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Maths in Year 4
End of Year Expectations for
Maths in Year 4
Autumn 1st half term objectives highlighted
Objectives previously taught are highlighted
Please note that in line with the progress children make this list is subject to
change and the objectives
are not necessarily taught in the order listed below.
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Learning Objectives |
Additional Information |
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Number and Place Value |
Count in multiples of 6, 7, 9, 25 and 1000. Find 1000 more or less than a given number.
Count backwards through zero to include negative numbers.
Recognise the place value of each digit in a four digit number (thousands, hundreds, tens and ones).
Order and compare numbers beyond 1000.
Identify, represent and estimate numbers using different representations.
Round any number to the nearest 10, 100 or 1000.
Solve number and practical problems that involve all of the above and with increasingly large positive numbers.
Read Roman numerals to 100 (I to C) and know that over time, the numeral
system changed to include the concept of zero and place value. |
Imagining the position of numbers on a horizontal number line helps us to order them: the number to the right on a number line is the larger number. So 5 is greater than 4, as 5 is to the right of 4. But –4 is greater than –5 as –4 is to the right of –5.
Rounding numbers in context may mean rounding up or down. Buying packets of ten cakes, we might round up to the nearest ten to make sure everyone gets a cake.
Estimating the number of chairs in a room for a large number of people we might round down to estimate the number of chairs to make sure there are enough.
We can think of place value in additive terms:
456 is 400 + 50 + 6, or in multiplicative terms: one hundred is ten times as large as ten.
Calculation policy page:
10
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Addition and Subtraction |
Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.
Estimate and use inverse operations to check answers to a calculation.
Solve addition and subtraction two step problems in
contexts, deciding which operations and methods to use
and why. |
It helps to round numbers before carrying out a calculation to get a sense of the size of the answer. For example, 4786 – 2135 is close to 5000 – 2000, so the answer will be around 3000. Looking at the numbers in a calculation and their relationship to each other can help make calculating easier. For example, 3012 – 2996.
Noticing that the numbers are close to each other might mean this is more easily calculated by thinking about subtraction as difference.
Calculation policy page: 12
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Multiplication and Division |
Recall and use
multiplication and
division facts for multiplication tables up to 12 x 12.
Use place
value, known and derived facts to
multiply and divide mentally, including: multiplying by
0 and 1; dividing by 1; multiplying together three numbers.
Recognise and use factor pairs and commutativity in mental calculations.
Multiply two digit and three digit numbers by a one digit number using formal written layout.
Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects. |
It is important for children not just to be able to chant their multiplication tables but to understand what the facts in them mean, to be able to use these facts to figure out others and to use them in problems.
It is also important for children to be able to link facts within the tables (e.g. 5× is half of 10×).
They understand what multiplication means and see division as both grouping and sharing, and to see division as the inverse of multiplication.
The distributive law can be used to partition numbers in different ways to create equivalent calculations.
For example, 4 × 27 = 4 × (25 + 2) = (4 × 25) + (4 × 2) = 108.
Looking for equivalent calculations can make calculating easier. For example, 98 × 5 is equivalent to 98 × 10 ÷ 2 or to (100 × 5) – (2 × 5).
The array model can help show equivalences.
Calculation policy page: 13
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Fractions |
Recognise and show, using diagrams, families of common equivalent fractions.
Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit
fractions where the answer is a whole number.
Add and subtract fractions with the same denominator.
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Fractions arise from solving problems, where the answer lies between two whole numbers.
Fractions express a relationship between a whole and equal parts of a whole. Children should recognise this and speak in full sentences when answering a question involving fractions.
For example, in response to the question What fraction of the chocolate bar is shaded? The child might say
Two sevenths of the whole chocolate bar is shaded.
Equivalency in relation to fractions is important. Fractions that look very different in their symbolic notation can mean the same thing. |
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Decimals |
Recognise and write decimal equivalents of any number of tenthsor hundredths.
Recognise and write decimal equivalents to ¼, ½, ¾
Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths.
Round decimals with one decimal place to the nearest whole number.
Compare numbers with the same number of decimal places up to two decimal places.
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Measurement |
Area and
Perimeter:
Find the area of rectilinear shapes by counting squares.
Convert between different units of measure eg kilometre to metre.
Measure and calculate the perimeter of a rectilinear figure (including squares) in cm and m
Time:
Convert between different units of measure, e.g. hour to minute.
Read, write and convert time between analogue and digital 12 and 24 hour clocks.
Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.
Money:
Solve simple measure and money problems involving fractions and decimals to two decimal places.
Estimate, compare and calculate different measures, including money in pounds and pence. |
The smaller the unit, the greater the number of units needed to measure (that is, there is an inverse relationship
between size of unit and measure). |
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Geometry |
Angles:
Identify acute and obtuse angles and compare and order angles up to two right angles by size.
Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.
Shape and Symmetry:
Identify lines of symmetry in 2D shapes presented in different orientations.
Complete a simple symmetric figure with respect to a specific line of symmetry.
Position and Direction :
Describe positions on a 2D grid as coordinates in the first quadrant.
Describe movements between positions as translations of a given unit to the left/ right and up/ down.
Plot specified points and draw sides to complete a given polygon.
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During this year, pupils increase the range of 2-D and 3-D shapes that they are familiar with.
They know the correct names for these shapes, but, more importantly, they are able to say why certain shapes are what they are by
referring to their properties, including lengths of sides, size of angles and number of lines of symmetry.
The naming of shapes sometimes focuses on angle properties (e.g. a rectangle is right-angled), and sometimes on properties of sides
(e.g. an equilateral triangle is an equal sided triangle).
Shapes can belong to more than one classification. For example, a square is a rectangle, a parallelogram, a rhombus and a quadrilateral.
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Statistics |
Interpret and present discrete and continuous data using appropriate graphical methods,
including bar charts and time graphs.
Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.
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