Year 6: Negative numbers
Part of the Year 6 place value and negative numbers chapter. Chapter overview · whole chapter on one page
Negative numbers
A negative number is a number less than zero. We write a minus sign in front of it, so −4 is “negative four”. Negative numbers are used every day. A thermometer shows −3 °C on a cold winter morning, a submarine can be at −120 m below sea level, and a lift can go down to the basement at −3.
On a number line, numbers get bigger as you move to the right and smaller as you move to the left. So −10 is further left than −4, which means −10 is less than −4. Zero is neither positive nor negative.
Key ideas
- A negative number is less than zero. It has a minus sign in front.
- For negative numbers, the bigger the number after the minus sign, the smaller the number: −9 is less than −3.
- To count down through zero, go 3, 2, 1, 0, −1, −2, −3…
- For a temperature change, move up for a rise and down for a fall. Count through zero when you cross it.
- Zero is neither positive nor negative.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Put the negative numbers first, then zero, then the positive numbers, all in the right order.
- Split the numbers into groups. Negative numbers are less than zero, and positive numbers are greater than zero.negative: −10, −4; zero; positive: 2, 7
- Order the negative numbers. For negatives, the bigger number after the minus sign is the smaller number: −10 is less than −4.−10, −4
- Write the whole list from the smallest. Put the smallest number first.−10, −4, 0, 2, 7
Check. Each number is in the right place: −10 < −4 < 0 < 2 < 7. ✓
Watch out. A bigger minus number is colder. −10 °C is colder than −4 °C, even though 10 is bigger than 4.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 7 steps down. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at 3 °C
- Move 7 steps down. Count one step at a time. Each step changes the number by 1.3 − 7
- Write the new number. −4 °C
Check. 3 − 7 = −4. Going back: −4 + 7 = 3. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Both numbers are negative, so the one with the bigger number after the minus sign is colder.
- Find where each number is on a thermometer. Start at zero and count down.−12 is 12 steps below zero. −8 is 8 steps below zero.
- Compare the two numbers. Further below zero means colder.−12 is further below zero than −8.
- Write the answer. −12 °C is colder
Check. Count down from zero: 8 steps reaches −8, and 12 steps reaches −12. ✓
Watch out. Do not choose the number that looks bigger: 12 is bigger than 8, but the temperature is colder.
Watch out
Do not think that −9 is bigger than −3 because 9 is bigger than 3. With negative numbers, the bigger number after the minus sign is the colder, smaller number. Also, zero is not a negative number, so 0 is greater than every negative number.Exercise 1D Negative numbers
Non-calculatorKey words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 1 steps down. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at 0
- Move 1 steps down. Count one step at a time. Each step changes the number by 1.0 − 1
- Write the new number. −1
Check. 0 − 1 = −1. Going back: −1 + 1 = 0. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Method. Count down from 3 one step at a time, through zero.
- Start at 3 and count down. Each step takes away 1.3, 2, 1, 0
- Keep counting into the negative numbers. Below zero the numbers have a minus sign.−1, −2, −3
- Write the missing numbers. −1, −2, −3
Check. Count up from −3 again: −3, −2, −1, 0. ✓
Watch out. The next number after 0 going down is −1, not −0 or 1.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Put the negative numbers first, then zero, then the positive numbers, all in the right order.
- Split the numbers into groups. Negative numbers are less than zero, and positive numbers are greater than zero.negative: −9, −5; zero; positive: 3
- Order the negative numbers. For negatives, the bigger number after the minus sign is the smaller number: −10 is less than −4.−9, −5
- Write the whole list from the smallest. Put the smallest number first.−9, −5, 0, 3
Check. Each number is in the right place: −9 < −5 < 0 < 3. ✓
Watch out. A bigger minus number is colder. −10 °C is colder than −4 °C, even though 10 is bigger than 4.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Both temperatures are below zero. The one nearer to zero is the warmer one.
- Find each temperature on a thermometer. Start at zero and count down.−2 is 2 below zero. −6 is 6 below zero.
- Compare them. The number closer to zero is warmer.−2 is closer to zero than −6.
