Mathematics · Year 4 · The Power of Place Value · Term 1

Decimal Discovery: Tenths

Introducing tenths as part of a whole, linking them to common fractions and visual models.

• ACARA Content Descriptions
• AC9M4N01
• AC9M4N02

About This Topic

Decimal Discovery introduces students to the world of parts-of-a-whole through tenths and hundredths. In the Australian Curriculum, this is a pivotal moment where students link their existing knowledge of common fractions to the decimal system. They learn that the decimal point is a separator between whole units and fractional parts, and they begin to see how our currency and metric measurement systems rely on this logic.

Understanding decimals requires a shift in thinking, as students must realize that a longer decimal number isn't necessarily 'bigger' than a shorter one. This topic is deeply connected to place value and provides the mathematical language needed for science and geography. Students grasp this concept faster through structured discussion and peer explanation where they compare different representations of the same value.

Key Questions

1. Evaluate when it is more useful to use a decimal instead of a whole number.
2. Design a visual representation to differentiate between a tenth and a whole.
3. Justify the use of a decimal point to separate whole units from parts.

Learning Objectives

• Compare the value of a given number of tenths to the value of a whole unit using visual models.
• Explain the relationship between a fraction with a denominator of 10 and its decimal representation.
• Calculate the total value when combining whole units and tenths, expressed as a decimal.
• Design a visual representation to differentiate between a tenth and a whole.
• Justify the use of a decimal point to separate whole units from fractional parts.

Before You Start

Fractions as Parts of a Whole

Why: Students need to understand the concept of dividing a whole into equal parts and representing those parts as fractions before connecting them to decimals.

Introduction to Place Value

Why: Understanding the value of digits in whole numbers is essential for grasping the concept of place value for tenths.

Key Vocabulary

Tenth	One part of a whole that has been divided into 10 equal parts. It is represented as 1/10 or 0.1.
Decimal point	A symbol used to separate the whole number part from the fractional part of a number. In tenths, it separates whole units from tenths.
Place value	The value of a digit based on its position in a number. For tenths, the position immediately to the right of the decimal point represents tenths.
Fraction	A number that represents a part of a whole. Tenths can be written as both fractions (e.g., 3/10) and decimals (e.g., 0.3).

Watch Out for These Misconceptions

Common Misconception

Thinking that 0.10 is larger than 0.8 because 10 is larger than 8.

What to Teach Instead

This 'whole number thinking' is common. Use 10x10 grids to shade in the values, showing that 0.8 covers 80 squares while 0.10 only covers 10. Peer comparison of these visual models helps students see the value of the tenths place.

Common Misconception

Believing the decimal point moves when multiplying or dividing by ten.

What to Teach Instead

Teach that the digits move across the fixed decimal point. Using a physical 'sliding' place value chart where the decimal point is taped to the desk helps students see that the value of the digits changes, not the position of the point.

Active Learning Ideas

Gallery Walk: Decimal Representations

Students create posters showing a decimal (e.g., 0.75) as a fraction, a shaded grid, a location on a number line, and a collection of coins. The class moves around the room with sticky notes to leave 'I notice' or 'I wonder' comments on each representation.

40 min·Small Groups

Simulation Game: The Decimal Shop

Set up a classroom shop with items priced in dollars and cents. Students use play money to pay for items, focusing on how 10 cents represents one tenth of a dollar and 1 cent represents one hundredth, recording their transactions in decimal form.

50 min·Pairs

Inquiry Circle: Human Number Line

Give each student a card with a decimal or a fraction (e.g., 0.5, 1/10, 0.25). Without speaking, students must organize themselves into a physical number line from zero to one, justifying their position to their neighbors once the line is formed.

25 min·Whole Class

Real-World Connections

• Australian currency uses dollars and cents, where a cent is one hundredth of a dollar. Understanding tenths is a foundational step towards understanding currency systems.
• Measuring lengths in metres and centimetres, or volumes in litres and millilitres, often involves decimal notation. For example, 1.5 metres means one whole metre and five tenths of a metre.

Assessment Ideas

Quick Check

Present students with a set of number lines marked with tenths. Ask them to circle the number 0.7 and write the fraction it represents. Then, ask them to shade a visual model (like a rectangle divided into 10 parts) to represent 0.7.

Discussion Prompt

Pose the question: 'When might it be more useful to write 1.5 metres instead of 1 metre and 50 centimetres?' Facilitate a discussion where students compare the efficiency and clarity of using decimals for measurements.

Exit Ticket

Give each student a card with a picture of a whole divided into 10 equal parts, with some parts shaded. Ask them to write the decimal and fraction that represents the shaded part, and to explain in one sentence why the decimal point is important.

Frequently Asked Questions

How can active learning help students understand decimals?

Decimals can feel abstract on paper. Active learning strategies like simulations and human number lines force students to physically relate decimals to whole numbers. By 'becoming' a number on a line or using decimals in a mock shop, students see the practical utility of tenths and hundredths. This social learning environment encourages them to verbalize their reasoning, which is crucial for moving past whole-number misconceptions.

What is the best way to introduce hundredths?

Start with a one-dollar coin. Show that it takes 100 cents to make a dollar, so one cent is 1/100 or 0.01. Using money is a culturally relevant and practical way for Australian students to understand the hundredths place.

Why do we teach fractions and decimals together?

They are two different ways of naming the same parts of a whole. Linking them early helps students develop a flexible number sense, allowing them to choose the most efficient representation for a problem later in secondary school.

How do I help a student who says 0.3 is 'zero point three' but doesn't know what it means?

Ask them to model it using a 'tenth' of a physical object, like a decimetre strip of a meter ruler. Shifting the language from 'zero point three' to 'three tenths' helps reinforce the place value connection.