Fractions and decimals on a number line

What it looks like when your child can do it

• — Given a line from 0 to 1 cut into fourths, your child counts three spaces from 0 and marks 3/4.
• — Asked where 2.5 goes, your child says halfway between 2 and 3 and marks it there.
• — Your child reads a pencil against a ruler as 4 1/2 inches, seeing that it ends halfway between the 4 and the 5.

How to teach it at the kitchen table

1. 01

   Start with a ruler or tape measure

   A ruler is a number line. Point to the marks between 0 and 1 inch and ask how many equal spaces there are. Those spaces are the fractions of an inch.

2. 02

   The bottom number sets the cuts

   To place 3/4, cut the space from 0 to 1 into 4 equal parts, because the bottom number is 4. Then count 3 parts from 0 and mark the spot.

3. 03

   Count spaces, not tick marks

   A line from 0 to 1 cut into fourths has 5 tick marks but only 4 spaces. Your child counts the jumps, and 3/4 is where the third jump lands. The grade 6 book calls those jumps steps, counted from zero.

4. 04

   Past one, keep counting

   5/4 is one fourth past 1, and 1 1/2 is halfway between 1 and 2. Every space between whole numbers gets cut the same way.

5. 05

   Decimals are tenths and hundredths

   0.5 is 5/10, halfway to 1. 0.3 is 3 of 10 equal jumps from 0. Money helps: 2.5 is 2 dollars and 50 cents, halfway between 2 and 3 dollars.

You will need: A ruler or tape measure · Paper and a pencil · Masking tape for a floor line

Try it together

1. Try 1

   Draw a line from 0 to 1 and cut it into 8 equal spaces. Ask your child to mark 3/8 and 6/8.

   Listen for  3/8 is the third jump from 0 and 6/8 is the sixth. Ask what else 6/8 could be called; it sits on the same spot as 3/4.

2. Try 2

   Draw a line from 0 to 3 with each whole cut into halves. Mark 1 1/2 and 5/2.

   Listen for  1 1/2 is halfway between 1 and 2. 5/2 is five halves, which is 2 1/2, halfway between 2 and 3. Watch that your child does not put 5/2 out near 5.

3. Try 3

   On a line from 0 to 1 marked in tenths, where does 0.7 go? Which is closer to 1, 0.7 or 0.65?

   Listen for  0.7 is the seventh jump. 0.65 sits halfway between 0.6 and 0.7, so 0.7 is closer to 1. A child who picks 0.65 is reading the digits instead of the places, so line both up on the same tenths line and look.

4. Try 4

   Which sits farther right on the line, 2/3 or 3/4?

   Listen for  3/4. Draw two lines from 0 to 1, one cut in thirds and one in fourths, and line them up. 3/4 is 0.75 and 2/3 is about 0.67.

Watch for

• — Counting tick marks instead of spaces. Counting the mark at 0 as "one" puts 3/4 where 2/4 belongs.

If it is not there yet

• — Go back to a ruler and read whole inches and half inches only, then quarter inches, before moving to a drawn number line.
• — Walk it: tape a line on the floor from 0 to 1 with four equal steps, and have your child stand on 1/4, 2/4 and 3/4.

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

• Grade 6 Math Practice Workbook · Lesson 11

  Every Number Has a Place on the Line

  Needs it because the line now runs in both directions, but placing three quarters between 0 and 1 has not changed.

• Grade 6 Math Practice Workbook · Lesson 14

  Absolute Value: How Far from Zero

  Needs it because distance from zero is read off the line, so your child has to be able to find a number's spot on it first.

• Grade 6 Math Practice Workbook · Lesson 23

  At Least, At Most: Inequalities

  Needs it because the solution set is drawn on one.

• Grade 6 Math Practice Workbook · Lesson 32

  Three Pictures of the Same Data

  Needs it because every one of these plots sits on a number line.