Year 5: Time and solving problems with measures
Part of the Year 5 units, perimeter, area, volume and time chapter. Chapter overview · whole chapter on one page
Time and solving problems with measures
Units of time do not go up in tens. There are 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in 1 day and 7 days in 1 week. To change to a smaller unit, multiply. To change to a bigger unit, divide.
A decimal number of hours can be split up. For example, 2.5 hours is 2 hours and half an hour, which is 2 hours 30 minutes.
Key ideas
- 1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours, 1 week = 7 days.
- Decimal hours: 0.5 hour = 30 minutes, 0.25 hour = 15 minutes, 0.1 hour = 6 minutes.
- Measures use all four operations: add lengths, take away to find the difference, multiply for equal amounts, and divide to share or to find how many.
- Scaling: find the amount for 1 first, then multiply to make a different amount. Use a bar model to show the steps.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 60 = 150
- Write the answer with the new unit. 150 minutes
Check. 150 ÷ 60 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change the hours to minutes, then add the extra minutes.
- Change the hours to minutes. Each hour is 60 minutes.3 × 60 = 180 minutes
- Add the extra minutes. The 20 minutes are added to the 180 minutes.180 + 20 = 200 minutes
- Write the answer. 200 minutes
Check. 200 minutes ÷ 60 = 3 remainder 20, which is 3 hours 20 minutes. ✓
Watch out. Do not write 3 hours 20 minutes as 3.20 hours. The 20 is minutes.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Find the amount for 1 person, then multiply by the number of people.
- Find the amount for 1 person. Share the 250 g between the 4 people in the recipe.250 ÷ 4 = 62.5 g
- Multiply by 6 people. Each of the 6 people needs the same amount.62.5 × 6 = 375 g
- Write the answer. 375 g
Check. 375 ÷ 6 = 62.5 g, which matches the amount for 1 person. ✓
Watch out. Find the amount for 1 first. Multiplying 250 by 6 is wrong, because 250 g is for 4 people.
Watch out
When you change a unit of time, do not use the decimal point as a separator. 2.5 hours is 150 minutes, not 250 minutes. Check your answer by asking whether the bigger unit gives a smaller number.Exercise 8F Time and problems with measures
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.5 × 60 = 90
- Write the answer with the new unit. 90 minutes
Check. 90 ÷ 60 = 1.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.25 × 60 = 195
- Write the answer with the new unit. 195 minutes
Check. 195 ÷ 60 = 3.25, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.4 × 60 = 24
- Write the answer with the new unit. 24 minutes
Check. 24 ÷ 60 = 0.4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.5 × 60 = 300
- Write the answer with the new unit. 300 minutes
Check. 300 ÷ 60 = 5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 60 = 150
- Write the answer with the new unit. 150 seconds
Check. 150 ÷ 60 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.2 × 60 = 252
- Write the answer with the new unit. 252 seconds
Check. 252 ÷ 60 = 4.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.5 × 60 = 30
- Write the answer with the new unit. 30 seconds
Check. 30 ÷ 60 = 0.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.6 × 60 = 360
- Write the answer with the new unit. 360 seconds
Check. 360 ÷ 60 = 6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2 × 24 = 48
- Write the answer with the new unit. 48 hours
Check. 48 ÷ 24 = 2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.5 × 24 = 36
- Write the answer with the new unit. 36 hours
Check. 36 ÷ 24 = 1.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.25 × 24 = 6
- Write the answer with the new unit. 6 hours
Check. 6 ÷ 24 = 0.25, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3 × 24 = 72
- Write the answer with the new unit. 72 hours
Check. 72 ÷ 24 = 3, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 week = 7 days
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3 × 7 = 21
- Write the answer with the new unit. 21 days
Check. 21 ÷ 7 = 3, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 week = 7 days
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 7 = 17.5
- Write the answer with the new unit. 17.5 days
Check. 17.5 ÷ 7 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 week = 7 days
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.6 × 7 = 42
- Write the answer with the new unit. 42 days
Check. 42 ÷ 7 = 6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change the hours to minutes, then add the extra minutes.
