Materials & Prep
- Project or draw a place-value chart with ones, tenths, hundredths, and thousandths.
- Prepare one half-sheet practice page with the problems in the Independent practice section.
- Usual pencils and whiteboards or scrap paper.
Fraction comparison hook
DisplayWrite 45/100 and 5/10. Ask students to silently choose which amount is greater, then show a thumb for the left fraction, right fraction, or equal.
Turn and talkPartners justify their choice using last year's fraction knowledge. Listen for students renaming 5/10 as 50/100, so 45/100 is less than 50/100.
ConnectWrite 0.45 below 45/100 and 0.5 below 5/10. Say, “The same amounts have new names. If 45 hundredths is less than 50 hundredths, then 0.45 is less than 0.5, even though 0.45 has more written digits.” This confronts the class's digit-counting prediction with evidence they already trust.
Model decimal names and comparisons
IntroduceUse the place-value chart. Explain that the decimal point separates ones from parts of one whole. Each place to the right is a smaller piece: tenths, hundredths, then thousandths.
AnalogyA dollar has tenths of a dollar, like dimes, then hundredths, like pennies. More places written does not mean a larger amount. It tells how precisely the amount is named.
Worked examplePlace 0.450 in the chart: 0 ones, 4 tenths, 5 hundredths, 0 thousandths. Think aloud: “I read the whole-number part first, then name the digits to the right by their last place: four hundred fifty thousandths. I do not say ‘four hundred fifty’ alone, because that would be a whole number.” Write 0.450 = 450/1000 = 45/100 = 0.45.
Worked exampleCompare 0.45 and 0.5 by writing 0.450 and 0.500. Think aloud: “I compare the largest place first. Both have 0 ones. In tenths, 4 is less than 5, so 0.450 < 0.500. I stop there because that place decides.”
MisconceptionShow the incorrect claim 0.45 > 0.5 because 45 is greater than 5. Clarify that decimal digits cannot be treated as a whole number after the point. Aligning decimal points and adding zeros at the end shows the place values being compared. Zeros may be added to the right, but never change the value.
Check for understandingDisplay 0.307. Students write its word name on a whiteboard: “three hundred seven thousandths.” Then ask, “Which is greater, 0.307 or 0.37?” Students hold up >, <, or = and explain that 0.37 is 0.370, so 3 tenths are equal and 7 hundredths are greater than 0 hundredths.
Guided practice
Have studentsComplete each item with a partner on whiteboards. After each, select one pair to explain the place-value reasoning.
- Write 0.608 in words.
- Write “nine tenths, four hundredths, and two thousandths” as a decimal.
- Compare 0.706 0.76.
- Compare 1.009 1.01.
ModelFor item 3, prompt students to write 0.760 before comparing. Ask, “What is the first place where the digits differ?” Expected: the hundredths place, where 0 is less than 6, so 0.706 < 0.760.
ScaffoldKeep the place-value chart projected and give students this comparison checklist: line up decimal points; add ending zeros if helpful; compare ones, then tenths, then hundredths, then thousandths; write <, >, or =; read the result aloud. Provide the spoken stem: “I know is greater because at the place, is greater than .”
ExtensionAsk ready students whether 0.600 and 0.6 are equal and to prove it using both a place-value chart and fractions.
Independent practice
StudentsComplete this focused practice page independently, using the checklist. Circulate and confer first with students who still read the digits after the decimal as a whole number.
A. Read and write.
- Write 2.045 in words.
- Write 0.918 in words.
- Write “six and twenty-three thousandths” as a decimal.
- Write “four hundredths” as a decimal.
B. Compare. Add zeros to the right when useful, then use <, >, or =.
- 0.639 0.64
- 3.105 3.015
- 0.700 0.7
- 1.999 2.000
C. Explain.
- A student says 0.82 is greater than 0.803 because 82 is greater than 803. Is the student correct? Write the two decimals with the same number of places and explain which is greater.
SupportOffer a place-value chart with the whole-number and decimal-point columns already marked. For item 9, provide the frame: “ is greater than . When I write them as and , I see that the first different place is the place.”
ChallengeCreate two different decimals to the thousandths that are equal, then write each in words and prove equality with equivalent fractions. Create a second pair in which the decimal with more digits is smaller, and explain why.
Closing check
Exit ticketOn a small slip, students answer: 1. Write 0.504 in words. 2. Compare 0.59 0.604 and give one place-value reason.
Look for“five hundred four thousandths” and 0.590 < 0.604 because at the tenths place, 5 is less than 6. Clarify during collection that the tenths decide this comparison, so no place farther right needs to be compared. Sort slips quickly into secure, needs decimal-name support, and needs comparison support for the next lesson's opening group.