Year 4: Reading scales, weighing scales and jugs
Part of the Year 4 perimeter, area and measures chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Reading scales, weighing scales and jugs
Mass is how heavy something is. We measure it in grams (g) and kilograms (kg). Capacity is how much a container can hold, or how much liquid is in it. We measure it in millilitres (ml) and litres (l). A weighing scale and a measuring jug both have a scale, which works just like a number line.
Step 1: find the unit (g or kg, ml or l). Step 2: work out the step. Different scales have different steps, so never guess. Look at two numbers next to each other. Count the gaps between them and divide. On the first scale there are 5 gaps from 300 to 400, so each small mark is 100 ÷ 5 = 20 g. On the second scale there are 2 gaps from 3 to 4, so each small mark is 1 ÷ 2 = 0.5 kg.
Step 3: count on. The first pointer is 2 small marks after 300. So it shows 300 + 20 + 20 = 340 g. The second pointer is 1 small mark after 3 kg, so it shows 3 + 0.5 = 3.5 kg.
Reading a jug. Look at the top of the liquid and read the mark level with it. A scale can also be a straight line, like a tiny ruler. Here each mark is 2 mm. The numbers are 0, 10, 20 … and there are 5 gaps between them, so each mark is 10 ÷ 5 = 2 mm.
Key words. The scale is the line of marks. The step (or interval) is the amount between two small marks. Mass is measured in g and kg. Capacity is measured in ml and l.
Key ideas
- Mass: grams (g) and kilograms (kg). Capacity: millilitres (ml) and litres (l).
- Find the unit first.
- Count the gaps between two numbered marks and divide to find the step.
- Read the number below the pointer, then count on in steps.
- For a jug, read at the top of the liquid.
- Do not assume each mark is 1. Always work out the step.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 100 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 100 there are 5 gaps.
100 − 0 = 100 g
100 ÷ 5 = 20 g for each small mark - Write the answer. Each small mark is 20 g.
Check. 5 small marks × 20 g = 100 g, which is the gap from 0 to 100. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 300 and 400.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 300 to 400 there are 5 gaps.
400 − 300 = 100 g
100 ÷ 5 = 20 g for each small mark - Count on from 300. Count how many small marks the pointer is past 300.2 small marks × 20 g = 40 g
300 + 40 = 340 g - Write the reading with its unit. A measure always needs a unit.340 g
Check. Count back from 400: 3 small marks below it. 400 − 60 = 340. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 3 and 4.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 3 to 4 there are 2 gaps.
4 − 3 = 1 kg
1 ÷ 2 = 0.5 kg for each small mark - Count on from 3. Count how many small marks the pointer is past 3.1 small mark × 0.5 kg = 0.5 kg
3 + 0.5 = 3.5 kg - Write the reading with its unit. A measure always needs a unit.3.5 kg
Check. Count back from 4: 1 small mark below it. 4 − 0.5 = 3.5. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 600 and 800.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 600 to 800 there are 4 gaps.
800 − 600 = 200 ml
200 ÷ 4 = 50 ml for each small mark - Count on from 600. Count how many small marks the top of the liquid is past 600.3 small marks × 50 ml = 150 ml
600 + 150 = 750 ml - Write the reading with its unit. A measure always needs a unit.750 ml
Check. Count back from 800: 1 small mark below it. 800 − 50 = 750. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is l (litres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 1 and 1.5.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 1.5 there are 5 gaps.
1.5 − 1 = 0.5 l
0.5 ÷ 5 = 0.1 l for each small mark - Count on from 1. Count how many small marks the top of the liquid is past 1.3 small marks × 0.1 l = 0.3 l
1 + 0.3 = 1.3 l - Change to millilitres. 1 l = 1,000 ml, so multiply by 1,000.1.3 l = 1,300 ml
Check. Count back from 1.5: 2 small marks below it. 1.5 − 0.2 = 1.3. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the arrow, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is mm (millimetres).
- Find the two numbered marks either side of the arrow. We read the number below it first, then count on.The arrow is between 10 and 20.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 10 to 20 there are 5 gaps.
20 − 10 = 10 mm
10 ÷ 5 = 2 mm for each small mark - Count on from 10. Count how many small marks the arrow is past 10.2 small marks × 2 mm = 4 mm
10 + 4 = 14 mm - Write the reading with its unit. A measure always needs a unit.14 mm
Check. Count back from 20: 3 small marks below it. 20 − 6 = 14. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read the scale, then find the difference between the two amounts.
