Home Mathematics Grade 3 Mathematics · Grade 3 Skills Read and write numbers to 10,000 Reads 6,205 aloud and writes "four thousand and nine" as 4,009, handling zeros inside the number. Compare and order 4-digit numbers Puts 5,342; 5,324; 4,999 in order and says which is greater by comparing thousands first, then hundreds. Place a number on a line to 10,000 Puts 6,250 on a line labelled 0 and 10,000 by working out which thousand it lies between and roughly where in it. Read unlabelled marks on a zoomed line Reads the number at an unlabelled mark on a line from 6,000 to 7,000 split into tens of hundreds (the mark is 6,400). Count in 4s, 6s, 7s, 8s and 9s Counts forward and back in 4s, 6s, 7s, 8s and 9s from any multiple (42, 49, 56, 63, 72). Count in 25s, 50s, 100s and 1000s Counts 25, 50, 75, 100, 125, in 50s and 100s (350, 400, 450), and 3,000, 4,000, 5,000, and says the next number after 975. Roman numerals to C (non-gating) Reads XXXIV as 34 and writes 49 as XLIX using I, V, X, L, C. Local extra. Compare temperatures below zero (introduce) Says −3 °C is colder than −1 °C and orders −4, −1, 2 on a vertical thermometer. Explore only. Count back through zero (introduce) Counts 3, 2, 1, 0, −1, −2 and says which floor is two below the ground floor. Explore only. Value of each digit in 4-digit numbers Says the 3 in 4,306 is worth 300 and the 4 is worth 4,000. Partition 4-digit numbers; zero as placeholder Writes 4,306 as 4,000 + 300 + 6 and says what the 0 in the tens place is doing. Add or subtract 1, 10, 100, 1000 Says 10 more than 4,396 is 4,406 and 1000 less than 5,090 is 4,090 without a written sum. Round to the nearest 10 Rounds 4,376 to 4,380 and 2,455 to 2,460, deciding by the ones digit. Round to the nearest 100 Rounds 4,376 to 4,400 and 2,450 to 2,500, deciding by the tens digit. Multiply by 10 and 100 by shifting digits Explains 35 × 100 = 3,500 as each digit moving two places left, with zeros holding the empty places. Read a 4-digit number with blocks Reads 2,345 as 2 thousands, 3 hundreds, 4 tens, 5 ones with blocks. Moved from G2. Column addition to 4 digits Adds 3,478 + 2,356 in columns, carrying in any column. Column subtraction to 4 digits Subtracts 6,254 − 2,876 in columns, exchanging from the next place when needed. Subtract across zeros Works out 5,003 − 2,768 by exchanging through the zeros. Check with inverse and estimates Checks 5,003 − 2,768 = 2,235 by adding 2,235 + 2,768 and by rounding to check it is near 2,200. All multiplication facts to 10 × 10 Knows 7 × 8 = 56 and 56 ÷ 7 = 8 and every other fact to 10 × 10. Commutativity and fact families Uses 6 × 4 = 4 × 6 to halve the facts to learn, and writes the four facts 6 × 4, 4 × 6, 24 ÷ 4, 24 ÷ 6; knows division is not commutative. The 11 and 12 tables with division facts Knows 12 × 7 = 84 and 96 ÷ 12 = 8, and 11 × 9 = 99. Multiply 2- and 3-digit numbers by 1 digit Works out 47 × 6 and 308 × 4 with a grid, partial products or short multiplication. Divide 2- and 3-digit numbers by 1 digit with a remainder Works out 87 ÷ 4 = 21 remainder 3 and 453 ÷ 5 = 90 remainder 3, saying the remainder is what is left over. Divide 4-digit numbers by 1 digit (introduce) Works out 4,375 ÷ 5 = 875 by short division and checks by multiplying. Explore only. 2-digit × 2-digit with an area model (introduce) Splits 23 × 14 into 20 × 10, 20 × 4, 3 × 10, 3 × 4 and adds the four partial products. Explore only. Brackets and order of operations (introduce) Says 3 × (4 + 2) = 18 but 3 × 4 + 2 = 14 because brackets go first. Explore only. Multiply three numbers in any order (introduce) Reorders 2 × 7 × 5 as 2 × 5 × 7 = 10 × 7 = 70 and says why the order does not matter. Explore only. Distributive law as a strategy (introduce) Works out 7 × 14 as 7 × 10 + 7 × 4 = 98. Explore only. ×0 and ×1 facts Says 7 × 0 = 0 and 7 × 1 = 7, and 0 ÷ 5 = 0, knowing multiplying by 1 changes nothing and by 0 gives 0. (OP-13/14 stay explore-only.) Instant recall of table facts Answers 7 × 8 or 54 ÷ 6 within about 3 seconds. Judge table facts instantly Says at a glance that 6 × 8 = 48 is true and 7 × 8 = 54 is false. Bridge through 10 Works out 68 + 7 as 68 + 2 + 5 = 75, and 8 + 6 as 8 + 2 + 4. Bridge through 100 Works out 396 + 8 as 396 + 4 + 4 = 404, and 504 − 7 as 504 − 4 − 3. Mental 2-digit ± 2-digit Works out 47 + 36 as 47 + 30 + 6 = 83 and 62 − 29 as 62 − 30 + 1 = 33, by partitioning or compensation. Multiply by 10 and 100 mentally Answers 64 × 10 = 640 and 35 × 100 = 3,500 instantly. Multiply by multiples of 10 Works out 4 × 60 = 240 as 4 × 6 tens. Estimate sums and differences by rounding Says 298 + 405 is about 700 and 4,980 − 2,010 is about 3,000. Estimate products by rounding Says 49 × 6 is about 50 × 6 = 300. Multiples