Challenge A — Integers in the real world
Challenge A — Integers in the real world
These problems go beyond ordering integers — you will need to find differences that cross zero and reason about change. Sketch a number line whenever you get stuck.
Q1. Read each thermometer: A = B = C = D =
Q2. How many degrees apart are the coldest and warmest thermometers? Show your counting.
Q3. Overnight, thermometer B falls by 11°. What does it read now?
Q4. A lift starts on floor −3 (3 levels of car park). It goes up 9 floors, down 4, then up 2. Which floor is it on? Show each step.
Q5. The temperature in Perth was 19°C. In Thredbo it was 23° colder. What was Thredbo's temperature?
Q6. Prove it. Marcus says “−10 is bigger than −2 because 10 is bigger than 2.” Is he correct? Use a number line to explain.
Q7. Open task. Write three different real-world situations that could each be represented by the integer −6.
Challenge B — Place-value puzzles
Challenge B — Place-value puzzles
Each place in our number system is ten times the place to its right. Reading a number in a place value chart helps you reason about how its digits change when you multiply or divide by 10, 100 or 1000.
Q1. In 4.56, write the value of each digit: 4 = , 5 = , 6 =
Q2. Make the number 10 times larger and then 100 times smaller than 4.56. Write both.
Q3. Digit puzzle. I am a number between 4 and 5. My tenths digit is double my hundredths digit, and my digits add to 7 with the 4. What number could I be? Is there more than one answer?
Q4. Use the digits 7, 3, 0, 9 once each to make the number closest to 5 in the form _ . _ _ _.
Q5. Prove it. Is 0.4 the same as 0.40? Explain using place value, not just “they look the same”.
Q6. Reasoning. Jess writes 3.7 > 3.65 because “7 is bigger than 65 has more digits”. Her answer is right but her reason is wrong. Write a correct explanation.
Q7. Challenge. Counting by 0.01, how many steps from 4.56 to 4.6?