Icing One Whole

Overview

Students explore whether Ravi has iced one whole cake by combining fractions with the same denominator. They use part–whole models and fraction notation to add eighths within one whole, building on prior learning about equal parts, numerators and denominators.

Learning intentions

• WALT add fractions with the same denominator within one whole.
• WALT read, write and represent eighths as fractions.
• WALT use a part–whole model to explain why fractions are equal to one whole.
• WALT communicate mathematical thinking using precise fraction vocabulary.

Success criteria

• I can identify the denominator and numerator in a fraction.
• I can add eighths by combining the numerators and keeping the denominator the same.
• I can show my answer with a model, fraction sentence or diagram.
• I can explain when fractions are equal to one whole.

Curriculum links

• Mathematics and Statistics — fractions, part–whole relationships and addition within one whole.
• Mathematics and Statistics — communicating mathematical ideas using representations, symbols and appropriate vocabulary.
• Mathsteasers — using challenging questions to deepen understanding and encourage higher-order thinking.
• Mathsteasers / Alignment — connecting mathematical challenge with relevant textbook learning.

Lesson structure (30 minutes)

1. 0–4 min · Hook: Is it one whole? Teacher displays a picture of a cake divided into eight equal parts and asks, “Has Ravi put icing on one whole cake?” Open with the cake investigation hook and accept estimates without confirming. Students quietly notice the iced and uniced parts, then share a first idea with a partner.

2. 4–9 min · Build the model. Teacher uses the fraction circles cut-out pack or a large drawn circle to model eighths, explicitly naming part, part–whole model, numerator and denominator. Teacher demonstrates that 3/8 + 4/8 = 7/8: the denominator stays eight because the parts are still eighths, while the numerators are combined. Students build or sketch examples and chorally read each fraction.

3. 9–14 min · Solve the investigation. Teacher presents Ravi’s icing as a fraction addition problem through the worked icing example and asks, “How many eighths are iced altogether? Is that equal to one whole?” Students solve using a drawing, fraction circles or an equation, then explain their reasoning to a partner. Prompt students to use: “___ eighths and ___ eighths make one” and “___ eighths and ___ eighths are equal to one.”

4. 14–24 min · Guided and independent practice. Teacher refers students to textbook pages 149–151, modelling the first question and checking that students identify the denominator before calculating. Students complete selected questions independently, then compare strategies with a partner. Students may record working on the eighths addition practice sheet; encourage a model alongside every equation. Circulate and ask, “What does the denominator tell us?” and “How do you know your answer is less than, or equal to, one whole?”

5. 24–28 min · Apply and discuss. Teacher selects two different solutions, including one visual model, and displays them using the strategy comparison slides. Students decide whether each solution is correct and justify their thinking. Address the misconception that both numerator and denominator should be added: contrast 2/8 + 3/8 = 5/8 with the incorrect 5/16.

6. 28–30 min · Exit check. Teacher asks students to complete the final question on the two-minute exit check: “4/8 + 3/8 = ___; draw or describe a model. Is the answer equal to one whole? Explain.” Students hand in the response before beginning the next lesson or pack-up routine.

Resources

• the complete investigation slide deck
• the eighths addition practice sheet
• the fraction circles cut-out pack
• Mathematics textbook, pages 149–151
• Mathematics workbook, pages 117–118
• Board and markers
• Pencils and coloured pencils
• Optional large paper cake model divided into eight equal parts

Assessment

• During modelling, check whether students can identify the numerator and denominator and explain what each represents.
• During practice, listen for students keeping the denominator unchanged when adding eighths; ask them to justify answers with a model or words.
• Use the exit check to identify students who can add within one whole and recognise when a sum equals 8/8, or one whole.

Differentiation

• Support students with the fraction circles, a pre-drawn eight-part cake and the sentence starters. Read questions aloud and rehearse the vocabulary orally before writing.
• Work with a small group using concrete eighths: physically combine parts, count them, and match the model to the equation.
• For EAL learners, pair each word with a labelled visual and provide repeated language frames: “The denominator is ___ because…” and “The numerator shows ___ parts.”
• Extend confident students by asking them to find two different additions that make one whole, such as 3/8 + 5/8, and explain why any numerator pair totalling eight equals 8/8.