Year 3 - Maths



NRICH problems linked to the Framework for teaching mathematics in Years 3, 4, 5 and 6

A list of recent updates can be found at the end of this document. The stars indicate the level of confidence and competence needed to begin the activity. One star problems will be suitable for the whole class, two stars for the majority and three stars for those who like a serious challenge.

N.B. This is work in progress – we would really appreciate your comments. Please email emp1001@cam.ac.uk

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 1 - Using and Applying |

|Solve one-step and two-step problems involving |Solve one-step and two-step problems involving |Solve one-step and two-step problems |Solve multi-step problems, and problems |Solve problems by breaking down complex|

|numbers, money or measures, including time, |numbers, money or measures, including time; |involving whole numbers and decimals and all |involving fractions, decimals and percentages; |calculations into simpler steps; choose|

|choosing and carrying out appropriate |choose and carry out appropriate calculations, |four operations, choosing and using |choose and use appropriate calculation |and use operations and calculation |

|calculations |using calculator methods where appropriate |appropriate calculation strategies, including|strategies at each stage, including calculator |strategies appropriate to the numbers |

|NRICH: A Square of Numbers * |NRICH: The Puzzling Sweet Shop ** |calculator use |use |and context; try alternative approaches|

|NRICH: How Do You See it? * | |NRICH: Money Bags ** |NRICH: Two Primes Make One Square ** |to overcome difficulties; present, |

| | |NRICH: Amy’s Dominoes ** |NRICH: Escape from the Castle ** |interpret and compare solutions |

|Represent the information in a puzzle or problem|Represent a puzzle or problem using number |Represent a puzzle or problem by identifying |Tabulate systematically the information in a |Represent information or unknown |

|using numbers, images or diagrams; use these to |sentences, statements or diagrams; use these to |and recording the information or calculations|problem or puzzle; identify and record the steps|numbers in a problem, for example in a |

|find a solution and present it in context, where|solve the problem; present and interpret the |needed to solve it; find possible solutions |or calculations needed to solve it, using |table, formula or equation; explain |

|appropriate using £.p notation or units of |solution in the context of the problem |and confirm them in the context of the |symbols where appropriate; interpret solutions |solutions in the context of the problem|

|measure |NRICH: Buying a Balloon * |problem |in the original context and check their accuracy|NRICH: Square Subtraction *** |

| |NRICH: Take Three Numbers * |NRICH: Sealed Solution ** |NRICH: Counting Cards *** | |

| |NRICH: Three Neighbours ** |NRICH: Prison Cells ** |NRICH: This Pied Piper of Hamelin ** | |

| |NRICH: Fifteen Cards * |NRICH: Spot Thirteen * |NRICH: Junior Frogs ** | |

| | | |NRICH: Inky Cube *** | |

|Follow a line of enquiry by deciding what |Suggest a line of enquiry and the strategy needed|Plan and pursue an enquiry; present evidence |Suggest, plan and develop lines of enquiry; |Develop and evaluate lines of enquiry; |

|information is important; make and use lists, |to follow it; collect, organise and interpret |by collecting, organising and interpreting |collect, organise and represent information, |identify, collect, organise and analyse|

|tables and graphs to organise and interpret the |selected information to find answers |information; suggest extensions to the |interpret results and review methods; identify |relevant information; decide how best |

|information |NRICH: How Tall? * |enquiry |and answer related questions |to represent conclusions and what |

|NRICH: Sweets in a Box * |NRICH: Eye View * |NRICH: Planning a School Trip * | |further questions to ask |

|NRICH: Going for Gold * |NRICH: In Order * | | | |

|NRICH: The Domesday Project * | | | | |

|NRICH: Birdwatch * | | | | |

|Describe patterns and relationships involving |Identify and use patterns, relationships and |Explore patterns, properties and |Represent and interpret sequences, patterns and |Generate sequences and describe the |

