Measurement: units, formulas, and word problems
Converting measurement units, applying area and perimeter formulas, and solving multi-unit measurement word problems
About three lessons of 45 to 60 minutes
Real measuring needs converting, formulas, and multi-step thinking
A recipe, a garden, and a road trip all use measurement, but rarely in the one unit you started with. This unit ties together three real skills: converting between units of the same kind (kilometres to metres, kilograms to grams), using a formula instead of counting for a rectangle's area and perimeter, and solving word problems that mix units, fractions, or money.
The three skills combine constantly in real life: converting is often the first step inside a bigger word problem, and a formula is just a fast, reliable shortcut for something you could still count by hand.
- A hiking trail that is 3 km long3 km = 3000 m, since 1 km is 1000 m
- A rectangular garden 8 m by 5 mperimeter = 2 x (8+5) = 26 m, area = 8 x 5 = 40 sq m
- 750 mL of milk poured from a 2 L jug2000 - 750 = 1250 mL left, a word problem mixing volume and subtraction
What students will be able to do
Students will convert measurements within one system (length, mass, volume, and time), apply the area and perimeter formulas for rectangles to real problems, and solve multi-step measurement word problems, including problems involving fractions, decimals, and money.
- I can convert a measurement to a smaller or larger unit within the same system.
- I can find the perimeter of a rectangle using 2 x (length + width).
- I can find the area of a rectangle using length x width.
- I can solve a word problem that combines measurement units, and give my final answer in the unit the question asked for.
Standards this unit teaches
- 4.MD.A.1Common Core (US)Convert measurement units
Convert measurements within one system, such as kilometres to metres, and record the conversions.
- 4.MD.A.3Common Core (US)Area and perimeter formulas
Apply area and perimeter formulas for rectangles to real world and mathematical problems.
- 4.MD.A.2Common Core (US)Measurement word problems
Solve word problems involving distances, time, volume, mass, and money, including fractions and decimals.
- AC9M4M01Australian Curriculum v9 (ACARA)Measure with metric units
Measure and compare objects with familiar metric units of length, mass and capacity using labelled instruments.
- AC9M3M02Australian Curriculum v9 (ACARA)Perimeter and area (Year 3 bridge)
Measure and approximate the perimeter and area of shapes and enclosed spaces using suitable formal and informal units. This unit's formula work reaches toward the Year 4 use of this Year 3 descriptor.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Converting measurement units
AbstractEvery system of units has a fixed relationship between its steps: 1 km = 1000 m, 1 kg = 1000 g, 1 L = 1000 mL. Going from the bigger unit to the smaller unit means there will be MORE of them, so multiply; going from smaller to bigger means there will be FEWER, so divide.
Time is the one exception to the metric 'multiply or divide by 1000, 100, or 10' pattern: there are 60 minutes in an hour and 60 seconds in a minute, not a power of ten, so time conversions must be learned as their own special case.
Convert 3 km to metres, and convert 4500 m to kilometres and metres.
- 3 km to m: bigger to smaller, so multiply by 1000. 3 x 1000 = 3000 m.
- 4500 m to km and m: smaller to bigger, so divide by 1000. 4500 ÷ 1000 = 4 remainder 500.
- The remainder stays in the smaller unit: 4 km 500 m.
Answer: 3 km = 3000 m, and 4500 m = 4 km 500 m.
- Convert 2 kg 750 g to grams. Is that bigger-to-smaller or smaller-to-bigger, and which operation does that mean?
- Why doesn't the 'divide or multiply by 1000' rule apply directly to converting hours to minutes?
2. Area and perimeter formulas for rectangles
AbstractPerimeter is the distance all the way around a shape's edge: for a rectangle, add all four sides, or use the shortcut 2 x (length + width) since opposite sides match. Area is how much space is inside, found for a rectangle by multiplying length x width, the formula version of counting unit squares row by row.
A rectangular garden is 8 m long and 5 m wide. Find its perimeter and its area.
- Perimeter: 2 x (length + width) = 2 x (8 + 5) = 2 x 13 = 26 m.
- Area: length x width = 8 x 5 = 40 square metres.
Answer: Perimeter = 26 m, Area = 40 square metres.
- For a rectangle 12 cm by 7 cm, what is the perimeter, and what is the area?
- Why does area use square units (like square metres) while perimeter uses plain length units (like metres)?
3. Multi-step measurement word problems
AbstractReal measurement problems often need a conversion AND an operation, sometimes more than once, and always finish by checking that the final answer is stated in the unit the question actually asked for.
A second common pattern is measuring what's left after using some of a total, such as a jug of liquid: convert everything to the same unit first, then subtract.
A ribbon is 4 metres long and is cut into 5 equal pieces. How long is each piece, in centimetres?
- Convert the total length to centimetres first: 4 m = 400 cm.
- Divide into the 5 equal pieces: 400 ÷ 5 = 80.
