Decimal Investigation

Overview

Lesson 5 of 5 in Decimal Place Value Explorers. Students consolidate their understanding of tenths, hundredths and thousandths by representing, reading, comparing and justifying decimal values through hands-on investigations and meaningful contexts.

Learning intentions

• WALT represent tenths, hundredths and thousandths as fractions and decimals.
• WALT read and write decimal numbers accurately.
• WALT compare decimal values using place value, models and number lines.
• WALT explain our mathematical thinking clearly.

Success criteria

• I can represent tenths, hundredths and thousandths as fractions and decimals.
• I can read and write decimal numbers accurately.
• I can compare decimal values and use place value or a model to justify my answer.
• I can connect decimals to money and measurement contexts.

Curriculum links

• Number: understand and represent decimal place value and equivalent fractional forms.
• Number: compare, order and locate decimals on a number line.
• Mathematical and statistical thinking: reason, communicate, represent and connect ideas.
• Make sense of problems, choose useful representations and explain the reasonableness of answers.

Lesson structure (30 minutes)

1. 0–5 min – Daily review and learning focus Open with the review and learning-intention slides. Students answer independently in books or on the decimal investigation recording sheet:

• Write 47/100 as a decimal.
• Write 0.006 as a fraction.
• Which is greater: 0.62 or 0.602? Ask students to turn and explain one answer. Clarify that 0.62 can be written as 0.620, so it is greater than 0.602.

2. 5–8 min – Model the investigation routine Use the place-value chart on the place-value modelling slide to model one example, such as 0.407. Show that the 4 represents four tenths, the 0 represents zero hundredths and the 7 represents seven thousandths. Demonstrate the group roles: reader, builder, recorder and checker.

3. 8–22 min – Rotating investigation stations Place students in five mixed-ability groups of four. Groups spend approximately three minutes at each station, moving clockwise when prompted. They record one example and one explanation at each station on the station recording page.

• Decimal puzzle: build a decimal from digit cards, then write it in fraction and expanded form using the place value mat.
• Matching challenge: match fraction and decimal representations, then explain why they are equivalent using the fraction-decimal-percentage matching cards. Students may focus on the fraction and decimal columns.
• Number-line challenge: place teacher-prepared decimal cards between 0 and 1 on a floor or desk number line. Students justify the position by identifying the nearest tenths or hundredths.
• Money context: compare prices such as $2.60 and $2.605. Students decide which is greater and explain what the extra thousandths mean mathematically.
• Measurement context: compare lengths or capacities such as 0.7 m, 0.68 m and 0.705 m. Students order them and explain their strategy. Display the station instructions and countdown on the rotating-stations slides. Confer with groups, asking, “Which place value decides the comparison?” and “How could you prove it with a model?”

4. 22–26 min – Share and correct reasoning Bring the class together and show two comparison examples on the reasoning discussion slide. Invite groups to share different representations, including a place-value model, equivalent zeros, a number line or a context. Address common errors, especially treating a longer decimal as automatically greater or ignoring zero place values.

5. 26–30 min – Individual exit task and reflection Distribute the final section of the individual exit task. Students complete independently:

• Represent 0.308 as a fraction and in words.
• Write a decimal for 6/10 + 4/100 + 2/1000.
• Which is greater: 0.506 or 0.56? Justify your answer using place value or a model. Finish with the reflection slide: students identify one representation that helped them and one place-value idea they now understand better.

Resources

• the Decimal Investigation slide deck
• the decimal investigation recording sheet
• the place value mat
• the fraction-decimal-percentage matching cards
• Digit cards or numeral cards
• Teacher-prepared decimal cards
• Floor or desk number line
• Pencils, mini-whiteboards and erasers
• Timer and station signs

Assessment

• Listen to explanations during the review and stations, noting whether students identify the first differing place value when comparing decimals.
• Check station recording for accurate fraction-decimal representations, ordering and justification.
• Use the individual exit task to identify students requiring further support with equivalent representations, zero place values or comparison.

Differentiation

• Support learners with the place-value mat, concrete counters, pre-filled examples and a visible chart naming tenths, hundredths and thousandths.
• Offer choice of building with materials, drawing a model, using a number line or explaining orally before recording.
• Provide sentence stems: “I know ___ is greater because the ___ place is ”; “/1000 is equivalent to ___ because…”
• Confer with students needing support; extend confident learners by asking them to compare decimals with trailing zeros and defend more than one strategy. Provide vocabulary and visual examples for English language learners and allow oral explanations or a scribe where appropriate.

Extension

Students design and solve a decimal mystery involving at least five clues. It must include equivalent fraction and decimal representations, a number-line clue and at least two comparisons. A partner solves the mystery and explains which clues were most useful.