Representing Money Different Ways

Overview

In this third lesson of the six-lesson unit, students build on their understanding of Australian coins, notes and dollar–cent relationships. They make, record and explain equivalent representations of money values, including coins, notes, cents, decimal notation and expanded forms.

Learning intentions

Students will:

• recognise that $1 is equal to 100 cents
• represent the same money value in several different ways
• use addition and place-value partitioning to explain equivalent representations
• communicate and justify their thinking using mathematical language

Success criteria

• I can make a money amount using coins and notes.
• I can write the same amount using dollars, cents, decimal notation and an expanded form.
• I can find more than one combination with the same value.
• I can explain why two representations are equivalent.

Curriculum links

• Measurement — recognise the relationship between dollars and cents and represent money values in different ways.
• Number — add and subtract using place value to partition, rearrange and regroup numbers.
• Number — follow and create step-by-step procedures and describe emerging patterns.
• Number — model and solve practical problems involving additive situations and financial contexts.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Open with the money mystery introduction and display the question: “Is $2.50 always made with the same coins?” Show $2.50 as two $1 coins and one 50c coin, then ask students to think of another representation. Students discuss with a partner and share possible answers; the teacher records different combinations without confirming them yet.

2. 5–13 min · Explicit teaching. Use the dollars, cents and expanded-form slides to model that $1 = 100c and $2.50 = 250c. Represent the amount as $2 + 50c, $1 + $1 + 50c, 250c, and $2 + 0.50. Model an expanded form such as $2 + 50c, explaining that the parts combine to make the whole. Students help write matching number sentences and identify which representations use dollars, cents, coins or notes.

3. 13–25 min · Guided investigation. Organise students into pairs and provide play Australian coins and notes. Display the task from the pair investigation instructions: “Make $1.35 in at least three ways. Record each way using coins or notes, decimal notation, cents and an expanded form.” Distribute the equivalent money representations worksheet. Students build each amount, draw or list their coins and notes, and record matching representations. Circulate and ask: “How do you know your combinations have the same value?” and “Can you use fewer coins?”

4. 25–35 min · Partner challenge. Display the challenge on the mystery amount challenge slide. Each pair chooses or is given one amount: $2.50, $3.05, $1.85 or $4.20. Students create at least three equivalent representations, including one representation entirely in cents and one using an expanded form. They then cover one representation and ask another pair to work out the missing amount. Partners check by counting, adding or regrouping the values, and explain any errors respectfully.

5. 35–41 min · Share and reason. Bring the class together using the comparison and discussion slides. Select two pairs to present different representations of the same amount. Discuss why $1 + $1 + 50c and 250c are equal, and how regrouping 100 cents creates another dollar. Highlight efficient counting patterns with 5c, 10c, 20c and 50c coins. Students complete the final worksheet question: “Which representation is easiest to check, and why?”

6. 41–45 min · Exit check. Show the final prompt on the exit-ticket slide: “Represent $3.40 in two different ways. Write it in cents and as an expanded form.” Students complete the response independently on the worksheet or in their maths books, then hold up their answer for a quick teacher scan before packing away materials.

Resources

• the money representations slide deck
• the equivalent money representations worksheet
• Play Australian coins and notes for pairs
• Whiteboard and markers
• Mini-whiteboards or scrap paper
• Pencils and coloured pencils
• Pair trays or envelopes for money materials
• Maths books for students who need extra recording space

Assessment

• During modelling, check whether students can state that $1 equals 100 cents and connect $2.50 with 250 cents.
• During pair work, observe whether students count accurately, record representations clearly and justify equivalence rather than simply copying a combination.
• Use the exit check to identify students who can independently represent $3.40 in two ways, in cents and in expanded form. Re-teach the dollar–cent relationship and regrouping to students who confuse dollars with cents or omit the decimal point.

Differentiation

• Support students with a place-value mat labelled dollars and cents, a reference showing common coin values, and sentence starters such as “These are equal because…” and “I counted…”.
• Begin some students with amounts under $2 and allow them to use physical coins while recording one representation at a time. Pair students strategically and provide adult prompting for counting and regrouping.
• For EAL students, pre-teach and display: amount, value, dollars, cents, equal, combination and expanded form. Use gestures, coin images and repeated oral rehearsal before written recording.
• Extend confident students by asking them to find the greatest number of coins and the fewest number of coins for an amount, then explain why both totals are equal.