Whole Numbers 1 Know that a whole number is a normal counting MNU 0-0a number such as 0, 1,, 3, 4, Count past 10 MNU 0-03a 3 Know why place value is important MNU 1-0a 4 Know that approximating means to get an answer MNU 1-01a close to the actual (true) answer 5 Add whole numbers (no carrying) without a calculator (e.g. 1 + 35) MNU 1-03a 6 Add whole numbers (carrying) without a calculator (e.g. 68 + 79) MNU 1-03a 7 Add whole numbers mentally MNU 1-03a 8 Approximate answers to adding sums (e.g. 7 + 59 90) MNU 1-01a 9 Subtract whole numbers (no borrowing) without a calculator MNU 1-03a (e.g. 65 ) 10 Subtract whole numbers (borrowing) without a calculator MNU 1-03a (e.g. 7 38) 11 Subtract whole numbers mentally MNU 1-03a 1 Approximate answers to subtraction sums (e.g. 138 71 70) MNU 1-01a 13 Add and subtract whole numbers in real-life problems MNU 3-03a 14 Multiply a whole number by a single digit without a calculator MNU 1-03a (e.g. 3 5, 56 9, 879 8) 15 Know how to make the times tables MNU 1-03a 16 Know the times tables up to 1 1 MNU 1-03a 17 Multiply whole numbers mentally (e.g. 7 8, 1 4, 35 6) MNU 1-03a 18 Approximate answers to multiplication sums (e.g. 9 5 150) MNU 1-01a 19 Multiply a whole number by 10, 100 and 1 000 MNU 1-03a (e.g. 5 10, 6 100, 1 000, 30 10, 40 100, 90 1 000) 0 Multiply a whole number by multiples of 10, 100 and 1 000 MNU 1-03a (e.g. 4 0, 3 400, 6 5 000, 78 90) 1 Multiply two -digit whole numbers without a calculator MNU 1-03a (e.g. 53 96, 44 75) Multiply bigger whole numbers (e.g. 987 64) MNU 1-03a 3 Multiply whole numbers in real-life situations MNU 3-03a 4 Know that a power of a whole number is that number multiplied by MTH 3-06a 3 itself so many times (e.g. = ) 5 Divide a whole number by a single digit (no remainder) (e.g. 38 7) MNU 1-03a 6 Divide whole numbers (no remainder) mentally (e.g. 36 9) MNU 1-03a 7 Divide whole numbers (remainder) mentally (e.g. 40 7) MNU 1-03a 8 Approximate answers to division sums (e.g. 53 5 50) MNU 1-01a 1
9 Divide whole numbers (no remainder) without a calculator (e.g. 84 6, 119 7) 30 Divide whole numbers (remainder) without a calculator (e.g. 87 5, 13 9) MNU 1-03a MNU 1-03a 31 Divide a whole number by 10, 100 and 1 000 MNU 1-03a (e.g. 60 10, 5 000 100, 90 000 1 000, 370 10, 40 300 100, 708 000 1 000) 3 Divide whole numbers by multiples of 10, 100 and 1 000 MNU 1-03a (e.g. 40 0, 1 500 300, 60 000 5 000) 33 Divide whole numbers in real-life situations MNU 3-03a 34 List even and odd numbers MNU 0-0a 35 Find factors of a whole number (e.g. 10 has 1,, 5 and 10) MTH -05a 36 Know that a whole number is prime if its only factors MTH 3-05b are 1 and the whole number itself 37 Know why 1 is not prime MTH 3-05b 38 Know why is the only even prime MTH 3-05b 39 Find the prime numbers up to 100 using the Sieve of Eratosthenes, MTH 3-05b or otherwise 40 Find prime factors of a whole number (e.g. 0 has and 5) MTH 3-05b 41 Write a whole number as a product of powers of primes (e.g. 7 = 3 3, 50 = 5 ) MTH 3-05b, MTH 3-06a 4 Know that rounding means to approximate (estimate) MNU -01a 43 Round a whole number to the nearest 10 (e.g. 9, 35, 85) MNU 3-01a 44 Round a whole number to the nearest 100 (e.g. 47, 149, 1 55) MNU 3-01a 45 Round a whole number to the nearest 1 000 (e.g. 459, 499, 3 500) MNU 3-01a 46 Find the square of a number (e.g. 1, 4, 10, 1 ) MTH 3-06a 47 Find the square root of a number (e.g. 1, 49, 11 ) MTH 4-06a 48 Know that BODMAS means Brackets, Orders, Division, MTH -03c Multiplication, Addition and Subtraction 49 Use BODMAS without brackets (e.g. 3 + 7 8 = 59) MTH -03c 50 Use BODMAS with brackets (e.g. 1 (5 ) = 7) MTH 4-03b
Fractions, Percentages and Decimals 1 Know that a fraction is (usually) part of a whole and written as, MNU 1-07a numerator denominator Work out unitary fractions (numerator = 1) of a whole number without a calculator (e.g. half of 0, quarter of 48) 3 Work out other fractions of a whole number without a calculator such as, MNU 1-07b MNU 1-07b 3 4 of 16 of 84 7 4 Know that a proper fraction is one where the numerator is smaller than the denominator (e.g. /3) 5 Know that an improper fraction (aka top-heavy) is one where the numerator is bigger than the denominator (e.g. 5/4) MNU 1-07a MNU 1-07a 6 Know that a mixed number is a whole number plus a proper fraction MNU 1-07a 7 Change a mixed number into an improper fraction, for example, MTH 3-07c 3 7 = 3 7 8 Change an improper fraction into a mixed number, for example, 14 3 = 4 3 9 Know that equivalent fractions are ones that are the same (e.g. /4 = 1/) 10 Simplify fractions and write fractions in simplest form such as, 0 4 = 5 6 11 Add and subtract fractions with the same denominator such as, MTH 3-07c MTH 1-07c MTH -07c MTH 3-07b 9 + 3 9 = 5 16 5, 9 1 1 = 11 1 1 Add and subtract fractions with different denominators such as, MTH 3-07b 3