- Read the amount now. First we need to know how much there is.650 ml
- Take the smaller amount away from the bigger. The difference is how much more (or less) there is.1000 − 650 = 350 ml
- Write the answer with its unit. 350 ml
Check. 650 + 350 = 1000. ✓
Watch out. Write the unit in the answer.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Work out the step of the scale, read every jug, then pick the one that matches.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 100 there are 5 gaps.
100 − 0 = 100 ml
100 ÷ 5 = 20 ml for each small mark - Read each one. Count on from the numbered mark below.A: 200 + 3 × 20 = 260 ml
B: 300 + 2 × 20 = 340 ml
C: 400 + 1 × 20 = 420 ml - Choose the jug that shows 340 ml. B
Check. B shows 340 ml. ✓
Watch out. Check the step first. A different scale can make the same-looking pointer mean a different amount.
Watch out
Count the gaps, not the marks. Between 300 and 400 there are 5 gaps (and 6 marks). Do not say each mark is 1 or 10 without checking. Also keep an eye on the unit: a scale marked in kg gives an answer in kg.Exercise 7B Weighing scales
Non-calculatorKey words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 100 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 100 there are 5 gaps.
100 − 0 = 100 g
100 ÷ 5 = 20 g for each small mark - Write the answer. Each small mark is 20 g.
Check. 5 small marks × 20 g = 100 g, which is the gap from 0 to 100. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 200 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 200 there are 4 gaps.
200 − 0 = 200 g
200 ÷ 4 = 50 g for each small mark - Write the answer. Each small mark is 50 g.
Check. 4 small marks × 50 g = 200 g, which is the gap from 0 to 200. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 50 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 50 there are 5 gaps.
50 − 0 = 50 g
50 ÷ 5 = 10 g for each small mark - Write the answer. Each small mark is 10 g.
Check. 5 small marks × 10 g = 50 g, which is the gap from 0 to 50. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 200 and 300.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 200 to 300 there are 5 gaps.
300 − 200 = 100 g
100 ÷ 5 = 20 g for each small mark - Count on from 200. Count how many small marks the pointer is past 200.3 small marks × 20 g = 60 g
200 + 60 = 260 g - Write the reading with its unit. A measure always needs a unit.260 g
Check. Count back from 300: 2 small marks below it. 300 − 40 = 260. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 600 and 800.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 600 to 800 there are 4 gaps.
800 − 600 = 200 g
200 ÷ 4 = 50 g for each small mark - Count on from 600. Count how many small marks the pointer is past 600.1 small mark × 50 g = 50 g
600 + 50 = 650 g - Write the reading with its unit. A measure always needs a unit.650 g
Check. Count back from 800: 3 small marks below it. 800 − 150 = 650. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 100 and 150.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 100 to 150 there are 5 gaps.
150 − 100 = 50 g
50 ÷ 5 = 10 g for each small mark - Count on from 100. Count how many small marks the pointer is past 100.3 small marks × 10 g = 30 g
100 + 30 = 130 g - Write the reading with its unit. A measure always needs a unit.130 g
Check. Count back from 150: 2 small marks below it. 150 − 20 = 130. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 1 and 2.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 2 there are 2 gaps.
2 − 1 = 1 kg
1 ÷ 2 = 0.5 kg for each small mark - Count on from 1. Count how many small marks the pointer is past 1.1 small mark × 0.5 kg = 0.5 kg
1 + 0.5 = 1.5 kg - Write the reading with its unit. A measure always needs a unit.1.5 kg
Check. Count back from 2: 1 small mark below it. 2 − 0.5 = 1.5. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 1 and 1.5.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 1.5 there are 5 gaps.
1.5 − 1 = 0.5 kg
0.5 ÷ 5 = 0.1 kg for each small mark - Count on from 1. Count how many small marks the pointer is past 1.3 small marks × 0.1 kg = 0.3 kg
1 + 0.3 = 1.3 kg - Write the reading with its unit. A measure always needs a unit.1.3 kg
Check. Count back from 1.5: 2 small marks below it. 1.5 − 0.2 = 1.3. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 6 and 8.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 6 to 8 there are 4 gaps.