of a number Lists the first multiples of 6 and says 42 is a multiple of 6. Factor pairs as rectangles Builds every rectangle from 12 or 24 tiles and reads off 24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6. Find all factor pairs of a number to 100 Lists 36 = 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 in an organised way and knows when to stop. Use "factor" and "multiple" correctly Says "6 is a factor of 18; 18 is a multiple of 6" and sorts numbers into each group. Count in tenths Counts 1/10, 2/10, … 10/10 and past, knowing tenths come from cutting a whole in ten. Count in hundredths Counts 1/100, 2/100 … and says ten hundredths make one tenth (introduce). Fractions on a 0–1 line and past 1 Places 3/4 and 5/4 on a line from 0 to 2, seeing fractions as numbers with a position. Equivalent fractions on a fraction wall Shows ½ = 2/4 = 4/8 by lining up strips, models only. Tenths equal hundredths Shows 3/10 = 30/100 on a 100-square by shading three columns (models only, no simplifying). Compare same-denominator and same-numerator fractions Says 3/8 > 2/8 (same size parts, more of them) and 1/3 > 1/5 (fewer cuts, bigger parts), and justifies with a model. Add same-denominator fractions Works out 3/8 + 2/8 = 5/8 with a bar. Add beyond one whole Works out 5/8 + 7/8 = 12/8 and sees it is more than one whole. No conversion rule yet. G4 preview, going beyond G3.FR.6 "within 1". Subtract same-denominator fractions Works out 7/8 − 5/8 = 2/8 and 7/10 − 3/10 = 4/10. G4.FR.4 preview only: 12/8 − 5/8 = 7/8. Fraction of a quantity Finds ¼ of 20 = 5 and ¾ of 20 = 15, and solves a simple problem with them. Name a/b as a parts of size 1/b Says 3/4 is three pieces each worth 1/4, for denominators 2, 3, 4, 6, 8 and 10. Whole numbers as fractions Says 3 = 3/1 and 4/4 = 1, and that 6/3 sits on the same spot as 2. The decimal point in prices and measures Reads $3.45 and 1.5 m, knowing the point separates whole units from parts. Value of decimal digits to hundredths Says 3.45 is 3 ones, 4 tenths, 5 hundredths. Hundredths introduce-only. Compare decimals to 2 places Says 3.45 is less than 3.5 by comparing tenths first. Order decimals on a number line Places 2.7, 2.07, 2.75 on a line from 2 to 3. Round decimals to the nearest whole number Rounds 3.6 to 4 and 3.2 to 3, looking at the tenths digit (tenths only). Tenths and hundredths as decimals Writes 3/10 as 0.3 and 7/100 as 0.07 and places them on a line. ½, ¼ and ¾ as decimals Knows ½ = 0.5, ¼ = 0.25, ¾ = 0.75. Add and subtract tenths Works out 0.4 + 0.3 = 0.7 and 1.2 − 0.5 = 0.7 (tenths only). Missing number in a multiplication Solves ☐ × 6 = 42 by thinking 6 times what makes 42. Missing number in a division Solves 56 ÷ ☐ = 8 and ☐ ÷ 7 = 6 using the matching multiplication. Patterns in the tables Explains why even × any number is even and spots the 9s digit pattern. Complete an input–output machine Fills the outputs of a "× 3" machine for inputs 2, 5, 9. Find the machine's rule Sees inputs 2, 4, 6 give outputs 8, 16, 24 and says the rule is × 4. Continue a number sequence Continues 7, 14, 21, … or 100, 90, 80, … for several terms. State a sequence rule in words Says "start at 4 and add 6 each time". Know the metric units and their links Knows 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 l = 1000 ml. Compare and order measures Orders 3 ribbons by length and says which jug holds more. Add and subtract measures Works out 2 m 40 cm + 1 m 75 cm and 3 kg − 1 kg 500 g. Convert between adjacent units Says 2 kg = 2,000 g and 350 cm = 3 m 50 cm; also 1 m 25 cm = 125 cm. Read scales in steps of 2, 5, 10 Reads a thermometer in steps of 2 and a ruler in steps of 5 mm. Read scales with unlabelled divisions Works out the step from two labelled marks and reads 250 g on a scale in steps of 50 g, or 100 ml. Estimate with benchmarks Says a door is about 2 m and a bottle about 1 l, and picks the sensible unit. Perimeter of a polygon Measures and adds the sides of a rectangle or a polygon: 5 + 3 + 5 + 3 = 16 cm. Find a missing side from the perimeter Finds the unknown side of a rectangle with perimeter 20 cm and sides 7 and ☐. Area by counting squares Counts unit squares to say a shape covers 12 cm² (and m² squares for a floor or mat). Area of a rectangle as rows × columns Says 4 rows of 6 squares is 24 and writes length × width. Area of shapes made of rectangles Splits an L-shape into two rectangles and adds their areas, comparing with the perimeter. Read an analog clock to the minute Reads 4:37 and "23 minutes past 6" on an analog clock. Roman-numeral clock faces Reads the time on a clock with Roman numerals, e.g. VII for 7. Write the same time three ways Writes 7:35 digitally, says "twenty-five to eight" and matches