|numbers or shapes, and use these to solve |properties of numbers or shapes; investigate a |relationships and propose a general statement|relationships involving numbers and shapes; |general term; use letters and symbols |

|problems |statement involving numbers and test it with |involving numbers or shapes; identify |suggest and test hypotheses; construct and use |to represent unknown numbers or |

|NRICH: Ip Dip * |examples |examples for which the statement is true or |simple expressions and formulae in words then |variables; represent simple |

|NRICH: Cuisenaire Spirals * |NRICH: Break It Up * |false |symbols (e.g. the cost of c pens at 15 pence |relationships as graphs |

|NRICH: That Number Square! * |NRICH: Count the Digits * |NRICH: Up and Down Staircases * |each is 15c pence) | |

|NRICH: Unlocking the Case * | |NRICH: Magic Vs ** |NRICH: Sticky Triangles *** | |

|NRICH: It’s a Scrabble * | |NRICH: Number Differences * |NRICH: Light the Lights Again * | |

|NRICH: Carrying Cards * | |NRICH: Exploring Wild & Wonderful Number | | |

| | |Patterns * | | |

| | |NRICH: Exploring Number Patterns You Make **| | |

| | |NRICH: Become Maths Detectives * | | |

| | |NRICH: The Numbers Give the Design * | | |

| | |NRICH: Button-up Some More ** | | |

| | |NRICH: Sitting Round the Party Tables * | | |

| | |NRICH: Follow the Numbers * | | |

|Describe and explain methods, choices and |Report solutions to puzzles and problems, giving |Explain reasoning using diagrams, graphs and |Explain reasoning and conclusions, using words, |Explain and justify reasoning and |

|solutions to puzzles and problems, orally and in|explanations and reasoning orally and in writing,|text; refine ways of recording using images |symbols or diagrams as appropriate |conclusions, using notation, symbols |

|writing, using pictures and diagrams |using diagrams and symbols |and symbols |NRICH: Make 37 ** |and diagrams; find a counter-example to|

|NRICH: Dotty Six * | |NRICH: Beads and Bags * |NRICH: GOT IT ** |disprove a conjecture; use step-by-step|

| | | | |deductions to solve problems involving |

| | | | |shapes |

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 2 - Counting and Understanding Number |

|Read, write and order whole numbers to at least |Recognise and continue number sequences formed by|Count from any given number in whole-number |Find the difference between a positive and a |Compare and order integers and decimals|

|1000 and position them on a number line; count |counting on or back in steps of constant size |and decimal steps, extending beyond zero when|negative integer, or two negative integers, in |in different contexts |

|on from and back to zero in single-digit steps |NRICH: Number Tracks * |counting backwards; relate the numbers to |context | |

|or multiples of 10 | |their position on a number line |NRICH: Consecutive Numbers ** | |

| | |NRICH: Swimming Pool* |NRICH: Sea Level * | |

| | |NRICH: Tug Harder! * | | |

| | |NRICH: First Connect Three * | | |

|Partition three-digit numbers into multiples of |Partition, round and order four-digit whole |Explain what each digit represents in whole |Use decimal notation for tenths, hundredths and |Order a set of fractions by converting |

|100, 10 and 1 in different ways |numbers; use positive and negative numbers in |numbers and decimals with up to two places, |thousandths; partition, round and order decimals|them to decimals |

| |context and position them on a number line; state|and partition, round and order these numbers |with up to three places, and position them on | |

| |inequalities using the symbols less than and | |the number line | |

| |greater than (e.g. -3 greater than -5, -1 less | | | |

| |than plus1) | | | |

| |NRICH: Some Games That May Be Nice or Nasty * | | | |

|Round two-digit or three-digit numbers to the |Use decimal notation for tenths and hundredths |Express a smaller whole number as a fraction |Express a larger whole number as a fraction of a|Recognise approximate proportions of a |

|nearest 10 or 100 and give estimates for their |and partition decimals; relate the notation to |of a larger one (e.g. recognise that 5 out of|smaller one (e.g. recognise that 8 slices of a |whole and use fractions and percentages|

