Compare, Order, Total

Overview

In this 20-minute small-group lesson, students use place value to compare and order two-digit numbers, then apply the same reasoning to order and group New Zealand coins and notes by value. The teacher makes the mathematical thinking visible through talk, materials and quick explanations.

Learning intentions

• WALT the place value of digits helps with comparing and ordering.
• WALT New Zealand coins and notes can be ordered and grouped to find the total value.
• We are learning to explain our mathematical thinking using words, materials and symbols.
• We are learning to check whether our answer makes sense.

Success criteria

• I can identify the tens and ones in a two-digit number.
• I can compare two numbers by looking at the tens first, then the ones.
• I can order New Zealand coins and notes from least to greatest value.
• I can group coins and notes and find the total value.

Curriculum links

• Practices — representing, reasoning, communicating and checking mathematical ideas.
• Number — recognising that the position of a digit determines its value.
• Number — comparing, ordering and combining numbers and money amounts.
• Mathsteasers — using challenging questions to deepen understanding and explain more than one possible strategy.

Lesson structure (20 minutes)

1. 0–3 min · Notice and wonder. Teacher displays 24 and 42 on the opening comparison slide and asks, “Which number is greater? How do you know?” Students tell their partner, then point to the tens and ones in each number. Prompt: “What changed when the digits changed places?” Accept drawings, materials or spoken explanations.

2. 3–7 min · Build the strategy. Teacher models 34 and 39 using tens-and-ones drawings or place-value equipment, recording 34 < 39. Revisit the place-value strategy slide and explicitly compare the tens first, then the ones if the tens are equal. Students use the hundreds chart and 100-square pack to locate selected numbers and explain which is greater, less or equal. Ask: “What would you look at first?” and “What tells you that 39 is only five more than 34?”

3. 7–12 min · Guided money sort. Teacher places a small selection of New Zealand coins and notes where both students can see them and uses the money ordering slide to establish the task: order the money from least to greatest, then group amounts that have the same total. Students handle the money, discuss their choices and arrange it in order. Include examples such as 10c, 20c, 50c, $1, $2, $5 and $10, using only real or clearly labelled play money. Ask: “How do you know $2 is worth more than 50c?” and “Can two different groups have the same total?”

4. 12–17 min · Independent practice with teacher conferencing. Teacher distributes the compare, order and total-value worksheet and supports each student to complete the short tasks: identify tens and ones, compare two-digit numbers, order money amounts, and calculate two totals. Students record a number sentence or drawing for at least one answer. Confer with one student at a time: “Show me the part that helped you decide.” Encourage the other student to rehearse an explanation with the materials while waiting.

5. 17–20 min · Share and check. Teacher returns to the final reasoning and exit question slide and presents: “Which is greater: 46 or 64? Which is worth more: $1 and 20c or 50c and 50c? Prove it.” Students answer individually, explain their reasoning, and complete a final verbal check: “First I looked at…, then I…”. Correct misconceptions immediately, particularly treating the digit 6 as having the same value in 46 and 64, or confusing the number of coins with their total value.

Resources

• the place-value and money comparison slide deck
• the compare, order and total-value worksheet
• New Zealand play coins and notes, or labelled coin and note images
• Tens-and-ones equipment, place-value cards or quick drawings
• the hundreds chart and 100-square pack
• Pencils and a suitable writing surface

Assessment

• Listen for students comparing tens before ones and using language such as greater than, less than, equal to, tens, ones and total.
• Observe whether students order money by value rather than by size, colour or number of pieces.
• Use the final two comparison questions as an exit check. Record whether each student can compare numbers and calculate a money total independently, with prompts or with materials.

Differentiation

• For support, limit number comparisons to numbers below 50, provide tens-and-ones equipment, and use sentence starters: “___ is greater because…” and “The total is…”.
• Keep labelled money values visible and allow students to touch, move and recount the coins or notes. Accept oral explanations, pointing, drawing or recording as evidence.
• For a student ready for challenge, ask them to find two different groups of coins with the same total, or to explain why 58 is greater than 49 without using the hundreds chart.
• For EAL learners, pair the spoken terms with symbols and gestures: greater than (>), less than (<), equal to (=), tens, ones and total. Repeat and rephrase questions rather than increasing the amount of written work.