Lesson 1 — Reading and Writing Decimals to Thousandths

Summary

Learners read and write decimals to the thousandths. They build numbers on a place-value chart, name each place (tenths, hundredths, thousandths), and write the same number three ways — standard form (3.456), word form (“three and four hundred fifty-six thousandths”), and expanded form (3 + 4/10 + 5/100 + 6/1000). They see that the decimal point is just a marker between whole ones and the parts smaller than one.

Objectives

• Read, write, and expand decimals to the thousandths and name the value of each place. (D05.S1.05.01)

Connection

You already know whole numbers — ones, tens, hundreds. Now think about one single chapatis or flatbread torn into ten equal strips. Each strip is one tenth of the bread. Tear one strip into ten again and you get one hundredth; tear again and you get one thousandth. Decimals are how we write those small parts next to whole ones — and people use them every day for money, medicine, measurements, and weather. In many parts of the world the decimal point is written as a comma instead (3,456), but the idea is the same: a marker between whole ones and parts of one.

Materials

• Place-value chart to thousandths
• Digit cards (0–9) and a decimal-point card
• Decimal recording page

Preparation

• Print or draw the place-value chart (ones · tenths · hundredths · thousandths).
• Copy digit-card sets for pairs and a recording page for each learner.
• Have two or three example numbers ready to build (3.456, 0.205, 12.7).

Facilitator note

This lesson is written to the learner (“you”). The idea to land is that a decimal point separates whole ones from parts smaller than one, and that each place to the right is ten times smaller — tenths, then hundredths, then thousandths. Because this is a foundational skill, use explicit instruction and worked examples before independent practice (Kirschner, Sweller & Clark, 2006): model building 3.456 step by step, name each place, then guide a second number together before learners work alone. Watch for two common slips: reading “3.456” as “three point four five six” only (also teach the place-value reading “three and four hundred fifty-six thousandths”), and skipping the value of a zero (in 3.05, the zero holds the tenths place — there are 0 tenths). Note the global point: many countries use a comma as the decimal separator and a space or period for thousands — this is a difference of convention, not of correctness. The number facts here are evidence; the claim that no system is “better” is a value we hold (docs/philosophy.md §4–5).

Procedure

1. Gather (5 min). Think of the smallest amount of money you know. A whole coin or bill is “one.” What about a part of it? Today you learn how to read and write parts of one using decimals.
2. Meet the chart (10 min). Look at the place-value chart. To the left of the decimal point are whole ones; to the right are parts: tenths (1/10), hundredths (1/100), thousandths (1/1000). Each place to the right is ten times smaller than the one before it.
3. Worked example (10 min). Build 3.456 together. Put a 3 in the ones column, a 4 in the tenths, a 5 in the hundredths, and a 6 in the thousandths. Read it two ways: “three point four five six,” and “three and four hundred fifty-six thousandths.” Write it in expanded form: 3 + 4/10 + 5/100 + 6/1000. Notice the 4 means 4 tenths, the 5 means 5 hundredths, the 6 means 6 thousandths.
4. Build your own (15 min). With a partner, build 0.205 and 12.7. For each, say each digit’s place and value aloud, then write it in standard, word, and expanded form. Check: in 0.205, what is the 0 in the hundredths place doing? (Holding the place — there are 0 hundredths.)
5. Close (5 min). Remember: the decimal point is just a marker. Every digit in a decimal has a name and a value, and now you can read and write them all the way to the thousandths.

Differentiation

• Support: Start with tenths and hundredths only; use a place-value chart with the value of each column printed in it. Describe each place aloud and trace the digits with a finger so learners with low vision can follow by listening and touch.
• Extension: Write decimals with a zero in a middle place (3.05, 0.040) and explain the zero’s role; extend the chart one more place to ten-thousandths and name it.

Assessment

• Formative (observation/self): Can the learner place digits of a decimal to the thousandths and name each place’s value?
• Self-check: The learner asks, “Can I read 3.456 two ways, and can I write any decimal to thousandths in expanded form?”

Home connection

Ask someone at home where they see decimals — on a receipt, a scale, a medicine label, a weather report — and read one decimal aloud together.

Resources

• Place value with decimals is standard in elementary mathematics; see John A. Van de Walle, Elementary and Middle School Mathematics (10th ed., 2019) for place-value teaching models. The note that a comma serves as the decimal separator in many countries is a documented convention (ISO 80000-1, which stipulates the decimal sign is “either a comma or a point on the line,” and national standards); treating all conventions as valid is a value commitment (docs/philosophy.md §4).