Converting units of measurement
Converting between different-sized units within one measurement system, and using conversions in multi-step problems
About three lessons of 45 to 60 minutes
Is a 2-litre bottle enough for 9 cups of soup?
A recipe needs 9 cups of soup. You only have a 2-litre bottle of stock and no cup measure. Can you tell if there is enough without pouring it out and guessing? You can, if you can convert between units: change everything into the same-sized unit, then compare or combine like normal numbers.
Every measurement system, metric or customary, is really a chain of fixed ratios: 1 metre is always 100 centimetres, 1 foot is always 12 inches. Once you know a chain's conversion factor, converting is just multiplying or dividing by it, and multi-step real problems become ordinary arithmetic once every measurement speaks the same unit.
- 3.5 m to cm3.5 x 100 = 350 cm, since 1 m is 100 cm
- 2 kg to g2 x 1000 = 2000 g, since 1 kg is 1000 g
- A 2 L bottle poured into 250 mL cups2000 mL / 250 mL = 8 cups worth, not quite enough for 9
- A ribbon 2 m 40 cm cut into 30 cm pieces240 cm / 30 cm = 8 equal pieces
What students will be able to do
Students will convert among different-sized measurement units within the metric system (length, mass, capacity) and within the customary system (length, weight, capacity) by multiplying or dividing by the fixed conversion factor between units, and will use these conversions to solve multi-step real-world problems.
- I can name the conversion factor between common metric units, such as 1 m = 100 cm.
- I can convert a larger unit to a smaller one by multiplying.
- I can convert a smaller unit to a larger one by dividing.
- I can convert customary units, such as feet to inches or pounds to ounces.
- I can solve a multi-step word problem that requires converting units before finishing the calculation.
Standards this unit teaches
- 5.MD.A.1Common Core (US)Convert within a measurement system
Convert among different sized units within one measurement system and use the conversions to solve problems.
- AC9M5M01Australian Curriculum v9 (ACARA)Convert metric units (Year 5)
Convert between common metric units of length, mass and capacity and use decimal measurements suited to the problem.
- AC9M6M01Australian Curriculum v9 (ACARA)Choose metric units (Year 6)
Choose suitable metric units for length, mass and capacity, combining units where needed for a more accurate measure.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
- Grade 5 multiplication teaching unitconverting to a smaller unit means multiplying by the conversion factor
- Grade 5 long division teaching unitconverting to a larger unit means dividing by the conversion factor
- How to teach measurementthe units and tools used to measure length, mass and capacity
- Place valuemetric conversions are powers-of-ten shifts, just like place value
Words to teach and display
- Measurement system
- a family of units that all measure the same kind of thing, such as the metric system (metres, grams, litres) or the customary system (feet, pounds, gallons)
- Conversion factor
- the fixed number that relates two units, such as 100 (1 m = 100 cm) or 12 (1 ft = 12 in)
- Convert
- to rewrite a measurement in a different-sized unit without changing the actual amount
- Metric system
- the base-ten measurement system using metres, grams and litres, where units relate by powers of ten
- Customary system
- the US measurement system using inches, feet, pounds and gallons, where units relate by varied conversion factors
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. Every unit pair has a fixed conversion factor
ConcreteTwo units that measure the same kind of quantity, such as metres and centimetres, always relate by one fixed number, the conversion factor. 1 metre is always 100 centimetres -- not sometimes 90, not sometimes 110, always exactly 100. Once you know that factor, you can move between the two units for any amount, forever.
The double number line below shows metres and centimetres scaling up together: as the metres count 0, 1, 2, 3, the centimetres count 0, 100, 200, 300 at the very same points, because the ratio between them, 1 to 100, never changes.
- How many centimetres are in 1 metre?
- Why does the conversion factor between two units never change?
2. Bigger to smaller: multiply. Smaller to bigger: divide.
PictorialConverting a bigger unit into a smaller one means the number gets bigger (it takes more small units to make the same amount), so you multiply by the conversion factor. Converting a smaller unit into a bigger one means the number gets smaller, so you divide.
3.5 m to cm: metres to centimetres is bigger unit to smaller unit, so multiply: 3.5 x 100 = 350 cm. 250 cm to m: centimetres to metres is smaller unit to bigger unit, so divide: 250 / 100 = 2.5 m. The same multiply-or-divide logic works for any pair: 3 lb to oz (bigger to smaller, multiply by 16, giving 48 oz), or 24 in to ft (smaller to bigger, divide by 12, giving 2 ft).
Convert 2 kg 300 g into grams, and convert 5 ft 3 in into inches.
- 2 kg 300 g: convert the 2 kg part to grams (bigger to smaller, multiply): 2 x 1000 = 2000 g. Add the 300 g already there: 2000 + 300 = 2300 g.
- 5 ft 3 in: convert the 5 ft part to inches (bigger to smaller, multiply): 5 x 12 = 60 in. Add the 3 in already there: 60 + 3 = 63 in.
Answer: 2 kg 300 g = 2,300 g. 5 ft 3 in = 63 in.
- When converting metres to centimetres, do you multiply or divide? Why?
- When converting centimetres to metres, do you multiply or divide? Why?
3. Multi-step real-world problems
AbstractReal problems rarely ask you to convert and stop -- they ask you to convert, then do something else with the answer. The key habit is to convert every measurement into the same unit first, then solve the rest of the problem as ordinary arithmetic.