3 8 + 1 4 = 5 7, 8 1 36 = 19 36 13 Multiply fractions, for example, MTH 4-07b 11 7 3 = 14 33 14 Know that a percentage is a fraction with denominator = 100 MNU -07a 15 Know that 100 % = 1 whole and 1 % = 1 out of 100 MNU -07a 16 Know other important equivalences between fractions and common percentages such as, MNU -07b 50 % = 5 % = 75 % = 0 % = 10 % = 1 1 4 3 4 1 5 1 10 33 1 % = 1 3 3 17 Change simple percentages to fractions such as, MNU -07a 70 % = 70 100 = 7 10 18 Work out common or simple percentages of a whole number without MNU -07a a calculator (e.g. 5 % of 64, 60% of 740) 19 Know that a decimal (number) is a whole number with a decimal point MNU -0a and a number of digits (fractional part) after the point 0 Round a decimal to the nearest unit (e.g. 0 4, 3 5, 5 9), tenth MNU 3-01a (e.g. 1 45, 449) or hundredth (e.g. 0 56, 0 909 9) 1 Find a decimal on a number scale (up to hundredths) MNU -07a Add decimals (up to 3 d.p.) without a calculator MNU -07a 4
(e.g. 3 105 + 4 07) 3 Subtract decimals (up to 3 d.p.) without a calculator (e.g. 15 1 879) 4 Multiply a decimal (up to 3 d.p.) by a single digit whole number (e.g. 8 195 6) 5 Multiply a decimal (up to 3 d.p.) by 10, 100 and 1 000 (e.g. 6 436 10, 6 436 100, 6 436 1 000) 6 Multiply a decimal (up to 3 d.p.) by a multiple of 10, 100 or 1 000 (e.g. 8 70 0, 8 70 600, 8 70 7 000) 7 Divide a decimal (up to 3 d.p.) by a single digit whole number (e.g. 8 196 6) 8 Divide a decimal (up to 3 d.p.) by 10, 100 and 1 000 (e.g. 6 436 10, 6 436 100, 6 436 1 000) 9 Divide a decimal (up to 3 d.p.) by a multiple of 10, 100 or 1 000 (e.g. 8 196 60, 8 196 00, 8 196 3 000 ) MNU -07a MNU -07a MNU -07a MNU -07a MNU -07a MNU -07a MNU -07a 30 Know simple decimals such as 50 % = 0 5 and 5 % = 0 5 MNU -07a 31 Work out commonly used percentages (such as 60 %, 5 % ) MNU -07a of a whole number or decimal without a calculator 3 Work out other percentages with a calculator MNU 3-07a (e.g. 3 % of 43, 1 7 % of 65, 37 % of 9 3) 33 Work out one number as a percentage of another with a calculator (e.g. 1 as a percentage of 47) MNU 3-07a 34 Know that every fraction can be written as a decimal that either terminates (stops) or goes on forever (recurs), for example, 5 = 0 4 MNU -07b 5 = 0 555... = 0 5& 9 35 Change simple fractions and percentages to decimals MNU -07b 36 Divide two small whole numbers without a calculator, giving the MNU 3-07a answer to a certain number of decimal places (e.g. /3 = 0 667 correct to 3 d.p.) 5
Temperature and Integers 1 Know that an integer is a whole or negative whole number MNU -04a Know that temperature is a measure of hotness or coldness MNU -04a 3 Know units of temperature (e.g. degrees Celsius ( C )) MNU -04a 4 Read temperature from a thermometer MNU 3-04a 5 Add small integers without a calculator (e.g. 3 + ( 5)) MNU -04a 6 Add other integers with a calculator (e.g. 3 45 + 5 978) MNU -04a 7 Subtract small integers without a calculator (e.g. 11 ( 17)) MNU -04a 8 Subtract other integers with a calculator (e.g. 671 ( 53)) MNU -04a 9 Work out temperature differences MNU 3-04a 10 Multiply integers (e.g. 3 4, 5 ( 4), ( 6) ( 7)) MNU -04a 11 Divide integers (e.g. 0 5, 56 ( 7), ( 60) ( 1)) MNU -04a Patterns and Sequences 1 Spot a number pattern and continue it MTH 1-13b Give the rule used to get the next number in a number pattern MTH 1-13b 3 Spot a picture pattern and continue it MTH 0-13a 4 Describe the rule used to get the next picture in a picture pattern MTH 0-13a 5 Make a table from a picture pattern with constant differences MTH 1-13b 6 From a table, work out a rule for the number of items in the n th MTH 3-13a, MTH 4-13a picture (n th term formula) for a simple picture pattern with constant differences (e.g. n, 3n, 4n, 5n) 7 From a table, work out a rule for the number of items in the n th MTH 3-13a, picture for a complicated picture pattern with constant MTH 4-13a differences (e.g. n + 3, 3n 1, 5n ) 8 Use the n th term rule to find the number of items in the n th MTH 4-13a picture 9 Use the n th term formula to find which picture (value of n) MTH 4-13a has a certain number of items 10 Solve real-life problems using sequences MTH 4-13a 11 Spot triangular numbers and know how they are made from pictures MTH 0-13a 1 Spot square numbers and know how they are made from pictures MTH 0-13a 13 Explore other figurate numbers MTH -13a 14 Build up the Fibonacci sequence MTH -13a 15 Explore how Fibonacci numbers arise in real-life MTH 0-13a 6
