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Comparing Decimals to Hundredths

A 45-minute Grade 4 lesson on comparing decimals to hundredths by their size rather than their length, and on why a comparison only means something when both decimals refer to the same whole.

Comparing Decimals to Hundredths is a free 45-minute Grade 4 math lesson plan for Common Core standard 4.NF.C.7 — compare two decimals to hundredths and record the result with >, = or <. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 4
Length:
45 minutes
Standard:
4.NF.C.7

Grade 4 · Number & Operations — Fractions

4.NF.C.7

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Objective

Students will be able to compare two decimals to hundredths by reasoning about their size, record the comparison with >, = or <, and justify it with a visual model.

Students are successful when they can

  • Rewrites tenths as hundredths, such as 0.5 as 0.50, before comparing.
  • Records comparisons with >, = and < and justifies one with a hundredths grid or with money.
  • Explains that 0.5 of one thing and 0.4 of another cannot be compared unless the wholes are the same size.

What you need

  • Hundredths grids, ten by ten
  • Play money: dimes, pennies and dollar bills
  • Decimal cards for comparing and ordering
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — which is more money?

5 min
  1. Ask which is more money: $0.75 or $0.80. Then write 0.75 and 0.8 without the dollar sign and ask again.
  2. Most students get the money right and the plain decimals wrong. The money is the bridge for the rest of the lesson.

Teach — compare the size, not the length

14 min
  1. Shade 0.45 and 0.5 on two hundredths grids. 0.5 is five columns, 50 squares; 0.45 is 45 squares. 0.5 > 0.45.
  2. Write 0.5 as 0.50. Adding the zero names the same amount in hundredths, so the two numbers can be compared digit by digit.
  3. Compare from the left: tenths first, then hundredths. 0.62 and 0.6: same tenths, then 2 hundredths against 0. 0.62 > 0.6.
  4. Connect to money: $0.80 is 8 dimes, and $0.75 is 7 dimes and 5 pennies. Eight dimes is more, whatever the pennies say.
  5. Ask whether 0.5 of a small pizza is more than 0.4 of a large one. It may not be. Draw both. The comparison only works when the wholes are the same.
  6. Order 0.4, 0.38, 0.6 and 0.06 from least to greatest, shading where unsure: 0.06, 0.38, 0.4, 0.6.
“Compare decimals by how much they are, not by how many digits they have. Write both in hundredths, then compare tenths first. And check they are parts of the same whole.”

Guided practice — shade and prove

12 min
  1. Pairs compare six pairs of decimals, writing >, = or < and shading grids for any pair they disagree about.
  2. Include one equal pair, such as 0.3 and 0.30, and one pair where the longer decimal is smaller, such as 0.7 and 0.65.
  3. For one pair, they write the comparison as money and check it with coins.

Independent practice

11 min
  1. Students complete a comparing decimals page.
  2. A pattern of choosing the longer decimal as larger is the whole-number error; a pattern of choosing the shorter one is its overcorrection. Both need the grid, not a rule.

Close

3 min
  1. Ask: Maria ran 0.6 of her route and Sam ran 0.5 of his. Who ran farther?
  2. It depends on the routes. Saying why is the point of the standard's 'same whole', and it is worth ending on.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Says 0.45 > 0.5 because 45 is bigger than 5.

Why: The digits after the point are being read as a whole number, so more digits seems to mean a bigger number, exactly as it does for 45 and 5.

Fix: Shade both on hundredths grids, then write 0.5 as 0.50. Fifty hundredths against forty-five hundredths is a comparison the student already knows how to make.

Says 0.4 > 0.52 because tenths are bigger than hundredths.

Why: A true fact — one tenth is bigger than one hundredth — has been overextended into a rule that a decimal ending in tenths beats one ending in hundredths.

Fix: Compare tenths first: 4 tenths against 5 tenths. 0.52 already has more tenths, so the hundredths do not need to be looked at. A grid makes it visible.

Says 0.5 of a small bottle is more water than 0.4 of a large jug.

Why: The numbers have been compared correctly, but the wholes they refer to have been ignored, because every comparison so far used the same unstated whole.

Fix: Draw both containers to scale and shade each part. When the wholes differ, the decimals alone cannot settle it — that is what the standard means by the same whole.

If they are not there yet

  • Compare amounts of money first, using dimes and pennies, before comparing plain decimals.
  • Write every decimal in hundredths on a place-value chart before comparing.

If they finish early

  • Find three decimals between 0.4 and 0.5 and order them.
  • Write a pair of decimals where the comparison changes if the wholes are different, and explain it.
  • Order five decimals that mix tenths and hundredths, then check with a number line from 0 to 1.

Exit ticket

Write >, = or <: 0.6 __ 0.59, 0.3 __ 0.30, 0.08 __ 0.1. Then: Ana drank 0.5 of her bottle and Ben drank 0.4 of his. Can you be sure Ana drank more?

What to look for: >, = and <, and no — only if the bottles are the same size. Choosing 0.59 as larger is the whole-number error; saying 0.3 and 0.30 differ means the zero is read as adding value; a plain yes means the whole is not yet part of the comparison.

Printable practice for 4.NF.C.7

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Comparing Decimals to Hundredths

How long does the Comparing Decimals to Hundredths lesson take?

45 minutes, split across 5 timed sections: warm-up 5 min, teach 14 min, guided practice 12 min, independent practice 11 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Comparing Decimals to Hundredths teach?

CCSS.MATH.CONTENT.4.NF.C.7 — 4.NF.C.7, Number & Operations — Fractions for Grade 4: “Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.” In plain terms, compare two decimals to hundredths and record the result with >, = or <.

What do I need to teach this lesson?

Hundredths grids, ten by ten, play money: dimes, pennies and dollar bills, decimal cards for comparing and ordering and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: says 0.45 > 0.5 because 45 is bigger than 5; says 0.4 > 0.52 because tenths are bigger than hundredths and says 0.5 of a small bottle is more water than 0.4 of a large jug. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “Write >, = or <: 0.6 __ 0.59, 0.3 __ 0.30, 0.08 __ 0.1. Then: Ana drank 0.5 of her bottle and Ben drank 0.4 of his. Can you be sure Ana drank more?.” >, = and <, and no — only if the bottles are the same size. Choosing 0.59 as larger is the whole-number error; saying 0.3 and 0.30 differ means the zero is read as adding value; a plain yes means the whole is not yet part of the comparison. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Comparing Decimals to Hundredths?

Yes — 1 printable 4.NF.C.7 worksheet, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Comparing Decimals to Hundredths free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on October 22, 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-10-22. Aligned to 4.NF.C.7 of the Common Core State Standards for Mathematics.