Answer: Each piece is 80 centimetres long.
- A recipe needs 750 mL of milk from a 2 L jug. How much milk is left in the jug after measuring it out?
- Why is converting to a single common unit usually the first move in a multi-step measurement problem?
Common misconceptions and how to address them
MisconceptionMultiplying when converting from a smaller unit to a bigger unit, or dividing when converting from bigger to smaller, the operation direction reversed.
Why it happens: Without a check step, it is easy to guess the operation rather than reason about whether the new unit will need more or fewer of it.
How to address it: Before converting, ask: will the new unit need MORE pieces or FEWER pieces to describe the same amount? Bigger to smaller needs more (multiply); smaller to bigger needs fewer (divide).
MisconceptionApplying the metric 'multiply or divide by a power of ten' pattern to converting hours, minutes, and seconds, for example treating 1 hour as 100 minutes.
Why it happens: Every other conversion in this unit is a power of ten, so time gets swept into the same expectation even though it genuinely is not.
How to address it: Call out time as a special case every time it appears: 60 minutes in an hour, 60 seconds in a minute, not 10 or 100.
MisconceptionMixing up the area and perimeter formulas, for example multiplying length by width to find perimeter, or adding the sides to find area.
Why it happens: Both formulas use the same two side lengths, so without a clear anchor for what each formula actually measures, they are easy to swap.
How to address it: Say the meaning before the formula every time: perimeter is walking the edge (so you add lengths), area is filling the inside (so you multiply lengths to count square units).
MisconceptionStopping a multi-step word problem after the first calculation and reporting that number, without converting the final answer into the unit the question asked for.
Why it happens: Getting a correct-looking number feels like finishing, so the last check (does this match the units the question asked?) gets skipped under time pressure.
How to address it: Re-read the question's last sentence before writing a final answer, and underline the unit it asks for; compare that to the unit of your last calculation.
Guided practice (with answers)
1. Convert 5 kg 400 g to grams.
Answer: 5400 g, since 5 kg = 5000 g and 5000 + 400 = 5400.
2. Convert 6200 mL to litres and millilitres.
Answer: 6 L 200 mL, since 6200 ÷ 1000 = 6 remainder 200.
3. Find the perimeter and area of a rectangle 10 m by 6 m.
Answer: Perimeter = 2 x (10+6) = 32 m. Area = 10 x 6 = 60 square metres.
4. A wall is 9 m long and 3 m tall. How much paint-coverage area does it have?
Answer: 27 square metres, since 9 x 3 = 27.
5. A jug has 2 L 500 mL of water. After using 900 mL for a recipe, how much is left in millilitres?
Answer: 1600 mL, since 2 L 500 mL = 2500 mL and 2500 - 900 = 1600.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Split practice across a lesson each for converting, formulas, and word problems.
Differentiation
- Keep a laminated conversion reference card (1 km=1000 m, 1 kg=1000 g, 1 L=1000 mL, 1 hr=60 min) on the desk during early practice.
- For formulas, always draw or tile the rectangle before applying the formula, so the formula stays connected to counting.
- Break word problems into an explicit two-step template: 'first I will ___, then I will ___' before calculating.
- Convert between two non-adjacent units in one step, such as millimetres directly to kilometres.
- Find the missing side length of a rectangle given its perimeter or area and one side.
- Write a three-step measurement word problem of your own, mixing at least two different unit types (such as length and money).
Assessment: exit ticket
A short exit ticket sampling converting, formulas, and a word problem.
1. Convert 7200 m to kilometres and metres.
Answer: 7 km 200 m, since 7200 ÷ 1000 = 7 remainder 200.
2. Find the perimeter and area of a rectangle 15 cm by 4 cm.
Answer: Perimeter = 2 x (15+4) = 38 cm. Area = 15 x 4 = 60 square cm.
3. A bottle holds 1 L 400 mL. After pouring out 550 mL, how much is left?
Answer: 850 mL, since 1400 - 550 = 850.
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 converting units (section 1), Lesson 2 area and perimeter formulas (section 2), Lesson 3 measurement word problems plus the exit ticket (section 3 and assessment).
- Language to keep saying: more pieces means multiply, fewer pieces means divide; perimeter walks the edge, area fills the inside; check the final unit against the question.
- The area formula in section 2 is deliberately linked back to the Grade 3 counting-unit-squares unit; if that unit has been taught, open this lesson by asking students to derive the formula themselves from the counting method rather than presenting it as new.
- Curriculum note: ACARA's AC9M4M01 covers measuring with metric units at Year 4, matching the conversion half of this unit closely; the area-and-perimeter-formula half bridges from the Year 3 AC9M3M02 descriptor, since ACARA folds formal formula use into general measurement fluency rather than a separate Year 4 code.
- Present mode and print both work: use Present to model the paint-coverage and jug word problems live, then print the worksheets for independent practice.