Symmetry and Tilings 1 Know that a shape has symmetry if, after changing it, the shape looks the same MTH 1-19a Know that a reflection involves a line of symmetry MTH -19a, 3 Find a line of symmetry on a shape MTH -19a, 4 Draw a vertical line of symmetry on a picture (e.g. capital W) MTH -19a, 5 Complete a picture that has a vertical line of symmetry MTH -19a, 6 Make a picture that has a vertical line of symmetry MTH -19a, 7 Draw a horizontal line of symmetry on a picture (e.g. capital H) MTH -19a, 8 Complete a picture that has a horizontal line of symmetry MTH -19a, 9 Make a picture that has a horizontal line of symmetry MTH -19a, 10 Draw more than 1 line of symmetry on a picture (e.g. rectangle) MTH -19a, 11 Draw a diagonal line of symmetry on a picture (e.g. square) MTH -19a, 1 Complete a picture that has a diagonal line of symmetry MTH -19a, 13 Make a picture that has a diagonal line of symmetry MTH -19a, 14 Know that a rectangle does not have a diagonal line of symmetry MTH 1-19a 15 Investigate reflection symmetry in real-life MTH 1-19a 16 Know that a rotation involves a turning about MTH 4-19a the middle of a picture 17 Know that the order of rotational symmetry is the number of MTH 4-19a times the picture must be turned to get it back to the original picture 18 Complete a picture which has half-turn symmetry MTH 4-19a 19 Complete a picture on squared paper which has half-turn symmetry MTH 4-19a 0 Complete a picture which has quarter-turn symmetry MTH 4-19a 7
1 Complete a picture on squared paper which MTH 4-19a has quarter-turn symmetry Investigate rotational symmetry in real-life MTH 1-19a 3 Know that a glide symmetry involves sliding (translating) a picture a given distance along a straight line and reflecting it MTH 1-19a 4 Complete a pattern that has glide symmetry MTH -19a, 5 Make a pattern that has glide symmetry MTH 0-19a 6 Investigate glide symmetry in real-life MTH 1-19a 7 Know that a tiling (tessellation) is a way of covering a flat surface without overlaps or gaps (like bathroom tiles) MTH 1-16b 8 Know that any square, triangle or rectangle makes a tiling MTH 1-16b 9 Know that any quadrilateral or regular hexagon makes a tiling MTH 1-16b 30 Know that there are 3 regular (aka Platonic) tilings MTH 1-16b 31 Continue a regular tiling pattern MTH 1-16b 3 Make a regular tiling pattern MTH 1-16b 33 Know that there are 8 semiregular tilings MTH 1-16b 34 Continue a semiregular tiling pattern MTH 1-16b 35 Make a semiregular tiling pattern MTH 1-16b 36 Know why a pentagon does not make a tiling MTH 1-16b 37 Investigate other shapes that don t tile MTH 1-16b 38 Investigate Penrose tilings MTH 1-16b Mass and Weight 1 Know that mass is a measure of how much material there is MNU 0-11a Know that weight is a measure of how heavy something is MNU 0-11a 3 Know that in maths, weight is often (incorrectly) used for mass MNU 0-11a 4 Estimate the weight of an object MNU 1-11a 5 Weigh objects using various devices MNU 1-11a 6 Know that units of mass include grams (g) and kilograms (kg) MNU 1-11a 7 Know that 1 kg = 1 000 g MNU -11b 8 Change kilograms to grams MNU -11b 9 Change grams to kilograms MNU -11b 10 Know that 1 tonne = 1 000 kg MNU -11b 11 Change kilograms to tonnes MNU -11b 1 Change tonnes to kilograms MNU -11b 8
Time, Distance and Speed 1 Know that time is a measure of how long something lasts MNU 0-10a Know different units of time (e.g. seconds, minutes, hours, days) MNU 0-10a 3 Use a clock or watch to tell the time MNU 0-10a 4 Use a stopwatch to accurately measure times MNU 0-10a 5 Estimate how long something takes MNU 1-10c 6 Know that 60 seconds = 1 minute MNU 0-10a 7 Change minutes to seconds (e.g. 7 min = 40 s) MNU 0-10a 8 Change seconds to minutes (e.g. 10 s = 3 5 min) MNU 0-10a 9 Change minutes into minutes and seconds MNU 0-10a 10 Change minutes and seconds into minutes only MNU 0-10a 11 Know that 60 minutes = 1 hour MNU 0-10a 1 Change hours to minutes (e.g. 4 h = 40 min) MNU 0-10a 13 Change minutes to hours (e.g. 150 min = 5 h) MNU 0-10a 14 Change hours and minutes into hours only MNU 0-10a 15 Change hours into hours and minutes MNU 0-10a 16 Know that 4 hours = 1 day MNU 0-10a 17 Change days to hours (e.g. 5 days = 10 h) MNU 0-10a 18 Change hours to days (e.g. 36 h = 1 5 days) MNU 0-10a 19 Know the 7 days of the week and their order MNU 0-10a 0 Know how many days are in each month MNU 0-10a 1 Know the 1 months of the year and their order MNU 0-10a Know that a leap year has 366 days MNU 0-10a 3 Decide whether or not a specific year is a leap year MNU 0-10a 4 Change 1 hour time to 4-hour time (e.g. 1.57 pm 13 57) MNU 1-10a 5 Change 4 hour time to 1-hour time (e.g. 06 3 6.3 am) MNU 1-10a 6 Write time in words and figures (e.g. 19 35 or twenty-five to eight) MNU 0-10a 7 Add times, especially in hours and minutes MNU 0-10a 8 Subtract times, especially in hours and minutes MNU 0-10a 9 Work out time differences in the same day (e.g. 13 45 to 3 13) MNU 0-10a 30 Work out time differences over midnight (e.g. 11 pm to 6 am) MNU 0-10a 31 Use a timetable (e.g. bus or train) to plan a journey MNU -10a 3 Plan a personal routine using a clock or diary MNU 1-10b 33 Know that Earth has 4 time zones MNU 0-10a 34 Plan a journey that involves travelling between time zones MNU -10a 35 Know that an Earth day is not the same as a day on other planets MNU 0-10a 36 Know that distance is a measure of how far away something is MNU 0-10a 37 Know different units of distance (e.g. metres, kilometers, miles) MNU 0-10a 9
