REDBRIDGE VERSION 2014

Year 4 Block B: Three units

Securing number facts, understanding shapes

Objectives / Units
1 / 2 / 3
·  Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes / ü / ü / ü
·  Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate / ü / ü
·  Use knowledge of rounding, number operations and inverses to estimate and check calculations / ü / ü / ü
·  Identify the doubles of two digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves. / ü / ü
·  Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols / ü / ü / ü
·  Derive and recall multiplication and division facts for multiplication tables up to 12 x 12 / ü / ü / ü
·  Identify lines of symmetry in 2-D shapes presented in different orientations Complete a simple symmetric figure with respect to a specific line of symmetry. / ü / ü
·  Identify acute and obtuse angles and compare and order angles up to two right angles by size / ü / ü

Vocabulary

problem, solution, calculate, calculation, equation, operation, inverse, answer, method, explain, predict, reason, reasoning, pattern, relationship, rule, sequence, sort, classify, property

Place value, add, subtract, multiply, divide, sum, total, difference, plus, minus, product, quotient, remainder, double, halve, factor, multiple, divisor, round

3-D, three-dimensional, 2-D, two-dimensional, geometric, geometry construct, regular, irregular, polygon, concave, convex, symmetrical, line of symmetry, vertex, vertices, face, edge, polygon, equilateral triangle, isosceles triangle, quadrilateral, rectangle, square, oblong, hexagon, heptagon, octagon, angle, right-angle, obtuse, acute

Building on previous learning

Check that children can already:

• recall addition and subtraction facts for each number to 50

• recall multiplication and division facts for the 2, 3, 4, 5, 8 and 10 times-tables

• say a subtraction fact that is the inverse of an addition fact, and a multiplication fact that is the inverse of a division fact, and vice versa

• identify the calculation needed to solve a one-step problem

• name common 2-D shapes

• draw a line of symmetry in a 2-D shape

• choose their own criterion for sorting a set of shapes.

Year 4 Block B: Securing number facts, understanding shapes

Extracts from New National Curriculum

The national curriculum for mathematics aims to ensure that all pupils:
 become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
 can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Number – Number and Place Value
Pupils should be taught to
 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 / Notes and guidance (non-statutory)
Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1000, including counting in tens and hundreds, and maintaining fluency in other multiples through varied and frequent practice.
They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far.
They connect estimation and rounding numbers to the use of measuring instruments.
Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were introduced over a period of time.
Number – Addition and Subtraction
Pupils should be taught to:
 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. / Notes and guidance (non-statutory)
Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency (
Number – Multiplication and Division
Pupils should be taught to:
 recall multiplication and division facts for multiplication tables up to 12 × 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. / Notes and guidance (non-statutory)
Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.
Pupils practise mental methods and extend this to three-digit numbers to derive facts, (for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).
Geometry – Properties of shape
Pupils should be taught to:
 compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
 identify acute and obtuse angles and compare and order angles up to two right angles by size
 identify lines of symmetry in 2-D shapes presented in different orientations
 complete a simple symmetric figure with respect to a specific line of symmetry. / Notes and guidance (non-statutory)
Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium).
Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.
Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the original shape.

Addition and Subtraction

Short multiplication

Long multiplication

Short division

Long division

Year 4 Block B: Securing number facts, understanding shapes
Unit 1

Objectives Unit 1 / Assessment for Learning /
·  Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
I can compare and classify geometric shapes, using their properties and sizes. / Sort these irregular polygons into those with no right angles, one right angle, two right angles, three right angles.
Here are four shapes.
They each have a different number of right angles.

Write the letter for each shape in the correct order. One has been done for you.

• Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations
I can work out how to solve problems with one or two steps
I can decide what calculation to work out
I can think about the numbers in a calculation and choose a good way to do the calculation / Consider this problem.
Jack bought some butter for 87p, some flour for £1.27 and some sugar for £2.15. What did he pay altogether?
Explain what you did to get your answer. What made you decide which calculation to do? How would you work out Jack's change from a £10 note?
Make up a word problem that would lead to each calculation:
9×5 63÷9 54–17 48+19+ 27
What are the important things to remember when you solve a word problem?
• Use knowledge of rounding, number operations and inverses to estimate and check calculations
I can round numbers in a calculation to help me estimate the answer to the calculation
I can check using inverse / Circle the number that is about the same as the right answer to 49+48.
10 50 40 100 70 200
• Identify the doubles of two digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves.
Because I know that double 7 is 14, I know that double 70 is 140.
I can work out doubles of numbers with two digits. / If double 6 is 12 what is double 60? 600?
Explain to someone how you double 32.
Why is double 46 more difficult?
·  Derive and recall multiplication and division facts for multiplication tables up to 12 x 12 and the corresponding division facts
I can work out division facts for the times-tables.
I can multiply by 0 and 1 and divide by 1 / If someone has forgotten the 6 times-table, what tips would you give them to help them work it out?
If you know 4×6=24, how does this help you to work out 24÷6?
If I know that 3 x 4 = 12, what other facts do I know / can I derive?
The product is 40. What could the two numbers be? Convince me.
The quotient is 5. What could the two numbers be? Convince me.
• Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols
I can explain to the class how I solved a problem
I can draw a diagram to show how I solved a problem / Here is part of a number square. The shaded numbers are part of a sequence. Explain the rule for the sequence.

Explain what you did to get your answer to the problem.
What sort of diagram did you draw to solve this problem?
How was it helpful?
Could you have chosen a different diagram?

Year 4 Block B: Securing number facts, understanding shapes

Unit 2

Objectives Unit 2 / Assessment for Learning /
·  Compare and classify geometric shapes including quadrilaterals and triangles, based on their properties and sizes
I can solve problems using properties of geometric shapes
(e.g. I can spot a rule about the number of lines of symmetry that regular polygons have) / Here are four shapes in a Carroll diagram.
Regular / Not regular
Quadrilateral / /
Not a
quadrilateral / /

Use this information to write the letters A, B and D in the Venn diagram below.
• Use knowledge of rounding, number operations and inverses to estimate and check calculations
If I add two numbers I can use subtraction to check whether my answer is correct
If I divide one number by another I can use multiplication to check whether my answer is correct / If the answer to a subtraction is 59 and I subtracted 45, what number did I start with? How do you know?
Michael wrote: 300 ÷ 6 = 40. How do you know this is wrong?
• Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols
I can write an explanation of how I solved a problem.
I can include number sentences using the +, –, × or ÷ signs where I need to / A shop has these special offers.

Joe wants to buy six pencils. Which is the cheaper offer: half price, or 3 packets for the price of 2? Explain how you know.
·  Recall the multiplication and division facts for multiplication tables up to 12 x 12
I can tell you answers to the times-tables, even when the questions are not in order. / How can doubling help you work out multiples of 8?
Which are the multiples of 8 in this list of numbers?
18 32 56 68 72
Find the missing numbers in the table below
X / 5 / 9 / 8
4
54
8
3 / 21
·  Identify acute and obtuse angles and compare and order angles up to two right angles by size
I can identify acute and obtuse angles and compare and order angles up to 1800 / Here are four triangles drawn on a square grid.

Write the letter for each triangle in the correct region of the sorting diagram.
One has been done for you.

·  Identify lines of symmetry in 2D shapes presented in different orientations
I can identify lines of symmetry in 2D shapes when the shapes have been turned around / Here is a square grid.
Two sides of a kite are drawn on the grid.
Complete the kite by drawing the two missing sides.
Use a ruler.

Year 4 Block B: Securing number facts, understanding shapesUnit 3

Objectives Unit 3 / Assessment for Learning /
·  Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples.
I can draw polygons on triangular grid paper and pick out some of the properties they have in common. /