Mathematics · 5th Class

Active learning ideas

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.

• NCCA Curriculum Specifications
• NCCA: Primary - Decimals

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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?'

What to look for

Provide students with a card showing a decimal like 0.38. 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. Draw a simple grid to represent 0.38.

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

Activity 02

• 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.

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.

What to look for

Display two decimal numbers on the board, such as €0.50 and €0.05. Ask students to hold up fingers to indicate which number represents a greater value. Follow up by asking a few students to explain their reasoning using the terms 'tenths' and 'hundredths'.

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

Activity 03

• 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.

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.

What to look for

Pose the question: 'Imagine you have €1.50 and your friend has €1.05. Who has more money and why?' Encourage students to use the terms 'tenths' and 'hundredths' in their explanations to justify their answers.

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

Activity 04

• 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.

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

What to look for

Provide students with a card showing a decimal like 0.38. 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. Draw a simple grid to represent 0.38.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• 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.

  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.

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

  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.

• 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.

  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.

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Methods used in this brief

• Concept Mapping