Using the number line
Type a range and the line is drawn for it. 0 to 20 gives one tick per whole number; -10 to 10 crosses zero; 0 to 1 by 1/4 marks quarters, labelled as fractions; and 0 to 1 by 0.1 marks tenths as decimals. Leave out the step and one is picked that keeps the line readable.
Type a sum, like 3 + 5 or 12 - 7, and it's drawn as hops: one hop per count for small numbers, or tens first and then ones for bigger ones, the way it's taught with an open number line. A single number, like 2.5, is marked on a line around it.
Printable number lines
Printable number linesstringmash.com/number-line
Adding and taking away on a number line
Adding is moving to the right and taking away is moving to the left. For 3 + 5, start on 3 and make five hops to the right, landing on 8. For 12 - 7, start on 12 and make seven hops to the left, landing on 5.
Counting in ones gets slow past 10, so bigger numbers jump in tens. For 23 + 18, jump a ten from 23 to 33, then 8 more to 41. It's the same sum, in two hops instead of eighteen.
Negative numbers, fractions and decimals
Numbers to the left of zero are negative. On a line from -10 to 10, -3 sits three steps left of zero, and -2 + 5 means starting at -2 and hopping five to the right, which lands on 3.
Between any two whole numbers there's room for more. Cut the gap from 0 to 1 into four equal steps and the ticks are quarters, 1/4, 1/2 and 3/4. Cut it into ten and they're tenths, 0.1 to 0.9. The line shows that 1/2 and 0.5 are the same point.
Where the number line came from
John Wallis described adding and taking away on a number line in his Treatise of Algebra in 1685, as a person walking forwards and backwards. An earlier picture of the numbers 1 to 12 in a row appears in John Napier's book on logarithms from 1616, though it doesn't use them for sums.
Questions
How do I print a number line?
Press Print chart above the printable lines. They print on their own sheet, with nothing else from the page.
How do I put fractions on a number line?
Type the range with a fraction step, like 0 to 1 by 1/4 or 0 to 2 by 1/3. The ticks are labelled as fractions.
What's an open number line?
A line with no fixed ticks, where you mark only the numbers you need and draw jumps between them. It's used to show mental methods, like jumping in tens.
How long can the line be?
Up to 40 steps. For bigger ranges, use a bigger step, like 0 to 1000 by 50.