Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Decimals: Place Value and Ordering

Active learning builds lasting understanding of decimals by letting students manipulate concrete objects and move their bodies in space. Moving from whole euros to cents or stepping along a number line makes invisible place values visible and memorable. Physical actions reduce confusion between tenths and hundredths by connecting symbols to real quantities.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.5

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 25 min · Pairs

Money Build: Decimal Place Value

Give play euros and cents. Students build amounts like €1.34 by selecting coins, then trade with partners to match written decimals. Record the number and explain each place's value.

Analyze how the position of a digit affects its value in a decimal number.

Facilitation Tip

During Money Build, circulate with play coins and ask students to verbalize each digit’s value (e.g., ‘The 2 stands for 20 cents, which is 2 tenths of a euro.’).

What to look for

Present students with a number line marked from 0 to 1. Ask them to place a marker for 0.7 and 0.2. Then, ask them to write the decimal that comes halfway between 0.1 and 0.3.

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

Activity 02

• Stations Rotation
• 30 min · Small Groups

Number Line Sort: Ordering Decimals

Create a floor number line with tape from 0 to 2. Provide decimal cards (0.23, 0.8, 1.05). Small groups place and order them, discussing comparisons step-by-step.

Compare the process of ordering decimals to ordering whole numbers.

Facilitation Tip

For Number Line Sort, provide sentence stems like ‘I placed 0.3 after 0.2 because…’ to scaffold explanations during the activity.

What to look for

Give each student a card with a fraction (e.g., 7/10 or 23/100). Ask them to write the equivalent decimal and draw a picture representing it using a 10 or 100 grid.

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

Activity 03

• Stations Rotation
• 20 min · Whole Class

Fraction-Decimal Match: Bingo Game

Prepare boards with decimals, fractions, and pictures. Call fractions like 7/10; students mark 0.7. Review matches as a class after each round.

Explain the relationship between fractions with denominators of 10, 100, or 1000 and their decimal equivalents.

Facilitation Tip

In Fraction-Decimal Match Bingo, pause after each call to ask the whole group to repeat the fraction and decimal aloud together for reinforcement.

What to look for

Pose the question: 'If you have €0.80 and your friend has €0.75, who has more money? Explain how you know by looking at the digits after the decimal point.'

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

Activity 04

• Stations Rotation
• 40 min · Small Groups

Place Value Station Rotation

Set up stations: coin building, grid drawing, ordering cards, fraction matching. Groups rotate every 8 minutes, noting one key learning per station.

Analyze how the position of a digit affects its value in a decimal number.

Facilitation Tip

At Place Value Station Rotation, set a two-minute timer at each station to keep the pace lively and prevent over-focusing on one task.

What to look for

Present students with a number line marked from 0 to 1. Ask them to place a marker for 0.7 and 0.2. Then, ask them to write the decimal that comes halfway between 0.1 and 0.3.

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

A few notes on teaching this unit

Teach decimals by starting with money and grids before introducing symbols, as research shows concrete-representational-abstract sequences build stronger understanding. Avoid rushing to abstract symbols; instead, give students time to explain their thinking aloud. Use peer talk to correct misunderstandings, because explaining to others reveals gaps in reasoning more clearly than teacher corrections alone.

Students will confidently read, write, and order decimals up to hundredths using place value language. They will explain why 0.45 is less than 0.5 by comparing digits in the tenths and hundredths places. Learners will also convert simple fractions to decimals and justify their conversions with drawings or models.

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Watch Out for These Misconceptions

• During Number Line Sort, watch for students who place 0.9 far to the left of 1 or 2.3 before 2, indicating they view decimals as separate from whole numbers.

  Have them re-trace their steps on the number line while saying each number aloud, then ask them to compare 0.9 and 1 by holding up one finger for 0.9 and two fingers for 1 to visualize the gap.

• During Place Value Station Rotation, watch for students who ignore the decimal point and compare 0.52 and 0.6 as 52 and 6, leading to incorrect ordering.

  Provide grid paper for vertical alignment and colored pencils to box the tenths and hundredths digits separately before comparing.

• During Money Build, watch for students who think the tenths place is smaller than the units place because the digit appears after the decimal point.

  Ask students to exchange 10 tenths (€0.10 coins) for 1 whole euro coin so they see that 10 tenths make one whole, clarifying the relative sizes.

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Methods used in this brief

• Stations Rotation