Remember the important ideas

A three-digit number is made of hundreds, tens and ones. The place of each digit tells you its value. Use this to read, write, compare and order numbers to 1000, and to find 10 or 100 more or less.

Key words

digit

A single symbol used to write a number. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

hundreds, tens and ones

The three places in a three-digit number. 538 has 5 hundreds, 3 tens and 8 ones.

place value

The place of a digit in a number tells you how much the digit is worth.

value

How much a digit is worth in its place. In 538, the digit 3 has the value 30.

greater than (>)

Has a higher value than another number. 538 > 358.

less than (<)

Has a lower value than another number. 358 < 538.

smallest to largest

An order that starts with the smallest number and ends with the largest: 358, 538, 853.

multiple

A number you say when you count in equal steps from 0. The multiples of 4 are 4, 8, 12, 16 and so on.

estimate

A sensible answer that is close, but not exact. Use the labelled numbers on a number line to estimate.

Key facts

• The place of a digit gives its value. In 538, the 5 is worth 500, the 3 is worth 30 and the 8 is worth 8.
• You can partition a number into hundreds, tens and ones: 538 = 500 + 30 + 8.
• A zero holds a place. 406 has 4 hundreds, 0 tens and 6 ones.
• Read and write numbers as numerals and in words: 406 is four hundred and six.
• To compare, look at the hundreds digits first. If they match, compare the tens. If those match, compare the ones.
• The open end of < or > faces the greater number: 352 > 325 and 325 < 352.
• 10 more or 10 less changes the tens digit. 100 more or 100 less changes the hundreds digit. 100 less than 612 is 512.
• 100 more than 900 is 1000.
• Count in steps of 4, 8, 50 and 100 from 0. Keep the step the same every time.

Pictures to remember

• Steps of 4048121620
• Steps of 80816243240
• Steps of 50050100150200250
• Steps of 1000100200300400500

Worked examples

Common reminders

• Read the value, not just the digit. In 538, the digit 3 is worth 30, not 3.
• A zero keeps a place. 305 has 3 hundreds, 0 tens and 5 ones. It is not the same as 35.
• Start with the hundreds when you compare. 419 < 421 because 1 ten is less than 2 tens, even though 9 ones is more than 1 one.
• The order of the digits matters. 305 and 350 use the same digits but they are different numbers.
• Keep the step the same when you count. In steps of 50: 0, 50, 100, 150, 200. Each number is 50 more than the one before.

Remember: Check the place of each digit before you decide what a number is worth.

To add and subtract numbers with up to three digits, use what you know about hundreds, tens and ones. You can work in your head, with partitioning, or in columns. Estimate first, then use the inverse to check.

Key words

add

Put numbers together to find a total. You can read + as plus.

total

The answer when you add. 235 + 124 has a total of 359.

subtract

Take one number away from another. You can read − as minus.

difference

How far apart two numbers are. The difference between 120 and 350 is 230.

column method

A written way to add or subtract. Line up the ones, tens and hundreds, then start with the ones.

exchange

Swap 1 ten for 10 ones, or 1 hundred for 10 tens, or the other way round, so a column has enough to work with.

estimate

Find a close value first. For example, round each number to the nearest 100, then calculate.

inverse

The opposite operation. Addition and subtraction undo each other.

missing number

A gap in a number sentence for you to fill, such as ___ + 150 = 430.

Key facts

• Work out which place changes. 246 + 30 = 276 changes the tens only.
• Add to put amounts together and find a total. Subtract to take away, or to find a difference.
• How many more? and What is the difference? both mean subtract. The difference between 297 and 482 is 185.
• In the column method, line up ones under ones, tens under tens and hundreds under hundreds. Start with the ones.
• Exchange when a column does not have enough. 10 ones make 1 ten. 10 tens make 1 hundred.
• Estimate first, calculate, then check that your answer is sensible.
• Check with the inverse. 257 + 134 = 391, so 391 − 134 = 257.
• Use the inverse to find a missing number. ___ + 150 = 430, so 430 − 150 = 280.

