Extending Place Value to Thousandths

Active learning helps students grasp the abstract concept of thousandths by making it concrete. Moving beyond whole numbers requires students to physically manipulate materials and visualize how each decimal place shrinks by a factor of ten. These hands-on experiences build lasting understanding that paper-and-pencil exercises alone cannot achieve.

• Grade 5
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

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

Stations Rotation

⏱ 35 min·Small Groups

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.

Prepare & details

Differentiate between the value of a digit in the ones place and the tenths place.

Facilitation Tip: During Manipulative Build: Decimal Blocks, circulate to ensure students correctly assign block values to tenths, hundredths, and thousandths before building their numbers.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 25 min·Pairs

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.

Prepare & details

Construct a model to represent a decimal number to the thousandths.

Facilitation Tip: For Grid Shading: Place Value Art, remind students to label each shaded section with its decimal value to reinforce the connection between visuals and written numbers.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 40 min·Small Groups

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.

Prepare & details

Explain how the decimal point acts as a separator between whole numbers and fractional parts.

Facilitation Tip: In Place Value Chart Relay, move between groups to clarify any confusion about digit placement before the next team continues.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 30 min·Pairs

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.

Prepare & details

Differentiate between the value of a digit in the ones place and the tenths place.

Facilitation Tip: During Measurement Hunt: Decimal Lengths, provide rulers with both centimeter and millimeter markings to highlight the thousandths place as a subdivision.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Teaching This Topic

Teachers should approach this topic by first solidifying whole number place value, then gradually introducing decimals through visual and tactile models. Avoid rushing to procedural rules before students have internalized the magnitude of each place. Research suggests that students need repeated exposure to decimal fractions through multiple representations—concrete, pictorial, and symbolic—to build deep understanding. Misconceptions often stem from overgeneralizing whole number rules to decimals, so address these early with targeted comparisons.

What to Expect

Successful learning looks like students confidently identifying, comparing, and explaining the value of digits in the tenths, hundredths, and thousandths places. They should articulate how the decimal point separates whole numbers from fractional parts and use precise language to describe each place's value. Misconceptions should be addressed in the moment through guided discussion and peer explanation.

Watch Out for These Misconceptions

Common Misconception

During Manipulative Build: Decimal Blocks, watch for students who treat tenths, hundredths, and thousandths as interchangeable. Redirect them by having them build 0.3, 0.03, and 0.003 side-by-side, then compare the total sizes of each model to clarify the tenfold decrease.

What to Teach Instead

Ask students to explain why the same block represents different values in each position. Reinforce that the digit’s value depends on its place, not the block itself.

Common Misconception

During Place Value Chart Relay, watch for students who believe shifting the decimal point changes the digits' values. Pause the relay and have students physically slide digits on their mats while keeping the decimal fixed to see that the digits' values stay the same.

What to Teach Instead

Challenge the group to write both the original and altered numbers, then compare the digits in each place to prove their values haven't changed.

Common Misconception

During Measurement Hunt: Decimal Lengths, watch for students who assume the thousandths place is larger because it has more digits. Bring them back to the ruler and have them measure the same length in centimeters, millimeters, and tenths of a millimeter to see how the thousandths place is the smallest subdivision.

What to Teach Instead

Ask students to explain why 0.1 cm is larger than 0.001 cm by comparing the actual lengths they measured on the ruler.

Assessment Ideas

Exit Ticket

After Manipulative Build: Decimal Blocks, provide the number 9.473. Ask students to: 1. Write the value of the digit 7. 2. Write the value of the digit 9. 3. Explain what the decimal point separates in this number.

Quick Check

During Grid Shading: Place Value Art, display a grid representing 0.564. Ask students to write the decimal number shown. Then, present the number 0.821 and ask students to shade a grid to match, labeling each section with its decimal value.

Discussion Prompt

After Place Value Chart Relay, pose the question: 'How is the digit 6 in the number 6.345 different from the digit 6 in the number 0.634?' Guide students to discuss the place value of each digit and its corresponding value, using their chart mats as visual support.

Extensions & Scaffolding

• Challenge students to create their own decimal numbers using base-ten blocks and then trade with a partner who must write the number in word form and expanded form.
• For students who struggle, provide pre-labeled place value mats with color-coded sections for tenths (blue), hundredths (yellow), and thousandths (green) to visually anchor their understanding.
• Deeper exploration: Have students research and present real-world examples where thousandths are used, such as precision measurements in science or engineering, and explain why accuracy matters in those contexts.

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.