Decimal Names and Fractions

Overview

Students rename decimals by connecting each decimal place to its fraction denominator. Using place-value charts, grids and fraction representations, they explain why (0.7=7/10), (0.86=86/100), (0.04=4/100), and (1.25=1\frac{25}{100}=125/100). The lesson builds on reading decimals, place value and familiar fractions.

Learning intentions

Students will:

• connect tenths, hundredths and thousandths to denominators 10, 100 and 1000
• rename decimals as fractions and mixed numerals
• use zeroes correctly when naming decimal places
• explain the difference between a digit’s place and the total value of a decimal

Success criteria

• I can say and write a decimal as tenths, hundredths or thousandths.
• I can choose the correct fraction denominator from the final decimal place.
• I can rename numbers greater than one as a mixed number or improper fraction.
• I can explain why (0.86) is (86/100), not (8/10+6/100).

Curriculum links

• Number — interpret, compare and order decimals with more than two decimal places using place value and number lines.
• Number — compare and connect fractions with related denominators, including mixed numerals.
• Number — represent familiar fractions and decimals using visual models and equivalent forms.

Prior knowledge and vocabulary

Students should read decimals to hundredths, identify ones, tenths and hundredths, understand that 10 tenths make one whole, and recognise familiar fractions such as (1/2), (1/4) and (3/4).

Vocabulary: decimal, digit, place value, ones, tenths, hundredths, thousandths, numerator, denominator, fraction, mixed numeral, improper fraction, equivalent, whole.

Lesson structure (90 minutes)

1. 0–8 min · Hook and diagnostic. Display (0.86), (0.8), (0.06), (0.04) and ask, “Which fraction names (0.86): (8/10+6/100) or (86/100)? Why?” Open with the decimal mystery hook and diagnostic question. Students silently choose, justify to a partner, then show answers on mini-whiteboards. Note students who omit zeroes or combine place values incorrectly.

2. 8–23 min · Explicit teaching. Use the Place Value Mat and a large place-value chart. Model (0.7): the 7 is in the tenths column, so it means 7 tenths, or (7/10). Model (0.86): 8 is in the tenths column and 6 is in the hundredths column, but together the number is 86 hundredths, (86/100). Emphasise: the final place tells the denominator; the digits together tell the numerator. Record:

• tenths → denominator 10
• hundredths → denominator 100
• thousandths → denominator 1000 Model (0.04=4/100), explaining that the zero holds the tenths place. Students echo-read each form and annotate the chart.

3. 23–35 min · Concrete and visual investigation. In groups of three, students use a (10\times10) base-ten grid or fraction strips to shade and label (0.7), (0.86) and (0.04). They write the decimal, words and fraction beside each model. Ask: “How many hundredths are shaded in (0.7) when renamed?” Guide students to see (0.7=70/100), while its simplest place-value name is 7 tenths. Checkpoint: each group holds up the denominator card for a displayed decimal.

4. 35–47 min · Numbers greater than one. Model (1.25) on the chart and grid: 1 whole and 25 hundredths, so (1.25=1\frac{25}{100}=125/100). Clarify that (125/100) describes 125 hundredths, while (1\frac{25}{100}) shows one whole plus 25 hundredths. Briefly model (2.04=2\frac4{100}=204/100). Students explain the role of the zero in (2.04). Checkpoint: ask, “Is (1.25) greater or less than (125/100)? Explain.”

5. 47–67 min · Guided practice. Open the guided examples and partner prompts. Pairs complete the first six examples on the decimal renaming practice sheet, pausing after each for partner explanation: (0.3), (0.58), (0.04), (1.6), (1.25), (2.007). Teacher circulates and asks, “What is the last named place? What denominator matches it?” Stop for feedback after questions 2 and 4. Students correct in a different colour.

6. 67–82 min · Differentiated independent practice. Students finish the worksheet independently. Support students complete a place-value table and sentence frames: “___ is in the ___ place, so the denominator is ___.” Core students rename decimals and match equivalent forms. Challenge students explain two correct names for (0.7), rename (3.406) as a mixed numeral and improper fraction, and order (0.86), (0.806) and (0.8), justifying with place value. Teacher conferences with a focus group of students needing support.

7. 82–90 min · Exit ticket and plenary. Use the final reflection and exit questions. Students answer:

8. Rename (0.86) as a fraction and explain the denominator.

9. Rename (1.25) as a mixed numeral and improper fraction.

10. Correct this statement: “(0.04=4/10).” Collect tickets and invite two students to share different representations.

Resources

• the decimal renaming teaching deck
• the decimal renaming practice sheet
• the Place Value Mat
• Mini-whiteboards and markers
• Large place-value chart
• (10\times10) base-ten grids or fraction strips
• Decimal and fraction cards
• Pencils, highlighters and counters

Assessment

• Use the hook and denominator-card checkpoint to identify misconceptions before teaching.
• During modelling and guided practice, listen for explanations linking the final decimal place to the denominator; inspect grid labels and worksheet responses.
• Use the exit ticket to determine whether students can rename decimals below and above one and retain zeroes.

Differentiation

• Support: provide a completed example, colour-code each place-value column, use the Place Value Mat, and rehearse sentence frames orally before writing.
• EAL/D and students needing language support: pair numerals with word cards (“four hundredths”), display vocabulary with visuals, and accept oral explanations alongside written work.
• Students requiring additional adjustment: use fewer examples, manipulatives and a reduced worksheet selection; provide teacher or peer scribing where appropriate.
• Extension: ask students to rename (0.7) as (70/100) and (700/1000), then explain why all forms are equivalent but use different denominators.

Anticipated misconceptions and answers

• (0.86) is not (8/10+6/100) as its single fraction name; it is (86/100). The 8 and 6 combine to make 86 hundredths.
• (0.04) is not (4/10); the zero holds the tenths place, so it is 4 hundredths, (4/100).
• The denominator is not chosen from the number of digits alone: it names the final place represented.
• Answers: (0.3=3/10); (0.58=58/100); (0.04=4/100); (1.6=1\frac6{10}=16/10); (1.25=1\frac{25}{100}=125/100); (2.007=2\frac7{1000}=2007/1000). The corrected statement is (0.04=4/100).