38 Know that speed is a measure of how fast something moves MNU 0-10a 39 Know different units of speed (e.g. miles per hour) MNU 0-10a 40 Work out distance D when told speed S and time T using, MNU 3-10a D = S T without a calculator (e.g. S = 5 5 mph, T = h) 41 Work out distance D when told speed S and time T using, MNU 3-10a D = S T with a calculator (e.g. S = 3 9 m/s, T = 7 6 s) 4 Calculate speed using, MNU 3-10a S = D T without a calculator (e.g. D = 56 m, T = 4 s) 43 Calculate speed using, MNU 3-10a S = D T with a calculator (e.g. D = 39 miles, T = 7 h) 44 Calculate time using, MNU 3-10a T = D S without a calculator (e.g. D = 10 km, S = 6 km/s ) 45 Calculate time using, MNU 3-10a T = D S with a calculator (e.g. D = 63 m, S = 13 m/s ) 46 Draw a distance-time graph MNU 4-10b 47 Know that the steepness of a distance-time graph shows speed MNU 4-10b 48 Know what a flat part of a distance-time graph means MNU 4-10b 49 Use a distance-time graph to solve problems MNU 4-10b 50 Estimate how long a journey may take at a certain speed MNU -10c 10
Angles 1 Know that an angle is the shape made by lines (arms) sharing a common endpoint and that a unit of angle is the degree MTH -17a Use 3 letters to name an angle MTH 3-17a 3 Know that an acute angle is strictly between 0 and 90, an obtuse MTH -17a angle is strictly between 90 and 180 and a reflex angle is strictly between 180 and 360 4 Know that a right angle has 90 MTH -17a 5 Know that complementary angles add up to 90 MTH -17a 6 Work out a missing angle at a right angle MTH 3-17a 7 Know that a straight line has 180 MTH -17a 8 Know that supplementary angles add up to 180 MTH -17a 9 Work out a missing angle at a straight line MTH 3-17a 10 Know that a circle has 360 MTH -17a 11 Work out a missing angle in a circle MTH 3-17a 1 Use a protractor to measure an angle smaller than 180 MTH -17b 13 Use a protractor to measure an angle bigger than 180 MTH -17b 14 Use a protractor to draw an angle MTH -17b 15 Estimate sizes of angles MTH -17a 16 Know that parallel lines are ones that never meet MTH 3-17a 17 Know that a transversal is a line that crosses MTH 3-17a or more lines at different points 18 Know that corresponding angles (aka F-angles) are made MTH 3-17a when a transversal crosses a pair of parallel lines 19 Know that corresponding angles are equal MTH 3-17a 0 Know that alternate angles (aka Z-angles) are made MTH 3-17a when a transversal crosses a pair of parallel lines 1 Know that alternate angles are equal MTH 3-17a Know that vertically opposite angles (aka X-angles) are made when two straight lines cross each other MTH 3-17a 3 Know that vertically opposite angles are equal MTH 3-17a 4 Know that the 3 angles in any triangle add up to 180 MTH 3-17a 5 Find a missing angle in a triangle when told the other angles MTH 3-17a 6 Know that the 4 angles in a quadrilateral add up to 360 MTH 3-17a 7 Find a missing angle in a quadrilateral when told the other 3 angles MTH 3-17a 8 Find the sum of the interior angles in a polygon MTH 3-17a 9 Find the sum of the exterior angles in a polygon MTH 3-17a 30 Find missing angles in various constructions and geometric figures MTH 3-17a 11
Ratio and Proportion 1 Know that things are in direct proportion (aka direct variation) if one increases at the same rate as the other Solve simple proportion problems such as, if identical bottles weigh 40 grams, find the weight of 1 of these bottles 3 Solve more difficult problems involving proportion such as, if 3 identical items cost 1 36, find the cost of 5 of these items 4 Know that a ratio is a way of dividing up something into or more segments, each segment being made up of equal parts 5 Know that a ratio of a to b (written a : b) means that for each amount of a there is an amount b (and that the total number of parts = a + b); for example, a ratio of boys to 3 girls means that for every boys, there are 3 girls ( : 3) 6 Know that a ratio of a : b does not equal a ratio of b : a unless a = b MNU 3-08a MNU 3-08a MNU 3-08a MNU 3-08a MNU 3-08a MNU 3-08a 7 Know that a ratio of 1 : 1 means equal parts MNU 3-08a 8 Simplify ratios such as, : 4, 17 : 51, 35 : 5 and 00 : 350 MNU 3-08a 9 Work out problems involving ratios by considering the total number of parts 10 Work out problems involving proportion by multiplying or dividing the relevant whole numbers 11 Know that a graph of direct proportion is a straight line passing through the origin of a coordinate system 1 Solve direct proportion problems such as, if the cost of a carpet varies directly as its length and a 5 metre long carpet costs 340 (i) how much will a carpet of 8 metres cost (ii) how long is a carpet which costs 38? MNU 3-08a MNU 3-08a MTH 4-13d MNU 3-08a 1
