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

Extending Place Value to Thousandths

Students will extend their understanding of place value to include decimals, identifying the value of digits in the tenths, hundredths, and thousandths places.

• Ontario Curriculum Expectations
• 5.NBT.A.1

About This Topic

Extending place value to thousandths builds on students' whole number knowledge by introducing decimal positions. A digit in the tenths place equals 0.1 or one-tenth of a whole, in the hundredths 0.01 or one-hundredth, and in the thousandths 0.001 or one-thousandth. Students identify these values in numbers like 3.456, where 4 is 4 tenths, 5 is 5 hundredths, and 6 is 6 thousandths. They also explain how the decimal point divides whole numbers from fractional parts, comparing 4.56 to 0.456 to see position shifts.

This concept strengthens number sense within Ontario's Grade 5 curriculum, linking to standards like 5.NBT.A.1 on place value relationships. Students construct models and answer key questions, such as differentiating ones from tenths or building decimals to thousandths. It lays groundwork for decimal operations and real-world applications like measurements or money.

Active learning shines here because abstract positions become visible through manipulatives. When students build numbers with blocks or shade grids, they physically regroup ten thousandths into a hundredth. Group discussions reveal thinking, while hands-on tasks make patterns stick, cutting confusion and deepening understanding.

Key Questions

1. Differentiate between the value of a digit in the ones place and the tenths place.
2. Construct a model to represent a decimal number to the thousandths.
3. Explain how the decimal point acts as a separator between whole numbers and fractional parts.

Learning Objectives

• Identify the value of each digit in a decimal number up to the thousandths place.
• Compare decimal numbers expressed to the thousandths place.
• Construct a visual model (e.g., base-ten blocks, grid paper) to represent a given decimal number to the thousandths.
• Explain the role of the decimal point in separating whole number and fractional parts of a number.
• Represent decimal numbers to the thousandths using expanded notation.

Before You Start

Understanding Place Value to Thousands

Why: Students need a solid foundation in the place value of whole numbers before extending it to decimal places.

Introduction to Decimals (Tenths and Hundredths)

Why: Prior exposure to tenths and hundredths helps build the conceptual bridge to thousandths.

Key Vocabulary

Decimal Point	A symbol used to separate the whole number part of a number from its fractional part. It indicates the transition from ones to tenths.
Tenths	The first place value to the right of the decimal point, representing one out of ten equal parts of a whole (0.1).
Hundredths	The second place value to the right of the decimal point, representing one out of one hundred equal parts of a whole (0.01).
Thousandths	The third place value to the right of the decimal point, representing one out of one thousand equal parts of a whole (0.001).
Expanded Notation	Writing a number to show the value of each digit. For decimals, this includes showing the value of digits to the right of the decimal point.

Watch Out for These Misconceptions

Common Misconception

Digits after the decimal point all represent the same small fraction.

What to Teach Instead

Students often overlook how position determines size, thinking tenths and thousandths are similar. Use decimal grids where they shade one tenth versus one thousandth side-by-side; visual comparison in pairs clarifies the tenfold decrease per place. Active regrouping reinforces this pattern.

Common Misconception

Moving the decimal point changes the number's value.

What to Teach Instead

Some believe shifting the point alters worth without digit moves. Hands-on slides with place value mats show fixed digit values; students physically shift digits instead. Group challenges to rewrite numbers expose the error through peer explanation.

Common Misconception

The thousandths place is larger than the tenths place.

What to Teach Instead

Confusion arises from left-to-right reading habits. Build models where students stack blocks to compare 0.1 versus 0.001; measuring total lengths in small groups quantifies the difference. Discussion ties back to the ten-times rule.

Active Learning Ideas

Manipulative Build: Decimal Blocks

Give students base-10 blocks adapted for decimals, including thousandths strips. Assign numbers like 1.234; they build by placing flats for tenths, longs for hundredths, and units for thousandths. Regroup ten thousandths into one hundredth and record digit values.

35 min·Small Groups

Grid Shading: Place Value Art

Distribute 10x10 grids for hundredths and smaller for thousandths. Students shade sections to represent decimals like 0.375, labeling each place. Pairs compare models and trade shaded areas to match different numbers.

25 min·Pairs

Place Value Chart Relay

Set up large charts to thousandths. Teams draw digit cards and race to place them correctly, stating the value aloud. Switch roles; correct as a class and rebuild with changes like moving a digit left.

40 min·Small Groups

Measurement Hunt: Decimal Lengths

Students measure classroom objects to thousandths using rulers marked in centimetres. Record as decimals, like 5.247 cm, and identify place values. Share findings and order measurements on a class line.

30 min·Pairs

Real-World Connections

• Pharmacists use decimal values to the thousandths when measuring precise dosages of medication, ensuring patient safety and treatment effectiveness.
• Engineers and scientists measure distances, weights, or other quantities to the thousandths of a unit (e.g., millimeters, grams) for highly accurate calculations in construction or research.
• Financial analysts examine stock prices that are often quoted to the thousandths of a dollar, requiring an understanding of these small decimal values to track market changes.

Assessment Ideas

Exit Ticket

Provide students with the number 7.382. Ask them to: 1. Write the value of the digit 3. 2. Write the value of the digit 2. 3. Explain what the decimal point separates in this number.

Quick Check

Display a set of base-ten blocks or a grid representing a decimal. Ask students to write the decimal number shown. Then, present a decimal number (e.g., 0.567) and ask students to draw a representation using base-ten blocks or shading a grid.

Discussion Prompt

Pose the question: 'How is the digit 5 in the number 5.234 different from the digit 5 in the number 0.523?' Guide students to discuss the place value of each digit and its corresponding value.

Frequently Asked Questions

How do I teach place value to thousandths in Grade 5?

Start with familiar whole numbers, then expand rightward across the decimal. Use visuals like expanded form: 3.456 = 3 + 4/10 + 5/100 + 6/1000. Progress to manipulatives for building and decomposing. Daily practice with Ontario expectants reinforces patterns, preparing for operations. Connect to measurements for relevance.

What manipulatives best show decimal place value?

Decimal squares, base-10 blocks with thousandths units, or centimeter grid paper work well. Students represent 0.123 by shading or stacking proportionally. These tools let them trade ten smaller pieces for one larger, mirroring place value rules. Store in kits for repeated use across the unit.

How can active learning help students understand extending place value to thousandths?

Active methods like building with blocks or shading grids turn abstract places into tangible models. Students regroup physically, grasp the ten-times pattern, and explain to peers, solidifying concepts. Collaborative relays or hunts apply skills to real contexts, boosting engagement and retention over worksheets alone.

What are common errors in decimal place value for Grade 5?

Errors include ignoring position shifts or misplacing the decimal point. Address with peer model-sharing where students justify digit values. Targeted practice decomposing numbers like 2.307 helps. Track progress via exit tickets; reteach using varied active tasks to correct mental models.