8 − 6 = 2 kg
2 ÷ 4 = 0.5 kg for each small mark - Count on from 6. Count how many small marks the pointer is past 6.1 small mark × 0.5 kg = 0.5 kg
6 + 0.5 = 6.5 kg - Write the reading with its unit. A measure always needs a unit.6.5 kg
Check. Count back from 8: 3 small marks below it. 8 − 1.5 = 6.5. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 2 and 3.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 2 to 3 there are 2 gaps.
3 − 2 = 1 kg
1 ÷ 2 = 0.5 kg for each small mark - Count on from 2. Count how many small marks the pointer is past 2.1 small mark × 0.5 kg = 0.5 kg
2 + 0.5 = 2.5 kg - Change to grams. 1 kg = 1,000 g, so multiply by 1,000.2.5 kg = 2,500 g
Check. Count back from 3: 1 small mark below it. 3 − 0.5 = 2.5. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 1 and 2.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 2 there are 4 gaps.
2 − 1 = 1 kg
1 ÷ 4 = 0.25 kg for each small mark - Count on from 1. Count how many small marks the pointer is past 1.3 small marks × 0.25 kg = 0.75 kg
1 + 0.75 = 1.75 kg - Change to grams. 1 kg = 1,000 g, so multiply by 1,000.1.75 kg = 1,750 g
Check. Count back from 2: 1 small mark below it. 2 − 0.25 = 1.75. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Work out the step of the scale, read every scale, then pick the one that matches.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 200 there are 4 gaps.
200 − 0 = 200 g
200 ÷ 4 = 50 g for each small mark - Read each one. Count on from the numbered mark below.A: 200 + 3 × 50 = 350 g
B: 400 + 1 × 50 = 450 g
C: 600 + 2 × 50 = 700 g - Choose the scale that shows 450 g. B
Check. B shows 450 g. ✓
Watch out. Check the step first. A different scale can make the same-looking pointer mean a different amount.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read the scale, then find the difference between the two amounts.
- Read the amount now. First we need to know how much there is.340 g
- Take the smaller amount away from the bigger. The difference is how much more (or less) there is.500 − 340 = 160 g
- Write the answer with its unit. 160 g
Check. 340 + 160 = 500. ✓
Watch out. Write the unit in the answer.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read the scale, then find the difference between the two amounts.
- Read the amount now. First we need to know how much there is.3.5 kg
- Take the smaller amount away from the bigger. The difference is how much more (or less) there is.4 − 3.5 = 0.5 kg
- Write the answer with its unit. 0.5 kg
Check. 3.5 + 0.5 = 4. ✓
Watch out. Write the unit in the answer.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Look at where the pointer is. It is exactly on a numbered mark, so we can read the number straight off.The pointer is on 400.
- Write the reading with its unit. A measure always needs a unit.400 g
Check. 400 is one of the numbers written on the scale. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 600 and 800.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 600 to 800 there are 4 gaps.
800 − 600 = 200 g
200 ÷ 4 = 50 g for each small mark - Count on from 600. Count how many small marks the pointer is past 600.1 small mark × 50 g = 50 g
600 + 50 = 650 g - Write the reading with its unit. A measure always needs a unit.650 g
Check. Count back from 800: 3 small marks below it. 800 − 150 = 650. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in grams, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.400 g + 650 g = 1,050 g
Th H T O 4 0 0 + 6 5 0 1 0 5 0 1 - Write the answer with its unit. A measure always needs its unit.1,050 g
Check. Use the inverse: 1,050 − 650 = 400. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. First read the scale, then share the mass equally between the 3 books.
- Read the scale. The pointer is on a numbered mark, so we can read the number straight off.The pointer is on 600 g.
- Divide by 3. The 3 books are the same, so they share the 600 g equally.600 ÷ 3 = 200 g
Check. 3 × 200 = 600. ✓
Watch out. Divide the total by the number of books. Do not divide by the step.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Work out what each small mark is worth first. Then count on from 300.
- Find the step. There are 5 gaps from 300 g to 400 g, so we divide 100 by 5.100 ÷ 5 = 20 g for each small mark, not 10 g
- Count on from 300. The pointer is 2 small marks after 300.2 × 20 = 40, so 300 + 40 = 340 g
- Find Mia’s mistake. Mia said 350 g. That would be halfway between 300 and 400, and the pointer is not halfway.She used 10 g for each mark, or guessed the middle. The correct reading is 340 g.
