Tenths on Number Lines

Overview

Lesson 1 of 16 in Place Value Decimal Journeys. Students connect one tenth with the fraction (1/10) and decimal (0.1), then use place-value grids, tenths strips and number lines to represent tenths between whole numbers.

Learning intentions

• WALT represent one tenth as a fraction and a decimal.
• WALT use place-value grids and tenths strips to show tenths.
• WALT place tenths accurately on a number line.
• WALT explain how fractions and decimals can represent the same value.

Success criteria

• I can identify one tenth as one of ten equal parts.
• I can write one tenth as (1/10) and (0.1).
• I can place tenths between whole numbers on a number line.
• I can explain why (0.1), (0.10) and (1/10) have the same value.

Curriculum links

• Number: recognise, represent and compare decimals to at least tenths using place value.
• Number: connect simple fractions and decimals, including tenths.
• Algebraic thinking: use number lines and patterns to describe the position and size of numbers.
• Mathematical communication and reasoning: represent ideas in more than one way, explain thinking and respond to others’ strategies.

Lesson structure (60 minutes)

1. 0–7 minutes – Hook and prior knowledge

Open with the hook and learning intention slides. Show a strip divided into ten equal parts and ask: “If one person gets one equal part, what fraction of the strip is that? How could we write it another way?” Students think, pair-share, then briefly revisit whole numbers and the meaning of place value.

2. 7–17 minutes – Build the meaning of one tenth

Model folding or partitioning a strip into ten equal parts. Shade one part and connect the representations: one out of ten parts is (1/10), which is one tenth, written (0.1). Use colour coding to show that the 1 in (0.1) is in the tenths column. Refer to the tenths modelling slides and ask students to explain what the zero and the one represent.

3. 17–28 minutes – Concrete and visual modelling

Organise students into groups of three or four. Give each group a place-value mat, tenths strips and digit cards; groups can use the Place Value Mat to build and discuss (0.1), (0.2), (0.5) and (1.0). Students record each number as a fraction and decimal on mini-whiteboards. Circulate and ask: “How many tenths make one whole?” and “Where does the digit belong?”

4. 28–40 minutes – Number-line demonstration

Display a line from 0 to 1. Mark the endpoints, divide the interval into ten equal spaces and label the points (0.1) to (1.0). Repeat with a line from 1 to 2, explaining that each step is still one tenth. Use the number-line teaching slides for a visual sequence, then have students place a marker at (1.3), (1.7) and (1.9) on individual whiteboards.

5. 40–52 minutes – Paired practice

Distribute the tenths representation and number-line worksheet. Students complete tasks in pairs, then independently complete the final two questions. Tasks should include matching (1/10) with (0.1), filling missing tenths on a place-value grid, and placing tenths on number lines from 0–1 and 1–2. Use partially marked lines and concrete strips with students who need support.

6. 52–57 minutes – Explain and compare

Show three cards: (0.1), (0.10) and (1/10). Ask pairs to decide whether they have the same value and prepare a short explanation. Invite several responses, emphasising that (0.10) is ten hundredths, which is equivalent to one tenth, while the focus today is tenths.

7. 57–60 minutes – Plenary and check

Return to the review and exit-question slides. Students answer orally or on a whiteboard: “Where would you place (0.6), and how do you know?” Collect responses and note who can connect the fraction, decimal and number-line representations.

Resources

• the complete tenths lesson slide deck
• the tenths representation and number-line worksheet
• the Place Value Mat
• Tenths strips or paper strips divided into ten equal parts
• Mini-whiteboards, pens and erasers
• Counters or small classroom objects
• Enlarged number lines and sticky notes
• Colour-coded place-value chart: ones and tenths

Assessment

• Listen during modelling and group work for accurate use of “one tenth”, (1/10), (0.1), “equal parts” and “tenths column”.
• Check whiteboard responses and worksheet number lines for correct partitioning, labels and placement.
• Record students who need further teaching with equal parts, decimal notation or locating tenths between whole numbers.

Differentiation

• Support: provide concrete tenths strips, enlarged colour-coded grids, oral rehearsal frames such as “One tenth is ___ out of ___ equal parts”, and partially marked number lines.
• Support: read instructions aloud, reduce copying, offer a quiet workspace and present one question at a time. Use uncluttered visuals, a clear sans-serif font and high-contrast colours for dyslexia-friendly access.
• Extension: ask students to explain why (0.1), (0.10) and (1/10) represent the same value, using a model or number line. Challenge them to place (1.05) or (1.25) and explain why these require smaller subdivisions.
• EAL learners: pre-teach and display “whole”, “equal parts”, “tenth”, “fraction”, “decimal” and “number line”; accept pointing, drawing, partner explanation or home-language rehearsal before written responses.