them. Duration within the hour Works out the time from 3:20 to 3:45 is 25 minutes. Duration across the hour Works out 3:50 to 4:20 is 30 minutes by jumping to 4:00. Find an end or start time from a duration Says a film starting 2:15 that lasts 50 minutes ends at 3:05. Convert hours, minutes and seconds Says 2 hours = 120 minutes and 3 minutes = 180 seconds. Leap years (non-gating) Knows a leap year has 366 days and 29 February, and finds which year in a list is one. Write money in decimal notation Writes 4 dollars 5 cents as $4.05. Convert dollars and cents Says $4.05 = 405 cents and 250 cents = $2.50. Add and subtract amounts Works out $3.45 + $2.80 and $10.00 − $6.35. Give change by counting on Gives change from $5 for $3.40 by counting 60 cents, then $1. Compare prices Says which of $4.50 and $4.05 is cheaper and by how much. Decide what can be afforded Says $7.50 buys the $3.20 book and the $4 toy but not two toys. Squares and rectangles Says a rectangle has 4 right angles and equal opposite sides, and a square is also a rectangle. Rhombuses, parallelograms, trapezoids and kites Names a shape with 4 equal sides but no right angles a rhombus, a shape with one pair of parallel sides a trapezoid, and knows a square is also a rhombus. Sort quadrilaterals by properties Sorts shapes into overlapping groups (4 equal sides, right angles, parallel sides). Equal parts as unit fractions Splits a square into 4 equal-area parts and names each as 1/4. Equal area, different shapes Shows two pieces cut differently from the same square are both halves. An angle as a turn; the right angle Says a right angle is a quarter turn and finds right angles in a room. Smaller than, equal to, larger than a right angle Tells which of three angles is smaller than a right angle, using a checker. Parallel and perpendicular lines Spots parallel and perpendicular pairs in a drawing and a floor plan. Horizontal and vertical lines; drawing lines Names horizontal and vertical lines and draws a line parallel to one on a grid. Make 3D shapes from materials Builds a cube and a pyramid from straws and clay and counts the edges. Recognise 3D shapes from different views Matches the top, front and side views to the solid. Compass directions N, E, S, W Says which way a character moves and gives directions like "go east 3". Quarter, half and full turns Says a quarter turn is 1 right angle, a half turn 2, a full turn 4. Grid references on a map Finds the museum at C4 on a map. Describe a route Says "north 2, turn right, east 3" to get across a map. Read coordinates (introduce) Reads the point (3, 5) as 3 across and 5 up. Plot points (introduce) Plots (3, 5) and joins points to draw a shape. Read scaled pictograms Reads a pictogram where 1 symbol = 5 and says 3½ symbols is 17 or 18, giving the total. Draw scaled pictograms Draws 20 as 4 symbols when 1 symbol = 5. Read and draw bar charts with a scale Reads a bar to the nearest tick on a scale of 2, 5 or 10 and draws a bar for 35. Read a table and compare Says which group has the most using a table, including a simple two-way table (e.g. boys/girls by favourite pet). "How many more or fewer" Works out 35 − 28 = 7 more. Two-step data questions Works out the total of two groups, then how many more than a third. Read line plots in halves and quarters Reads a plot where crosses sit at 2½, 2¾. Draw line plots in halves and quarters Measures lengths and marks crosses on a line plot. Plan an investigation Writes a question and a plan for collecting data (e.g. favourite fruit). Show data and give a conclusion Draws a chart and says what it shows. List every outcome Lists the six faces of a die or the colours of a spinner. More or less likely Says on a spinner with 3 red and 1 blue that red is more likely. Compare results with expectation Rolls a die 30 times and says why the tally is not exactly even. Two-step problem with an equation Solves "28 apples, 3 boxes of 6 removed" with 28 − 3 × 6 = ☐. Choose the operations Decides a problem needs × then + and why. Comparison bar models Draws two bars, 24 and 17, and shows the difference is 7. "Times as many" bar models Shows "3 times as many" with a short bar and one three times longer. Judge whether an answer makes sense Says 78 + 49 = 227 is wrong because it should be near 130. Spot missing information Says "How much change?" needs the amount paid. Spot surplus information Crosses out the fact not needed. Explain a method Says in order how 24 × 3 was worked out. Compare two methods Says which of two methods for 99 + 36 is quicker and why. Organised lists for all solutions Lists all pairs of numbers with sum 10 in order. Tables to find all solutions Uses a table to find every outfit from 3 tops and 2 skirts.