Now we have come to what is expected of children aged between 8 and 9: as defined by the English Primary Framework for Mathematics (part of the National Curriculum). In year 4 there is a greater emphasis on written methods, with the standard or efficient method expected for both addition and subtraction. Children are expected to know all their tables and there is a lot more work on decimals.

**Counting and understanding number:**

By the end of year 4 children should

• read and write whole numbers up to thousands.

(eg write in words 4009.)

• be able to continue number sequences counting on and back in even steps.

(eg count back 60 in tens from 645.)

• partition 4-digit numbers into thousands, hundreds, tens and units.

(eg know that 2547 is 2 000 + 500 + 40 + 7.)

• order and round 4-digit numbers.

(eg round 3456 to the nearest hundred.)

• use negative numbers and place them on a number line.

(eg reading a thermometer below zero.)

• state inequalities using < and > signs.

(eg -4<0)

• use the decimal point to show tenths and hundredths.

(eg 6.3 is 6 and three tenths.)

• partition decimals.

(eg know that 2.45 is 2 units + 4 tenths + 5 hundredths.)

• relate decimals to money and measurement.

(eg write 465 cm as 4.65 metres.)

• recognise the equivalence between fractions and decimals of half, quarters, tenths and hundredths.

(eg 35/100 = 0.35.)

• use diagrams to show equivalent fractions.

(eg 4/5 and 8/10.)

• understand mixed numbers and place them on a number line.

(place 3 and four fifths on a number line from 0 to 10.)

• begin to use the vocabulary of ratio and proportion.

(eg 2 cars in every 5 cars….)

• estimate a proportion.

(eg about a quarter of the grapes are red.)

**Knowing and using number facts:**

By the end of year 4 children should

• use their knowledge of addition to add pairs of multiples of 10, 100 or 1 000.

(eg 600 + 700.)

• use their knowledge of subtraction to subtract pairs of multiples of 10, 100 or 100.

(eg 1300 – 600.)

• identify doubles of 2-digit numbers and use these to calculate doubles of multiples of 10 and 100.

(eg double 1 200.)

• derive halves of 2-digit numbers and use these to calculate halves of multiples of 10 and 100.

(eg half of 1 400.)

• know all multiplication facts (tables) up to 10×10.

(eg 6 x 7.)

• derive division facts from knowledge of tables.

(eg work out mentally 42 divided by 7.)

• use knowledge to derive multiples of numbers to 10 up to the tenth multiple/

(eg 60 x 5/)

• use knowledge of rounding to estimate and check calculations

(eg estimate 234 + 899 by adding 200 to 900).

• use knowledge of number operations and inverses to check answers.

(eg if 345 + 567 = 912 then 912 – 567 = 345.)

• identify pairs of fractions which total 1.

(eg 3/5 + 4/10.)

**Calculating:**

By the end of year 4 children should

• be able to add mentally two 2-digit numbers.

(eg 45 + 37.)

• be able to subtract mentally two 2-digit numbers.

(eg 65 – 37.)

• use efficient (standard) written methods to add 3-digit whole numbers and £.p.

(eg 245 + 456/)

• use efficient (standard) written methods to subtract 3-digit whole numbers and £.p.

(eg £4.56 – £2.15.)

• multiply or divide numbers up to 1 000 by 10 and understand the effect.

(eg each digit moves one place to the left/right.)

• multiply or divide numbers up to 1 000 by 100 and understand the effect.

(eg each digit moves two places to the left/right.)

• develop written methods for multiplication of 2-digits by 1-digit, but not the efficient or standard method.

(eg 48 x 6.)

• develop written methods for division of 2-digits by 1-digit (but not the efficient or standard method) including remainders.

(eg divide 59 by 6.)

• find fractions of numbers, quantities or shapes.

(eg find 1/5 of 35 apples.)

• use a calculator to carry out one-step and two-step operations.

(eg double 67 and add 42.)

• recognise negative numbers on the calculator display.

(eg recognise -4 as negative 4.)

• interpret money correctly from the display.

(eg know that 4.2 on the calculator is £4.20.)

**Understanding shape:**

By the end of year 4 children should

• be able to draw polygons and classify them according to their properties.

(eg identify all the pentagons in a group of shapes.)

• identify lines of symmetry in shapes.

(eg identify whether logos and adverts have line symmetry.)

• visualise 3-D objects from 2-D drawings.

(identify the properties of a cube from a 2-D drawing.)

• make nets of solids.

(eg using card and glue make a square based pyramid.)

• recognise horizontal and vertical lines.

• Use the 8 compass points to describe direction.

(eg move a counter on a grid 2 places south west.)

• Know that angles are measured in degrees and that one whole turn is 360 degrees.

• Compare and order angles less than 180 degrees.

(eg place in order of size 5 angles.)

**Measuring:**

By the end of year 4 children should

• know the standard metric units and their abbreviations.

(eg kg, g, km, m, cm. l, ml.)

• choose and use metric units when estimating, measuring and recording weight, length and capacity.

(eg suggest a metric unit for measuring the height of a door.)

• begin to use decimal notation to record measurements.

(eg know that 140cm is 1.4m.)

• record readings from scales accurately, where appropriate to the nearest tenth of a unit.

(eg read how much water there is in a measuring jug marked in 100 ml divisions.)

• measure and calculate the perimeter of rectangles.

(eg find the perimeter of a 3cm by 6cm rectangle.)

• find the area of shapes by counting squares.

(eg cover a shape with a transparent cm square grid and count the squares.)

• read the time to the nearest minute.

(eg know that 4:40 is twenty to five.)

• use am and pm.

(eg understand that 9:05 am is in the morning.)

• choose sensible units to estimate and measure time.

(eg suggest a suitable unit to time a 100m race.)

• calculate an interval of time between two events.

(eg read a train timetable to see how long it takes between two stations.)

**Handling data:**

By the end of year 4 children should

• collect and organise data.

(eg collect data on number of cars passing the gate at different times of day.)

• use tables, diagrams, tally charts, pictograms and bar charts to present results.

(eg use a bar chart to show times and number of cars.)

• analyse the data collected.

(draw conclusions from the bar chart above.)

• Compare the impact of graphs which use different scales.

(eg be aware that graphs with intervals of different size can impact of the effectiveness of a presentation.)

**Using and applying mathematics:**

By the end of year 4 children should

• solve one-step and two-step problems involving money, measures, time, and numbers by choosing appropriate calculations.

(eg decide what calculations to carry out to reach an answer.)

• solve puzzles and present the solution.

(eg arrange the numbers 1-9 in a square so that each side adds up to 12.)

• suggest a line of enquiry and collect the necessary information to find the answer.

(describe a short way to work out the perimeter of a rectangle.)

• make a statement and test it with examples.

(eg half way between any two multiples of 10 is a multiple of 5.)