Directions, Bearings and Scale Drawings 1 Give directions for a journey using the words left, right, back and forward MTH 0-17a Follow directions for a journey MTH 1-17a 3 Know that the four cardinal compass directions are North (N), MTH -17c South (S), East (E) and West (W) and know where they point 4 Know that a bearing is an angle (i) written using 3 digits (ii) measured clockwise from a North line MTH -17c 5 Work out the bearing of a point B from a point A by drawing the North line at A and measuring clockwise to B MTH -17c 6 Measure the bearing of one point from another MTH -17c 7 Know the bearings of the 4 cardinal compass directions, i.e. N (0 ), MTH -17c E (090 ), S (180 ) and W (70 ) 8 Know that four of the intercardinal compass directions are North East (NE), North West (NW), South East (SE) and South West (SW) and know where they point MTH -17c 9 Know the bearings of the 4 intercardinal compass directions, i.e. MTH -17c NE (045 ), SE (135 ), SW (5 ) and NW (315 ) 10 Describe a given journey using compass directions MTH -17c 11 Know the meaning of back-bearing MTH -17c 1 Know that if a point B has a bearing from A that is bigger than MTH -17c 180, the back-bearing is the bearing minus 180 13 Know that if a point B has a bearing from A that is smaller than MTH -17c 180, the back-bearing is the bearing plus 180 14 Use bearings and back-bearings to solve navigational problems MTH -17c 15 Know that a scale is a rule for working out an actual (real-life) length when told the measured length (and vice versa) MTH -17d 16 Know that a scale is usually written as a ratio MTH -17d 17 Work out a real-life length when told the MTH 3-17c scale and the measured length 18 Know what a scale drawing is MTH -17d 19 Make a scale drawing of a line MTH 3-17c 0 Make a scale drawing of a square or rectangle MTH 3-17c 1 Make scale drawings of other shapes and figures MTH 3-17c Use scale drawings to solve practical problems MTH 3-17b such as designing a house 3 Plot a point given the bearing and distance from another point MTH 3-17b 4 Plot point C given the bearing and distance from points A and B MTH 3-17b 13
Coordinates 1 Know that a coordinate is a pair of things (usually numbers) (x, y), x being the x - coordinate and y the y - coordinate Know that a coordinate grid consists of an equally spaced (usually numbered) horizontal line (x - axis), an equally spaced (usually numbered) vertical line (y - axis) and the origin (where the axes cross) 3 Know that (x, y) is not the same as (y, x) unless x and y are the same MTH -18a, MTH 3-18a MTH -18a, MTH 3-18a MTH -18a, MTH 3-18a 4 Know that points such as (3, 0), (8, 0) and (0, 0) are on the x - axis MTH -18a, MTH 3-18a 5 Know that points such as (0, ), (0, 9) and (0, 0) are on the y - axis MTH -18a, MTH 3-18a 6 Know that the origin has coordinates (0, 0) MTH -18a, MTH 3-18a 7 Plot a coordinate when x and y are positive or zero MTH -18a, MTH 3-18a 8 Find and give the coordinates of an object on a grid with numbers and/or letters MTH 1-18a, MTH -18a, MTH 3-18a 9 Know that a coordinate grid can be divided into 4 quadrants MTH 4-18a 10 Plot coordinates in all four quadrants MTH 4-18a 11 Given 3 points on any coordinate grid, plot another point to complete a quadrilateral 1 Given points on any coordinate grid, plot other points to complete a quadrilateral 13 Given the area of a quadrilateral and 1 or vertices as coordinates on any coordinate grid, plot a coordinate (or ) to complete the quadrilateral MTH 4-18a MTH 4-18a MTH 4-18a 14
Statistics and Probability 1 Use tally marks to count MNU 0-0a Know that data (aka information) is a list of things, usually numbers MNU 0-0a 3 Collect data MNU 0-0a 4 Know that a frequency table (aka tally chart) is a way of MTH 1-1a recording how many times something happens 5 Make a tally chart MTH 1-1a 6 Know the meaning of grouped data MNU 1-0b 7 Make a frequency table using grouped data MNU 1-0b 8 Make a frequency polygon using grouped data MTH 1-1a 9 Know that the mode is the most common thing and MTH 4-0b work out the mode from a list of things 10 Calculate the mode from a frequency table MTH 4-0b 11 Calculate the range of data using the equation, MTH 4-0b Range = Highest number Lowest number 1 Calculate the range from a frequency table MTH 4-0b 13 Work out the mean using the equation, MTH 4-0b Mean = Total How many numbers there are 14 Calculate the mean of data that has 0 and negative numbers MTH 4-0b 15 Calculate the mean from a frequency table MTH 4-0b 16 Know that the median of a data set is the middle number when the MTH 4-0b list is written from lowest to highest; in the case of numbers in the middle, the mean of these is taken to find the median 17 Calculate the median of some data MTH 4-0b 18 Calculate the median from a frequency table MTH 4-0b 19 Read information from a bar graph MNU -0a 0 Draw a bar graph MTH 1-1a 1 Read information from a pictograph MNU -0a Draw a pictograph MTH 1-1a 3 Read information from a line graph MNU -0a 4 Draw a line graph MTH 1-1a 5 Read information from a pie chart MNU -0a 6 Draw a pie chart MTH 1-1a 7 Use statistics in real-life situations MNU 0-0c, MNU 3-0a, MNU 3-0b 15
