Hundredths And Place Value

Overview

Lesson 8 of 15 in Number Connections: Fractions, Decimals, Percentages. Students use 10-by-10 grids and place-value representations to understand that one hundredth is one of 100 equal parts, then connect hundredths, fractions and decimals.

Learning intentions

• WALT represent and interpret hundredths.
• WALT connect hundredths to fractions and decimals.
• WALT use place value to explain the value of each digit.
• WALT partition one whole into 100 equal parts.

Success criteria

• I can identify the value of each digit in a decimal to hundredths.
• I can represent hundredths on a 10-by-10 grid.
• I can convert familiar hundredths to decimals, such as 25/100 = 0.25.
• I can explain why 0.5 and 0.50 are equivalent.

Curriculum links

• Number knowledge: recognise, represent and compare fractions and decimals, including hundredths.
• Place value: explain the value of digits in numbers with up to two decimal places.
• Number strategies: use models, partitioning and equivalent representations to solve and explain problems.
• Mathematical communication: use diagrams, symbols, words and precise mathematical language to justify thinking.

Lesson structure (45 minutes)

1. 0–5 minutes – Engage and connect

Display the question from the opening hook slide: “Is 0.5 the same as 0.50? How could you prove it?” Students make a quick individual prediction, then share with a partner. Introduce the WALT and explain that today’s focus is the hundredths place.

2. 5–13 minutes – Build the model

Use the place-value teaching slides and draw a large 10-by-10 grid. Establish that the whole grid represents 1, each small square represents 1/100, and 1/100 is written as 0.01. Shade examples such as 1/100, 10/100 and 25/100, recording each as a fraction and decimal.

Explicitly model the place-value chart: ones, tenths, hundredths. Use examples such as 3.47: 3 ones, 4 tenths and 7 hundredths. Ask: “What is the value of the 7? What would change if it moved to the tenths place?”

3. 13–21 minutes – Guided MNP examples

Work through the concrete–visual–symbolic sequence using mini-whiteboards. Students first describe a shaded grid, then write the fraction out of 100, and finally write the decimal. Include 40/100 = 0.40 = 0.4 and 7/100 = 0.07.

Pause after each example for students to show answers. Address the common misconception that 0.7 and 0.07 have the same value by comparing seven tenths with seven hundredths on grids.

4. 21–30 minutes – Partner matching activity

In pairs, students match representations using the fraction-decimal-percentage matching cards. Direct students to focus on the fraction and decimal columns first, using grids or drawings to justify matches. Circulate and ask: “How do you know these two representations are equivalent?” and “Where is the hundredths place?”

Students who finish early create a new matching example for another pair, ensuring the decimal has two places.

5. 30–40 minutes – Independent workbook practice

Distribute the hundredths and place-value practice worksheet. Students complete tasks involving shading 10-by-10 grids, identifying digit values, converting familiar fractions with denominator 100 to decimals, and ordering decimals to hundredths.

Model the first question together, then release students to work independently. Confer with selected learners, asking them to explain their representation rather than simply state an answer.

6. 40–45 minutes – Reflect and assess

Use the review and exit-question slides for a whole-class check. Students respond on whiteboards:

• Write 63/100 as a decimal.
• What is the value of the 6 in 0.63?
• Explain why 0.5 = 0.50.

Invite two or three students to share different explanations. Revisit the success criteria and ask students to identify one representation that helped them learn.

Resources

• the complete lesson slide deck
• the hundredths and place-value practice worksheet
• the fraction-decimal-percentage matching cards
• Large 10-by-10 grid drawn on the board or displayed
• Enlarged 10-by-10 grids for support
• Place-value charts
• Coloured pencils or highlighters
• Mini-whiteboards and pens
• Student mathematics books or workbooks

Assessment

• Listen to partner explanations and inspect whiteboard responses for accurate links between shaded grids, fractions and decimals.
• Check worksheet responses for correct digit values, leading zeroes in hundredths such as 0.07, and equivalence such as 0.40 = 0.4.
• Use the final three questions to identify students needing further teaching with tenths, hundredths or equivalent decimals.

Differentiation

• Support lower learners with enlarged grids, colour coding for tenths and hundredths, a labelled place-value chart, and paired teacher conferencing. Provide sentence frames: “The whole is divided into __ equal parts” and “__/100 is written as __.”
• Allow students to build or shade each answer before recording symbols. Pair students strategically and revisit 0.7 versus 0.07 with concrete grid comparisons.
• Extend advanced learners by asking them to explain 0.5 = 0.50 and generate decimals between given values, such as between 0.42 and 0.45. Ask them to justify which values are possible using place value.
• Support EAL and students with additional learning needs through clear worked examples, repeated oral language, visual vocabulary, deliberate partner talk and reduced worksheet quantity without reducing the key learning.