- Write the answer. −2 °C is warmer
Check. Count down from zero: −2 is reached first, so it is the warmer one. ✓
Watch out. The warmer temperature is the one with the smaller number after the minus sign.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Find the level of the liquid on the thermometer and read the number beside it.
- Find the top of the liquid. The liquid stops at the line marked with a number below zero.The liquid stops 6 steps below zero.
- Read the number. Each step below zero is a negative number.The line is −6, so the temperature is −6 °C.
Check. Count down from zero: 0, −1, −2, −3, −4, −5, −6. ✓
Watch out. Read the labels. The liquid is below zero, so the number has a minus sign.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 4 steps up. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at −7
- Move 4 steps up. Count one step at a time. Each step changes the number by 1.−7 + 4
- Write the new number. −3
Check. −7 + 4 = −3. Going back: −3 − 4 = −7. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 3 steps up. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at −5
- Move 3 steps up. Count one step at a time. Each step changes the number by 1.−5 + 3
- Write the new number. −2
Check. −5 + 3 = −2. Going back: −2 − 3 = −5. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 4 steps down. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at 1
- Move 4 steps down. Count one step at a time. Each step changes the number by 1.1 − 4
- Write the new number. −3
Check. 1 − 4 = −3. Going back: −3 + 4 = 1. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 6 steps down. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at −1
- Move 6 steps down. Count one step at a time. Each step changes the number by 1.−1 − 6
- Write the new number. −7
Check. −1 − 6 = −7. Going back: −7 + 6 = −1. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Method. Mark the numbers on the number line and count between them.
- Look at the first box. Count up from −6: −6, −5, then the box.−6, −5, −4
- Look at the second box. Count on from −4 to −1 through the boxes.−4, −3, −2, −1
- Write the missing numbers. The two boxes hold these numbers.−4 and −1
Check. From −6 to 2 there are 9 whole numbers, including both ends, and each step is 1. ✓
Watch out. The steps are all 1 apart, so count each one.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Put the negative numbers first, then zero, then the positive numbers, all in the right order.
- Split the numbers into groups. Negative numbers are less than zero, and positive numbers are greater than zero.negative: −20, −15, −3; zero; positive: 4
- Order the negative numbers. For negatives, the bigger number after the minus sign is the smaller number: −10 is less than −4.−20, −15, −3
- Write the whole list from the largest. Put the largest number first.4, 0, −3, −15, −20
Check. Each number is in the right place: 4 > 0 > −3 > −15 > −20. ✓
Watch out. A bigger minus number is colder. −10 °C is colder than −4 °C, even though 10 is bigger than 4.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Use the number line to compare the two numbers.
- Look at where each number is. Start at zero and count down.−9 is 9 steps below zero. −3 is 3 steps below zero.
- Compare the two numbers. The number further to the left is smaller.−9 is further left, so −9 is less than −3.
- Explain the mistake. Ben forgot that the minus sign changes the order.−3 is greater than −9.
Check. Count the steps: −3 is reached first going down, so it is bigger. ✓
Watch out. With negatives, the bigger number after the minus sign is the smaller number.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Start at the first number and move 45 steps up. Count through zero if you need to.
- Start at the first number. Find it on the number line or thermometer.Start at −120 m
- Move 45 steps up. Count one step at a time. Each step changes the number by 1.−120 + 45
- Write the new number. −75 m
Check. −120 + 45 = −75. Going back: −75 − 45 = −120. ✓
Watch out. Going down past zero makes the number negative. Count through zero, do not stop at zero.
Key words. A negative number is a number less than zero. It has a minus sign in front of it, such as −4. Zero is neither positive nor negative. On a number line, numbers get smaller as you move left.
Method. Do the two changes one at a time, and keep the sign of the answer each time.
- Fall 5 degrees. Going down 5 from −4 takes you 5 steps down.−4 − 5 = −9
- Rise 9 degrees. Going up 9 from −9 takes you 9 steps up. Count through zero.−9 + 9 = 0
- Write the answer. 0 °C
Check. Going back: 0 − 9 = −9, and −9 + 5 = −4. ✓
Watch out. The temperature reached zero exactly. Zero is not negative.