Mathematics · Grade 5 · The Power of Place: Large Numbers and Decimals · Term 1

Reading and Writing Decimals

Students will read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

• Ontario Curriculum Expectations
• 5.NBT.A.3.A

About This Topic

Reading and writing decimals to thousandths strengthens students' place value knowledge for numbers like 2.349. They represent these in base-ten numerals, number names such as "two and three hundred forty-nine thousandths," and expanded form: 2 + 3/10 + 4/100 + 9/1000. This directly supports Ontario Grade 5 Mathematics expectations in the unit on large numbers and decimals, where students construct expanded forms, explain correct oral reading with terms like "tenths" and "and" for the decimal point, and compare these to whole number expansions.

These skills build precise mathematical communication and number sense, essential for upcoming decimal operations and real-world applications like measurements or money. Students see how decimal place values mirror whole number ones but extend to fractional parts, fostering flexibility in number representation.

Active learning benefits this topic greatly with hands-on tools and partner tasks. When students use base-ten blocks to model decimals or match forms in games, they physically manipulate place values, clarify confusions through discussion, and retain concepts longer than through worksheets alone.

Key Questions

1. Construct the expanded form of a decimal number to the thousandths.
2. Explain how to correctly read a decimal number aloud.
3. Compare the expanded form of a whole number to that of a decimal number.

Learning Objectives

• Construct the expanded form of decimal numbers to the thousandths using base-ten numerals, fractions, and addition.
• Explain the process of reading decimal numbers aloud, including the use of 'and' for the decimal point and specific place value names.
• Compare the expanded form of a whole number to the expanded form of a decimal number, identifying similarities and differences in place value representation.
• Write decimal numbers to the thousandths in base-ten numerals, given their number name or expanded form.
• Represent decimal numbers to the thousandths using base-ten numerals, number names, and expanded form.

Before You Start

Place Value to Thousands

Why: Students need a strong understanding of whole number place value to extend this concept to decimal places.

Introduction to Fractions

Why: Understanding unit fractions like tenths and hundredths is foundational for comprehending decimal place values.

Reading and Writing Whole Numbers

Why: Students must be able to read and write whole numbers to apply the same principles to decimal numbers.

Key Vocabulary

Thousandths	The place value that represents one-thousandth of a whole. It is the third digit to the right of the decimal point.
Expanded Form	A way to write a number showing the value of each digit. For decimals, this includes whole number parts and fractional parts of the whole.
Base-Ten Numerals	The standard way we write numbers using digits 0-9 and place value, such as 123.456.
Number Name	Writing a number using words. For decimals, this includes terms like 'tenths', 'hundredths', and 'thousandths'.
Decimal Point	A dot that separates the whole number part of a number from the fractional part.

Watch Out for These Misconceptions

Common Misconception

Decimals like 0.7 mean 'zero and seven wholes.'

What to Teach Instead

This ignores place value; 0.7 is seven tenths. Grid paper activities where students shade tenths reveal the fractional part. Partner explanations during shading help students articulate and correct their views.

Common Misconception

Expanded form combines digits after decimal, like 1.23 as 1 + 23.

What to Teach Instead

Each digit needs its place value fraction. Base-ten block builds show separate 2/10 and 3/100 pieces. Group rotations with blocks prompt peer questions that resolve bundling errors.

Common Misconception

Read 3.405 as 'three point four zero five' without place names.

What to Teach Instead

Proper reading uses 'four hundred five thousandths.' Choral practice and recording playback in pairs build fluency. Matching audio to written forms reinforces naming conventions.

Active Learning Ideas

Partner Match: Decimal Forms

Pairs receive cards showing decimals in standard, word, or expanded form. They match sets of three matching representations, then create their own sets to trade. Discuss and verify as a class.

25 min·Pairs

Small Group: Place Value Mats

Provide mats marked with place value columns to thousandths. Groups build numbers using base-ten blocks or drawings, then write all three forms. Rotate materials to try teacher-chosen numbers.

35 min·Small Groups

Whole Class: Read Aloud Chain

Display a decimal on the board. First student reads it aloud correctly; next writes it in expanded form; continue around the room with variations. Correct as a group.

20 min·Whole Class

Individual: Number Journal

Students pick five decimals from daily life (e.g., measurements), write in all forms, and explain one orally to a partner. Collect for feedback.

15 min·Individual

Real-World Connections

• Measuring ingredients for recipes often requires precise decimal measurements, such as 0.25 cups of flour or 1.5 teaspoons of vanilla extract. Bakers and chefs use these numbers daily.
• Financial transactions, like calculating sales tax or discounts, involve decimals to the hundredths place. A cashier at a grocery store or a bank teller uses these skills to accurately process payments and give change.
• Scientific measurements, such as the length of a specimen or the volume of a liquid, frequently use decimals to the thousandths place. A lab technician might record a measurement as 3.141 millimeters.

Assessment Ideas

Exit Ticket

Provide students with a card displaying a decimal number (e.g., 5.678). Ask them to write the number in words, write its expanded form, and state the value of the digit in the hundredths place.

Quick Check

Write a decimal number in expanded form on the board (e.g., 10 + 0.5 + 0.02 + 0.009). Ask students to write the base-ten numeral for this number on a mini-whiteboard and hold it up. Then, ask them to read the number aloud.

Discussion Prompt

Present two decimal numbers written in expanded form, one as a whole number expansion and one as a decimal expansion (e.g., 123 and 12.3). Ask students: 'How are these expanded forms similar? How are they different? What does the decimal point do?'

Frequently Asked Questions

How do you teach expanded form for decimals to Grade 5 students?

Start with familiar whole numbers, then extend to decimals using visuals like place value charts. Have students build 2.34 with blocks: 2 ones, 3 tenths rods, 4 hundredths flats. Write as 2 + 3/10 + 4/100. Practice progresses from guided examples to independent construction, with peer review to check place values. This scaffolds from concrete to abstract.

What are common errors when reading decimals aloud?

Students often omit 'and' after the whole number or misname places, like 'three point two four' instead of 'three and twenty-four hundredths.' They confuse zero placeholders. Address with explicit modeling, choral reading of varied examples, and student-recorded audios for self-assessment. Daily practice with money or measurements embeds correct phrasing.

What manipulatives work best for decimal place value?

Base-ten blocks with added decimal mats excel, as students layer flats for tenths, skinny rods for hundredths, and units for thousandths. Grid paper or decimal squares offer paper alternatives. Combine with digital tools like virtual manipulatives for flexibility. These make fractional parts visible and support transitions to symbolic forms.

How does active learning help with reading and writing decimals?

Active approaches like partner matching games and block builds turn abstract place values into tangible experiences. Students discuss representations, catch errors in real time, and explain reasoning, which deepens understanding. Collaborative tasks build confidence in oral reading, while hands-on repetition improves accuracy and retention over passive drills. Expect stronger number sense and fewer misconceptions.

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