Tenths In Three Forms

Overview

Lesson 7 of 15 in Number Connections: Fractions, Decimals, Percentages. Students connect tenths shown as fractions, decimals, lengths and money, then locate them on a number line. The lesson uses the refreshed New Zealand Curriculum emphasis on making connections, representing ideas in multiple ways, explaining thinking and using mathematical language.

Learning intentions

• WALT represent tenths as fractions, decimals and positions on a number line.
• WALT connect a fraction with denominator 10 to its decimal representation.
• WALT explain the value of digits in tenths using place-value language.
• WALT use tenths in familiar measurement and money contexts.

Success criteria

• I can read and write tenths as fractions and decimals.
• I can explain why (3/10 = 0.3).
• I can place tenths correctly on a 0–1 number line.
• I can explain that the digit after the decimal point shows tenths.

Curriculum links

• Number: recognise, represent and compare fractions and decimals, including tenths.
• Number: use place value to explain the meaning of digits in decimal numbers.
• Measurement: interpret tenths in metre lengths and everyday quantities.
• Mathematical practices and key competencies: use representations, connect ideas, communicate reasoning and participate in collaborative problem-solving.

Lesson structure (45 minutes)

1. 0–5 min – Hook and prior knowledge

Open with the hook and learning intention slides. Display a one-metre strip and ask: “If this metre is divided into ten equal parts, how much is each part? How could we write three parts as a fraction, a decimal and a length?”

Students discuss with a partner, then share examples. Record both correct and incorrect ideas for later checking.

2. 5–13 min – Explicit teaching: tenths and place value

Use the tenths model and place-value slides alongside a place-value chart. Fold or mark a metre strip into ten equal intervals. Establish that one interval is one tenth, written (1/10) or 0.1, and that three intervals are (3/10) or 0.3.

Model reading and writing 0.1, 0.3, 0.7 and 1.0. Emphasise that the 3 in 0.3 means three tenths, not three ones. Students show each number with fingers or mini-whiteboards.

3. 13–23 min – Partner representation activity

In pairs, students use metre strips, tenths grids and place-value charts to build and record tenths. Call out or display numbers such as (2/10), 0.5 and seven tenths. Partners represent each in at least two ways and explain the connection.

Use the fraction-decimal-percentage matching cards for a short matching challenge, focusing on the fraction and decimal columns. Students should justify each match rather than simply rely on visual similarity.

4. 23–32 min – Number-line investigation

Open the number-line instructions and discussion prompts. Students draw a 0–1 number line on the tenths practice worksheet and divide it into ten equal intervals. They label 0, 0.1, 0.2 and 1, then plot 0.3, 0.6 and 0.9.

Connect this to money: $0.30 is 30 cents, or three tenths of a dollar. Connect it to measurement: 0.3 m is 30 cm. Ask: “Which is greater, 0.3 or 0.7? How does the number line prove it?”

5. 32–40 min – Independent application

Students complete the remaining questions on the tenths practice worksheet. Include reading and writing tenths, matching (3/10) with 0.3, explaining the tenths digit, and placing decimals on a number line.

Pause midway for a quick peer check: partners compare one answer and explain their reasoning using the sentence frame, “I know ___ equals ___ because ___.”

6. 40–45 min – Plenary and assessment

Return to the final reflection slides. Ask students to complete these prompts orally or on their worksheet: “0.8 means…”, “(4/10) is the same as…”, and “The digit ___ in 0.__ shows…”.

Invite two students to explain why (3/10 = 0.3). Collect worksheets or photograph selected responses to identify who is ready to move to hundredths and who needs further work with one decimal place.

Resources

• the complete tenths teaching deck
• the tenths practice worksheet
• Place-value charts and mini-whiteboards
• Base-ten blocks and tenths grids
• One-metre strips, rulers and pencils
• Play money or price tags showing amounts such as $0.30 and $0.70
• Relevant MNP textbook/workbook pages for decimals and tenths
• Prepared 0–1 number-line examples

Assessment

• Listen for accurate use of “tenths”, “decimal point”, “numerator” and “denominator” during partner explanations.
• Check representations for correct equivalence, especially (3/10 = 0.3), and accurate spacing on number lines.
• Use the final responses to group students for the next lesson: secure, developing or requiring concrete support.

Differentiation

• Support learners with base-ten blocks, tenths grids, pre-marked metre strips and a place-value chart. Keep examples to one decimal place and provide: “___ tenths is written as ___/10 and ___.”
• Pair students strategically and rehearse language orally before written work. Allow students to point, build or draw their explanation before recording it.
• For EAL and students requiring additional support, display visuals for whole, tenth, fraction, decimal and number line; repeat instructions one step at a time and provide sentence frames.
• Extend advanced learners by investigating patterns when tenths are added or subtracted, such as 0.2 + 0.1, 0.3 + 0.1 and 0.9 + 0.1. Ask them to explain what changes at 1.0 and generalise the pattern.