Tenths Beyond One

Overview

This introductory Year 4 lesson builds on understanding of whole numbers, equal parts and place value. The learner explores how the base-10 system continues to the right of ones, representing one tenth as both (\frac{1}{10}) and 0.1.

Learning intentions

• WALT understand that one whole can be split into ten equal parts.
• WALT represent one tenth as a fraction and a decimal.
• WALT read and write simple decimals to tenths.
• WALT explain the value of digits to the right of the ones place.

Success criteria

• I can split one whole into ten equal parts.
• I can match (\frac{1}{10}), 0.1 and a picture showing one tenth.
• I can read and write decimals such as 0.3 and 1.7.
• I can explain that the first digit after the decimal point shows tenths.

Curriculum links

• Te Mātaiaho Mathematics and Statistics, Phase 2 Number: place value extends to tenths.
• Decimals are fractions whose denominators are powers of 10.
• Tenths can be represented using fractions, decimals, place-value materials and money contexts.
• Mathsteasers: using visual and conceptual challenges to deepen mathematical understanding.

Lesson structure (45 minutes)

1. 0–6 min · Diagnostic check. Teacher displays the opening diagnostic questions and asks: “What does the 3 mean in 35?” “What is one half?” and “How could we share one whole equally?” Students respond orally, draw or use materials; teacher notes confidence with place value, equal parts and fraction language.

2. 6–13 min · Hook and connect. Teacher shows a chocolate bar or strip divided into ten equal parts and asks, “If I take one part, how much of the whole do I have?” using the whole-and-tenths visual. Students fold a paper strip into ten equal parts, shade one part, and describe it as “one out of ten” and (\frac{1}{10}).

3. 13–23 min · Explicit modelling. Teacher models the folded strip, a 10-by-1 place-value chart and a $1 coin context: ten 10-cent coins make one dollar, so 10 cents is one tenth of a dollar. Record: 1 whole = 10 tenths; (\frac{1}{10}=0.1). Use the place-value modelling slides to show ones, the decimal point and tenths. Students help place digit cards and read 0.1, 0.4 and 0.9, explaining what each tenths digit means.

4. 23–31 min · Guided practice. Teacher draws or builds amounts with the strip and asks the learner to match each representation to a fraction and decimal on the tenths representation worksheet. Students complete examples such as three shaded tenths → (\frac{3}{10}) → 0.3, then explain their thinking using the sentence frame: “___ tenths is ___ out of ten, so it is ___.”

5. 31–39 min · Independent practice. Teacher gives the learner the remaining questions on the tenths representation worksheet and prompts them to work independently before checking. Students shade tenths, write fractions and decimals, read decimals aloud, and place 0.2, 0.6 and 0.9 on a number line from 0 to 1. Include one item such as “Which is greater: 0.3 or 0.8? How do you know?”

6. 39–43 min · Formative conference and misconception check. Teacher asks the learner to explain why 0.5 means five tenths and presents two deliberate errors: “0.7 means seven ones” and “0.4 is greater than 0.9 because 4 is bigger than 9.” Students correct the statements using the strip, chart or number line. Teacher records whether the learner can connect the three representations without prompting.

7. 43–45 min · Exit and reflect. Teacher asks the learner to complete the final reflection prompt: “Draw, write and say three tenths.” Students give the answer as a picture, (\frac{3}{10}) and 0.3, then state one thing they learned.

Resources

• the tenths introduction and teaching deck
• the tenths representation worksheet
• Paper strips, pencils and crayons
• Place-value chart showing ones, decimal point and tenths
• Digit cards 0–9
• 10-cent coins and a $1 coin, or pictures of them
• 0–1 number line
• Optional counters or linking cubes

Assessment

• Use the diagnostic check to identify prior knowledge of place value, equal sharing and fractions.
• During modelling and guided practice, listen for accurate use of “whole”, “tenths”, “fraction” and “decimal”; check that the learner understands the decimal point separates ones from tenths.
• Use the final response to decide whether the next lesson should revisit concrete tenths or move towards comparing and ordering tenths.

Differentiation

• For support, keep the folded strip and place-value chart visible, use only 0–1 initially, and build one tenth at a time. Accept drawing, pointing and oral explanations before requiring written notation.
• Provide dyslexia-friendly access: use a clear sans-serif font, large spacing, uncluttered worksheet sections, short instructions read aloud, and allow the learner to answer orally or with manipulatives. Avoid requiring rapid copying from the board.
• For EAL learners, rehearse the words “whole”, “equal”, “tenth”, “fraction”, “decimal” and “point” with pictures and sentence frames. Model “zero point three” rather than “zero comma three”.
• For an advanced learner, ask them to find every tenth between 0 and 1, explain why 0.1 + 0.1 = 0.2, and create a money or measurement story for 1.6. Keep the focus on tenths; do not require hundredths.

Extension

• Challenge the learner to prove, using the strip or number line, that ten tenths make one whole.
• Ask: “Can you find two different representations for 0.7 and explain why they show the same amount?”