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

Decimal Discovery: Hundredths

Extending decimal understanding to hundredths, connecting them to fractions and real-world contexts like money.

• ACARA Content Descriptions
• AC9M4N01
• AC9M4N02

About This Topic

Hundredths build on students' tenths knowledge by partitioning wholes into 100 equal parts, represented as 0.01. Students connect this to the fraction 1/100 and see it in money, where one cent equals one hundredth of a dollar. Contexts like measuring fabric to the nearest centimetre or dividing pizzas equally show why hundredths offer greater precision than tenths.

This topic supports AC9M4N01, recognising place value patterns in decimals, and AC9M4N02, representing, ordering and comparing them to hundredths. Students compare a tenth to ten hundredths using models, create scenarios like timing races where hundredths matter more than tenths, and informally link 100 hundredths to 100%. These skills strengthen number sense for future topics like operations with decimals.

Active learning benefits this topic because students physically manipulate tools like decimal mats or coins to build and rename numbers, clarifying relationships that diagrams alone miss. Group tasks, such as constructing real-world problems together, encourage explanation and debate, solidifying understanding through talk and trial.

Key Questions

1. Compare the value of a tenth and a hundredth using models.
2. Construct a scenario where hundredths are more precise than tenths.
3. Explain how hundredths relate to percentages (informally).

Learning Objectives

• Compare the value of a tenth and a hundredth using base-ten blocks and decimal grids.
• Construct a word problem where the precision of hundredths is necessary for an accurate solution.
• Represent decimal numbers to the hundredths place using various models.
• Order a set of decimal numbers including tenths and hundredths.
• Explain the relationship between hundredths and percentages using concrete examples.

Before You Start

Understanding Tenths

Why: Students must have a solid grasp of tenths and their representation as decimals and fractions before extending to hundredths.

Introduction to Fractions

Why: Understanding the concept of a fraction as a part of a whole is fundamental to grasping the meaning of hundredths as 1/100.

Key Vocabulary

Hundredth	One part of one whole when the whole is divided into 100 equal parts. It is represented as 0.01 or 1/100.
Decimal Grid	A visual tool, often a 10x10 grid, used to represent decimal values, with each small square representing a hundredth.
Place Value	The value of a digit based on its position within a number. For hundredths, the position is two places to the right of the decimal point.
Fraction	A number that represents a part of a whole. In this topic, fractions like 1/100 and 1/10 are directly related to decimal hundredths and tenths.

Watch Out for These Misconceptions

Common Misconception

A hundredth is larger than a tenth.

What to Teach Instead

Students often reverse place value hierarchy. Use concrete models like filling decimal strips where 0.1 covers ten squares but 0.01 covers one, allowing hands-on comparison. Peer teaching in pairs helps them articulate and correct the error through visual evidence.

Common Misconception

Hundredths have no connection to fractions.

What to Teach Instead

Many see decimals as separate from fractions. Activities shading hundredths grids alongside fraction circles reveal 37/100 = 0.37 directly. Group discussions of shared models build the link, reducing abstraction.

Common Misconception

Decimals always align perfectly when adding place values.

What to Teach Instead

Students add digits without considering place, like 0.2 + 0.03 = 0.23 instead of 0.05. Manipulatives like base-10 rods renamed to hundredths flats show regrouping needs. Collaborative building tasks expose and fix this through shared correction.

Active Learning Ideas

Modelling Station: Hundredth Grids

Provide decimal grids divided into 100 squares. Students shade sections for numbers like 0.47, then compare to 0.4 by overlaying grids and counting differences. Partners explain why 0.47 needs hundredths. Record findings on mini whiteboards.

35 min·Pairs

Money Hunt: Cent Scenarios

Distribute play money and scenario cards, such as 'Buy items totalling $1.23'. Students select exact coins, noting how cents represent hundredths. Groups create their own shopping problems and solve peers'. Discuss precision over tenths.

40 min·Small Groups

Ordering Relay: Decimal Line-Up

Write decimals to hundredths on cards. Teams line up in order on a floor number line, justifying placements with models. Switch roles for verification. Whole class reviews errors as a group.

30 min·Small Groups

Fraction Link-Up: Matching Pairs

Create cards with fractions (e.g., 23/100), decimals (0.23) and money amounts ($0.23). Students match in pairs, then build models to prove equivalence. Share one match with the class.

25 min·Pairs

Real-World Connections

• Retail pricing often uses hundredths of a dollar, like $1.99, where the '99' represents 99 cents, or 99 hundredths of a dollar. This precision is crucial for business transactions.
• Sports timing, particularly in events like swimming or athletics, frequently measures performance to the hundredth of a second. A difference of 0.01 seconds can determine a winner.
• Measuring ingredients in baking recipes may require precision to the hundredth of a unit, for example, 0.25 cups of flour, to ensure the correct chemical reactions occur for the desired texture.

Assessment Ideas

Quick Check

Present students with a decimal grid shaded to represent a number. Ask them to write the decimal and the equivalent fraction. Then, ask: 'If this grid represented 1 dollar, how many cents would be shaded?'

Discussion Prompt

Pose the question: 'Imagine you are timing a race. One runner finishes in 10.5 seconds, and another finishes in 10.52 seconds. Who won and by how much? Explain why using the terms tenths and hundredths.'

Exit Ticket

Give each student two cards. On one card, they write a number with tenths (e.g., 0.7). On the other, they write a number with hundredths that is equivalent to the tenths number (e.g., 0.70). They then draw a simple picture showing the relationship.

Frequently Asked Questions

How do I introduce hundredths using money in Year 4?

Start with familiar dollars and cents: show $1.00 as 100 hundredths using play money. Have students exchange 10 dimes (tenths) for 100 pennies (hundredths) to visualise equivalence. Extend to problems like splitting $2.50 equally, reinforcing precision. This grounds abstract decimals in everyday transactions students recognise.

What activities link hundredths to fractions?

Use hundred-square grids where students shade 1/100 and label 0.01, scaling to 45/100 = 0.45. Pair with fraction walls adjusted to hundredths. Groups justify matches verbally, connecting notation systems. This builds flexible thinking for AC9M4N02 while addressing common disconnects.

How can active learning help teach decimal hundredths?

Active methods like manipulating decimal grids, coins or number lines let students physically partition wholes, making place value relationships concrete. Small group challenges, such as racing to order decimals accurately, promote talk and error-checking. These approaches outperform worksheets by engaging multiple senses and building confidence through immediate feedback and collaboration.

How to compare tenths and hundredths effectively?

Model with strips: colour 0.1 as 10 units, then subdivide into 100 for 0.01. Students overlay and count, creating sentences like 'One tenth equals ten hundredths'. Real scenarios, like track times (3.2s vs 3.24s), show precision needs. Rotate stations for varied practice, ensuring all grasp the hierarchy.