|sums and differences |money and measurement; position one-place and |8 is five eighths); find equivalent fractions|5-slice pizza represents eight fifths or 1three |to describe and compare them, for |

| |two-place decimals on a number line |(e.g. seven tenths equals fourteen |fifths pizzas); simplify fractions by cancelling|example when interpreting pie charts |

| | |twentieths, or nineteen tenths equals 1nine |common factors; order a set of fractions by | |

| | |tenths); relate fractions to their decimal |converting them to fractions with a common | |

| | |representations |denominator | |

| | |NRICH: Fractions in a Box ** |NRICH: Chocolate ** | |

|Read and write proper fractions (e.g. three |Recognise the equivalence between decimal and |Understand percentage as the number of parts |Express one quantity as a percentage of another |Use ratio notation, reduce a ratio to |

|sevenths, nine tenths), interpreting the |fraction forms of one half, quarters, tenths and |in every 100 and express tenths and |(e.g. express pound400 as a percentage of |its simplest form and divide a quantity|

|denominator as the parts of a whole and the |hundredths |hundredths as percentages |pound1000); find equivalent percentages, |into two parts in a given ratio; solve |

|numerator as the number of parts; identify and | | |decimals and fractions |simple problems involving ratio and |

|estimate fractions of shapes; use diagrams to | | | |direct proportion (e.g. identify the |

|compare fractions and establish equivalents | | | |quantities needed to make a fruit drink|

|NRICH: Matching Fractions * | | | |by mixing water and juice in a given |

| | | | |ratio) |

| |Use diagrams to identify equivalent fractions |Use sequences to scale numbers up or down; |Solve simple problems involving direct | |

| |(e.g. six eighths and three quarters, or seventy |solve problems involving proportions of |proportion by scaling quantities up or down | |

| |hundredths and seven tenths); interpret mixed |quantities (e.g. decrease quantities in a |NRICH: Orange Drink ** | |

| |numbers and position them on a number line (e.g. |recipe designed to feed six people) |NRICH: Pumpkin Pie Problem ** | |

| |3 one half) |NRICH: Blackcurrantiest *** | | |

| |Use the vocabulary of ratio and proportion to | | | |

| |describe the relationship between two quantities | | | |

| |(e.g. 'There are 2 red beads to every 3 blue | | | |

| |beads, or 2 beads in every 5 beads are red'); | | | |

| |estimate a proportion (e.g. 'About one quarter of| | | |

| |the apples in the box are green') | | | |

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 3 - Knowing and Using Number Facts |

|Derive and recall all addition and subtraction |Use knowledge of addition and subtraction facts |Use knowledge of place value and addition and|Use knowledge of place value and multiplication |Consolidate rapid recall of number |

|facts for each number to 20, sums and |and place value to derive sums and differences of|subtraction of two-digit numbers to derive |facts to 10 multiplied by 10 to derive related |facts, including multiplication facts |

|differences of multiples of 10 and number pairs |pairs of multiples of 10, 100 or 1000 |sums and differences and doubles and halves |multiplication and division facts involving |to 10 multiplied by 10 and the |

|that total 100 |NRICH: Which Is Quicker? * |of decimals (e.g. 6.5 plus over minus 2.7, |decimals (e.g. 0.8 multiplied by 7, 4.8 divided |associated division facts |

| | |half of 5.6, double 0.34) |by 6) | |

|Derive and recall multiplication facts for the |Identify the doubles of two-digit numbers; use |Recall quickly multiplication facts up to 10 |Use knowledge of multiplication facts to derive |Recognise the square roots of perfect |

|2, 3, 4, 5, 6 and 10 times-tables and the |these to calculate doubles of multiples of 10 and|multiplied by 10 and use them to multiply |quickly squares of numbers to 12multiplied by12 |squares to 12 multiplied by 12 |

