Decimal Place Value: Tenths and Hundredths

Active learning helps students grasp decimal place value by connecting abstract numbers to tangible models, which is essential for this topic. Hands-on activities correct common errors where students confuse tenths and hundredths or misapply whole number rules to decimals.

• 5th Class
• Mathematical Mastery: Exploring Patterns and Logic
• 4 activities
• 25 min–40 min

Learning Objectives

1. Compare the value of a digit in the tenths place to the value of the same digit in the hundredths place within a given decimal number.
2. Construct a visual model, such as a decimal grid or money representation, to accurately depict a two-digit decimal number.
3. Explain the relationship between decimal place value (tenths and hundredths) and the representation of monetary values in Euros and cents.
4. Differentiate between decimal numbers based on their place value, identifying which is larger or smaller.
5. Justify the importance of understanding decimal place value for accurate calculations involving currency.

Ready-to-Use Activities

Concept Mapping

⏱ 35 min·Pairs

Manipulative Mats: Building Tenths and Hundredths

Provide decimal mats divided into tenths and hundredths grids. Students use small squares for hundredths and larger strips for tenths to build numbers like 0.45. They trade ten hundredths for one tenth and record the model. Pairs compare and justify their builds.

Prepare & details

Differentiate the value of a digit in the tenths place versus the hundreds place.

Facilitation Tip: During the Manipulative Mats activity, circulate to ensure students trade tenths for hundredths correctly, asking guiding questions like 'How many tenths make one whole?'

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 30 min·Small Groups

Money Matching Game: Decimal Values

Prepare cards with decimals (e.g., 0.75), euro notes/coins, and expanded forms (7/10 + 5/100). In small groups, students match sets and explain why 0.75 equals 75 cents. Extend by creating their own cards for peers to solve.

Prepare & details

Construct a model to represent a decimal number like 0.45.

Facilitation Tip: In the Money Matching Game, model how to verbalize the value of each coin (e.g., 'This nickel is five hundredths of a dollar') to reinforce place value language.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 25 min·Small Groups

Number Line Relay: Place Value Positioning

Draw large decimal number lines from 0 to 2 on the floor. Call out numbers like 1.37; teams race to place cards on correct spots, naming the tenths and hundredths values. Discuss placements as a class to reinforce positioning.

Prepare & details

Justify why understanding decimal place value is crucial for working with money.

Facilitation Tip: For the Number Line Relay, emphasize precise placement of decimals by having students explain their reasoning to peers before marking the line.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 40 min·Pairs

Grid Art: Decimal Designs

Students draw 10x10 grids on paper to shade decimals like 0.36, using colors for tenths and hundredths. They partner to critique and rewrite partner designs in words or symbols. Display for whole-class gallery walk.

Prepare & details

Differentiate the value of a digit in the tenths place versus the hundreds place.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Teaching This Topic

Teach this topic by starting with concrete models before moving to symbolic notation, as research shows this deepens understanding. Avoid rushing to abstract representations, and instead use peer teaching where students explain their models to each other. Always connect decimals to real-world contexts like money or measurements to build relevance and retention.

What to Expect

Successful learning looks like students accurately modeling decimals with manipulatives, explaining the difference between tenths and hundredths, and justifying their reasoning with terms like '4 tenths' or '5 hundredths.' They should also compare decimals correctly and represent them visually on grids or with money.

Watch Out for These Misconceptions

Common Misconception

During the Manipulative Mats activity, watch for students who treat tenths and hundredths as equal parts or fail to trade ten tenths for one whole.

What to Teach Instead

Ask students to physically trade ten tenths manipulatives for one whole mat, then ask them to explain why this trade makes sense. Have them count aloud to verify that ten tenths equal one whole before moving to hundredths.

Common Misconception

During the Number Line Relay activity, watch for students who place decimals randomly or ignore the left-to-right increase in value.

What to Teach Instead

Have students first mark tenths (0.1, 0.2, etc.) on the line, then insert hundredths between them. Ask them to justify each placement by explaining which whole number it is closer to or between.

Common Misconception

During the Money Matching Game activity, watch for students who confuse the value of coins, such as thinking a dime is 0.01 or a penny is 0.10.

What to Teach Instead

Start the game with only dimes and pennies, asking students to verbalize 'one dime is ten hundredths' and 'one penny is one hundredth.' Then add nickels to reinforce the relationship between tenths and hundredths.

Assessment Ideas

Exit Ticket

After the Manipulative Mats activity, give students a card showing a decimal like 0.57. Ask them to write: 1. The value of the digit in the tenths place, 2. The value of the digit in the hundredths place, 3. Use tally marks to show how many hundredths are in the tenths place of this number.

Quick Check

During the Money Matching Game, display two decimal amounts such as $0.30 and $0.03 on the board. Ask students to hold up fingers to indicate which amount is greater, then call on a few to explain their choice using terms like 'tenths' and 'hundredths'.

Discussion Prompt

After the Number Line Relay activity, pose the question: 'If you have $0.75 and your friend has $0.57, who has more money and why?' Encourage students to use the number line they created to justify their answers and explain the difference in place value.

Extensions & Scaffolding

• Challenge early finishers to create a decimal greater than 0.99 but less than 1.00 using their grid or money manipulatives, then explain their model to a peer.
• For struggling students, provide pre-labeled hundredths grids with some sections already shaded to help them focus on interpreting rather than drawing.
• Provide extra time for students to explore decimals beyond hundredths, such as thousandths, using the same grid or money models to extend their understanding.

Key Vocabulary

Decimal Point	A symbol used to separate the whole number part of a number from its fractional part. It indicates the transition to tenths and hundredths.
Tenths Place	The first digit to the right of the decimal point. It represents a value that is one-tenth (1/10) of a whole.
Hundredths Place	The second digit to the right of the decimal point. It represents a value that is one-hundredth (1/100) of a whole.
Place Value	The value of a digit based on its position within a number. In decimals, position determines if a digit represents tenths, hundredths, or other fractional parts.