Year 3 - NRICH



NRICH nrich. problems linked to

the Framework for teaching mathematics in Years 3, 4, 5 and 6

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

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

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

| |to the nearest 10 or 100 and give |hundredths and partition decimals; |fraction of a larger one (e.g. recognise|fraction of a smaller one (e.g. |whole and use fractions and percentages |

| |estimates for their sums and differences|relate the notation to money and |that 5 out of 8 is five eighths); find |recognise that 8 slices of a 5-slice |to describe and compare them, for |

| | |measurement; position one-place and |equivalent fractions (e.g. seven tenths |pizza represents eight fifths or 1three |example when interpreting pie charts |

| | |two-place decimals on a number line |equals fourteen twentieths, or nineteen |fifths pizzas); simplify fractions by | |

| | | |tenths equals 1nine tenths); relate |cancelling common factors; order a set | |

| | | |fractions to their decimal |of fractions by converting them to | |

| | | |representations |fractions with a common denominator | |

| | | | |NRICH: Chocolate | |

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

| | |fractions (e.g. six eighths and three |down; solve problems involving |proportion by scaling quantities up or | |

| | |quarters, or seventy hundredths and |proportions of quantities (e.g. decrease|down | |

| | |seven tenths); interpret mixed numbers |quantities in a recipe designed to feed |NRICH: Orange Drink | |

| | |and position them on a number line (e.g.|six people) |NRICH: Pumpkin Pie Problem | |

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

|  |  |  |  |  |  |

| |Derive and recall multiplication facts |Identify the doubles of two-digit |Recall quickly multiplication facts up |Use knowledge of multiplication facts to|Recognise the square roots of perfect |

| |for the 2, 3, 4, 5, 6 and 10 |numbers; use these to calculate doubles |to 10 multiplied by 10 and use them to |derive quickly squares of numbers to |squares to 12 multiplied by 12 |

| |times-tables and the corresponding |of multiples of 10 and 100 and derive |multiply pairs of multiples of 10 and |12multiplied by12 and the corresponding | |

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

| |2, 5 or 10 up to 1000 | |division facts |NRICH: One Wasn’t Square | |

| |NRICH: Growing Garlic | | | | |

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

|  |  |  |  |  |  |

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

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

| |this to derive and record related |three eighths of a 6 by 4 rectangle) |numbers and quantities (e.g. 10percent, | |with more than one step; use the square |

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

| |sentences |NRICH: Fractional Triangles | | | |

| |NRICH: Secret Number | | | | |

| |  |  |  |  |  |

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

| |half-division, scales that are numbered |partially numbered scales and record |two unnumbered divisions on a scale |measuring instruments, recognising that |and calculating; measure and calculate |

| |or partially numbered; use the |readings accurately, where appropriate | |the measurement made is approximate and |using imperial units still in everyday |

| |information to measure and draw to a |to the nearest tenth of a unit | |recording results to a required degree |use; know their approximate metric |

| |suitable degree of accuracy | | |of accuracy; compare readings on |values |

| | | | |different scales, for example when using| |

| | | | |different instruments | |

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

| |and to the nearest 5 minutes on an |calculate their perimeters; find the |millimetre; measure and calculate the |rectilinear shapes; estimate the area of|triangles given the lengths of the two |

| |analogue clock; calculate time intervals|area of rectilinear shapes drawn on a |perimeter of regular and irregular |an irregular shape by counting squares |perpendicular sides, and the volume and |

| |and find start or end times for a given |square grid by counting squares |polygons; use the formula for the area |NRICH: Numerically Equal |surface area of cubes and cuboids |

| |time interval |NRICH: Torn Shapes |of a rectangle to calculate the | |NRICH: Brush Loads |

| |NRICH: Two Clocks | |rectangle's area | |NRICH: More Transformations on a |

| |NRICH: Clocks | |NRICH: Fitted | |Pegboard |

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