|corresponding division facts; recognise |100 and derive the corresponding halves |pairs of multiples of 10 and 100; derive |and the corresponding squares of multiples of 10| |

|multiples of 2, 5 or 10 up to 1000 | |quickly corresponding division facts |NRICH: One Wasn’t Square ** | |

|NRICH: Growing Garlic *** | | |NRICH: Cycling Squares ** | |

|NRICH: Ordering Cards * | | | | |

|Use knowledge of number operations and |Derive and recall multiplication facts up to 10 |Identify pairs of factors of two-digit whole |Recognise that prime numbers have only two |Recognise and use multiples, factors, |

|corresponding inverses, including doubling and |multiplied by 10, the corresponding division |numbers and find common multiples (e.g. for 6|factors and identify prime numbers less than |divisors, common factors, highest |

|halving, to estimate and check calculations |facts and multiples of numbers to 10 up to the |and 9) |100; find the prime factors of two-digit numbers|common factors and lowest common |

| |tenth multiple |NRICH: Multiples Grid * |NRICH: Factors and Multiples Game * |multiples in simple cases |

| |NRICH: Multiplication Square Jigsaw * |NRICH: Music to My Ears * | |NRICH: What's in the Box? * |

| |NRICH: Shape Times Shape * |NRICH: Multiplication Squares * | |NRICH: Factor-multiple Chains ** |

| |NRICH: What do you Need? * |NRICH: Flashing Lights * | |NRICH: The Moons of Vuvv * |

| |NRICH: Table Patterns Go Wild! ** |NRICH: Mystery Matrix ** | |NRICH: Round and Round the Circle ** |

| |NRICH: Let’s Divide Up! * |NRICH: Factor Lines ** | |NRICH: Counting Cogs ** |

| | |NRICH: Zios and Zepts * | | |

| | |NRICH: Abundant Numbers * | | |

| | |NRICH: Factor Track ** | | |

| | | | | |

| |Use knowledge of rounding, number operations and |Use knowledge of rounding, place value, |Use approximations, inverse operations and tests|Make and justify estimates and |

| |inverses to estimate and check calculations |number facts and inverse operations to |of divisibility to estimate and check results |approximations to calculations |

| |NRICH: Make 100 ** |estimate and check calculations |NRICH: Curious Number *** | |

| | |NRICH: Four Go * | | |

| |Identify pairs of fractions that total 1 | | | |

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 4 - Calculating |

|Add or subtract mentally combinations of |Add or subtract mentally pairs of two-digit whole|Extend mental-methods for whole-number |Calculate mentally with integers and decimals: |Understand how the commutative, |

|one-digit and two-digit numbers |numbers (e.g. 47 plus 58, 91 - 35) |calculations, for example to multiply a |U.t plus over minus U.t, TU multiplied by U, TU |associative and distributive laws, and |

|NRICH: Super Shapes * |NRICH: Twenty Divided Into Six ** |two-digit by a one-digit number (e.g. 12 |divided by U, U.t multiplied by U, U.t divided |the relationships between operations, |

|NRICH: Roll These Dice ** | |multiplied by 9), to multiply by 25 (e.g. 16 |by U |including inverse operations, can be |

|NRICH: Strike it Out * | |multiplied by 25), to subtract one |NRICH: How Do You Do It? * |used to calculate more efficiently; use|

| | |near-multiple of 1000 from another (e.g. 6070|NRICH: Route Product** |the order of operations, including |

| | |- 4097) | |brackets |

|Develop and use written methods to record, |Refine and use efficient written methods to add |Use efficient written methods to add and |Use efficient written methods to add and |Consolidate and extend mental methods |

|support or explain addition and subtraction of |and subtract two-digit and three-digit whole |subtract whole numbers and decimals with up |subtract integers and decimals, to multiply and |of calculation to include decimals, |

|two-digit and three-digit numbers |numbers and pound.p |to two places |divide integers and decimals by a one-digit |fractions and percentages |

