Pack and Pour Problems

Overview

This is lesson 15 of 28 in Year 4 Maths Across Aotearoa. Learners use familiar metric relationships to convert and combine measures of length, mass, capacity and volume, choosing useful units and representations to solve practical problems.

Learning intentions

• WALT convert between familiar metric units.
• WALT choose an appropriate unit and representation before calculating.
• WALT combine measurement information to solve practical problems.
• WALT explain and compare solutions using mathematical language.

Success criteria

• I can convert 3 L to 3,000 mL.
• I can show a conversion using a number line, conversion card or calculation.
• I can solve a two-step measurement problem and explain my thinking.
• I can compare two designs with the same capacity.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge tasks are connected to familiar mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: open-ended reasoning and extension opportunities.
• Te Mātaiaho mathematical practices: reasoning, representing, communicating and persevering with problems.

Lesson structure (60 minutes)

1. 0–7 min · Hook and diagnostic. Teacher opens the hook and learning intention slides with an image of two differently shaped drink containers and asks, “Which container holds more? How could we prove it?” Students make a quick estimate, discuss with a partner and share what they already know about litres and millilitres. Record common strategies and misconceptions.

2. 7–17 min · Model conversions. Teacher displays the conversion modelling slides and uses the Units Conversion Ladder as a class reference. Model that 1 L = 1,000 mL, so 3 L = 3,000 mL; connect this to a marked number line and repeated groups of 1,000 mL. Briefly model familiar relationships such as 1 m = 100 cm and 1 kg = 1,000 g, stressing that the unit must be named before calculating. Students explain the direction of each conversion and complete two oral examples with a partner.

3. 17–25 min · Sort and justify. Teacher displays the unit-choice and matching prompt and provides pairs with accessible conversion cards or prepared measure labels. Students match equivalent measures, such as 2 L and 2,000 mL, then sort practical situations by a sensible unit: a classroom length, a lunchbox mass, a drink quantity and a playground distance. Pairs justify one choice using the sentence frame, “I chose ___ because ___.”

4. 25–43 min · Pack and Pour investigation. Teacher introduces the activity using the Pack and Pour instructions and safety slide. In groups of four, students use accessible containers, cups, water or dry rice, and pictorial word problems. They record each problem and solution on the Pack and Pour problem-solving sheet. Students must first circle or write the unit they will use, then represent the information with containers, a drawing, number line or equation. Include the must-do problem: “Convert 3 L to ___ mL.” Groups then solve a two-step problem, for example: “A jug holds 2 L. Sam pours in 500 mL, then adds another 750 mL. How much is in the jug now?” Encourage students to check whether their answer is reasonable.

5. 43–53 min · Compare designs. Teacher displays the design challenge and discussion prompts. Students complete the Try task: compare two container designs with the same capacity, such as 1 L and 1,000 mL, or 1 L made from two 500 mL containers. They draw or arrange the designs, label units and explain why the capacities are equivalent. Can Do learners solve a further two-step problem involving mixed units. Extension learners design two different packing or pouring arrangements with equivalent measures and prove that both work.

6. 53–60 min · Share and exit check. Teacher selects two contrasting solutions and uses the sharing and plenary slides to prompt: “Where did the unit change? How do you know the answer is sensible?” Students explain one representation and complete the final three questions on the reflection and exit questions: convert 3 L to mL, solve a short two-step measurement problem, and state how two designs can have the same capacity. Collect sheets for assessment.

Resources

• the complete measurement conversions and problem-solving slide deck
• the Pack and Pour problem-solving sheet
• the Units Conversion Ladder
• Conversion cards or teacher-prepared equivalent-measure cards
• Number lines and pencils
• Measuring jugs, cups and accessible containers
• Water, dry rice or another low-mess filling material
• Trays, cloths and handwashing supplies
• Pictorial measurement word problems

Assessment

• Listen for accurate unit choices and explanations during the conversion model and card sort; note whether learners understand that 3 L equals 3,000 mL.
• During Pack and Pour, check that learners identify the unit before calculating, represent the problem clearly and combine measures accurately.
• Use the exit questions to identify learners needing further practice with conversion, two-step reasoning or equivalence.

Differentiation

• Support learners with the conversion ladder, labelled containers, pre-marked number lines, pictorial problems and the sentence frames “___ is the same as ___” and “First I ___, then I ___.”
• Allow concrete, drawn, oral and symbolic solutions. Pair learners strategically and provide a reduced-choice set of conversion cards where needed.
• For learners developing English, explicitly teach and gesture the words capacity, volume, equivalent, litre, millilitre, kilogram and gram; accept oral explanations alongside written work.
• Challenge confident learners to design equivalent measures in different units, solve problems with more than one possible method and explain why their answers are reasonable.