Grade 5 Mathematics: Converting Between Common Fractions and Decimal Fractions – Week 43 Term 4

1. Common Fraction

A number that represents part of a whole, written with a numerator and denominator (e.g., 3/4, 1/2, 7/10)

2. Decimal Fraction

A fraction written using the decimal notation system with place value (tenths, hundredths, thousandths), using a comma in South Africa (e.g., 0,5; 0,25; 1,75)

3. Equivalent

Having the same value but in different forms (e.g., 1/2 = 0,5; 25/100 = 0,25)

4. Tenths

The first decimal place after the comma representing one part out of ten equal parts (e.g., 0,3 = 3 tenths = 3/10)

5. Hundredths

The second decimal place after the comma representing one part out of one hundred equal parts (e.g., 0,25 = 25 hundredths = 25/100)

Hook Activity:

Display a R10 note and ask: “If I share this R10 equally among 10 friends, how much does each person get?” (R1 = 1/10 of R10 = 0,1 of R10). Show real South African coins (50c, 20c, 10c) and discuss: “What fraction and decimal of one Rand is 50 cents?” This connects to learners’ everyday experience with money.

Introduction Activities:

• Quick Mental Warm-up (3 minutes): Count in tenths from 0 to 1 (0; 0,1; 0,2; 0,3… 1,0). Then count in hundredths from 0 to 0,5. Write these on the board showing both decimal and fraction notation side by side.
• Learning Intentions (2 minutes): Share today’s objectives clearly: “Today we will learn how to change common fractions like 3/10 into decimal form like 0,3, and also change decimals like 0,75 back into fractions like 75/100 or 3/4.”
• Success Criteria Display (2 minutes): Show learners what success looks like – display example conversions and explain that by the end they’ll be able to move confidently between these two forms.

Direct Instruction (12 minutes):

Phase 1: Fractions to Decimals (6 minutes)

• Use a large visual fraction strip divided into 10 equal parts. Shade 3 parts and show this is 3/10.
• Explain: “When we have tenths, we can write them as decimals. The 3 in 3/10 goes in the tenths place after the comma: 0,3”
• Demonstrate the pattern: 1/10 = 0,1; 2/10 = 0,2; 3/10 = 0,3; 4/10 = 0,4 (continuing to 10/10 = 1,0)
• Show a hundred square grid. Shade 25 squares and demonstrate: 25/100 = 0,25 (25 hundredths)
• Key teaching point: “The denominator tells us the place value – tenths or hundredths. The numerator tells us the digit.”

Phase 2: Decimals to Fractions (6 minutes)

• Write 0,7 on the board. Ask: “What place value is the 7 in?” (tenths)
• Show: “0,7 = 7 tenths = 7/10”
• Write 0,45 on the board. Explain: “This is 4 tenths and 5 hundredths = 45 hundredths = 45/100”
• Demonstrate using place value cards to show the conversion
• Show practical example: “R0,75 = 75 cents = 75/100 of a Rand = 3/4 of a Rand”

Guided Practice (15 minutes):

Activity 1: Conversion Practice with Visual Support (8 minutes)

• Distribute decimal grids (100-square grids) and fraction strips to each learner
• Work through examples together as a class:
  • Convert 6/10 to decimal (shade 6 parts of 10-part strip, write 0,6)
  • Convert 0,8 to fraction (shade 8 parts, write 8/10)
  • Convert 30/100 to decimal (shade 30 squares, write 0,30 or 0,3)
  • Convert 0,55 to fraction (shade 55 squares, write 55/100)
• After each example, have learners show their work to a partner and explain their thinking

Activity 2: Money Connections (7 minutes)

• Use South African money context: “Thandi has R0,50. What fraction of a Rand does she have?” (50/100 = 5/10 = 1/2)
• Work through problems:
  • “Sipho spent 3/10 of his R10. How much did he spend?” (R3,00 or R3)
  • “A shop sells cool drink for R6,50. What fraction of R10 is this?” (650/1000 or 65/100 of R10)
• Learners work in pairs to solve 3 similar problems with teacher circulating and supporting

Independent Practice (13 minutes):

Differentiated Worksheet Activity:

• Section A (Foundation Level): Convert simple fractions to decimals: 1/10, 5/10, 9/10, 20/100, 50/100, 75/100
• Section B (Core Level): Mixed conversions both ways: 0,4 to fraction; 7/10 to decimal; 0,65 to fraction; 35/100 to decimal
• Section C (Extension Level): Problem-solving: “A recipe needs 0,75 liters of milk. Express this as a common fraction.” “Nomsa walked 3/10 of a kilometer. Write this as a decimal.”
• Practical Application: Create your own real-world problem using either fractions or decimals, then convert it

Teacher circulates during independent work, providing targeted support and checking for understanding through questioning.