| | |NRICH: Reach 100 ** |integer, and to multiply two-digit and | |

| | | |three-digit integers by a two-digit integer | |

|Multiply one-digit and two-digit numbers by 10 |Multiply and divide numbers to 1000 by 10 and |Use understanding of place value to multiply |Relate fractions to multiplication and division |Use standard column procedures to add |

|or 100, and describe the effect |then 100 (whole-number answers), understanding |and divide whole numbers and decimals by 10, |(e.g. 6 divided by 2 equals one half of 6 equals|and subtract integers and decimals, and|

| |the effect; relate to scaling up or down |100 or 1000 |6 multiplied by one half ); express a quotient |to multiply two-digit and three-digit |

| |NRICH: The Deca Tree * | |as a fraction or decimal (e.g. 67 divided by 5 |integers by a one-digit or two-digit |

| | | |equals 13.4 or 13two fifths ); find fractions |integer; extend division to dividing |

| | | |and percentages of whole-number quantities |three-digit integers by a two-digit |

| | | |NRICH: Andy’s Marbles ** |integer |

| | | |NRICH: Would you Rather? * |NRICH: Two and Two *** |

| | | |NRICH: Forgot the Numbers ** |NRICH: Trebling * |

| | | |NRICH: Jumping * |NRICH: All the Digits ** |

|Use practical and informal written methods to |Develop and use written methods to record, |Refine and use efficient written methods to |Use a calculator to solve problems involving |Calculate percentage increases or |

|multiply and divide two-digit numbers (e.g. 13 |support and explain multiplication and division |multiply and divide HTU multiplied by U, TU |multi-step calculations |decreases and fractions of quantities |

|multiplied by 3, 50 divided by 4); round |of two-digit numbers by a one-digit number, |multiplied by TU, U.t multiplied by U and HTU| |and measurements (integer answers) |

|remainders up or down, depending on the context |including division with remainders (e.g. 15 |divided by U | | |

| |multiplied by 9, 98 divided by 6) | | | |

|Understand that division is the inverse of |Find fractions of numbers, quantities or shapes |Find fractions using division (e.g. one | |Use bracket keys and the memory of a |

|multiplication and vice versa; use this to |(e.g. one fifth of 30 plums, three eighths of a 6|hundredth of 5 kg), and percentages of | |calculator to carry out calculations |

|derive and record related multiplication and |by 4 rectangle) |numbers and quantities (e.g. 10percent, | |with more than one step; use the square|

|division number sentences |NRICH: A Bowl of Fruit *** |5percent and 15percent of pound80) | |root key |

|NRICH: Secret Number ** |NRICH: Fractional Triangles * | | | |

|NRICH: Journeys in Numberland * |NRICH: Bryony’s Triangle * | | | |

| | | | |Using a Calculator |

|Find unit fractions of numbers and quantities |Use a calculator to carry out one-step and |Use a calculator to solve problems, including| | |

|(e.g. one half, one third, one quarter and one |two-step calculations involving all four |those involving decimals or fractions (e.g. | | |

|sixth of 12 litres) |operations; recognise negative numbers in the |find three quarters of 150 g); interpret the | | |

|NRICH: Fair Feast * |display, correct mistaken entries and interpret |display correctly in the context of | | |

| |the display correctly in the context of money |measurement | | |

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 5 - Understanding Shape |

|Relate 2-D shapes and 3-D solids to drawings of |Draw polygons and classify them by identifying |Identify, visualise and describe properties |Describe, identify and visualise parallel and |Use correctly the vocabulary, notation |

|them; describe, visualise, classify, draw and |their properties, including their line symmetry |of rectangles, triangles, regular polygons |perpendicular edges or faces; use these |and labelling conventions for lines, |

|make the shapes |NRICH: Let’s Reflect * |and 3-D solids; use knowledge of properties |properties to classify 2-D shapes and 3-D solids|angles and shapes |

