Exploring, visualising, and converting fractions greater than 1
Understand, visualise, and convert between mixed numbers and improper fractions using concrete representations and numerical steps.
DO: Project slide while students log in or sit on floor. Introduce lesson goal clearly.
WORK: Read WALT and WILF aloud with the class. Ask 2-3 students to explain in their own words what a fraction greater than 1 looks like.
RECORD: Ensure student math exercise books are open to today's heading: Improper Fractions & Mixed Numbers.
FINISH: 2 minutes intro max.
CHECK: Quick thumbs up/middle if students recall what numerator and denominator mean.
Imagine ordering pizzas cut into equal slices. When we have more slices than one whole pizza, we can name the amount in two different ways!
🍕 Pizza Slices Activity: Slices make whole pizzas!
• 4 slices make 1 whole pizza.
• If you have 5 slices, you have 1 whole pizza and 1 slice left over!
• Written as a fraction: 5 quarters (54) = 114.
DO: Use the interactive buttons on the slide to test different slice numbers (e.g. 5 quarters, 7 thirds, 9 halves).
WORK: Ask students: "If 1 pizza has 4 slices, how many slices do 2 whole pizzas have? What about 3 pizzas?"
RECORD: Have students sketch 2 pizzas cut in quarters in their book and shade 5 slices.
FINISH: 5 minutes visual exploration.
CHECK: Ask: "Why is 5/4 called 'improper'? Because the top number is bigger than the bottom number!"
Has a whole number part AND a fraction part.
The numerator (top) is larger than or equal to the denominator (bottom).
DO: Click on tick marks along the number line (e.g., at 5/4, 6/4, 7/4).
WORK: Point out how 1 is equivalent to 4/4, 1 1/2 is equivalent to 6/4 or 3/2, and 2 is 8/4.
RECORD: Students write definitions in exercise books: Mixed Number = Whole + Fraction. Improper Fraction = Top ≥ Bottom.
FINISH: 4 minutes.
CHECK: Call on a student: "Is 4/4 an improper fraction? Yes! The numerator equals the denominator."
DO: Chant "Multiply the whole by the bottom, add the top!" with the class twice.
WORK: Model 3 1/4: 3 x 4 = 12, 12 + 1 = 13, result is 13/4. Note that the denominator NEVER changes!
RECORD: Have students copy the golden rule and example 3 1/4 = 13/4 into their books.
FINISH: 4 minutes.
CHECK: Ask: "Why does the denominator stay 4? Because the size of the pieces hasn't changed!"
DO: Walk through 11/4. Ask students: "What is 11 divided by 4?" (2 remainder 3).
WORK: Emphasise that the quotient (2) is the whole number, and the remainder (3) sits on top of the original denominator (4).
RECORD: Have students write 11/4 = 11 ÷ 4 = 2 3/4 in their books.
FINISH: 4 minutes.
CHECK: Ask: "What happens if there is no remainder? It's just a whole number!" (e.g. 12/4 = 3).
Work out these 4 conversions on your mini-whiteboard or exercise book. Click each card to check your steps!
DO: Give students 2-3 minutes to solve these 4 questions on mini-whiteboards.
WORK: Reveal answers one by one as students hold up whiteboards. Scan room for misconceptions (e.g. changing denominator).
RECORD: Note students who need Tier 1 support for the upcoming task stations.
FINISH: 5 minutes.
CHECK: 3/4 or 4/4 correct ready for Tier 2/3.
Select your entry tier or work through in order with your partner!
A. Convert to Improper:
B. Convert to Mixed:
A. Convert to Improper:
B. Convert to Mixed:
1. Compare: Which is larger: 325 or 165? Show why!
2. Pizza Context: Sam ordered 5 pizzas cut into 6 slices each. Friends ate 22 slices. Express the eaten pizza as a mixed number and improper fraction.
3. Convert: 578 to improper fraction.
DO: Direct students to choose Tier 1, 2, or 3 based on their mini-whiteboard check.
WORK: Teacher circulates to support Tier 1 table while Tier 2/3 work collaboratively.
RECORD: Answers written in exercise books with full working shown.
FINISH: 10-12 minutes station work.
CHECK: Reveal answers tier by tier for self-marking.
You are now ready to complete Page 1:11 (Improper fractions, mixed numbers) in your workbook!
Multiply whole number by denominator, add numerator!
(Questions 1a to 1l)
Divide bottom into top! Remainder is new numerator.
(Questions 2a to 2l)
How confident do you feel starting Page 1:11? Show your teacher 1 to 5 fingers before picking up your workbook!
DO: Hand out textbook page 1:11 or direct students to open workbooks.
WORK: Conduct Fist-to-Five check. Pull 1-2 finger students to teacher table for immediate scaffolded support.
RECORD: Independent completion of page 1:11.
FINISH: Remaining class time (15-20 mins).
CHECK: Collect or review completed 1:11 sheets at end of lesson.
Select a slide to see accompanying pedagogical notes and teaching tips.