Worked examples

Common reminders

• Line up the places. In 436 + 75, the 5 goes under the 6 and the 7 goes under the 3. 436 + 75 = 511.
• Exchange when the top digit is too small, even when there is a zero. In 702 − 345 there are 0 tens, so exchange 1 hundred for 10 tens first. Then exchange 1 ten for 10 ones. 702 − 345 = 357.
• Choose add or subtract from what is happening in the problem. Altogether means add. How many are left? and What is the difference? mean subtract.
• Use the inverse that matches the calculation. To check 391 − 134 = 257, add: 257 + 134 = 391.
• Check that your answer makes sense. If you estimate 400 + 300 = 700, an answer of 1700 is not sensible.

Remember: Estimate first, calculate carefully, then check with the inverse.

Multiplication and division are linked. Equal groups and arrays show both. Know the 3, 4 and 8 times tables, use them to work out other facts, and check a division with a multiplication.

Key words

multiply

Find the total of equal groups. Read × as times. 3 × 4 means 3 groups of 4.

divide

Share a total equally, or put it into equal groups. Read ÷ as divided by.

times table

The multiples of a number in order. The 4 times table is 4, 8, 12, 16, 20, 24 and so on.

multiple

A number in a times table. 12 is a multiple of 4.

product

The answer when you multiply. The product of 6 and 8 is 48.

equal groups

Groups with the same number in each group.

array

Counters in rows and columns, with the same number in every row. 3 rows of 4 is an array for 3 × 4.

share equally

Split a total into a number of equal groups. You find how many are in each group.

group equally

Put a total into groups of a set size. You find how many groups there are.

inverse

The opposite operation. Multiplication and division undo each other.

fact family

Linked facts that use the same three numbers, such as 6 × 8 = 48 and 48 ÷ 6 = 8.

double

Multiply by 2. Double 24 is 48.

Key facts

• Know the 3, 4 and 8 times tables. Counting in steps gives the multiples: 4, 8, 12, 16, 20, 24.
• 3 groups of 4 is 3 × 4 = 12. You can multiply in either order: 4 × 3 = 12.
• Every multiplication fact gives two division facts. 6 × 8 = 48, so 48 ÷ 6 = 8 and 48 ÷ 8 = 6.
• Division starts with the total. 48 ÷ 8 = 6. Division cannot be done in either order.
• Division is the inverse of multiplication. 56 ÷ 8 = 7 because 7 × 8 = 56.
• The 8 times table is double the 4 times table. 4 × 6 = 24, so 8 × 6 = 48.
• Place value helps. 3 × 4 = 12, so 3 × 40 = 120.
• To multiply a two-digit number, partition it into tens and ones. Multiply each part, then add. 26 × 3 = 60 + 18 = 78.
• Sharing finds how many are in each group. Grouping finds how many groups. Both are division.
• A missing number can be found with the inverse. ___ × 8 = 56, so 56 ÷ 8 = 7.

Pictures to remember

Worked examples

Common reminders

• Keep the 4 and 8 times tables apart. 4 × 6 = 24 but 8 × 6 = 48. The 8 times table is double the 4 times table.
• Division starts with the total. 24 ÷ 8 = 3. The total, 24, comes first. Division cannot be done in either order, so swapping the numbers does not give the same answer.
• Sharing and grouping both use division. 18 shared between 3 pots gives 18 ÷ 3 = 6 in each pot. 18 put into bags of 3 gives 18 ÷ 3 = 6 bags.
• Choose multiply or divide from the story. Equal groups with the total missing: multiply. A total split into equal groups: divide.
• Check a division with a multiplication. 56 ÷ 8 = 7 because 7 × 8 = 56.
• Multiply both parts of a two-digit number. 34 × 2: 30 × 2 = 60 and 4 × 2 = 8. Add both parts: 60 + 8 = 68. Do not forget the tens.