|NRICH: Building Blocks * |NRICH: National Flags * |to draw 2-D shapes, and to identify and draw |NRICH: Where Are They? * | |

|NRICH: The Third Dimension *** | |nets of 3-D shapes |NRICH: Sponge Sections ** | |

|NRICH: Cubes * | |NRICH: Square It * | | |

|NRICH: Rolling That Cube * | |NRICH: Cut Nets ** | | |

|NRICH: Triple Cubes * | |NRICH: Egyptian Rope ** | | |

|Draw and complete shapes with reflective |Visualise 3-D objects from 2-D drawings; make |Read and plot coordinates in the first |Make and draw shapes with increasing accuracy |Extend knowledge of properties of |

|symmetry; draw the reflection of a shape in a |nets of common solids |quadrant; recognise parallel and |and apply knowledge of their properties |triangles and quadrilaterals and use |

|mirror line along one side |NRICH: A Puzzling Cube * |perpendicular lines in grids and shapes; use |NRICH: Stringy Quads ** |these to visualise and solve problems, |

| | |a set-square and ruler to draw shapes with |NRICH: Making Cuboids ** |explaining reasoning with diagrams |

| | |perpendicular or parallel sides |NRICH: Making Spirals *** |NRICH: Nine-pin Triangles *** |

| | |NRICH: Cops and Robbers * | |NRICH: Transformations on a Pegboard *|

| | | | |NRICH: Cut it Out *** |

| | | | |NRICH: Quadrilaterals *** |

|Read and record the vocabulary of position, |Recognise horizontal and vertical lines; use the |Complete patterns with up to two lines of |Visualise and draw on grids of different types |Know the sum of angles on a straight |

|direction and movement, using the four compass |eight compass points to describe direction; |symmetry; draw the position of a shape after |where a shape will be after reflection, after |line, in a triangle and at a point, and|

|directions to describe movement about a grid |describe and identify the position of a square on|a reflection or translation |translations, or after rotation through |recognise vertically opposite angles |

| |a grid of squares | |90degrees or 180degrees about its centre or one | |

| |NRICH: Square Corners ** | |of its vertices | |

|Use a set-square to draw right angles and to |Know that angles are measured in degrees and that|Estimate, draw and measure acute and obtuse |Use coordinates in the first quadrant to draw, |Use all four quadrants to find |

|identify right angles in 2-D shapes; compare |one whole turn is 360degrees; compare and order |angles using an angle measurer or protractor |locate and complete shapes that meet given |coordinates of points determined by |

|angles with a right angle; recognise that a |angles less than 180degrees |to a suitable degree of accuracy; calculate |properties |geometric information |

|straight line is equivalent to two right angles | |angles in a straight line |NRICH: A Cartesian Puzzle * |NRICH: Coordinate Tan ** |

| | |NRICH: Six Places to Visit * |NRICH: Eight Hidden Squares ** |NRICH: Ten Hidden Squares *** |

| | | |Estimate angles, and use a protractor to measure|Identify all the symmetries of 2-D |

| | | |and draw them, on their own and in shapes; |shapes; transform images using ICT |

| | | |calculate angles in a triangle or around a point|NRICH: Symmetry Challenge *** |

| | | |NRICH: How Safe Are You? * |NRICH: Coordinate Challenge * |

| | | |NRICH: Olympic Turns *** | |

| | | |NRICH: Round a Hexagon * | |

| | | | |Construct a triangle given two sides |

| | | | |and the included angle |

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 6 - Measuring |

|Know the relationships between kilometres and |Choose and use standard metric units and their |Read, choose, use and record standard metric |Select and use standard metric units of measure |Convert between related metric units |

|metres, metres and centimetres, kilograms and |abbreviations when estimating, measuring and |units to estimate and measure length, weight |and convert between units using decimals to two |using decimals to three places (e.g. |

|grams, litres and millilitres; choose and use |recording length, weight and capacity; know the |and capacity to a suitable degree of accuracy|places (e.g. change 2.75 litres to 2750 ml, or |convert 1375 mm to 1.375 m, or vice |

