Home Mathematics Grade 4 Mathematics · Grade 4 Skills Read and write numbers to the millions Reads and writes 3,070,400 as "three million, seventy thousand, four hundred" and back. Compare and order numbers to the millions Decides that 4,206,090 is more than 4,196,999 by comparing from the highest place and orders a set of 4–5 such numbers. Read billions by 3-digit groups (enrichment, non-gating) Reads 2,340,000,000 as "two billion, three hundred forty million" by reading each group of three. Place big numbers on a number line Places 640,000 on a 0–1,000,000 line and finds the midpoint of 2,000,000 and 3,000,000 (the billions part is enrichment, non-gating; G4.NUM.1 covers only the to-1,000,000 part). Roman numerals to M (local, non-gating) Reads XIV, XLIX and MCMXC and the year on a monument. Lakh/crore commas (local, non-gating) Reads 12,50,000 as "twelve lakh fifty thousand" and knows it equals 1,250,000. Count back through zero Counts 3, 1, −1, −3 on a number line and says what comes after −2 going up. Gap between a negative and a positive number Finds the gap between −4 °C and 7 °C (11 degrees) or between floor −2 and floor 3 (5 floors). Digit value in numbers to millions Says that the 4 in 3,482,150 is worth 400,000 and the 3 is worth 3,000,000. Expanded form and the ten-times rule Writes 3,482,150 as 3,000,000 + 400,000 + … and says why the 8 is ten times the 8 one place to its right. Decimal place value to hundredths Says that each digit in 2.71 is worth 2, 7/10 and 1/100, and writes 3.47 = 3 + 4/10 + 7/100 in expanded form. Thousandths are G5-PV-6. Round whole numbers to any place Rounds 458,372 to 458,000 (nearest thousand) and 460,000 (nearest 10,000) and says why. Multiply and divide whole numbers by 10, 100, 1000 Shifts digits to get 45 × 100 = 4500 and 4500 ÷ 1000 = 4.5. Divide multiples of 10 and 100 by 10 and 100 Says 4,500 ÷ 100 = 45, the digits shifting right, as the undo of ×100. Decimal scaling is G5-PV-1. Column addition and subtraction of multi-digit numbers Adds 4,687 + 2,759 and subtracts 5,003 − 2,768 in columns, regrouping and trading across zeros. Check ± by estimate and inverse Checks 5,003 − 2,768 = 2,235 by rounding to 5,000 − 2,800 and by adding 2,235 + 2,768. Add and subtract decimals in columns Lines up the decimal point to compute 12.4 + 3.85 and 7 − 2.35, and a 3-place case, 2.375 + 1.4. Multiply 3- and 4-digit numbers by 1 digit Computes 4,237 × 6 with an area model and then in a column. Introduce 4-digit × 2-digit Computes 1,246 × 23 as two partial-product rows and adds them (introduce only). Multiply and divide a decimal by a whole number Gets 2.5 × 4 = 10, 3.2 × 3 = 9.6 and a hundredths case, 1.25 × 4 = 5, and shares 4.8 ÷ 4 = 1.2 (introduce only). Divide up to 4 digits by 1 digit Computes 735 ÷ 5 and 4,284 ÷ 6 by sharing place by place (short division). Decide what to do with a remainder Answers "58 children, 8 per bus" with 8 buses (round up) and "58 sweets, 8 per box" with 7 boxes (drop). Introduce division by a 2-digit number Works 156 ÷ 12 by chunking with multiples of 12 (introduce, whole-number remainder only). "Times as many" versus "more than" Says that 12 is "3 times as many as 4" but "8 more than 4". Distributive and associative properties Calculates 25 × 4 × 7 as 100 × 7 and 6 × 98 as 6 × 100 − 6 × 2. Order of operations without brackets Evaluates 3 + 4 × 2 = 11 and 20 − 12 ÷ 4 = 17, doing × ÷ before + −. Brackets in expressions Shows that (3 + 4) × 2 = 14 and places brackets in 2 + 3 × 4 to make 20. Multiply 2-digit by 2-digit Computes 34 × 27 with an area model (30 × 27 + 4 × 27), then in a column with two partial-product rows. Multiply and divide multiples of 10 and 100 mentally Computes 30 × 40 = 1,200 and 2,400 ÷ 6 = 400 from the basic fact. Add and subtract by rounding and compensating Computes 346 + 99 as 346 + 100 − 1 and 502 − 298 as 502 − 300 + 2. Double and halve to simplify Turns 16 × 25 into 8 × 50 into 4 × 100 = 400. Estimate products Estimates 48 × 6 as 50 × 6 = 300 and decides whether 288 is reasonable. Estimate quotients with friendly numbers Estimates 412 ÷ 8 as 400 ÷ 8 = 50 using compatible numbers. Choose the best mental strategy Picks compensation for 346 + 99, double-and-halve for 16 × 25 and tens-facts for 30 × 40. Recall facts to 12×12 and matching divisions Recalls 7 × 8 = 56, 12 × 11 = 132 and 132 ÷ 12 = 11 instantly. Find factor pairs to 100 Lists all factor pairs of 36: 1×36, 2×18, 3×12, 4×9, 6×6. Recognise multiples