Negative numbers and integers. Read a little, then play. Clear all six games!
What it is
Numbers less than zero are negative numbers, written with a minus sign like −3. On the number line they sit to the left of zero, and positive numbers to the right.
Why it works
As you move right along the line the numbers get bigger, and as you move left they get smaller. So moving 5 steps left from 3 lands you on −2, past zero into the negatives.
Why it matters
Negative numbers describe real things below a starting point, like floors below the ground or temperatures below zero.
A few examples
−2 is 2 steps left of 0. Starting at 3 and moving 5 left gives −2.
What it is
To compare two integers, the one further to the right on the number line is the bigger one.
Why it works
Zero is bigger than every negative, and among negatives the one closer to zero is bigger. So −3 is bigger than −5, because −3 is to the right of −5.
Why it matters
Comparing integers lets us say which temperature is warmer or which floor is higher.
A few examples
−3 is bigger than −5. 0 is bigger than −1. 2 is bigger than −9.
What it is
Every integer is positive (right of zero), negative (left of zero) or zero itself. The sign tells you which side of zero it is on.
Why it works
A number with a minus sign is negative and less than 0. A number with no sign (or a plus) is positive and more than 0. Zero is neither positive nor negative.
Why it matters
Sorting integers by sign and size is the first step to working with them.
A few examples
−4 and −1 are negative. 2 and 6 are positive. 0 is neither.
What it is
We can show integers with tokens: a +1 token and a −1 token. One of each together makes a zero pair and cancels out.
Why it works
To find the value, pair up every +1 with a −1 and remove those pairs, since each is worth 0. Whatever tokens are left over give the answer. 3 plus and 5 minus leave 2 minus, so −2.
Why it matters
The token model makes adding and subtracting integers easy to see.
A few examples
3 plus and 5 minus tokens make −2. 4 plus and 4 minus make 0.
What it is
To add integers, move that many steps on the number line: to the right for a positive, to the left for a negative.
Why it works
Start at the first number. Adding a positive moves you right, adding a negative moves you left. So −3 + 7 means start at −3 and move 7 right, landing on 4.
Why it matters
This is how we combine gains and losses, or rises and falls, in one calculation.
A few examples
−3 + 7 = 4. 5 + (−8) = −3. −2 + (−4) = −6.
What it is
Integers describe anything with an up and down from a zero point: temperature above and below freezing, floors above and below ground, and depth below sea level.
Why it works
We choose a zero (freezing point, ground floor, sea level) and count up as positive and down as negative, so a drop or a descent is subtracting, moving into negatives.
Why it matters
This lets us solve everyday problems about weather, lifts, submarines and money owed.
A few examples
2 degrees dropping 5 gives −3 degrees. A submarine at −20 m rising 8 m is at −12 m.
Have a go on paper first, then tap to see the clear steps.
Q1. Start at 2 on the number line and move 6 steps left. Where do you land?
Q2. Which is bigger, −2 or −7?
Q3. There are 4 positive tokens and 6 negative tokens. What is the total value?
Q4. Work out −5 + 8.
Q5. The temperature is 3 degrees and drops by 7 degrees. What is it now?
Q6. A submarine is at −12 m and rises 5 m. What is its new depth?