Remember: Ask two questions: how many groups, and how many in each group?

A fraction names equal parts of a whole. The denominator says how many equal parts the whole is split into and the numerator says how many you have. You can find fractions of amounts, show equivalent fractions, compare them and add them. Tenths are 10 equal parts, and they link to the number line from 0 to 1.

Key words

whole

The complete object, shape or amount before it is split into parts.

equal parts

Parts that are exactly the same size. A fraction needs equal parts.

fraction

A number that names equal parts of a whole, such as 3/4.

denominator

The bottom number of a fraction. It is the number of equal parts the whole is split into.

numerator

The top number of a fraction. It is the number of those equal parts you have.

unit fraction

A fraction with a numerator of 1, such as 1/4.

non-unit fraction

A fraction with a numerator greater than 1, such as 3/4.

equivalent

Fractions are equivalent when they name the same amount, such as 1/2 and 2/4.

tenths

10 equal parts of a whole. One tenth is 1/10.

Key facts

• A fraction names equal parts of a whole. The parts must be equal.
• The denominator is the number of equal parts the whole is split into. The numerator is the number of those parts you have.
• A unit fraction has a numerator of 1, such as 1/4. A non-unit fraction has a numerator greater than 1, such as 3/4.
• To find a fraction of an amount, share the amount into equal groups using the denominator, then take the number of groups the numerator names. 1/5 of 30: 30 ÷ 5 = 6.
• Equivalent fractions name the same amount: 1/2 = 2/4 and 1/3 = 2/6. Check by shading the same whole.
• Unit fractions: the more equal parts the whole is split into, the smaller each part is. 1/3 > 1/4.
• Fractions with the same denominator: the greater numerator is the greater fraction. 6/9 > 4/9.
• To add or subtract fractions with the same denominator, add or subtract the numerators and keep the denominator. 1/7 + 3/7 = 4/7 and 6/8 − 2/8 = 4/8.
• Count in tenths: 1/10, 2/10, 3/10 and so on up to 10/10. Ten tenths make one whole.
• One tenth is 1/10: one of 10 equal parts of a whole.
• Tenths can also be written as decimals: 1/10 is 0.1 and 3/10 is 0.3. This is another way to write the same tenths.

Pictures to remember

Worked examples

Common reminders

• The parts must be equal. A shape cut into 4 pieces of different sizes does not show quarters.
• The denominator counts all the equal parts, not just the shaded ones. A bar with 5 equal parts and 2 shaded is 2/5, not 2/2.
• Do not add the denominators. 1/7 + 3/7 = 4/7, not 4/14. The parts are still sevenths.
• A larger denominator does not mean a larger fraction. 1/8 < 1/2, because eighths are smaller parts than halves.
• To find a fraction of an amount, divide by the denominator. 1/5 of 30: 30 ÷ 5 = 6. Dividing by the numerator, 1, would only give 30.
• Equivalent means the same amount, not similar numbers. 1/3 and 2/6 cover the same part of a whole. 1/3 and 1/6 do not.
• Ten tenths make one whole. 10/10 is the whole, so 10/10 = 1. A tenth is a small part, not the number 10.

Remember: Check that the parts are equal, then use the denominator for the number of parts and the numerator for the parts you have.

Length, mass and capacity are measured in standard units. Read the scale carefully, write the unit, and use the same unit when you compare, add or subtract. Perimeter is a length: it is the distance all the way around the outside of a shape.

Key words

length

How long something is, or how far apart two points are. Height and width are also lengths. Length is measured in mm, cm and m.

perimeter

The distance all the way around the outside of a 2-D shape. You find it by adding all the side lengths.

mass

How heavy something is. Mass is measured in g and kg.

capacity

How much a container can hold. Capacity is measured in ml and l. You may also see this called volume.

millimetre (mm)

A very small unit of length. 10 mm is 1 cm.

centimetre (cm)

A small unit of length. 100 cm is 1 m.

metre (m)

A longer unit of length. 1 m is 100 cm.

gram (g)

A small unit of mass. 1000 g is 1 kg.

kilogram (kg)

A bigger unit of mass. 1 kg is 1000 g.

millilitre (ml)

A small unit of capacity. 1000 ml is 1 l.

litre (l)

A bigger unit of capacity. 1 l is 1000 ml.