|appropriate units to estimate, measure and |meaning of 'kilo', 'centi' and 'milli' and, where|(e.g. the nearest centimetre); convert larger|vice versa) |versa) |

|record measurements |appropriate, use decimal notation to record |to smaller units using decimals to one place | | |

|NRICH: Olympic Starters * |measurements (e.g. 1.3 m or 0.6 kg) |(e.g. change 2.6 kg to 2600 g) | | |

| | |NRICH: Discuss and Choose * | | |

|Read, to the nearest division and half-division,|Interpret intervals and divisions on partially |Interpret a reading that lies between two |Read and interpret scales on a range of |Solve problems by measuring, estimating|

|scales that are numbered or partially numbered; |numbered scales and record readings accurately, |unnumbered divisions on a scale |measuring instruments, recognising that the |and calculating; measure and calculate |

|use the information to measure and draw to a |where appropriate to the nearest tenth of a unit | |measurement made is approximate and recording |using imperial units still in everyday |

|suitable degree of accuracy | | |results to a required degree of accuracy; |use; know their approximate metric |

| | | |compare readings on different scales, for |values |

| | | |example when using different instruments | |

|Read the time on a 12-hour digital clock and to |Draw rectangles and measure and calculate their |Draw and measure lines to the nearest |Calculate the perimeter and area of rectilinear |Calculate the area of right-angled |

|the nearest 5 minutes on an analogue clock; |perimeters; find the area of rectilinear shapes |millimetre; measure and calculate the |shapes; estimate the area of an irregular shape |triangles given the lengths of the two |

|calculate time intervals and find start or end |drawn on a square grid by counting squares |perimeter of regular and irregular polygons; |by counting squares |perpendicular sides, and the volume and|

|times for a given time interval |NRICH: Torn Shapes * |use the formula for the area of a rectangle |NRICH: Numerically Equal ** |surface area of cubes and cuboids |

|NRICH: Two Clocks ** | |to calculate the rectangle's area |NRICH: Area and Perimeter * |NRICH: Brush Loads * |

| | |NRICH: Fitted *** |NRICH: Shaping It * |NRICH: More Transformations on a |

| | | | |Pegboard ** |

| | | | |NRICH: Making Boxes ** |

| | | | |NRICH: Next Size Up ** |

| |Read time to the nearest minute; use am, pm and |Read timetables and time using 24-hour clock | | |

| |12-hour clock notation; choose units of time to |notation; use a calendar to calculate time | | |

| |measure time intervals; calculate time intervals |intervals | | |

| |from clocks and timetables |NRICH: How Many Times? * | | |

| |NRICH: Wonky Watches ** |NRICH: 5 on the Clock *** | | |

| |NRICH: Clocks * |NRICH: The Time Is … ** | | |

| |NRICH: Watch the Clock *** | | | |

|Year 3 |Year 4 |Year 5 |Year 6 |Year 6-7 |

|Strand 7 - Handling Data |

|Answer a question by collecting, organising and |Answer a question by identifying what data to |Describe the occurrence of familiar events |Describe and predict outcomes from data using |Understand and use the probability |

|interpreting data; use tally charts, frequency |collect; organise, present, analyse and interpret|using the language of chance or likelihood |the language of likelihood |scale from 0 to 1; find and justify |

|tables, pictograms and bar charts to represent |the data in tables, diagrams, tally charts, |NRICH: Probably … * |NRICH: Domino Pick * |probabilities based on equally likely |

|results and illustrate observations; use ICT to |pictograms and bar charts, using ICT where | |NRICH: Odds or Sixes? * |outcomes in simple contexts |

|create a simple bar chart |appropriate | |NRICH: The Twelve Pointed Star Game ** | |

|NRICH: Our Sports * |NRICH: The Car That Passes * | |NRICH: Same or Different? ** | |