Says that 56 is a multiple of 7 and lists the multiples of 9 up to 100. Common factors of two numbers Finds that 12 and 18 share 1, 2, 3 and 6. Prime or composite to 100 Decides that 47 is prime and 51 (3 × 17) is composite. Divisibility rules for 2, 5, 10 Knows that 3,460 is divisible by 2, 5 and 10 and 1,375 only by 5. Square numbers and ² Builds 7² = 49 from tiles and recognises 36 and 81 as squares; knows the squares up to 12². Cube numbers and ³ Builds 3³ = 27 from blocks and reads 2³ as 2 × 2 × 2 = 8; knows the cubes up to 5³ (125). Common multiples of two numbers (non-gating, G5 lead-in) Lists multiples of 4 and 6 and finds the shared ones: 12, 24. Generate equivalent fractions Shows that 3/4 = 6/8 = 9/12 by multiplying numerator and denominator by the same number. Simplify to lowest terms Reduces 12/18 to 2/3 by dividing top and bottom by the common factor 6. Compare fractions with a benchmark Decides that 5/8 > 1/2 and 3/7 < 1/2 without a common denominator. Compare and order with a common denominator Orders 3/4, 2/3 and 5/6 by rewriting them as twelfths. Convert improper fractions and mixed numbers Writes 11/4 as 2¾ and 3½ as 7/2. Add and subtract fractions with the same denominator Computes 5/8 + 7/8 = 12/8 = 1½ and 1 − 3/8 = 5/8. Add and subtract related denominators Computes 2/3 + 1/6 = 4/6 + 1/6 = 5/6. Add and subtract mixed numbers Computes 2¼ + 1¾ = 4 and 3½ − 1¾ = 1¾. Decompose a fraction into a sum Writes 3/8 = 1/8 + 2/8 and 3/8 = 1/4 + 1/8. Multiply a fraction by a whole number Computes 3 × 2/5 = 6/5 = 1 1/5 as repeated addition. Find a fraction of a quantity Finds 3/5 of 40 as 3 × (40 ÷ 5) = 24 in a word problem. Compare decimals to 3 places Decides 0.45 > 0.405 by comparing place by place. Order and place decimals on a number line Places 0.405, 0.45 and 0.5 on a line that zooms from tenths to thousandths. Round decimals to the nearest whole Rounds 6.48 to 6 and 6.5 to 7. Add and subtract decimals in money and measures Computes €4.75 + €2.60 and 3.4 m − 1.85 m in context. Percent means "out of 100" Shades 25 squares of a 100-grid and says "25%, 25 out of 100". Link percent, fraction and decimal Matches 25% = 25/100 = 0.25 = ¼ for ½, ¼, ¾, ⅕, tenths (7/10 = 0.7) and hundredths. Continue a number pattern from its rule Continues 4, 7, 10, … from "add 3". Notice what a rule does not say Spots that 4, 7, 10, 13 alternates even and odd although the rule only says "add 3". Growing shape patterns Predicts how many matchsticks the 6th shape needs from the first four. Use a symbol for one unknown Solves □ + 17 = 40 and 6 × □ = 54. Unknown in a multi-step sentence Solves 3 × □ + 4 = 19 by undoing + 4 then × 3. State the rule between two columns Reads the table 1→5, 2→10, 3→15 and says "multiply by 5". Two-step column rules Finds that 1→5, 2→8, 3→11 follows "× 3, then + 2". Metric length relationships Converts 3.5 km to 3,500 m and 450 cm to 4.5 m. Metric mass and capacity relationships Converts 2.4 kg to 2,400 g and 750 ml to 0.75 l. Estimate length, mass and capacity Estimates the length of a desk as about 120 cm and a bottle as about 500 ml, then checks. Read scales with unlabelled divisions Reads a kitchen scale that goes up in 20 g steps with only 100 g labelled. Solve measurement problems with the four operations Works out how many 35 cm ribbons come from 2.4 m, with 10 cm left over. Area of a rectangle with a formula Computes 8 cm × 5 cm = 40 cm² and says why it is "squares in each row × rows". Area of shapes made of rectangles Splits an L-shape into two rectangles and gets 12 + 8 = 20 cm². Perimeter of rectangles and rectilinear shapes Gets 2 × (9 + 4) = 26 cm and walks round an L-shape to total its sides. Find a missing side from perimeter or area Finds that a 40 cm² rectangle that is 8 cm long is 5 cm wide, and a missing side from a perimeter of 26 cm. Same area, different perimeter Shows that 6 × 4 and 12 × 2 both have area 24 cm² but perimeters 20 and 28. Convert 12-hour and 24-hour times Converts 3:45 pm to 15:45 and 00:20 to 12:20 am. Read a timetable Finds the 14:25 bus from a station and its arrival time in a table. Plan a journey with a timetable Chooses the train that gets you to school by 08:30 with a 10-minute walk. Durations across the hour Works out 07:48 to 09:15 as 1 h 27 min using a time line. Durations across midnight Works out 22:40 to 01:15 as 2 h 35 min. Find a date weeks ahead or behind Finds the date 3 weeks after 14 March and the weekday it falls on. Total