Tenths in Three Forms

Overview

Students connect one tenth as a part of one whole, a fraction, and a decimal. They use visual models, number lines and equivalent representations to explain that ( \frac{1}{10} = 0.1 ), building on prior learning about equal parts and place value.

Learning intentions

• WALT represent one tenth using a visual model, fraction and decimal.
• WALT connect tenths to the tenths place in a decimal number.
• WALT explain why different representations can show the same amount.
• WALT use a number line to locate and compare tenths.

Success criteria

• I can divide one whole into ten equal parts.
• I can write a tenth as ( \frac{1}{10} ) and 0.1.
• I can match a model, fraction and decimal that represent the same amount.
• I can explain what the 1 in 0.1 means.

Curriculum links

• Mathematics and Statistics — number knowledge and the relationship between fractions, decimals and place value.
• Mathematics and Statistics — representing, comparing and communicating mathematical ideas.
• Mathsteasers — using higher-order questions to deepen understanding and challenge advanced learners.
• Mathsteasers — connecting mathematical topics with relevant textbook learning.

Lesson structure (40 minutes)

1. 0–5 min · Hook and prior knowledge. Teacher displays an image of a chocolate bar or rectangle divided into ten equal pieces using the opening visual and hook question and asks, “If one piece is shaded, how could we describe it?” Students think independently, share with a partner, then offer fraction, decimal or everyday-language responses.

2. 5–12 min · Make the connection. Teacher uses the tenths teaching slides to model one whole divided into ten equal parts, recording ( \frac{1}{10} ), “one tenth” and 0.1 beside the same shaded part. Emphasise that the denominator 10 tells how many equal parts there are, while the tenths digit tells how many tenths are represented. Students copy the three connected forms and explain the meaning of each to a partner.

3. 12–20 min · Number-line exploration. Teacher displays a 0–1 number line divided into tenths through the number-line modelling slide and asks students to locate 0.1, 0.5 and 0.9. Students use the blank number-line mats in pairs to label 0, 0.1, 0.2 and so on to 1, then write the matching fractions below the points. Check that students understand ( \frac{10}{10}=1 ) and 1.0 represents one whole.

4. 20–30 min · Guided practice. Teacher distributes the tenths connections worksheet and completes the first example with the class: a shaded model, ( \frac{3}{10} ), and 0.3. Students independently complete matching, shading, number-line and explanation questions, while the teacher works with a small group needing support. Pause halfway to discuss a common error, such as reading 0.4 as four wholes or writing ( \frac{1}{4} ) for one tenth.

5. 30–36 min · Reasoning challenge. Teacher presents the discussion prompts from the partner reasoning and challenge slides: “Which is greater, 0.6 or ( \frac{5}{10} )? How do you know?” and “Can you find two different ways to show 0.8?” Students solve with a partner, use a model or number line as evidence, and share explanations. Invite advanced learners to explain why ( \frac{10}{10}=1 ) and why 0.10 is equivalent to 0.1.

6. 36–40 min · Plenary and exit check. Teacher returns to the hook question using the plenary and exit-ticket slide and asks students to show one tenth in three forms. Students complete an exit response: “Draw or describe one tenth. Write its fraction and decimal. Explain what the 1 in 0.1 represents.” Collect responses to identify next steps.

Resources

• the tenths introduction, teaching, activity and plenary deck
• the tenths connections worksheet
• the blank number-line mats
• Whiteboard and markers
• Pencils, coloured pencils and rulers
• Optional tenths grids or paper strips
• One copy of the worksheet per student

Assessment

• Listen for accurate use of “one tenth”, “ten equal parts”, numerator, denominator and tenths place during partner talk.
• Check number-line labels and worksheet representations, especially whether students connect ( \frac{n}{10} ) with 0.n.
• Use the exit response to group students for the next lesson: secure connections, needs more modelling, or ready for hundredths and equivalent decimals.

Differentiation

• Support learners with a pre-divided tenths model, a labelled place-value chart and sentence starters: “The whole is divided into…”, “The fraction is…”, and “The decimal is…”.
• Provide dyslexia-friendly access through a clear sans-serif font, uncluttered worksheet spacing, short instructions, strong contrast and the option to have questions read aloud. Allow students to respond orally or by drawing.
• Pair students strategically and use concrete paper strips or tenths grids before expecting abstract notation. Reduce the number of worksheet questions while retaining one example of each representation.
• Extend advanced learners with the reasoning prompt “How many different tenths can you combine to make one whole?” and ask them to prove why 0.5, ( \frac{5}{10} ), ( \frac{1}{2} ) and 50% represent the same amount, where appropriate.

Extension

• Students create a “mystery tenth” clue card using a model, fraction and decimal, then swap with a partner to solve.
• Students investigate whether 0.3 is closer to 0, 0.5 or 1, justifying their answer on a number line.