8 Know that probability measures the likelihood (the chances ) of something (event or outcome) happening 9 Know that probability is worked out using the equation, MNU 4-0a MNU 1-a MNU 3-a Probability = f t where f = number of favourable outcomes and t = total number of outcomes 30 Write probability as a fraction, decimal or percentage MNU 3-a 31 Mark probability on a likelihood line MNU 3-a 3 Do probability experiments (e.g. with cards or dice) MNU -a 33 Predict what might happen in a probability experiment MNU -a 34 Know that the total probability of all possible outcomes of an event equals 1 35 Know that probability written as a fraction always has the numerator less than or equal to the denominator 36 Know that probability written as a decimal always has a value between 0 and 1 (including both these values) 37 Know that probability written as a percentage always has a value between 0 % and 100 % (including both these values) 38 Know that a probability of 0 (or 0 %) means no chance of a given event happening 39 Know that a probability close to 0 (or 0 %) means (very) unlikely to happen MNU -a MNU 3-a MNU 3-a MNU 3-a MNU 1-a MNU 1-a 40 Know that a probability of 1 (or 100 %) means certainty MNU 1-a 41 Know that a probability close to 1 (or 100 %) MNU 1-a means (very) likely to happen 4 Calculate the probability of simple events (such as obtaining a 5 MNU 3-a from rolling a fair 6-sided die numbered from 1 to 6), leaving the answer as a fraction 43 Calculate the probability of a value occurring in a MNU -a frequency table, leaving the answer as a fraction 44 Predict how many times an event is likely to occur MNU 4-a 45 Use probability in real-life situations MNU 4-a 16
Algebraic Expressions 1 Know the meaning of (algebraic) expression MTH 3-14a Know the meaning of term in an algebraic expression MTH 3-14a 3 Write down examples of expressions MTH 3-14a 4 Make expressions from real-life situations MTH 3-14a 5 Collect like terms together (e.g. x + 5x x) MTH 3-14a 6 Know the meaning of simplify an expression MTH 3-14a 7 Add and subtract expressions (e.g. 3x + 5 x 1) MTH 3-14a 8 Multiply and divide expressions (e.g. x 3x, 1x 4x) MTH 3-14a 9 Know when expressions are the same MTH 3-14a 10 Work out an expression by replacing letters with numbers (substitution) MTH 3-14a 11 Expand/break brackets (e.g. 3 (x 4)) MTH 4-14a 1 Use BODMAS to evaluate an expression MTH 3-14a 13 Find algebraic factors (factors of an algebraic term) MTH 4-14b 14 Find common factors of algebraic terms (e.g. 3x and 1x ) MTH 4-14b 15 Factorise simple algebraic expressions (e.g. 1x 7) MTH 4-14b Volume 1 Know that volume measures how much 3D space there is in a shape MNU 0-11a Know that units of volume include cubic centimetres (cm 3 ), cubic MNU 1-11a metres (m 3 ), litres (l) and millitres (ml) 3 Estimate volume MNU 1-11a 4 Know that 1 l = 1 000 ml MNU -11b 5 Change litres to millilitres MNU -11b 6 Change millilitres to litres MNU -11b 7 Work out the volume of a cube or cuboid by using the equations, MNU -11c V = L L L (Cube) V = L B H (Cuboid) 8 Work out the height of a cuboid when told its volume and sides MTH 3-11b 9 Work out the volume of a shape by counting cubes MNU -11c 10 Calculate the volume of a prism given the base area and length MTH 4-11c 11 Work out the volume of a compound 3D shape MTH 3-11b 17
Solving Equations and Inequations 1 Know that an equation links expressions that are the same (balanced) MTH 1-15a Solve simple equations involving pictures MTH 1-15b 3 Make an equation from a number machine or picture MTH 3-15a 4 Solve 1-step equations (e.g. 3x = 18, x = 0, 5 + x = 11) MTH 3-15a 5 Solve -step equations (e.g. 5x 3 = 17, 3x 3 = 18) MTH 3-15a 6 Solve equations with 4 terms (e.g. 3x + = 18 x) MTH 4-15a 7 Solve equations with brackets (e.g. 6 (x 1) = 4) MTH 4-15a 8 Solve equations involving multiplying brackets MTH 4-15a (e.g. (x + 1) (x + 1) = (x + ) (x 3)) 9 Solve equations with fractions (e.g. 1 (x 1) = 16) MTH 4-15a 10 Know that an inequation links expressions MTH 1-15a that are not necessarily the same 11 Know the meanings of the 4 inequality symbols ( <, >, and ) MTH 1-15a 1 Solve simple inequations using pictures MTH 4-15a 13 Make an inequation MTH 4-15a 14 Solve 1-step inequations (e.g. 3x < 4, x > 0, 6 + x 17) MTH 4-15a 15 Solve -step inequations (e.g. 4x 3 > 5, 4x 3 < 1) MTH 4-15a 16 Solve inequations with 4 terms ( of which involve the unknown) (e.g. 3x + 3 19 x) MTH 4-15a 17 Solve inequations with brackets (e.g. (x 3) 4) MTH 4-15a 18 Solve inequations involving multiplying brackets MTH 4-15a (e.g. (x + 1) (x + 1) (x + ) (x 3)) 19 Solve inequations with fractions (e.g. 1 (x 1) < 16) MTH 4-15a 18
