Learning Units of Length and Capacity — Build a Feel for Quantity Before Conversion
"1 L = 10 dL. 1 L = 1000 mL." Memorised as a table — and then the hand stops at "how many dL is 3 L 2 dL?"
I assumed at first that not enough had been memorised, and reached for more conversion problems. Looking into it, I had the order backwards. What the national curriculum commentary asks for isn't repetition of conversions but a richer feel for the size of quantities.
Units run from length and capacity in grade 2 through weight in grade 3 — a quietly long stretch where children get stuck.
Where it goes wrong
Cause 1: the unit has no felt size
Few adults can picture 1 dL. Children are the same, and a unit with no felt size becomes symbol memorisation that peels straight off. Deciliters in particular barely appear in daily life, which makes them the hardest of the school units to develop a feel for.
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), asks that teaching "actively incorporate activities of investigating and confirming the size of various concrete objects, so as to enrich the sense of the size of quantities" (Measurement). Schools are also expected to move through a sequence: compare directly, compare via something in between, measure with a handy unit of your own, and only then measure with a shared unit like cm or L. The shared unit comes last.
Cause 2: the conversion factor keeps changing
cm → mm is ×10, m → cm is ×100, km → m is ×1000, L → dL is ×10, L → mL is ×1000. The factors are all over the place, so a false generalisation like "unit conversion means ×10" falls apart.
Cause 3: compound notation like "3 L 2 dL"
Turning a quantity written in two units into one unit uses place value (groups of ten) and unit conversion at the same time. If either is weak, it shows up here.
How to teach it at home
Step 1: build one personal benchmark per unit
- 1 cm = the width of your child's finger (roughly)
- 1 m = arms spread wide (a little short for younger children)
- 1 L = one carton of milk
- 1 dL = half a measuring cup (100 mL)
- 1 kg = a 1 L bottle of water
Put one "this much is 1 ___" into the body at a time. A kitchen measuring cup is the finest teaching material there is. Pour barley tea 1 dL at a time and count how many cups fill a litre, and 1 L = 10 dL stops being memorisation and becomes experience.
Step 2: draw the conversion table as a "×10 staircase"
Draw mm → cm → m → km as one flight of stairs: "move one step across and a zero is added or removed." Because only the gap between m and cm is two steps (×100), drawing it makes that a memorable special case.
Step 3: use money for compound notation
A child who struggles with "3 L 2 dL" still understands "320 yen is three 100-yen coins and two 10-yen coins." Compound units have the same structure as place value, so money makes the bridge.
How to practise
- Grade 2 starts with Length (cm, mm, m) and Capacity (L, dL, mL). Measuring the real thing before solving makes a visible difference
- Grade 1's Comparing Length and Comparing Capacity compare without units at all. If that's shaky, going back is the fast route
- Grade 3 adds Length (km and Tape Measure), Weight (kg, g, t) and Decimal Units (Capacity and Length). Each time a new unit appears, add one more personal benchmark
Frequently asked questions
Q. Will lots of conversion problems fix it?
A. Working through volume without a felt sense tends to train guessing between ×10, ×100 and ×1000. Before the worksheet, ask "how much is 1 L?" and check that a milk carton comes back.
Q. Deciliters are never used in real life — why teach them?
A. They're used as material for experiencing a base-ten structure, where the unit changes every ten. Read as "practice ground for place value" rather than "never used, so it doesn't matter", and the connection to decimals becomes visible — Decimals in grade 3 starts from 0.1 L = 1 dL.
This is the topic you can push furthest at home, with nothing more than a kitchen and a tape measure. On days when the worksheets don't get done, measuring something is still progress.
This article is written by a parent who builds diglabo. I am not a teacher or an education specialist. The general guidance here is based on how the topic is taught in Japanese primary schools, checked against Japan's national curriculum guidelines.
diglabo's worksheets follow the Japanese curriculum. What that means if you are outside Japan