Check. Count back from 400: 3 marks of 20 g = 60 g. 400 − 60 = 340. ✓
Watch out. Never guess the step. Count the gaps and divide.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Think about different scales. The step depends on how many gaps there are between the numbers.
- Look at a scale where each mark is 1. On a ruler for tiny things, every mark can be 1 g.Step = 1 g: this is true for this scale.
- Look at a scale where each mark is 20 g. On the scale in this section, there are 5 gaps from 300 to 400, so each mark is 20 g, not 1 g.Step = 20 g: this is false for this scale.
- Decide. It is true for some scales and false for others.Sometimes.
Check. We found one scale where it is true and one where it is false. ✓
Watch out. Always work out the step for the scale you are looking at.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 1 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 1 there are 4 gaps.
1 − 0 = 1 kg
1 ÷ 4 = 0.25 kg for each small mark - Write the answer. Each small mark is 0.25 kg.
Check. 4 small marks × 0.25 kg = 1 kg, which is the gap from 0 to 1. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 1 and 2.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 2 there are 4 gaps.
2 − 1 = 1 kg
1 ÷ 4 = 0.25 kg for each small mark - Count on from 1. Count how many small marks the pointer is past 1.3 small marks × 0.25 kg = 0.75 kg
1 + 0.75 = 1.75 kg - Write the reading with its unit. A measure always needs a unit.1.75 kg
Check. Count back from 2: 1 small mark below it. 2 − 0.25 = 1.75. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is kg (kilograms).
- Find the two numbered marks either side of the pointer. We read the number below it first, then count on.The pointer is between 1 and 2.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 2 there are 4 gaps.
2 − 1 = 1 kg
1 ÷ 4 = 0.25 kg for each small mark - Count on from 1. Count how many small marks the pointer is past 1.3 small marks × 0.25 kg = 0.75 kg
1 + 0.75 = 1.75 kg - Change to grams. 1 kg = 1,000 g, so multiply by 1,000.1.75 kg = 1,750 g
Check. Count back from 2: 1 small mark below it. 2 − 0.25 = 1.75. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Exercise 7C Measuring jugs and straight scales
Non-calculatorKey words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 100 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 100 there are 5 gaps.
100 − 0 = 100 ml
100 ÷ 5 = 20 ml for each small mark - Write the answer. Each small mark is 20 ml.
Check. 5 small marks × 20 ml = 100 ml, which is the gap from 0 to 100. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 200 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 200 there are 4 gaps.
200 − 0 = 200 ml
200 ÷ 4 = 50 ml for each small mark - Write the answer. Each small mark is 50 ml.
Check. 4 small marks × 50 ml = 200 ml, which is the gap from 0 to 200. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Count the gaps between two numbered marks. Divide the difference between the numbers by the number of gaps.
- Look at two numbered marks next to each other. We need two marks where we know the numbers.The marks 0 and 50 are next to each other.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 50 there are 5 gaps.
50 − 0 = 50 ml
50 ÷ 5 = 10 ml for each small mark - Write the answer. Each small mark is 10 ml.
Check. 5 small marks × 10 ml = 50 ml, which is the gap from 0 to 50. ✓
Watch out. Count the spaces between the marks, not the marks themselves. 5 gaps have 6 marks.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 300 and 400.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 300 to 400 there are 5 gaps.
400 − 300 = 100 ml
100 ÷ 5 = 20 ml for each small mark - Count on from 300. Count how many small marks the top of the liquid is past 300.2 small marks × 20 ml = 40 ml
300 + 40 = 340 ml - Write the reading with its unit. A measure always needs a unit.340 ml
Check. Count back from 400: 3 small marks below it. 400 − 60 = 340. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 600 and 800.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 600 to 800 there are 4 gaps.
800 − 600 = 200 ml
200 ÷ 4 = 50 ml for each small mark - Count on from 600. Count how many small marks the top of the liquid is past 600.3 small marks × 50 ml = 150 ml
600 + 150 = 750 ml - Write the reading with its unit. A measure always needs a unit.750 ml
Check. Count back from 800: 1 small mark below it. 800 − 50 = 750. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 100 and 150.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 100 to 150 there are 5 gaps.
