Halves and Tenths

Overview

In this fifth lesson of the Fractions as Measures unit, students connect the familiar fraction one-half with tenths and decimal notation. Through folding, measuring, matching and explaining, they move from concrete models to pictorial and symbolic representations.

Learning intentions

• WALT recognise that one-half is equivalent to five-tenths and 0.5.
• WALT represent one-half using fraction strips, tenths grids and a number line.
• WALT explain why different representations can have the same value.
• WALT use mathematical language to compare and match equivalent representations.

Multilingual Instructions

中文（简体）

学习目标（WALT）： 我们正在学习识别和表示二分之一和十分之一。

学习指引：

• 和一位同伴一起学习。
• 将模型折叠或分成相等的部分。
• 标出各部分。
• 分享并解释你的想法。
• 检查各部分是否相等。

العربية

هدف التعلم (WALT): نحن نتعلّم تحديد وتمثيل الأنصاف والأعشار.

إرشادات العمل:

• اعمل مع زميل.
• اطوِ النموذج أو قسّمه إلى أجزاء متساوية.
• سمِّ الأجزاء.
• شارك أفكارك واشرحها.
• تحقّق من أن الأجزاء متساوية.

Success criteria

• I can recall that ( \frac{1}{2} = \frac{5}{10} = 0.5 ).
• I can explain why five out of ten equal parts is the same amount as one-half.
• I can match fraction, decimal, diagram and number-line representations.
• I can describe the pattern when one-half is renamed using tenths.

Curriculum links

• Mathematics and Statistics — Number: understanding fractions as measures and recognising equivalent representations.
• Mathematics and Statistics — Number: connecting fractions and decimals in familiar contexts.
• Mathematical practices: representing, reasoning, communicating and making connections.
• Mathsteasers: using higher-order thinking questions to deepen understanding and challenge advanced learners.

Lesson structure (45 minutes)

1. 0–5 min · Retrieval hook. Display the opening question in the introduction and retrieval slides: “Which is more: one-half or five-tenths?” Students silently record an answer, then discuss it with a partner using a quick sketch or explanation. Invite several responses without confirming the answer yet.

2. 5–13 min · Explicit teaching and modelling. Use the modelling slides to show a strip representing one whole. Fold it into two equal parts, shade one part, then overlay or mark a strip divided into ten equal parts. Model that the same length is covered by five tenths: ( \frac{1}{2} = \frac{5}{10} ). Show the same value on a tenths grid and number line, and write (0.5). Students echo-read the statement and explain it to a partner.

3. 13–23 min · Hands-on representation. In mixed-ability pairs, students use paper strips and tenths grids to make one-half, then label it ( \frac{1}{2} ), ( \frac{5}{10} ) and (0.5). Provide the fraction wall and strip cards for pairs that need a ready-made visual comparison. Circulate and ask: “How do you know the parts are equal?” and “What does the 5 tell us? What does the 10 tell us?” Students photograph a clear model if appropriate.

4. 23–32 min · Matching and retrieval game. Distribute the halves and tenths practice sheet. Students complete the matching section, linking diagrams, fraction notation, decimal notation and number-line points. In pairs, they take turns hiding one representation and asking their partner to retrieve it from memory. Students use the cue: “Same amount, different name.” Pause halfway for partners to check one another’s explanations.

5. 32–39 min · Reasoning and feedback. Display the discussion prompts in the partner reasoning and feedback slides. Students respond to: “Is ( \frac{4}{10} ) equal to one-half? How can you prove it?” and “Why is (0.5) not five wholes?” Partners compare answers, identify one strength and suggest one improvement. Select two pairs to share different representations and reasoning.

6. 39–45 min · Assessment and reflection. Students complete the final matching check on the halves and tenths practice sheet: match ( \frac{1}{2} ), ( \frac{5}{10} ), (0.5) and a shaded model, then finish the sentence, “Five-tenths equals one-half because…”. Review answers together using the plenary and answer-check slides. Take a Hero photo of selected completed models or explanations and upload it as evidence.

Resources

• the halves and tenths teaching deck
• the halves and tenths practice sheet
• the fraction wall and strip cards
• Blank paper strips, each the same length
• Pencils, rulers and coloured pencils
• Tenths grids or mini-whiteboards
• Classroom camera or tablet for Hero evidence
• Optional headphones or audio-recorded instructions

Assessment

• Listen for accurate use of whole, equal parts, tenths, equivalent and decimal during partner explanations.
• Check models and matching work for the connected representations ( \frac{1}{2} ), ( \frac{5}{10} ) and (0.5); note students who rely on a memorised fact without explaining why.
• Use the final matching check and explanation as an exit assessment. Upload a clear Hero photo of student work or a model that demonstrates the learning intention.

Differentiation

• Support learners through repeated concrete-to-pictorial-to-symbolic modelling, pre-drawn strips, colour coding and a personal reference card showing ( \frac{1}{2} = \frac{5}{10} = 0.5 ).
• Pair students strategically and provide sentence starters: “I know they are equivalent because…” and “The numerator shows…, while the denominator shows…”.
• Offer quiet independent practice, reduced visual clutter, widely spaced cards, icons and audio-recorded instructions for dyslexic learners. Read all written directions aloud and allow oral explanations.
• Challenge advanced learners to find other equivalent names for one-half, such as twentieths or hundredths, and explain the pattern using a diagram, number line or multiplication relationship.

Extension

• Find three different ways to represent one-half and explain how each representation shows the same measure.
• Investigate the pattern ( \frac{1}{2} = \frac{5}{10} = \frac{50}{100} ). Explain what changes and what stays the same.