Key facts

• Length is measured in millimetres (mm), centimetres (cm) and metres (m). Mass is measured in grams (g) and kilograms (kg). Capacity is measured in millilitres (ml) and litres (l).
• Choose a unit to fit what you measure. Use mm for very small lengths, cm for small objects and m for longer lengths.
• Equal measures: 10 mm = 1 cm, 100 cm = 1 m, 1000 g = 1 kg and 1000 ml = 1 l.
• Mass is how heavy something is. Capacity is how much a container holds. They are different things.
• Start at 0 on a ruler or scale. To find the step size, look at two numbered marks next to each other. A scale marked 0, 200, 400 and 600 goes up in steps of 200.
• Compare, add and subtract measures in the same unit. If the units are different, change them to the same unit first.
• Write the unit after every measure: 62 cm, 450 g or 350 ml.
• Perimeter is the distance all the way around the outside of a 2-D shape.
• To find a perimeter, add the lengths of all the sides. Write the total with a unit of length, such as cm or m.
• A rectangle has two pairs of equal sides. If one side is 11 cm and the next side is 6 cm, the perimeter is 11 cm + 6 cm + 11 cm + 6 cm = 34 cm.
• A square has 4 equal sides. If one side is 5 m, the perimeter is 5 m + 5 m + 5 m + 5 m = 20 m.

Pictures to remember

Worked examples

Common reminders

• Write the unit. 38 cm + 24 cm = 62 cm. The answer is 62 cm, not just 62.
• Use the same unit before you compare, add or subtract. To compare 3 kg and 2500 g, change 3 kg to 3000 g. Then 3000 g is greater than 2500 g.
• Check the step size of the scale. On a scale marked 0, 200, 400, each step is 200. It is not 1.
• Mass and capacity are different. Mass is how heavy something is, such as 750 g of flour. Capacity is how much a container holds, such as 750 ml of water.
• Add all the sides for perimeter. A rectangle that is 9 cm long and 4 cm wide has 4 sides. 9 cm + 4 cm + 9 cm + 4 cm = 26 cm, not 9 cm + 4 cm = 13 cm.
• Perimeter goes around the edge. Perimeter is the distance around the outside of a shape, not the space inside it. It is a length, so write it in cm or m.

Remember: Read the scale carefully, use one unit at a time and write the unit in your answer.

Money uses pounds (£) and pence (p), and 100p is £1. An amount such as £3.20 means £3 and 20p. Keep the pounds and the pence in their own places, and write £ or p in every answer.

Key words

pound

The larger unit of money. The symbol is £. 1 pound is 100 pence.

pence

The smaller unit of money. The symbol is p. 100p is the same as £1.

cost

The amount you must pay to buy something. You may also see this called the price.

total

The whole amount when you add amounts together.

pay

To give money for something. The amount you give is the amount paid.

change

The money you get back when you pay with more than the cost. Change = amount paid − cost.

Key facts

• Money is measured in pounds (£) and pence (p). 100p = £1.
• Coins are worth 1p, 2p, 5p, 10p, 20p and 50p, and £1 and £2. A £1 coin is worth 100p. Notes such as £5 and £10 are worth that many pounds.
• Write an amount with pounds and pence as £3.20. It means £3 and 20p. Write the pence with two digits: £3.05 is £3 and 5p, and £3.50 is £3 and 50p. They are different amounts.
• An amount less than £1 is written in pence, such as 65p. Use £ or p, never both on one amount.
• To change pounds into pence, count 100p for each pound and add the pence. £3.20 is 300p + 20p = 320p.
• To change pence into pounds, count the lots of 100p and keep the pence that are left. 450p is 400p + 50p, which is £4 and 50p.
• To add money, add the pounds and add the pence, or change both amounts to pence first. If the pence reach 100p, change 100p into £1.
• Change = amount paid − cost. You can check it by counting up from the cost to the amount paid.
• To compare amounts, look at the pounds first. If the pounds are the same, look at the pence. £3.50 is greater than £3.05 because 50p is more than 5p.
• A total is found by adding. Change is found by subtracting the cost from the amount paid.