A ribbon is 2 m 40 cm long and is cut into pieces 30 cm each. First convert the whole ribbon to centimetres: 2 m 40 cm = 200 cm + 40 cm = 240 cm. Now the division makes sense in matching units: 240 cm / 30 cm = 8 pieces.
A water tank holds 3 L 250 mL. It is poured into bottles that hold 250 mL each. How many full bottles can be filled?
- Convert the tank's capacity into millilitres, the same unit as the bottles: 3 L = 3 x 1000 = 3000 mL, plus the 250 mL already there: 3000 + 250 = 3250 mL.
- Divide by the size of one bottle: 3250 / 250 = 13.
Answer: 13 full bottles can be filled.
- Why must the tank and the bottles be in the same unit before dividing?
- What is the first step in any multi-step conversion problem?
Common misconceptions and how to address them
MisconceptionConverting to a smaller unit means the amount gets smaller, so you divide.
Why it happens: Students link 'smaller unit' with 'smaller number' without noticing it takes more of a small unit to equal the same amount.
How to address it: The actual amount never changes, only how it is counted. It takes 100 small centimetres to make 1 big metre, so converting metres to centimetres needs a bigger number: multiply. Ask 'does it take more or fewer of the new unit to measure the same thing?' every time.
MisconceptionYou can add or subtract measurements in different units directly, such as 2 m + 40 cm = 42.
Why it happens: Students treat the numbers as plain numbers and ignore that the units are different sizes.
How to address it: Convert to the same unit before combining. 2 m + 40 cm becomes 200 cm + 40 cm = 240 cm (or 2 m + 0.4 m = 2.4 m). Numbers with different-sized units cannot be combined until they match.
MisconceptionThe conversion factor between two units is the same for every pair, such as always multiplying or dividing by 100.
Why it happens: The metric system's most familiar conversions (m to cm, L to mL) do use 100 or 1000, so students assume every conversion, including customary ones, uses a round metric-style number.
How to address it: Every unit pair has its own conversion factor: 1 ft is 12 in, 1 lb is 16 oz, 1 gal is 4 qt. Keep a reference table of common conversion factors while these are being learned, rather than guessing.
Guided practice (with answers)
1. Convert 4 m to cm.
Answer: 400 cm, since 4 x 100 = 400.
2. Convert 1,500 mL to L.
Answer: 1.5 L, since 1500 / 1000 = 1.5.
3. Convert 3 lb to oz.
Answer: 48 oz, since 3 x 16 = 48.
4. Convert 2 gal to qt.
Answer: 8 qt, since 2 x 4 = 8.
5. A rope is 5 m long and is cut into pieces 20 cm each. How many pieces?
Answer: 25 pieces. Convert 5 m to 500 cm, then 500 / 20 = 25.
Independent practice worksheets
Set the matching ChalkBee measurement worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with single conversions before moving to the multi-step word problems.
Differentiation
- Keep a visible reference table of the common conversion factors (1 m = 100 cm, 1 kg = 1000 g, 1 ft = 12 in, 1 lb = 16 oz) while students are still learning them.
- Use the double number line to show any single conversion before asking for it as a bare calculation.
- Practise 'bigger to smaller, multiply; smaller to bigger, divide' as a spoken rule before applying it to unfamiliar unit pairs.
- Start multi-step problems with both measurements already in a compatible form, before requiring the conversion step to be spotted independently.
- Convert across more than two steps, such as millimetres to metres to kilometres in one problem.
- Solve problems that mix the metric and customary systems by first converting a real approximate rate (such as 1 inch is about 2.5 cm), discussing why this conversion is only approximate unlike within-system conversions.
- Write an original multi-step word problem that requires a conversion, and solve a partner's problem.
- Investigate why the metric system's conversions are always powers of ten while the customary system's are not, connecting to place value.
Assessment: exit ticket
A three-question exit ticket for the last five minutes, sampling both directions of conversion and a multi-step problem.
1. Convert 6.2 kg to g.
Answer: 6,200 g, since 6.2 x 1000 = 6200.
2. Convert 7 ft to in.
Answer: 84 in, since 7 x 12 = 84.
3. A tank holds 3 L 250 mL of water, poured into 250 mL bottles. How many bottles can be filled?
Answer: 13 bottles. Convert 3 L 250 mL to 3250 mL, then 3250 / 250 = 13.
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 the fixed conversion factor (section 1), Lesson 2 multiply-or-divide direction (section 2), Lesson 3 multi-step problems plus the exit ticket (section 3 and assessment).
- Language to keep saying: does it take more or fewer of the new unit, bigger to smaller multiply, smaller to bigger divide, convert first then solve. These target the three main misconceptions directly.
- This unit covers both metric and customary conversions since the US standard names 'a given measurement system' without restricting to one; most ChalkBee measurement worksheets default to metric with an imperial (customary) toggle, so use whichever matches your class's current unit of study.
- Curriculum note: ACARA v9 covers metric conversion across two years -- converting between common metric units at Year 5 (AC9M5M01), then choosing and combining suitable metric units at Year 6 (AC9M6M01) -- which together match the scope of this single US Grade 5 standard, since ACARA does not teach the US customary system.
- Present mode and print both work: use Present to build the double-number-line conversion live, then print for independent conversion and word-problem practice.