Divide by Ten

Overview

In this sixth lesson of Fractions as Measures, students connect sharing whole numbers into ten equal groups with decimal notation. Through place-value discs, grids and a place-value chart, they model how 1, 2, 10 and 24 ones become tenths and explain why (24 \div 10 = 2.4).

Learning intentions

• WALT divide one- and two-digit whole numbers by 10.
• WALT represent answers to division by 10 as decimals.
• WALT place digits correctly in a place-value chart.
• WALT identify the tenths digit and explain its meaning.

Success criteria

• I can divide a whole number by 10.
• I can place the whole-number and tenths digits in the correct columns.
• I can identify the tenths digit.
• I can show or explain my thinking using materials, a grid or an equation.

Curriculum links

• Mathematics and Statistics — Mathsteasers: challenging higher-order thinking questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge questions with taught mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: providing appropriate challenge and enrichment.
• Mathematical communication and reasoning are developed as students represent, explain and justify division by 10.

Lesson structure (45 minutes)

1. 0–5 min · Hook and retrieval. Display a ten-frame or ten equal groups and ask, “If 1 whole is shared equally between 10 people, how much does each person get?” Open with the sharing hook and retrieval slides. Students think, pair-share and show answers such as (1/10), 0.1 or “one tenth” on mini-whiteboards; invite several explanations.

2. 5–13 min · Explicit teaching with equipment. Use place-value discs to model 1, 2 and 10 ones shared into ten equal groups. Teacher physically trades each one for ten tenths, records the matching place-value chart and connects (1 \div 10 = 0.1), (2 \div 10 = 0.2) and (10 \div 10 = 1). Students rehearse the language aloud: “Dividing by ten makes ten equal groups; the tenths digit tells how many tenths.”

3. 13–21 min · Model 24 ÷ 10. Build 24 ones, share them across ten groups and represent the result as 2 ones and 4 tenths. Record (24 \div 10 = 2.4) on a vertical, colour-coded place-value chart and a 10-by-10 grid. Use the place-value modelling slides to reveal each representation one at a time. Students copy the chart, identify the tenths digit and explain why the answer is not 24.10 or 2.04.

4. 21–33 min · Guided hands-on practice. Organise 23 students into pairs, with one teacher-led support group as needed. Give each pair place-value discs, a chart and a grid, then distribute the divide-by-ten modelling and practice sheet. Students model and record examples including (1 \div 10), (2 \div 10), (10 \div 10), (24 \div 10), (16 \div 10) and (30 \div 10). Pause twice for partner checking: “Where is the tenths digit? How do you know?”

5. 33–40 min · Independent application and feedback. Students complete the remaining worksheet questions, showing at least one model and one equation. Teacher circulates, checks mini-whiteboards and gives immediate feedback using the prompts “Check the place-value columns”, “What does the tenths digit represent?” and “Can you prove it with another representation?” Students compare one answer with a partner and revise in a different colour.

6. 40–45 min · Share-back and evidence check. Show (37 \div 10) and ask students to solve it on mini-whiteboards before sharing. Students explain the answer using either a place-value chart and discs or a grid and equation; finish with a quick oral exit response: “The tenths digit in 3.7 is __ because __.” Photograph selected models, annotated worksheets and whiteboard responses for upload to Hero as evidence of the curriculum goals.

Resources

• the complete Divide by Ten teaching deck
• the divide-by-ten modelling and practice sheet
• Place-value discs or counters, including tenths discs
• Vertical place-value charts with ones and tenths columns
• 10-by-10 grids
• Mini-whiteboards, pens and erasers
• Arrow cards showing whole numbers and decimal place values
• Projector or interactive display
• Devices or camera for uploading evidence to Hero

Assessment

• Use mini-whiteboard responses at the hook, after modelling and during the (37 \div 10) check to identify misconceptions about decimal placement.
• During pair work, listen for accurate use of “ones”, “tenths”, “share equally” and “divide by ten”; record students needing further support.
• Check worksheet representations and exit responses, then upload a representative range of annotated evidence to Hero.

Differentiation

• Support learners with physical trading of ones for tenths, a reduced number range of 1, 2, 10 and 24, worked examples, arrow cards and colour-coded place-value columns.
• Provide a vertical place-value layout, uncluttered pages, clear sans-serif text and enlarged charts for dyslexic learners. Allow spoken rehearsal before writing and accept oral explanations alongside equations.
• Use mixed-ability pairs with clearly shared roles: builder, recorder and checker. Re-model with the teacher-led group while other students continue familiar examples.
• Extension learners explain why (37 \div 10 = 3.7) using two representations, then create a similar example for a partner and check whether the explanation is convincing.