Decimal Number Lines

Overview

Students connect tenths to familiar fractions, locate decimals such as 0.2 and 0.7 on a number line, rename decimals as fractions, and add tenths using a number line and part-part-whole thinking. The lesson extends students’ understanding of numbers to 1000, fractions and addition while introducing decimal notation in a concrete, accessible way.

Learning intentions

Students will:

• represent tenths as fractions and decimals;
• locate and label decimals between 0 and 1 on a number line;
• convert simple tenths between decimal and fraction notation;
• add decimals representing tenths using a number line and number sentences;
• explain their strategy using mathematical language.

Success criteria

• I can explain that 0.1 is the same as one-tenth.
• I can locate and label tenths on a number line from 0 to 1.
• I can write a decimal tenths number as a fraction, and a fraction as a decimal.
• I can add tenths and show my thinking on a number line.

Curriculum links

• Number — recognise, represent and order numbers using materials, numerals and number lines.
• Number — add and subtract one- and two-digit numbers using number sentences, number lines and part-part-whole reasoning.
• Number — count by fractions and locate fractions on number lines.
• Number — make connections between fractions and decimal notation.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Open with the hook and warm-up slides showing a 1-litre measuring strip divided into ten equal parts and ask, “How much is three parts of the whole?” Students discuss what they know about tenths, then place 0, 0.5 and 1 on a blank number line in their books. Quickly check that students understand equal intervals and the meaning of one-half.

2. 7–18 min · Build the connection. Use the tenths teaching slides to model a whole divided into ten equal parts. Teacher records one-tenth = 1/10 = 0.1, two-tenths = 2/10 = 0.2 and so on, emphasising that the digit after the decimal point shows tenths when the number is less than one. Students fold or mark a strip into ten equal intervals, label selected points as both fractions and decimals, and rehearse the sentence: “___ tenths is equal to ___.”

3. 18–30 min · Guided number-line practice. Display the worked example in the number-line modelling slides and jointly construct a number line from 0 to 1 with ten equal intervals. Teacher models locating 0.3, then asks students to justify the position of 0.6 and 9/10. Students work in pairs to locate and label 0.1, 0.4, 0.8, 1/10, 5/10 and 10/10 on their strip, checking that equivalent names occupy the same point. Address the misconception that a longer decimal notation automatically means a larger number.

4. 30–43 min · Independent application. Distribute the decimal number-line practice worksheet. Students complete tasks involving matching tenths and decimals, labelling points on number lines, ordering simple decimals from smallest to largest, and writing number sentences such as 0.3 + 0.4 = 0.7. Teacher conferences with individuals and pauses for a brief whole-class check after the first two questions.

5. 43–53 min · Add tenths on a number line. Use the decimal addition modelling and activity slides to model 0.2 + 0.5 by starting at 0.2 and jumping five tenths to reach 0.7. Connect this to 2/10 + 5/10 = 7/10. Students solve selected worksheet additions, drawing jumps and reading each answer aloud. Include examples that cross one whole, such as 0.6 + 0.5, and guide students to recognise 10/10 as one whole and record the result as 1.1.

6. 53–60 min · Reasoning and exit check. Display the discussion and plenary slides with the statement, “0.4 + 0.3 = 0.10 because four tenths plus three tenths makes ten tenths.” Students decide whether it is true, false or needs correcting, and explain their reasoning to a partner. Finish with the fractions-on-a-number-line strategy mat as a quick individual reflection: students plot 0.7, rename it as a fraction, and solve 0.7 + 0.2, showing one number-line jump.

Resources

• the complete decimal number-line slide deck
• the decimal number-line practice worksheet
• the fractions-on-a-number-line strategy mat
• Board or interactive whiteboard
• Paper strips or ten-frame strips
• Pencils, coloured pencils and rulers
• Individual mini-whiteboards and markers
• Anchor chart showing tenths, fractions and decimals

Assessment

• During modelling, ask students to point to 3/10, 0.3 and the third interval, checking that they identify the same position.
• Listen to partner explanations and inspect number-line jumps for accurate intervals, labels and addition.
• Use the final task to assess whether students can plot a decimal, convert it to a fraction and add tenths, including an answer that crosses one whole.

Differentiation

• Support students with pre-drawn number lines, highlighted equal intervals, paper tenths strips and sentence starters such as “I know ___ because there are ___ tenths.”
• Work with a small teacher-led group using numbers between 0 and 1 only; provide a place-value prompt showing tenths and the decimal point.
• For EAL/D students, explicitly model and display the terms whole, tenth, fraction, decimal, equal and number line, with gestures and repeated oral rehearsal.
• Extend confident students by asking them to solve and explain three different additions that equal 1, such as 0.4 + 0.6, and to represent each using both fraction and decimal notation.