|NRICH: Class 5’s Names * |NRICH: The Olympic Flame: Are You in the 95%? * | |NRICH: Tricky Track ** | |

| | | |NRICH: Winning the Lottery ** | |

| | | |NRICH: Now and Then ** | |

| | | |NRICH: A Bit of a Dicey Problem ** | |

|Use Venn diagrams or Carroll diagrams to sort |Compare the impact of representations where |Answer a set of related questions by |Solve problems by collecting, selecting, |Explore hypotheses by planning surveys |

|data and objects using more than one criterion |scales have intervals of differing step size |collecting, selecting and organising relevant|processing, presenting and interpreting data, |or experiments to collect small sets of|

|NRICH: Venn Diagrams * | |data; draw conclusions, using ICT to present |using ICT where appropriate; draw conclusions |discrete or continuous data; select, |

|NRICH: More Carroll Diagrams * | |features, and identify further questions to |and identify further questions to ask |process, present and interpret the |

|NRICH: Plants ** | |ask |NRICH: It's a Tie ** |data, using ICT where appropriate; |

| | |NRICH: Real Statistics *** | |identify ways to extend the survey or |

| | |NRICH: If the World Were a Village * | |experiment |

| | |Construct frequency tables, pictograms and |Construct and interpret frequency tables, bar |Construct, interpret and compare graphs|

| | |bar and line graphs to represent the |charts with grouped discrete data, and line |and diagrams that represent data, for |

| | |frequencies of events and changes over time |graphs; interpret pie charts |example compare proportions in two pie |

| | | |NRICH: Match the Matches ** |charts that represent different totals |

| | |Find and interpret the mode of a set of data |Describe and interpret results and solutions to |Write a short report of a statistical |

| | | |problems using the mode, range, median and mean |enquiry and illustrate with appropriate|

| | | | |diagram |

Updates in January 2011: The Car That Passes, Probably, Winning the Lottery

Updates in May 2011: Journeys in Numberland, Area and Perimeter, Discuss and Choose, The Time Is …

Updates in September 2011: Four Go, Sponge Sections, Plants

Updates in February 2013: How Do You See it?, Escape from the Castle, Take Three Numbers, Three Neighbours, Fifteen Cards, Spot Thirteen, This Pied Piper of Hamelin, Junior Frogs, Inky Cube, Square Subtraction, Going for Gold, The Domesday Project, Birdwatch, How Tall?, Eye View, In Order, Cuisenaire Spirals, That Number Square!, Unlocking the Case, It’s a Scrabble, Carrying Cards, Count the Digits, Number Differences, Exploring Wild & Wonderful Number Patterns, Exploring Number Patterns You Make, Become Maths Detectives, The Numbers Give the Design, Button-up Some More, Sitting Round the Party Tables, Follow the Numbers, Dotty Six, Beads and Bags, Some Games That May Be Nice or Nasty, Matching Fractions, Which is Quicker?, Ordering Cards, Let’s Divide Up!, Zios and Zepts, Abundant Numbers, Factor Track, Curious Number, Roll These Dice, A Bit of a Dicey Problem, Strike it Out, Jumping, Bryony’s Triangle, Cubes, Rolling That Cube, Triple Cubes, National Flags, Making Spirals, Olympic Turns, Round a Hexagon, Olympic Starters, Shaping It, Our Sports, Class 5’s Names, The Olympic Flame: Are You in the 95%?, Now and Then, If the World Were a Village.

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Thinking Mathematically

Patterns and Sequences

Thinking Mathematically

Counting and Ordering

Addition and Subtraction

Place Value

Fractions, Decimals and Percentages

Ratio and Proportion

Addition and Subtraction

Multiplication and Division

Factors and Multiples

Rounding, Approximating and Estimating

Addition and Subtraction

Multiplication and Division

Place Value

Fractions, Decimals and Percentages

Properties of Shape

Movement and Position

Units and Scales

Time

Area and Perimeter

Data

Probability

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