Pictures to remember

Worked examples

Common reminders

• Use £ or p for an amount, never both. An amount under £1 is written in pence, such as 45p. Do not put a £ and a p on one amount.
• Write the pence with two digits. £3.05 is £3 and 5p. £3.50 is £3 and 50p. They are not the same amount.
• Read 40p as forty pence, not £40. 40p is less than £1. £40 is the same as 4000p.
• Check whether the question wants the total or the change. Two items cost £1.20 and £2.00. Add to find the total: £1.20 + £2.00 = £3.20. If you pay £5.00, subtract to find the change: £5.00 − £3.20 = £1.80.
• Use the same form before you add or compare. To compare 175p and £1.65, change £1.65 to 165p. Then 175p is more than 165p.
• When the pence reach 100p, change 100p into £1. 65p + 50p = 115p. That is £1 and 15p.

Remember: Check whether you need a total or the change, keep the pounds and the pence in their own places, and write £ or p in your answer.

Time can be read from an analogue clock, written as a digital time, and measured as a duration. The hour hand and the minute hand work together. Use the facts about seconds, minutes, hours, days and months to compare and calculate.

Key words

o'clock

The time is exactly on the hour. The minute hand points to 12.

half past

30 minutes after the hour. The minute hand points to 6.

quarter past

15 minutes after the hour. The minute hand points to 3.

quarter to

15 minutes before the next hour. The minute hand points to 9.

analogue clock

A clock with hands that move round a dial.

digital clock

A clock that shows the time as numbers, such as 3:15.

12-hour clock

Uses am for the morning and pm for the afternoon and evening.

24-hour clock

Counts the hours from 00:00 to 23:59. It does not use am or pm.

am and pm

am is for times after midnight and before noon. pm is for times after noon and before midnight.

noon

12 o'clock in the middle of the day. It is 12:00 pm, or 12:00 in 24-hour time.

midnight

12 o'clock at night, when one day ends and the next begins. It is 12:00 am, or 00:00 in 24-hour time.

Roman numerals

Numbers written with letters. I is 1, V is 5 and X is 10.

duration

How long something lasts, such as 35 minutes.

timeline

A line that shows times in order, with the start, the end and the jumps between.

leap year

A year with 366 days. February has 29 days.

Key facts

• 60 seconds = 1 minute. 60 minutes = 1 hour. 24 hours = 1 day. 7 days = 1 week.
• A year has 365 days. A leap year has 366 days because February has 29 days instead of 28.
• Seven months have 31 days, four months have 30 days and February has 28 or 29 days.
• On a clock face each number is 5 minutes more than the one before. The 3 is 15 minutes, the 6 is 30 minutes and the 9 is 45 minutes.
• The hour hand moves slowly as the minutes pass. At quarter past it is just past the hour number. At quarter to it is almost at the next hour number.
• Roman numerals on a clock work in the same way. I is 1, V is 5, X is 10, IV is 4 and IX is 9.
• The 12-hour clock uses am for the morning and pm for the afternoon and evening. The 24-hour clock does not use am or pm.
• To write a pm time from 1:00 pm onwards in 24-hour time, add 12 to the hour. The minutes stay the same. 3:15 pm is 15:15.
• Noon is 12:00 pm, and the hour stays 12 just after noon: 12:30 pm is 12:30. Just after midnight the 12 becomes 00: 12:20 am is 00:20.
• To find a duration, count on from the start time to the end time. To find an end time, count on the duration from the start time. The next hour is a useful stepping stone.
• Compare durations in the same unit. For example, change minutes into seconds first.