Consolidation Activity (6 minutes):

• Pair-Share-Square: In pairs, learners explain to each other the steps for converting fractions to decimals and decimals to fractions
• Class Discussion: Select 2-3 learners to share their explanations with the whole class
• Quick Check Game: Hold up fraction cards (e.g., 4/10) and learners write the decimal equivalent on mini whiteboards, then show simultaneously
• Review key learning: “Remember – tenths go in the first place after the comma, hundredths in the second place”

Exit Ticket (4 minutes):

On a slip of paper, learners complete:

1. Convert 7/10 to a decimal: _______
2. Convert 0,40 to a common fraction: _______
3. Write one thing you learned today about fractions and decimals
4. Write one question you still have

Collect exit tickets as learners leave to inform tomorrow’s lesson planning and identify learners needing additional support.

📝 Formative Assessment

• Observation: Monitor learners during guided practice – check if they can shade correct portions of grids and strips
• Questioning: Ask targeted questions like “How do you know where to place the digit?” and “Why is 0,5 the same as 5/10?”
• Peer Discussion: Listen to pair conversations during consolidation to assess understanding
• Exit Ticket: Review responses to identify misconceptions and plan tomorrow’s revision
• Worksheet Completion: Check accuracy and strategy use during independent practice

📋 Success Criteria

• Learners can accurately convert at least 4 out of 5 fractions with denominators of 10 to decimals
• Learners can accurately convert at least 4 out of 5 fractions with denominators of 100 to decimals
• Learners can convert decimals back to common fractions with correct denominators
• Learners can explain the relationship between place value and fraction denominators
• Learners can apply conversions to solve at least one practical problem correctly

🤝 For learners who need support:

• Provide pre-shaded fraction strips and decimal grids to reduce cognitive load
• Work in small teacher-led group during independent practice
• Use only fractions with denominator of 10 initially before progressing to 100
• Provide a reference chart showing common conversions (1/10 = 0,1; 2/10 = 0,2, etc.)
• Allow use of concrete manipulatives (base-ten blocks) throughout the lesson
• Pair with a supportive peer buddy for guided practice activities

🚀 For advanced learners:

• Challenge with fractions requiring simplification: Convert 50/100 to 0,50 then simplify to 5/10 and 1/2
• Introduce conversion of mixed numbers: Convert 2 3/10 to 2,3
• Problem creation: Design their own word problems involving fraction-decimal conversion for classmates
• Extension to thousandths: Explore 0,125 = 125/1000
• Real-world research: Find examples of fractions and decimals in newspapers, packaging, or recipes and convert between them
• Mental mathematics challenge: Rapid conversion practice without visual aids

♿ For learners with barriers to learning:

• Provide enlarged visual aids with high contrast for learners with visual impairments
• Use tactile fraction strips and grids with raised edges for learners with visual challenges
• Offer oral instructions and verbal explanation for each step
• Allow extra time for processing and completing activities
• Reduce number of problems required (quality over quantity)
• Provide a scribe or allow verbal responses for learners with fine motor difficulties
• Use digital tools or apps that provide immediate feedback if available
• Break down instructions into smaller, sequential steps with visual cues

✅ What worked well:

[To be completed after lesson – Consider: Did the money context engage learners? Were the visual aids effective? Did learners grasp the place value connection?]

🔧 What could be improved:

[To be completed after lesson – Consider: Did timing work well? Were instructions clear? Did all learners have adequate resources? Which activities need modification?]

📝 Notes for next lesson:

[To be completed after lesson – Note: Which learners need additional support? What concepts need revision? Plan for follow-up activities on equivalent fractions or addition of decimals]