Exploring Thousandths

Overview

Lesson 3 of 5 in Decimal Place Value Explorers. Students use place-value sliders, layered representations and metre strips to see that a whole divided into 1,000 equal parts creates thousandths, then connect thousandths fractions with decimal notation.

Learning intentions

• WALT create thousandths by dividing one whole into 1,000 equal parts.
• WALT locate and use the thousandths place.
• WALT represent thousandths as fractions and decimals.
• WALT explain how tenths, hundredths and thousandths are connected.

Success criteria

• I can locate the thousandths place in a decimal.
• I can write thousandths as fractions and decimals.
• I can explain that (1/1,000 = 0.001).
• I can describe how a whole is divided into 1,000 equal parts.

Curriculum links

• Number: understand place value and represent, compare and order decimals.
• Number: make connections between fractions and decimals, including equivalent representations.
• Mathematical inquiry: use equipment, diagrams and mathematical language to explain thinking.
• Communication and participation: share strategies, listen to others and justify conclusions.

Lesson structure (30 minutes)

1. 0–4 minutes – Daily review and hook Open with the review and hook slides. Ask students to answer on mini-whiteboards: What is (1/100) as a decimal? How many hundredths are in one whole? Which is greater: 0.4 or 0.04? Reveal answers and ask, “If a whole is split into 1,000 equal pieces, how small is one piece?”

2. 4–9 minutes – Zoom through place value Display a whole metre strip or a drawn strip. Fold or mark it to show tenths, then hundredths, and explain that each hundredth can be divided into ten equal parts. Use the standard form place value slider to move a digit through tenths, hundredths and thousandths. Emphasise that moving one place right divides the value by 10.

3. 9–15 minutes – Build the representation In pairs, give students a place-value mat, digit cards and a metre strip. Use the place value mat to model (1/10=0.1), (1/100=0.01), and (1/1,000=0.001). Students say each example aloud using the sentence frame: “One thousandth is one of ___ equal parts, so it is written as ___.”

4. 15–22 minutes – Guided practice Distribute the thousandths representation worksheet. Model the first two questions: (3/1,000=0.003) and (125/1,000=0.125). Students complete examples by identifying the place value, writing the fraction and writing the decimal. Pause to check that zero placeholders are included in numbers such as 0.003.

5. 22–27 minutes – Partner explain and connect Display the partner discussion slides. Partners take turns explaining one answer using the prompt: “I know ___/1,000 equals ___ because…”. Ask selected students to show how 0.125 contains 1 tenth, 2 hundredths and 5 thousandths. Address the misconception that 0.125 means 125 tenths.

6. 27–30 minutes – Exit check and reflection Students complete the final section of the reflection and exit questions: locate the thousandths digit in 0.407, write (7/1,000) as a decimal, and explain what dividing a whole into 1,000 equal parts means. Invite two students to share different explanations, then preview that the next lesson will compare and order decimals.

Resources

• Slides-1: review, visual zoom, worked examples, discussion prompts and plenary.
• Worksheet-1: guided practice and exit questions.
• the place value mat for pair modelling.
• the standard form place value slider for moving digits.
• Metre strips or strips of paper.
• Digit cards or small counters.
• Mini-whiteboards and pens.
• Pencils and coloured pencils.
• One prepared decimal place-value chart for teacher modelling.

Assessment

• Listen for accurate use of “tenths”, “hundredths”, “thousandths” and “equal parts” during partner explanations.
• Check models and worksheet responses, particularly zero placeholders in 0.003 and 0.050.
• Use the exit questions to identify students needing further work with place-value columns or the fraction–decimal connection.

Differentiation

• Support learners with concrete metre strips, counters, the place-value mat and a completed example. Begin with familiar patterns: 0.1, 0.01, 0.001.
• Provide a place-value chart, enlarged digit cards and pronunciation support: “zero point zero zero three” and “three thousandths”. Allow students to rehearse explanations with a partner before sharing.
• For students requiring additional support, reduce the number of examples and use colour coding: tenths blue, hundredths green and thousandths red.
• Extend confident learners by asking them to convert between equivalent forms and justify them, for example (0.7=700/1,000), (0.25=250/1,000), and (0.125=125/1,000).