Pictures to remember

Worked examples

Common reminders

• The hour hand moves too. At quarter past 7 it is just past the 7. At ten to 5 it is just before the 5, but the hour is still 4.
• Check am or pm. 7:05 am and 7:05 pm are different times. In 24-hour time they are 07:05 and 19:05.
• Use one form at a time. Write 15:15 or 3:15 pm. Do not write 15:15 pm.
• Keep the units when you compare. 3 minutes is longer than 100 seconds, even though 3 is less than 100. 1 hour is 60 minutes, not 100 minutes.
• Read IV and VI carefully. IV is 4 and VI is 6. On a Roman numeral clock, IV is where the 4 would be.

Remember: Read the minute hand first, then use it to decide which hour the hour hand is showing.

Angles, lines and shapes are described with a few exact words. A right angle is a quarter turn. Parallel lines never meet, and perpendicular lines meet at a right angle. A shape keeps its name and its properties when it is turned.

Key words

angle

An angle is made where two lines meet. You can find angles in the corners of shapes and in turns.

right angle

The angle in the corner of a square. A right angle is a quarter turn, and it is 90 degrees.

quarter turn

One quarter of the way round. A quarter turn is 1 right angle.

half turn

Half of the way round. A half turn is 2 right angles.

three-quarter turn

Three quarters of the way round. A three-quarter turn is 3 right angles.

full turn

All the way round, back to where you started. A full turn is 4 right angles.

horizontal

A line that goes across, level like the horizon.

vertical

A line that goes straight up and down.

parallel

Parallel lines stay the same distance apart and never meet.

perpendicular

Perpendicular lines meet at a right angle.

2-D shape

A flat shape that you can draw on paper, such as a square or a circle.

side

A straight line that forms part of the edge of a 2-D shape.

polygon

A closed 2-D shape with straight sides, such as a triangle or a hexagon. A circle is not a polygon, because its edge is curved.

quadrilateral

A polygon with 4 sides. Squares and rectangles are quadrilaterals.

3-D shape

A solid shape that takes up space, such as a cube or a sphere.

face

A flat or curved surface of a 3-D shape.

edge

Where two faces of a 3-D shape meet.

vertex

A corner. In a 2-D shape, sides meet at each vertex. In a cube or cuboid, 3 edges meet at each vertex. The plural is vertices.

Key facts

• An angle is made where two lines meet. You can find angles in the corners of shapes and in turns.
• A right angle is a quarter turn. It is the angle in the corner of a square, and it is 90 degrees.
• Turns are made of right angles: a quarter turn is 1 right angle, a half turn is 2, a three-quarter turn is 3 and a full turn is 4.
• To compare an angle with a right angle, picture the corner of a square. An angle that opens less than that corner is less than a right angle. An angle that opens wider is greater than a right angle.
• The length of the arms does not change the size of an angle. Look at how wide the angle opens.
• Horizontal lines go across, level like the horizon. Vertical lines go straight up and down.
• Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle.
• A 2-D shape is flat. A polygon is a closed 2-D shape with straight sides, so a polygon has as many vertices as it has sides. A circle is not a polygon.
• A quadrilateral is a polygon with 4 sides. A triangle has 3 sides, a pentagon 5, a hexagon 6 and an octagon 8.
• A square and a rectangle each have 4 sides, 4 vertices and 4 right angles.
• A 3-D shape is solid. Its faces are flat or curved surfaces, its edges are where two faces meet and its vertices are its corners.
• A cube and a cuboid each have 6 faces, 12 edges and 8 vertices. A cylinder has 2 flat faces and 1 curved surface. A cone has 1 flat face, 1 curved surface and 1 vertex. A sphere has 1 curved surface and no edges or vertices.
• A shape keeps its name and its properties when it is turned. In a picture of a 3-D shape some faces, edges and vertices are hidden, but they are still there.