150 − 100 = 50 ml
50 ÷ 5 = 10 ml for each small mark - Count on from 100. Count how many small marks the top of the liquid is past 100.3 small marks × 10 ml = 30 ml
100 + 30 = 130 ml - Write the reading with its unit. A measure always needs a unit.130 ml
Check. Count back from 150: 2 small marks below it. 150 − 20 = 130. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is l (litres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 1 and 1.5.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1 to 1.5 there are 5 gaps.
1.5 − 1 = 0.5 l
0.5 ÷ 5 = 0.1 l for each small mark - Count on from 1. Count how many small marks the top of the liquid is past 1.3 small marks × 0.1 l = 0.3 l
1 + 0.3 = 1.3 l - Write the reading with its unit. A measure always needs a unit.1.3 l
Check. Count back from 1.5: 2 small marks below it. 1.5 − 0.2 = 1.3. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is l (litres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 2 and 3.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 2 to 3 there are 4 gaps.
3 − 2 = 1 l
1 ÷ 4 = 0.25 l for each small mark - Count on from 2. Count how many small marks the top of the liquid is past 2.1 small mark × 0.25 l = 0.25 l
2 + 0.25 = 2.25 l - Write the reading with its unit. A measure always needs a unit.2.25 l
Check. Count back from 3: 3 small marks below it. 3 − 0.75 = 2.25. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is l (litres).
- Look at where the top of the liquid is. It is exactly on a numbered mark, so we can read the number straight off.The top of the liquid is on 0.5.
- Write the reading with its unit. A measure always needs a unit.0.5 l
Check. 0.5 is one of the numbers written on the scale. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is l (litres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 1.5 and 2.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 1.5 to 2 there are 5 gaps.
2 − 1.5 = 0.5 l
0.5 ÷ 5 = 0.1 l for each small mark - Count on from 1.5. Count how many small marks the top of the liquid is past 1.5.2 small marks × 0.1 l = 0.2 l
1.5 + 0.2 = 1.7 l - Change to millilitres. 1 l = 1,000 ml, so multiply by 1,000.1.7 l = 1,700 ml
Check. Count back from 2: 3 small marks below it. 2 − 0.3 = 1.7. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is l (litres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 2 and 3.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 2 to 3 there are 4 gaps.
3 − 2 = 1 l
1 ÷ 4 = 0.25 l for each small mark - Count on from 2. Count how many small marks the top of the liquid is past 2.2 small marks × 0.25 l = 0.5 l
2 + 0.5 = 2.5 l - Change to millilitres. 1 l = 1,000 ml, so multiply by 1,000.2.5 l = 2,500 ml
Check. Count back from 3: 2 small marks below it. 3 − 0.5 = 2.5. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Work out the step of the scale, read every jug, then pick the one that matches.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 0 to 200 there are 4 gaps.
200 − 0 = 200 ml
200 ÷ 4 = 50 ml for each small mark - Read each one. Count on from the numbered mark below.A: 200 + 3 × 50 = 350 ml
B: 400 + 1 × 50 = 450 ml
C: 600 + 1 × 50 = 650 ml - Choose the jug that shows 450 ml. B
Check. B shows 450 ml. ✓
Watch out. Check the step first. A different scale can make the same-looking pointer mean a different amount.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the arrow, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is mm (millimetres).
- Find the two numbered marks either side of the arrow. We read the number below it first, then count on.The arrow is between 20 and 30.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 20 to 30 there are 5 gaps.
30 − 20 = 10 mm
10 ÷ 5 = 2 mm for each small mark - Count on from 20. Count how many small marks the arrow is past 20.3 small marks × 2 mm = 6 mm
20 + 6 = 26 mm - Write the reading with its unit. A measure always needs a unit.26 mm
Check. Count back from 30: 2 small marks below it. 30 − 4 = 26. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the arrow, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is g (grams).
- Find the two numbered marks either side of the arrow. We read the number below it first, then count on.The arrow is between 60 and 80.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 60 to 80 there are 4 gaps.
80 − 60 = 20 g
20 ÷ 4 = 5 g for each small mark - Count on from 60. Count how many small marks the arrow is past 60.1 small mark × 5 g = 5 g
60 + 5 = 65 g - Write the reading with its unit. A measure always needs a unit.65 g
Check. Count back from 80: 3 small marks below it. 80 − 15 = 65. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the arrow, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the arrow. We read the number below it first, then count on.The arrow is between 200 and 300.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 200 to 300 there are 4 gaps.
