Introduction to Decimals: Tenths and Hundredths

Active learning works for decimals because visual models and manipulatives transform abstract symbols into concrete understanding. When students shade grids or sort money, they see how 0.3 is three parts of ten and 0.25 is twenty-five parts of one hundred, building mental images that persist beyond the lesson.

• Year 5
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Compare decimal representations to their equivalent fraction forms, identifying commonalities and differences in notation.
2. Analyze the structure of decimal notation to explain the value of digits in the tenths and hundredths places.
3. Calculate decimal values by partitioning a whole unit into tenths and hundredths using visual aids.
4. Represent given fractions (e.g., 3/10, 7/100) as decimal numbers and vice versa.
5. Explain the relationship between a tenth and a hundredth, demonstrating how 1/10 is equivalent to 10/100.

Stations Rotation

⏱ 30 min·Small Groups

Hands-On: Decimal Grid Shading

Give each small group decimal grids divided into 10 or 100 squares. Students shade fractions like 4/10 or 23/100, record the decimal, and swap grids to read partners' work. Discuss equivalents as a group.

Prepare & details

Explain the relationship between a tenth of a unit and a hundredth of a unit.

Facilitation Tip: During Decimal Grid Shading, circulate and ask students to say the decimal aloud as they shade, reinforcing place value vocabulary like 'three tenths' or 'forty-five hundredths'.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 25 min·Pairs

Money Sort: Fraction-Decimal-Cents Match

Prepare cards showing fractions (e.g., 3/10), decimals (0.3), and money (30 cents). Pairs sort into matching sets three times, using play money to verify, then create their own sets to trade.

Prepare & details

Compare the representation of a fraction and its decimal equivalent.

Facilitation Tip: While running Money Sort, listen for students to name coins as fractions (e.g., 'a quarter is one-fourth') before matching to decimals, bridging prior knowledge to new concepts.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 35 min·Small Groups

Number Line Parade: Ordering Decimals

Draw floor number lines from 0 to 2 with tape. Distribute decimal cards (e.g., 0.12, 0.9, 1.05) to small groups. Students position themselves, justify spots to the class, and adjust based on feedback.

Prepare & details

Analyze how decimal notation extends the place value system to represent parts of a whole.

Facilitation Tip: In Number Line Parade, observe students’ placements and ask, 'Why did you put 0.15 here?' to prompt justification of place value reasoning.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 20 min·Individual

Place Value Build: Expanded Form Towers

Provide base-ten blocks adapted for decimals (strips for tenths, squares for hundredths). Individuals build models for numbers like 0.47, write expanded form (4/10 + 7/100), then pair to compare sizes.

Prepare & details

Explain the relationship between a tenth of a unit and a hundredth of a unit.

Facilitation Tip: During Place Value Build, challenge groups to build both 0.8 and 0.80 with place value blocks so they see the equivalence visually and physically.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

Research shows that integrating visual, auditory, and kinesthetic elements solidifies decimal understanding. Avoid rushing to abstract notation; let students grapple with models first. Use collaborative talk to normalize error and encourage peer correction. Emphasize reading decimals correctly ('zero point two five') to prevent place value confusion.

What to Expect

Students will confidently read, write, and compare decimals to hundredths using place value language. They will explain why 0.45 equals 0.450 and justify why 0.07 is less than 0.2, using models and number lines to support their reasoning.

Watch Out for These Misconceptions

Common Misconception

During Number Line Parade, watch for students who order 0.19 before 0.2 because they compare 19 and 2 as whole numbers.

What to Teach Instead

Pause the group and have them align 0.19 and 0.2 vertically on a chart, then model regrouping 0.19 as 0.2 - 0.01 to show it is less than 0.2. Ask them to adjust the placement on the line based on this reasoning.

Common Misconception

During Place Value Build, watch for students who insist 0.5 must be written as 0.50 to have two digits after the decimal.

What to Teach Instead

Provide decimal strips and have students fold a tenth strip into ten equal parts to see 0.5 = 0.50. Then challenge pairs to prove equivalence by trading place value blocks: five tenths for fifty hundredths.

Common Misconception

During Decimal Grid Shading, watch for students who read 0.03 as 'three tenths' because they overlook the leading zero.

What to Teach Instead

Have students shade exactly three hundredths squares and count aloud, 'one hundredth, two hundredths, three hundredths,' matching the count to the decimal notation. Practice reading decimals aloud in pairs to reinforce correct pronunciation.

Assessment Ideas

Exit Ticket

After Decimal Grid Shading, provide students with a hundred-grid. Ask them to shade 3 tenths and then shade another 4 hundredths. On the back, they should write the total amount shaded as a decimal and as a fraction.

Quick Check

During Number Line Parade, present students with a number line marked from 0 to 1 with only tenths indicated. Ask them to place a marker for 0.05 and explain why they chose that position relative to 0.1 and 0.2.

Discussion Prompt

After Place Value Build, pose the question: 'How is 0.7 the same as 0.70?' Guide students to discuss equivalent decimals using their expanded form towers and relate this to fractions like 7/10 and 70/100.

Extensions & Scaffolding

• Challenge students who finish early to create a decimal greater than 0.6 but less than 0.7 using hundredths grids, then present their decimal to the class with an explanation.
• For students who struggle, provide fraction cards (1/10, 2/10, etc.) to match with decimal cards before moving to hundredths, reinforcing the connection between fractions and decimals.
• Deeper exploration: Ask students to research how decimals appear in real-world contexts like sports statistics or measurements, then create a poster showing how decimals represent precision in their chosen context.

Key Vocabulary

Tenth	One part of ten equal parts of a whole. It is written as 1/10 or 0.1 in decimal form.
Hundredth	One part of one hundred equal parts of a whole. It is written as 1/100 or 0.01 in decimal form.
Decimal Point	A symbol used to separate the whole number part from the fractional part of a number written in decimal notation.
Place Value	The value of a digit based on its position within a number, extending to tenths and hundredths in decimal numbers.