Pictures to remember

Worked examples

Common reminders

• Compare with the corner of a square. A right angle matches the corner of a square exactly. A corner that is narrower or wider is not a right angle.
• The length of the arms does not change the angle. An angle with short arms can open wider than an angle with long arms.
• Parallel lines never meet. Perpendicular lines meet at a right angle. Two lines can cross without being perpendicular. They are perpendicular only if they cross at a right angle.
• Horizontal goes across. Vertical goes up and down. A lamp post is vertical. The horizon is horizontal. Parallel lines can be horizontal, vertical or sloping.
• Count the right angles in a turn. A half turn is 2 right angles, not 1. A full turn is 4 right angles.
• A shape keeps its name and its properties when it is turned. A cube on its edge is still a cube. A square standing on a corner is still a square.
• Count the faces, edges and vertices you cannot see. A picture of a cube shows 3 faces, but the cube has 6 faces.
• A face is not the whole shape, and an edge is not a vertex. One face of a cube is a square, but the cube is a 3-D shape. An edge is a line and a vertex is a corner.

Remember: Compare an angle with the corner of a square, name a shape from its properties and not its position, and count every face, edge and vertex, even the hidden ones.

Data can be shown in a table, a pictogram or a bar chart. Read the key or the scale first, then find the numbers you need. Use them to find a total or to find how many more.

Key words

data

Information that has been collected, such as how many children chose each lunch.

category

One group in the data, such as Pizza or Rice. Each category has its own number.

table

Data arranged in rows and columns. Find a category in its row, then read along to its number.

pictogram

A chart that uses symbols to show amounts. Each symbol is worth the number given in the key.

key

Tells you what one symbol stands for. A pictogram needs a key.

bar chart

A chart that uses bars to show amounts. The top of a bar shows the number.

scale

The numbers up the side of a bar chart. Check how much each step goes up by.

total

All the numbers added together.

how many more (difference)

How many more is the difference between two numbers. Subtract the smaller number from the larger.

tally chart

A chart that counts with tally marks. Four lines with a line across make 5.

Key facts

• Data is information that has been collected. A table, a pictogram and a bar chart are three ways to show it.
• Read the key or the scale first, before you answer a question.
• In a pictogram, the key tells you what one symbol is worth. Number of symbols × value of one symbol = the amount.
• If the key says one symbol stands for 5 children, 4 symbols show 4 × 5 = 20 children.
• In a bar chart, the scale shows the numbers up the side. Check how much each step goes up by. A scale marked 0, 2, 4, 6 goes up in 2s.
• The top of a bar is level with a number on the scale. That number is the amount.
• A table shows each category in a row. Read along the row to find its number.
• The total is all the numbers added together: 7 + 9 + 4 = 20.
• How many more? Find the difference. Subtract the smaller number from the larger: 20 − 15 = 5.
• A two-step question needs two calculations. Find the numbers you need, then answer what the question asks.
• When you show data, label every category and show the key or the scale.
• A tally chart counts with tally marks. Four lines with a line across make 5, so count in 5s: 5, 10, 15.

Pictures to remember

Worked examples

Common reminders

• Check what one symbol is worth. If the key says one symbol stands for 10 books, 3 symbols show 3 × 10 = 30 books, not 3.
• Read across to the scale. On a scale that goes up in 2s, a bar level with the third mark above 0 shows 6, not 3.
• A category is not a number. In a chart of lunches, Rice is the category and 8 is the number of children.
• How many more means subtract. Reading has 20 and Art has 15. How many more is 20 − 15 = 5. Adding gives 20 + 15 = 35, which is the total.
• Finish every step of a two-step question. To find how many more stickers were given on Tuesday and Wednesday together than on Monday, first add 9 + 15 = 24, then subtract 24 − 12 = 12.

Remember: Read the key or the scale first, then find the numbers you need and answer the question that was asked.