300 − 200 = 100 ml
100 ÷ 4 = 25 ml for each small mark - Count on from 200. Count how many small marks the arrow is past 200.3 small marks × 25 ml = 75 ml
200 + 75 = 275 ml - Write the reading with its unit. A measure always needs a unit.275 ml
Check. Count back from 300: 1 small mark below it. 300 − 25 = 275. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read the scale, then find the difference between the two amounts.
- Read the amount now. First we need to know how much there is.450 ml
- Take the smaller amount away from the bigger. The difference is how much more (or less) there is.600 − 450 = 150 ml
- Write the answer with its unit. 150 ml
Check. 450 + 150 = 600. ✓
Watch out. Write the unit in the answer.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read the jug first. Then take away the amount that was poured out.
- Read the jug. The top of the liquid is on a numbered mark, so we can read it directly.The jug shows 800 ml.
- Subtract the amount poured out. Take the smaller amount away from the bigger amount.800 − 350 = 450 ml
- Write the answer. 450 ml is left in the jug.
Check. 450 + 350 = 800. ✓
Watch out. Subtract: the water that is poured out is no longer in the jug.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 200 and 400.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 200 to 400 there are 4 gaps.
400 − 200 = 200 ml
200 ÷ 4 = 50 ml for each small mark - Count on from 200. Count how many small marks the top of the liquid is past 200.3 small marks × 50 ml = 150 ml
200 + 150 = 350 ml - Write the reading with its unit. A measure always needs a unit.350 ml
Check. Count back from 400: 1 small mark below it. 400 − 50 = 350. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.
- Find the unit on the scale. The unit tells us what the numbers mean.The unit is ml (millilitres).
- Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.The top of the liquid is between 200 and 300.
- Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.From 200 to 300 there are 5 gaps.
300 − 200 = 100 ml
100 ÷ 5 = 20 ml for each small mark - Count on from 200. Count how many small marks the top of the liquid is past 200.3 small marks × 20 ml = 60 ml
200 + 60 = 260 ml - Write the reading with its unit. A measure always needs a unit.260 ml
Check. Count back from 300: 2 small marks below it. 300 − 40 = 260. ✓
Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.
Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.
Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.
- Check the units. We can only add or subtract measures that are in the same unit.Both measures are in millilitres, so we can go straight to the calculation.
- Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.350 ml + 260 ml = 610 ml
H T O 3 5 0 + 2 6 0 6 1 0 1 - Write the answer with its unit. A measure always needs its unit.610 ml
Check. Use the inverse: 610 − 260 = 350. ✓
Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read the jug, then share the amount equally between 3 glasses.
- Read the jug. The top of the liquid is 3 small marks after 600 ml. The step is 50 ml.600 + 3 × 50 = 600 + 150 = 750 ml
- Divide by 3. The 3 glasses get equal amounts.750 ÷ 3 = 250 ml
Check. 3 × 250 = 750. ✓
Watch out. Read the scale before you divide.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. The step is not 10 ml. Work it out by counting the gaps.
- Find the step. There are 5 gaps from 300 ml to 400 ml.100 ÷ 5 = 20 ml, not 10 ml
- Count on from 300. The top of the liquid is 3 small marks after 300.3 × 20 = 60 and 300 + 60 = 360 ml
- Find Noah’s mistake. Noah used 10 ml for each mark: 300 + 3 × 10 = 330.He did not work out the step. The jug has 360 ml.
Check. Count back from 400: 2 marks of 20 = 40. 400 − 40 = 360. ✓
Watch out. Count the gaps and divide to find the step.
Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).
Method. Read both jugs. They have different scales, so find the step for each jug.
- Read jug A. Jug A: 5 gaps from 300 to 400, so a step of 20 ml. The liquid is on the 2nd mark after 300.300 + 2 × 20 = 340 ml
- Read jug B. Jug B: 4 gaps from 200 to 400, so a step of 50 ml. The liquid is 1 mark after 300.300 + 1 × 50 = 350 ml
- Compare and find the difference. The bigger number has more liquid.350 − 340 = 10 ml. Jug B has 10 ml more.
Check. 340 + 10 = 350. ✓
Watch out. A jug that looks fuller may not have more liquid. The scales are different.