- Change 1 hour to minutes. One hour is 60 minutes.1 × 60 = 60 minutes
- Add the extra 35 minutes. Add the minutes to the 60 minutes.60 + 35 = 95 minutes
- Write the answer. 95 minutes
Check. 95 minutes is 1 hour 35 minutes. ✓
Watch out. Do not write 1 hour 35 minutes as 135 minutes. Change the hour to 60 first.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change the minutes to seconds, then add the extra seconds.
- Change 2 minutes to seconds. One minute is 60 seconds.2 × 60 = 120 seconds
- Add the extra 45 seconds. Add the seconds to the 120 seconds.120 + 45 = 165 seconds
- Write the answer. 165 seconds
Check. 165 seconds ÷ 60 = 2 minutes 45 seconds. ✓
Watch out. Change the minutes to seconds before you add.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Find the total minutes, then change them to hours and minutes.
- Find the total minutes. Multiply the minutes for one day by the 7 days.25 × 7 = 175 minutes
- Change the minutes to hours. There are 60 minutes in 1 hour, so divide by 60.175 ÷ 60 = 2 remainder 55
- Write the answer. The remainder is the extra minutes.2 hours 55 minutes
Check. 2 hours is 120 minutes, and 120 + 55 = 175. ✓
Watch out. The remainder after dividing by 60 is the minutes, not hours.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Multiply the price of one notebook by the number of notebooks.
- Write the price of one notebook. Each notebook costs £1.85.£1.85
- Multiply by 3. Three notebooks cost three times as much. Multiply the decimal as if it were whole numbers, then put the point back.1.85 × 3 = 5.55
- Write the answer with £. £5.55
Check. £5.55 ÷ 3 = £1.85. ✓
Watch out. Keep two decimal places in money: £5.55, not £5.5.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Multiply the weight of one bag by the number of bags.
- Write the weight of one bag. Each bag weighs 2.5 kg.2.5 kg
- Multiply by 4 bags. Four bags weigh four times as much.2.5 × 4 = 10 kg
- Write the answer. 10 kg
Check. 10 kg ÷ 4 = 2.5 kg. ✓
Watch out. A decimal number of kilograms can be multiplied in the same way as whole numbers.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Find the amount for 1 person first, then scale up to 10 people.
- Find the amount for 1 person. The recipe serves 4 people, so share the 300 g between 4.300 ÷ 4 = 75 g
- Multiply by 10 people. Each of the 10 people needs 75 g.75 × 10 = 750 g
- Write the answer. 750 g
Check. 750 g ÷ 10 = 75 g, which matches the amount for 1 person. ✓
Watch out. Find the amount for 1 person first. Then multiply.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the litres to millilitres, then share the millilitres equally between the 5 cups.
- Change 2 litres to millilitres. There are 1,000 ml in 1 litre.2 × 1,000 = 2,000 ml
- Share the millilitres equally. Divide the total by the number of cups.2,000 ÷ 5 = 400
- Write the answer. 400 ml in each cup
Check. 5 × 400 ml = 2,000 ml. ✓
Watch out. Change to millilitres first, so that both amounts use the same unit.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change 2.5 hours to minutes, then compare.
- Change 2.5 hours to minutes. Each hour is 60 minutes, so multiply 2.5 by 60.2.5 × 60 = 150 minutes
- Compare with 250 minutes. The two numbers must be in the same unit.150 minutes ≠ 250 minutes
- Write the answer. No. The journey is 150 minutes, not 250 minutes.
Check. 150 minutes is 2 hours 30 minutes, which is 2.5 hours. ✓
Watch out. Ali has multiplied by 100 instead of 60. There are 60 minutes in each hour, so 2.5 hours is 2 hours plus half an hour.