Length 1 Know that length is a measure of how long something is MNU 0-11a Know that units of length are the same as those of distance MNU 1-11a 3 Estimate the length of an object MNU 1-11a 4 Measure lengths of objects using various devices MNU 1-11a 5 Know that 1 cm = 10 mm MNU -11b 6 Change millimetres into centimetres MNU -11b 7 Change centimetres into millimetres MNU -11b 8 Know that 1 m = 100 cm MNU -11b 9 Change metres into centimetres MNU -11b 10 Change centimetres into metres MNU -11b 11 Know that 1 km = 1 000 m MNU -11b 1 Change metres into kilometres MNU -11b 13 Change kilometres into metres MNU -11b 14 Add lengths in the same units (e.g. 3 cm plus 48 cm) MNU -11b 15 Add lengths in different units (e.g. 17 cm and 0 5 m) MNU -11b 16 Subtract lengths in the same units (e.g. 96 cm minus 37 cm) MNU -11b 17 Subtract lengths in different units (e.g. 0 5 m minus 4 cm) MNU -11b 18 Know that perimeter is the total distance once around a D shape MNU -11c 19 Work out the perimeter of a square MNU -11c 0 Work out the perimeter of a rectangle MNU -11c 1 Work out the perimeter of a shape that can MNU -11c be broken up into rectangles only Calculate the perimeter of a complicated shape MNU -11c made up of rectangles and triangles only 3 Know how the radius and diameter of a circle are linked MTH 4-16b 4 Know that the circumference of a circle with radius r is the perimeter and calculated using the equation, MTH 4-16b C = πr 5 Know that a semicircle is half a circle MTH 4-16b 6 Calculate the perimeter of a composite shape involving semicircles MTH 4-16b 19
Area 1 Know that area measures how much D space there is in a shape MNU 0-11a Know units for area (e.g. square centimetres (cm ) ) MNU 0-11a 3 Estimate the area of a shape MNU 1-11b 4 Know that 1 cm = 100 mm MNU -11b 5 Change square millimetres into square centimetres MNU -11b 6 Change square centimetres into square millimetres MNU -11b 7 Know that 1 m = 10 000 cm MNU -11b 8 Change metres into centimetres MNU -11b 9 Change centimetres into metres MNU -11b 10 Know that 1 km = 1 000 000 m MNU -11b 11 Change square metres into square kilometres MNU -11b 1 Change square kilometres into square metres MNU -11b 13 Know that 1 h = 10 000 m MNU -11b 14 Change hectares into square metres MNU -11b 15 Change square metres into hectares MNU -11b 16 Work out the area of a square (L = length) using, A = L L 17 Work out the area of a rectangle (L = length, B = breadth) using, MNU -11c, MNU 3-11a MNU -11c, MNU 3-11a A = L B 18 Work out the area of a triangle (H = height, B = breadth) using, A = B H MNU -11c, MNU 3-11a 19 Work out areas of shapes by counting squares and half-squares MNU -11c 0 Work out the area of a kite or rhombus (diagonals c and d ) using, MNU 3-11a A = c d 1 Work out the area of a parallelogram (base B and height H ) using, MNU 3-11a A = B H Work out the area of a circle (r = radius) using, MNU 3-11a A = πr 3 Work out the area of a composite shape MTH 3-11b 0
D and 3D Shapes 1 Know that a -dimensional (D) shape is a (closed) shape drawn on a (usually flat) surface MTH 1-16a Know the meaning of vertex MTH -16a 3 Know that a 3-sided shape is called a triangle MTH 1-16a 4 Know that a quadrilateral is a 4-sided shape MTH 1-16a 5 Know that a square is a quadrilateral with (i) all sides the same (ii) 4 right angles (iii) diagonals that bisect each other (iv) 4 lines of symmetry MTH -16a 6 Know that a rectangle is a quadrilateral with (i) pairs of parallel lines (different length) (ii) 4 right angles (iii) diagonals that bisect each other (iv) lines of symmetry 7 Know that a parallelogram is a quadrilateral with (i) pairs of parallel sides (different length) (ii) equal, opposite, acute and equal, opposite, obtuse angles (iii) diagonals that bisect each other (iv) half-turn symmetry, but no lines of symmetry 8 Know that a rhombus is a quadrilateral with (i) pairs of parallel lines (all 4 lines have the same length) (ii) equal, opposite, acute and equal, opposite, obtuse angles (iii) diagonals (different length) that bisect each other at 90 (iv) lines of symmetry 9 Know that a kite is a quadrilateral with (i) pairs of equal sides (each pair a different length), with none parallel (ii) equal opposite angles (iii) diagonals that bisect each other at 90 (iv) 1 line of symmetry MTH -16a MTH -16a MTH -16a MTH -16a 10 Know that a composite shape is one made up of simple shapes MTH 3-11b such as squares, rectangles, triangles and semi-circles 11 Know the meaning of polygon MTH 1-16a 1 Know important polygons such a triangles, rectangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons and decagons MTH 1-16a 13 Know the meaning of convex polygon MTH 1-16a 14 Know the meaning of concave polygon MTH 1-16a 15 Sketch convex and concave polygons MTH -16c 16 Draw convex and concave polygons with a given number of sides MTH 3-16a using a ruler and compass 17 Know real-life applications of polygons MTH -16a 18 Name a polygon using letters MTH 1-16a 19 Know that a circle is all points the same MTH 4-16b distance from a given point (centre) 1
