7-4
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I can compare and order integers using a number line.Puedo comparar y ordenar números enteros usando una recta numérica.

MissionMisión · Case FilesExpedientes · night shiftturno de noche

Follow the numbers to the truth.Sigue los números hasta la verdad.

A cold case is open again. Every clue is a number, and some are far below zero. Put them in the right order to open the evidence room.

Un caso sin resolver está abierto otra vez. Cada pista es un número y algunos están muy por debajo de cero. Ponlos en el orden correcto para abrir la sala de evidencias.

Word bankBanco de palabras 5 words5 palabrascompare, order, greater than (>), …comparar, ordenar, mayor que (>), …
comparecomparar
To decide whether a number is greater than, less than, or equal to another.Decidir si un número es mayor que, menor que o igual a otro.
orderordenar
To arrange numbers by size, from least to greatest or from greatest to least.Acomodar números por tamaño, de menor a mayor o de mayor a menor.
greater than (>)mayor que (>)
The symbol > shows that the number on its open side is greater.El símbolo > muestra que el número de su lado abierto es mayor.
less than (<)menor que (<)
The symbol < shows that the number on its small end is less.El símbolo < muestra que el número de su punta pequeña es menor.
inequalitydesigualdad
A statement that uses < or > to compare two numbers.Un enunciado que usa < o > para comparar dos números.

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.

  1. 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.

  1. Find the Comparison Error
  2. A student says: 'Negative numbers are always less than positive numbers, so -100 is less than 1.' Is this correct? Now the student says: '-100 is less than -1 because 100 is greater than 1.' Is THIS correct? Explain the difference.
  3. Four rooms at the scene were measured: freezer −18°C, attic 31°C, cellar −4°C, study 0°C. Rank them from coldest (1) to warmest (4), and count how many rooms are warmer than each one. Fill in every empty cell.
  4. Five clues are placed on the number line: A at −9, B at −4, C at 0, D at 3 and E at −12. Which list shows the clues in order from least to greatest?
    • D, C, B, A, E
    • C, D, B, A, E
    • E, A, B, C, D
    • B, A, E, C, D
  5. A detective scores six clues: −7, 4, −2, 0, −9 and −5. How many of the scores are greater than −3?
  6. A case ledger lists four balances: Smith −$45, Jones −$12, Park $8 and Lee −$30. Which list orders the balances from greatest to least?
    • $8, −$12, −$30, −$45
    • −$45, −$30, −$12, $8
    • $8, −$45, −$30, −$12
    • −$12, −$30, −$45, $8

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.

  1. Decide whether each comparison is true or false. Sort every card.
  2. Plan three underwater stops and one point above sea level. Write each elevation as a rational number. Order the four from least to greatest, then rank them by distance from sea level. Explain why the two lists are different.
  3. 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.

  1. Pru orders −9, 5, −2 and 0 from least to greatest. Find the step where her thinking goes wrong.
  2. Quin compares −3 and −8 and writes a statement with a symbol. Find the step where his work goes wrong.
  3. Rae compares 0 and −6 and says which is greater. Find the step where her thinking goes wrong.
  4. Ximena says −3 is greater than −7, because −3 is farther right on a number line. Yuri says −7 is greater than −3, because 7 is greater than 3. Zoe says −3 is less than −7, because negatives are less than positives. Who is right?
    • Only Yuri
    • Only Ximena
    • Only Zoe
    • None of them
  5. What is the best next move?
    • Order negatives: farthest from 0 is least.
    • List them by size, ignoring signs: 0, 4, 9, 11, 16.
    • Put 9 first, because it is the biggest number.
    • Put 0 at the far left, because it is the smallest.
  6. 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.

  1. Which list shows −7, 3, −10 and 0 in order from least to greatest?
    • −7, −10, 0, 3
    • 3, 0, −7, −10
    • 0, 3, −7, −10
    • −10, −7, 0, 3
  2. Which comparison is true?
    • −2.5 < −2.25
    • −0.3 < −0.8
    • −4 > −3.5
    • −1.2 > 0.1
  3. How many integers are between −4 and 3? Do not count −4 or 3 themselves.
  4. Three points are shown on the number line: P at −7, Q at −2 and R at 4. Which statement is true?
    • Q is less than P.
    • R is less than Q.
    • P is less than Q.
    • P is greater than R.
  5. Four rooms at a scene measure −6°C, 2°C, −11°C and −1°C. How many degrees apart are the coldest room and the warmest room?
  6. Create your own cold case. Write five integers as clues, with at least three negative, and put them in order from least to greatest. Use the symbols < and > in two true comparisons, and explain how a number line helped you.