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Capacity Chains: Pour, Drink, Top Up

Maths · Stage 3
Year 5
Lesson Guide
Explanation
Capacity uses litres and millilitres, and a litre is a thousand millilitres — the same times-a-thousand step as kilometres and metres. One and a half litres is fifteen hundred millilitres; seven hundred and fifty millilitres is zero point seven five litres. Before any chain of pouring starts, put everything into millilitres so the arithmetic stays in whole numbers, and keep a few sizes in mind as a check: a can is about three hundred and seventy-five, a carton a litre or two, a bucket ten.
Your Turn
Convert 2 L to mL and 2 500 mL to L. Check: 2 000 mL; 2.5 L.
Watch Out
1.5 L is 1 500 mL, not 150. Three columns, because a litre is a THOUSAND millilitres.
Explanation
A single move on a single container is an addition or a subtraction. A litre bottle with two hundred and sixty millilitres poured out has seven hundred and forty left. A chain is a sequence of those: a jug with eight hundred, drink one hundred and fifty, add four hundred — six hundred and fifty, then one thousand and fifty. When several equal amounts are poured, multiply first: three glasses of three hundred and fifty is one thousand and fifty, then subtract that from two litres. Write the amount after every move.
Your Turn
A jug has 800 mL. 150 mL is drunk, then 400 mL added. How much now? Check: 650, then 1 050 mL.
Watch Out
2 L minus 350 mL is 1 650 mL, not 1.65 or 165. Convert the 2 L to 2 000 mL before subtracting.
Explanation
The selective paper's chain uses two containers. Sooyoung has two hundred and fifty millilitres of cordial in a glass. She drinks ten: two hundred and forty. She tops the glass up to the five hundred mark — which means she adds five hundred minus two hundred and forty, two hundred and sixty. That water came from a one-litre bottle, which now has one thousand minus two hundred and sixty, seven hundred and forty. Track each container on its own; the amount that leaves one is exactly the amount that arrives in the other. The trap is topped up to the mark: the amount added is the mark minus what was already there.
Your Turn
A glass has 180 mL. It is topped up to 400 mL from a 750 mL jug. How much is left in the jug? Check: added 220; jug 530 mL.
Watch Out
"Topped up to 500" adds 500 − 240 = 260, not 500. The 500 is where the glass ENDS.
Explanation
Sharing a capacity is division in millilitres. One and a half litres into six glasses is fifteen hundred divided by six, two hundred and fifty each. Turned round, how many two-hundred-and-fifty glasses does one and a half litres fill — six. And the remainders lesson returns: two litres into three-hundred-and-fifty glasses fills five full glasses with two hundred and fifty left over, and whether the answer is five or six depends on whether the question asks how many can be filled or how many are needed to hold it all.
Your Turn
How many 250 mL glasses can be filled from a 1.5 L bottle? Check: 1 500 ÷ 250 = 6.
Watch Out
Divide millilitres by millilitres. 1.5 ÷ 250 is meaningless; 1 500 ÷ 250 = 6.
Explanation
A rate is an amount for each unit of time, and it turns capacity into multiplication or division. A tap that fills two hundred millilitres every minute fills one thousand two hundred in six minutes, and takes five minutes to fill a litre. A tank that leaks a hundred and fifty millilitres an hour loses one thousand two hundred in eight hours, so a five-litre tank has three thousand eight hundred left. Amount is rate times time; time is amount divided by rate; and keep everything in millilitres and one time unit. Quiz and exercises now.
Your Turn
A tap fills 200 mL a minute. How long to fill 2 L? Check: 2 000 ÷ 200 = 10 minutes.
Watch Out
Convert the litres before dividing by the rate. 2 ÷ 200 is not 10 minutes; 2 000 ÷ 200 is.
📌 Key Points — this lesson in a nutshell
  • 1 L = 1 000 mL. 1.5 L is 1 500 mL; 750 mL is 0.75 L. Work in millilitres so the numbers stay whole.
  • Track each container separately. What leaves one container arrives in another.
  • "Topped up to the 500 mL mark" means the amount ADDED is 500 minus what was already there.
  • Sharing: 1.5 L into 6 glasses is 1 500 ÷ 6 = 250 mL each. Rates: 200 mL a minute for 6 minutes is 1 200 mL.
Step 1: Introduction
Step 1 of 5
1 L = 1 000 mL 1.5 L× 10001 500 mL 750 mL÷ 10000.75 L L → mL is × 1000 (three columns left). mL → L is ÷ 1000. The same digit-sliding as kilometres and metres. 2 L = 2 000 mL. 2 500 mL = 2.5 L. 0.3 L = 300 mL. 750 + 250 = 1 000 mL = 1 L. A can of drink is about 375 mL; a water bottle 600 mL; a milk carton 1 or 2 L; a bucket 10 L. Use these to check sizes. Convert everything to mL before a chain starts, so no step mixes units.
A 1 L bottle. 260 mL is poured out. 5001000 → 5001000 1 000 − 260 = 740 mL left Pouring out subtracts. Adding in adds. Each move changes one container by the amount moved. Jug 800 mL: drink 150 → 650; add 400 → 1 050. Tank 2 L: pour out 3 glasses of 350 → 2 000 − 1 050 = 950. Write the amount after every move. A chain of three moves is three subtractions or additions, not one. "Three glasses of 350" is a multiplication first: 3 × 350 = 1 050, then one subtraction.
Sooyoung has 250 mL of cordial in a glass. She drinks 10 mL, then tops the glass up to the 500 mL mark from a 1 L bottle of water. 100200300400500glass: 250 100200300400500drinks 10: 240 100200300400500topped to 500 5001000bottle: 1 000 5001000bottle: 740 Glass: 250 → 240 after drinking. Topped up to 500 means 500 − 240 = 260 mL was ADDED. That 260 came from the bottle: 1 000 − 260 = 740 mL left in the bottle. Two containers, tracked separately. The link is the 260: it left the bottle and arrived in the glass. "Topped up to the mark" is the trap. The amount added is the mark minus what was there, not the mark itself.
1.5 L shared equally into 6 glasses 250500750100012501500 → 100200300100200300100200300100200300100200300100200300 1 500 ÷ 6 = 250 mL each Convert to mL, divide by the number of glasses. 1 500 ÷ 6 = 250. How many 250 mL glasses from a 1.5 L bottle? 1 500 ÷ 250 = 6. Four of those glasses hold 1 000 mL = 1 L. Division with remainders returns: 2 L into 350 mL glasses fills 5 full glasses (1 750) with 250 mL left over. "How many glasses can be filled" rounds down. "How many glasses to hold it all" rounds up.
A tap fills 200 mL every minute 01 min2002 min4003 min600……6 min1 200 In 6 minutes: 6 × 200 = 1 200 mL = 1.2 L. To fill 1 L: 1 000 ÷ 200 = 5 minutes. To fill 2 L: 10 minutes. A tank holds 5 L and leaks 150 mL an hour. After 8 hours: 5 000 − 8 × 150 = 5 000 − 1 200 = 3 800 mL. Amount = rate × time. Time = amount ÷ rate. Both in millilitres and the same time unit. A rate can be per minute, per hour, per glass — "per" means "for each one". Quiz and exercises now.
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