0 Draw a circle using a set of compasses MTH 3-16a 1 Know the meanings of radius (r) and diameter (D) and what they look like on a circle MTH 4-16b Know that D = r MTH 4-16b 3 Work out the diameter of a circle when told its radius MTH 4-16b 4 Work out the radius of a circle when told its diameter MTH 4-16b 5 Know that a 3-dimensional (3D) shape is a shape drawn in space MTH 0-16a 6 Recognise 3D shapes such as a cube, cuboid, cylinder, pyramid, cone and sphere and name them when shown pictures of them MTH 1-16a 7 Know that a net of a 3D shape is a flat (D) shape which, MTH -16b when folded up, makes the 3D shape 8 Know the properties of a cube MTH 1-16a 9 Recognise the net of a cube MTH -16b 30 Draw the net of a cube MTH -16b 31 Decide whether or not a given net can be used to make a cube MTH -16b 3 Make a cube from its net MTH -16b 33 Know the properties of a cuboid MTH 1-16a 34 Recognise the net of a cuboid MTH -16b 35 Draw the net of a cuboid MTH -16b 36 Decide whether or not a given net can be used to make a cuboid MTH -16b 37 Make a cuboid from its net MTH -16b 38 Know the properties of a pyramid MTH -16a 39 Draw the net of a pyramid MTH -16b 40 Know that a prism is a shape with a flat side (base) that is MTH 1-16a projected along a direction of 90 to the base 41 Recognise and name a triangular prism MTH 1-16a (prism with a triangle as base) 4 Know the properties of a triangular prism MTH -16a 43 Draw the net of a triangular prism MTH -16b 44 Know the meaning of polyhedron MTH 1-16a 45 Know the meaning of convex polyhedron MTH 1-16a 46 Know the meaning of concave polyhedron MTH 1-16a 47 Sketch convex and concave polyhedra MTH -16c 48 Know real-life applications of polyhedra MTH -16a 49 Name a polyhedron using letters MTH -16b 50 Make polyhedra using nets MTH -16b 51 Know the 5 Platonic solids MTH -16a 5 Investigate Euler s formula for the vertices, edges and faces of a convex polyhedron MTH -16a
Triangles 1 Know that a triangle is acute if all its angles are acute MTH 1-16a Know that a triangle is obtuse if it has an obtuse angle MTH 1-16a 3 Know that a right-angled triangle is one that has a right angle MTH 1-16a 4 Classify triangles by angle MTH 1-16a 5 Recognise right-angled triangles MTH 1-16a 6 Know the importance of right-angled triangles in real-life MTH 1-16a 7 Find lines of symmetry on different types of triangles MTH 1-16a, MTH -19a, 8 Know that a scalene triangle is one that has all MTH 1-16a sides of different lengths 9 Know that an isosceles triangle is one that has sides the same MTH 1-16a length and the remaining side different (equivalently, angles the same and the remaining angle different) 10 Know that an equilateral triangle has all sides the same length MTH 1-16a (equivalently, 3 angles the same) 11 Classify triangles by length MTH 1-16a 1 Find missing angles in a triangle MTH 4-16a 13 Draw triangles using a ruler and set of compasses MTH 3-16a 14 Know and explore Pythagoras Theorem MTH 4-16a 15 Use Pythagoras theorem to calculate the hypotenuse MTH 4-16a in a right-angled triangle 16 Use Pythagoras theorem to calculate a shorter side in a right-angled triangle MTH 4-16a 3
History of Maths Project 1 Work sensibly and properly in a small group MTH -1a Pick out information from a variety of sources MTH -1a 3 Find information (without plagiarizing) about a mathematician by using the internet and/or other resources MTH 3-1a 4 Know why the mathematician is important in history MTH 3-1a 5 Find information (without plagiarizing) about a mathematical topic MTH -1a by using the internet and/or other resources 6 Know why the mathematical topic is important in modern times MTH -1a 7 Present findings about a mathematician and/or mathematical topic to a class MTH -1a, MTH 3-1a 8 Give examples of mathematical skills needed in real-life MTH 4-1a Financial Maths Project 1 Know the different types of coins and notes used in this country MNU 0-09a Know that 1 = 100 p MNU 0-09a 3 Know the different types of coins and notes used in other countries MNU 0-09a 4 Use money to pay for items MNU 1-09a 5 Work out how much change is expected after buying an item MNU 1-09a, MNU 1-09b 6 Work out profit and loss MNU -09c 7 Fill out an application form to open a bank account MNU 3-09b 8 Fill out a budget planner MNU -09b 9 Use an ATM MNU 3-09b 10 Know the features of different types of cards (e.g. credit card, debit card, travel card) MNU -09b 11 Fill in a pay-slip or a cheque MNU 3-09b 1 Know the meaning of debt MNU 4-09a 13 Know that high levels of debt is a national issue MNU 4-09a 14 Know how to deal with debt MNU 4-09a 15 Describe ways of saving money and why this is important MNU 3-09b 16 Know the meaning of interest rate MNU 3-09a 17 Know that interest rates can be different from lenders MNU 3-09a 18 Know the dangers of borrowing with high interest rates MNU 3-09a 19 Know the advantages and disadvantages of borrowing money MNU 3-09a 4
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