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.)