Tenths and Hundredths

Overview

A 30-minute, hands-on lesson for Year 5/6 students to connect fractions, decimals, hundred grids and place value. Students work in pairs to represent, match and compare tenths and hundredths using mathematical language and reasoning.

Learning intentions

• WALT read and write tenths and hundredths as fractions and decimals.
• WALT represent decimals using hundred grids, place-value charts and number lines.
• WALT explain how the base-10 place-value system works.
• WALT compare tenths and hundredths using <, > and =.

Success criteria

• I can read and write tenths and hundredths as fractions and decimals.
• I can represent a decimal on a grid, place-value chart or number line.
• I can explain that one whole contains 100 hundredths.
• I can compare decimals and justify my answer using place value or a number line.

Curriculum links

• Number: understand and use the base-10 place-value system.
• Number: read, write, represent and compare fractions and decimals.
• Number: recognise equivalent representations, such as tenths and hundredths.
• Mathematical practices: use materials, diagrams, mathematical language and explanations to reason and communicate.

Lesson structure (30 minutes)

1. 0–5 minutes – Daily review and connection Open with the review and lesson introduction slides. Ask students to answer orally, with mini-whiteboards or fingers:

• What is the value of the 6 in 3,642?
• What happens to a digit’s value when it moves one place to the right?
• How many hundredths are in one whole?
• Which is greater: 0.4 or 0.3? Explain. Briefly connect the last question to today’s focus: digits have value because of their position.

2. 5–10 minutes – Model tenths and hundredths Use a large hundred grid and place-value chart, shown on the tenths and hundredths modelling slides. Shade one whole strip of 10 squares and explain that it represents one tenth: 1/10 = 0.1. Then shade 27 squares and model 27/100 = 0.27. Emphasise that dividing one whole into 100 equal parts creates hundredths, and each hundredth is 0.01.

3. 10–15 minutes – Build and represent In pairs, students use a hundred grid, digit cards and a place-value chart to build examples including 3/10 = 0.3, 27/100 = 0.27 and 0.6 = 60/100. Provide the guided decimal representation sheet for students to record each representation. Pause to ask: “What does the 2 mean in 0.27?” and “Why can 0.6 also be written as 0.60?”

4. 15–22 minutes – Match representations Give each pair a small set from the fraction-decimal-percentage matching cards. Students use only the fraction and decimal cards, matching equivalent representations and checking them against their grid or chart. Circulate and ask students to explain their matches rather than relying on visual guessing.

5. 22–25 minutes – Compare and justify Display comparison prompts from the partner comparison and discussion slides: 0.4 __ 0.3, 0.27 __ 0.7, 0.50 __ 0.5. Pairs place <, > or = and justify their decisions using place value, shaded grids or a number line. Select two contrasting explanations to share.

6. 25–30 minutes – Plenary and quick check Return to the plenary and exit-check slide. Students complete the final questions on the independent check section:

• Write 4/10 as a decimal.
• Write 0.36 as a fraction in hundredths.
• Circle the greater number: 0.48 or 0.5.
• Explain why. Invite students to share one sentence beginning, “I know this because…”

Resources

• the complete lesson slide deck
• the guided decimal representation sheet
• the fraction-decimal-percentage matching cards
• Hundred grids, one per pair
• Place-value charts showing ones, tenths and hundredths
• Decimal/fraction digit cards
• Mini-whiteboards or scrap paper
• Pencils, coloured pencils and erasers
• Optional concrete hundredths strips

Assessment

• Listen for accurate use of “tenths”, “hundredths”, “decimal point” and “place value” during partner work.
• Check whether students correctly match shaded grids, fractions and decimals, particularly 0.6 and 60/100.
• Use the independent check to identify students who can compare decimals and explain their reasoning, not just select an answer.

Differentiation

• Support learners with pre-labelled place-value charts, shaded grids, concrete hundredths strips, vocabulary cards and the guided examples on the scaffolded examples section.
• Begin with tenths before connecting to hundredths. Pair students strategically and allow students to explain orally, point to a model or use a number line.
• For EAL learners and students requiring additional support, provide sentence frames: “___ is greater because ___ hundredths is more than ___ hundredths.”
• Challenge confident learners to convert tenths into equivalent hundredths and explain why 0.4 = 0.40. They may also investigate thousandths by comparing 0.407 and 0.47, explaining the zero placeholder.