and change with decimal amounts Adds €3.45 + €2.80 and finds the change from €10. Multiply and divide with money Computes 4 × €2.45 = €9.80 and €7.80 ÷ 4 = €1.95 each. Multi-step shopping problems Plans a party list: 3 pizzas, 2 drinks each for 6 guests, then the change from €50. Estimate a bill and check the change Rounds €3.45 + €6.80 + €1.95 to about €12 and spots that change of €5 from €20 is wrong. Points, lines, segments and rays Tells a line segment from a ray and a line and names them (AB, ray CD). Parallel and perpendicular lines Finds the parallel and perpendicular pairs on a map or a letter shape and draws them. Name angle types Calls 45° acute, 90° right, 120° obtuse, 180° straight and 250° reflex. Measure and draw angles with a protractor Reads 65° from the correct scale and draws a 110° angle. Angles on a straight line and around a point Finds the missing angle as 180° − 125° = 55° on a line and 360° − 270° = 90° around a point. Classify triangles by sides Names a triangle with sides 5, 5 and 8 as isosceles. Classify triangles by angles Names a triangle with a 100° angle obtuse and one with a 90° angle right. Regular and irregular polygons Explains that a rhombus is irregular as its angles are not equal, while a square is regular. Find lines of symmetry Finds all 4 lines of symmetry of a square and the single line of an isosceles triangle. Complete a symmetric figure Draws the mirror half of a figure across a vertical, horizontal or diagonal line. Parts of a circle and drawing with compasses Names centre, radius and diameter (diameter = 2 × radius) and draws a circle of radius 3 cm. Faces, edges and vertices of prisms and pyramids Says a triangular prism has 5 faces, 9 edges and 6 vertices and a square pyramid has 5, 8 and 5. Plot and read coordinates in the first quadrant Plots (3, 5) and says that the point is 3 across and 5 up. Draw a polygon from its vertices Plots (1, 1), (4, 1), (4, 3), (1, 3) and joins them to see a rectangle. Eight compass points Names the direction between north and east as north-east and plans a route using them. Turns of 90°, 180°, 270° Faces north, turns 270° clockwise and says which way you face (west). Translate a shape and describe the move Slides a triangle "left 2, up 3" and describes the move from start and end. Reflect a point in a mirror line Reflects (2, 5) in a vertical mirror line at x = 4 to get (6, 5). Reflect a shape in a horizontal or vertical mirror Reflects a whole polygon by reflecting each vertex. Draw and read bar charts with a scale Draws a bar chart with a scale of 2 per square and reads a bar that ends between labels. Double bar charts Compares boys and girls on a double bar chart ("5 more preferred swimming"). Draw and read line graphs Plots temperature at each hour and reads the value between two marks. Describe the trend of a line graph Says "it rose until noon, then fell" and which period changed fastest. Read and complete two-way tables Fills in a two-way table (class × favourite sport) and answers "how many girls chose football?". Line plots with fractions of a unit Plots pencil lengths in ¼ cm on a line plot and finds the difference between the longest and shortest. Pose a question and collect data Rewrites "Do you like sport?" as "Which sport do you like best?" and tallies answers. Pick the graph that fits the data Chooses a line graph for temperature over a week and a bar chart for favourite fruits. List all outcomes of an experiment Lists the 6 outcomes of a die and the 4 of two coins (HH, HT, TH, TT). Equally likely or not Says a 3-colour spinner with unequal slices is not fair and why. Design a fair or unfair game Re-slices a spinner so one player wins about twice as often, or makes it fair. Multi-step problems with mixed operations and units Solves "3 packs of 250 g plus 1.5 kg, how many kg?" by converting first. Bar models for "times as many" Draws a bar for "Tom has 3 times as many as Mia" and finds both amounts. Bar models for fraction problems Draws 5 equal parts to show that 3/5 of a bar is 24 and finds the whole (40). Work systematically to find all solutions Lists every 2-coin total from {1, 2, 5, 10} in an organised table or tree and knows none is missing. Explain and critique a method Explains 36 × 5 as "half of 36 × 10" so a friend can follow it and says what is wrong in someone else's steps. Conjectures and counterexamples Tests "all numbers ending in 5 are divisible by 10" and finds 15 as a counterexample.