Read a number line

What it looks like when your child can do it

• — On a line with only 0 and 10 written and a mark for every whole number, your child finds 7 by counting seven jumps from zero.
• — Your child counts the gaps between marks, not the marks themselves, before deciding what one step is worth.
• — Reading a measuring cup, your child finds two numbered marks and works out the unmarked ones in between.

How to teach it at the kitchen table

1. 01

   Draw a line and number every mark

   Draw a line with 11 evenly spaced marks and number them 0 to 10. Put a coin on one mark and ask what number it sits on. Start where every mark has a number.

2. 02

   Count gaps, not marks

   Hold up five fingers. There are five fingers but only four gaps between them. Distance on a number line lives in the gaps, so the gaps are what your child counts.

3. 03

   Rub out some of the numbers

   Now write only 0, 5 and 10 on the line. Put the coin down and ask for its value. Your child counts steps from the nearest numbered mark.

4. 04

   Work out what one step is worth

   Draw a line with 0 and 60 written at the ends and 3 equal gaps between them. Take the difference, 60, and divide by the 3 gaps. Each step is worth 20.

5. 05

   Find number lines around the house

   A ruler, a measuring cup and an oven dial are all number lines. Pick one, find two numbered marks, and work out what one small mark is worth.

You will need: Paper, a pencil and a ruler · A coin or a small toy · A measuring cup from the kitchen

Try it together

1. Try 1

   Draw a line from 0 to 10 with a mark for every whole number, but write only 0 and 10. Point to the third mark after zero.

   Listen for  3. Watch that your child counts jumps from zero and does not count the zero mark itself as one.

2. Try 2

   Draw a line with 0 and 50 written at the ends and 5 equal gaps between. Ask what each small step is worth.

   Listen for  10. The difference is 50 and there are 5 gaps, so 50 divided by 5 is 10. The marks read 0, 10, 20, 30, 40, 50.

3. Try 3

   Draw a line with 20 and 40 written at the ends and 4 equal gaps between. Point to the third mark above 20.

   Listen for  35. The difference is 20 and there are 4 gaps, so each step is 5. Three steps above 20 is 35.

4. Try 4

   On the 0 to 50 line with 5 gaps, ask your child how many marks there are and how many gaps.

   Listen for  6 marks and 5 gaps. If your child tries 50 divided by 6, it does not come out even, which is the clue that the marks were counted instead of the gaps.

Watch for

• — Counting marks instead of gaps. Five marks have four gaps, and dividing by the wrong one gives the wrong step every time.
• — Assuming every step is worth one. Ask what a step is worth before reading anything off the line.

If it is not there yet

• — Go back to a line with every mark numbered and hop a small toy along it, one hop per gap, saying each number it lands on.
• — Stay with lines that count by ones up to 10 before trying lines that count by fives or by tens.

A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.

Where this skill comes up

• How Scientists Actually Find Out · Lesson 7

  Reading the Line on the Cup

  Needs it because A measuring cup, a ruler and a thermometer are number lines wrapped around an object.

• How Scientists Actually Find Out · Lesson 22

  Turning Numbers Into a Picture

  Needs it because the vertical axis is a number line stood on end, and a wrong scale makes a lying graph.