Comparing whole numbers and decimals

What it looks like when your child can do it

• — Comparing 0.5 and 0.45, your child writes 0.5 as 0.50 and says 0.50 is greater.
• — Your child writes 4,089 < 4,098 and reads it aloud as 4,089 is less than 4,098.
• — Given four gas prices, your child lines up the decimal points and puts them in order from cheapest to most expensive.

How to teach it at the kitchen table

1. 01

   The pointed end aims at the smaller number

   Write 3 < 8 and 8 > 3. Both say the same thing. The open side faces the bigger number, the point faces the smaller one, and either number can go first.

2. 02

   Whole numbers: count digits, then compare from the left

   A number with more digits is greater, so 1,020 > 999. When the digit counts match, compare from the left until two digits differ. 4,089 and 4,098 match until the tens place, where 8 is less than 9.

3. 03

   Decimals: line up the points first

   Stack the numbers with their decimal points in one column and add zeros so both have the same number of places. 0.5 becomes 0.50, and now 50 hundredths against 45 hundredths is a fair comparison.

4. 04

   Picture a number line

   Greater numbers sit farther right. When a comparison feels slippery, sketch a line from 0 to 1 and mark both decimals. In the book the same line runs left past zero into the negatives, and farther left still means less.

You will need: Paper and a pencil · A few dimes and pennies

Try it together

1. Try 1

   Write 4,089 and 4,098. Ask which is greater, and ask your child to write the symbol between them.

   Listen for  4,089 < 4,098, or 4,098 > 4,089. Watch that your child starts at the left and stops at the first place that differs, the tens place.

2. Try 2

   Ask which is greater, 0.5 or 0.45.

   Listen for  0.5 is greater. Writing it as 0.50 shows 50 hundredths against 45. If your child picks 0.45 because it has more digits, that is the classic mix-up.

3. Try 3

   Ask which is greater, 2.305 or 2.35.

   Listen for  2.35 is greater. With a zero added it is 2.350, and 350 thousandths is more than 305 thousandths.

4. Try 4

   Ask your child to put these in order from least to greatest: 0.7, 0.07, 0.707, 0.77.

   Listen for  0.07, 0.7, 0.707, 0.77. Writing each with three places, 0.070, 0.700, 0.707, 0.770, shows the order. This one takes patience, so let your child work it on paper.

5. Try 5

   Gas costs 4.59 dollars a gallon at one station and 4.6 at another. Which is cheaper?

   Listen for  4.59 is cheaper, by one cent, because 4.6 is 4.60. A child who says 4.6 is cheaper because 6 looks smaller than 59 needs to line up the points.

Watch for

• — Deciding that the decimal with more digits is greater, so 0.45 beats 0.5. Adding zeros until both have the same number of places fixes it.

If it is not there yet

• — Go back to money. 0.5 of a dollar is 50 cents and 0.45 is 45 cents, and a child who would rather have 50 cents already knows which is greater.
• — Mark decimals on a number line drawn from 0 to 1 in ten equal sections, one for each tenth, until the picture of left and right is solid.
• — Practice the symbols with whole numbers under 100 before mixing them with decimals.

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 13

  Which Is Colder? Ordering Rational Numbers

  Needs it because the move extends to negatives; the symbols are the same.