Interactive number line

What a number line is for

A number line puts numbers in order with equal gaps between them, so a child can see that 9 is one step from 10 and that 0.5 sits halfway between 0 and 1. Adding becomes moving right and subtracting becomes moving left. The same picture later carries fractions, decimals and negative numbers.

This tool has six ranges: 0 to 10, 0 to 20, 0 to 100, -10 to 10, 0 to 1 in tenths, and 0 to 2 in quarters. Drag the pointer, tap a spot or use the arrow buttons, and it snaps to the nearest tick, with a readout of where it sits. On 0 to 100 the ticks go up in tens, and the quarters line is labeled in quarters, such as 2/4 and 6/4, so a child counts equal parts.

Why moving a pointer helps

Counting on a number line makes a child count the jumps, not the marks. A common slip when working out 8 + 5 is to count 8 as the first step and land on 12. Moving a pointer one tick at a time shows that the first jump goes from 8 to 9, so the answer is 13. The line also builds a sense of size: 47 would sit much nearer the 50 tick than the 40 tick, which is the whole idea behind rounding.

Fractions are numbers too, with their own place on the line. Common Core standard 3.NF.A.2 asks third graders to represent fractions on a number line diagram, and 6.NS.C.6 extends the line past zero to negative numbers. The quarters and negative ranges on this page cover both.

Ideas by grade

• Kindergarten and grade 1: use 0 to 10 and 0 to 20 for counting on and counting back. Ask "what is one more?" and "what is one less?"
• Grade 2: use 0 to 100 to count in tens, and use 0 to 20 to add and subtract within 20 by counting on and back.
• Grades 3 and 4: use 0 to 100 for rounding to the nearest ten by naming the tens on either side, and 0 to 2 in quarters to show that 4/4 and 1 are the same point.
• Grades 4 and 5: use 0 to 1 in tenths to place decimals such as 0.3 and 0.8 and to see that 0.5 is one half.
• Grades 6 and 7: use -10 to 10 for temperatures, opposites such as 4 and -4, and adding or subtracting across zero.

A 10-minute number line routine

• Pick the range that matches the child's work this week.
• Call out a number and ask the child to place the pointer. Do three of these quickly as a warm-up.
• Give a move: "start at 6, go forward 7." Ask the child to predict the landing number first, then move the pointer to check.
• Turn it round: "you landed on 15 and you started on 9. How many jumps did you make?" This is subtraction as finding the gap.
• Finish by asking the child to make up a move for you. Explaining a problem is harder than solving one.

Keep it brisk. If a prediction is wrong, let the pointer settle it and ask what happened.

Where this leads

Number lines appear throughout Eurekami's interactive lessons, drawn from the real numbers in each question and narrated in English or Spanish. When a child is stuck on a word problem, the AI tutor can ask guiding questions about where to start and which way to move, rather than jumping to the answer.