Redbridge Version 2014
Year 6 Block B: Three units
Securing number facts, understanding shapes
Mental methods:
multiplication and division
facts applied to decimals
Patterns, relationships
and properties of
numbers and shapes;
suggesting hypotheses
Representing a problem
using calculations, symbols,
formulae, diagrams
Solving algebraic problems
Multiples, factors, primes
and prime factors
Tables to 10 × 10; squares,
squares of multiples of 10
Tests of divisibility
Block B
Securing number
facts, understanding
shapes
Using a calculator,
including to find inverses
Visualising and classifying
3-D and 2-D shapes,
including quadrilaterals
Making and drawing shapes
Units
Objectives
1

•
Tabulate systematically the information in a problem or puzzle; identify and
record the steps or calculations needed to solve it, using symbols where
appropriate; interpret solutions in the original context and check their accuracy
2
3


Represent and interpret sequences, patterns and relationships involving
numbers and shapes; suggest and test hypotheses; construct and use simple
expressions and formulae in words then symbols (e.g. the cost of c pens at 15
pence each is 15c pence)



Express missing number problems algebraically. Find pairs of numbers that
satisfy an equation with two unknowns. Enumerate possibilities of
combinations of two variables.



Recognise that prime numbers have only two factors and identify prime
numbers less than 100; find the prime factors of two-digit numbers identify
common multiples and common factors of numbers




Use knowledge of multiplication facts to derive quickly squares of numbers to
12 × 12 and the corresponding squares of multiples of 10.


Solve multi-step problems, and problems involving fractions, decimals and
percentages; choose and use appropriate calculation strategies at each stage,
including calculator use.

•


•
Use approximations, inverse operations and tests of divisibility to estimate and
check results



•
Describe, identify and visualise parallel and perpendicular edges or faces; use
these properties to classify 2-D shapes and 3-D solids; compare and classify
geometric shapes based on their properties and sizes and find unknown angles
in any triangles, quadrilaterals and regular polygons


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Redbridge Version 2014
•

Make and draw shapes with increasing accuracy and apply knowledge of their
properties including nets

Illustrate and name parts of circles including radius, diameter and
circumference and know that the diameter is twice the radius



Vocabulary
problem, solution, calculate, calculation, equation, method, explain, reasoning, reason, predict,
rule, formula, relationship, sequence, pattern, classify, property, criterion/criteria, generalise,
construct
integer, decimal, fraction, square number, multiple, factor, factorise, divisor, divisible,
divisibility, prime, prime factor, consecutive, operation, inverse, product, quotient, round,
estimate, approximate
parallel, perpendicular, regular, irregular, face, edge, vertex/vertices, polyhedron,
dodecahedron, octahedron, tetrahedron, polygon, quadrilateral, rhombus, kite, parallelogram,
trapezium, triangle, isosceles, equilateral, scalene, radius, diameter, circumference,
intersecting, intersection, plane
Building on previous learning
Check that children can already:
• propose a general statement involving numbers or shapes
• organise information in a table
• use knowledge of place value and addition and subtraction of two-digit numbers to derive
sums, differences, doubles and halves of decimals, e.g. 6.5 ± 2.7, halve 5.6, double 0.34
• identify pairs of factors of two-digit whole numbers and find common multiples
• recognise parallel and perpendicular lines
• identify, visualise and describe properties of rectangles, regular polygons and 3-D solids.
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Redbridge Version 2014
Year 6 Block B: Securing number facts, understanding shape
Extracts from the New National Curriculum
The national curriculum for mathematics aims to ensure that all pupils:
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
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.
Algebra
Notes and guidance (non-statutory)
Pupils should be taught to:
linear number
sequences
Pupils should be introduced to the use of symbols and
letters to represent variables and unknowns in
mathematical situations that they already understand,
such as:
algebraically
with two unknowns
ions (for example, a + b = b + a)
variables.
add up to).
Number – Multiplication and Division
Notes and guidance (non-statutory)
Pupils should be taught to:
Pupils practise and extend their use of the formal written
methods of short multiplication and short division (see
Mathematics Appendix 1). They apply all the multiplication
tables and related division facts frequently, commit them
to memory and use them confidently to make larger
calculations.
all factor pairs of a number, and common factors
of two numbers
numbers, prime factors and composite (nonprime) numbers
and recall prime numbers up to 19
mbers up to 4 digits by a one- or
two-digit number using a formal written method,
including long multiplication for two-digit
numbers
upon known facts
They use and understand the terms factor, multiple and
prime, square and cube numbers.
Pupils interpret non-integer answers to division by
expressing results in different ways according to the
context, including with remainders, as fractions, as
decimals or by rounding (for example, 98 ÷ 4 = 98/4 = 24 r
2 = 24½ = 24.5 ≈ 25).
-digit
number using the formal written method of short
division and interpret remainders appropriately
for the context
Pupils use multiplication and division as inverses to
support the introduction of ratio in year 6, for example, by
multiplying and dividing by powers of 10 in scale drawings
or by multiplying and dividing by powers of a 1000 in
converting between units such as kilometres and metres.
involving decimals by 10, 100 and 1000
Distributivity can be expressed as a(b + c) = ab + ac.
They understand the terms factor, multiple and prime,
square and cube numbers and use them to construct
equivalence statements (for example, 4 x 35 = 2 x 2 x 35;
3 x 270 = 3 x 3 x 9 x 10 = 92 x 10).
Pupils use and explain the equals sign to indicate
equivalence, including in missing number problems (for
example, 13 + 24 = 12 + 25; 33 = 5 x
).
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Redbridge Version 2014
Geometry – properties of shape
Notes and guidance (non-statutory)
Pupils should be taught to:
Pupils draw shapes and nets accurately, using measuring
tools and conventional markings and labels for lines and
angles.
-D shapes using given dimensions and
angles
-D
shapes, including making nets
on their properties and sizes and find unknown
angles in any triangles, quadrilaterals, and
regular polygons
Pupils describe the properties of shapes and explain how
unknown angles and lengths can be derived from known
measurements.
These relationships might be expressed algebraically for
example, d = 2 × r; a = 180 – (b + c).
radius, diameter and circumference and know
that the diameter is twice the radius
a point,
are on a straight line, or are vertically opposite,
and find missing angles.
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Redbridge Version 2014
Year 6 Block B: Securing number facts, understanding shape
Unit 1
Objectives Unit 1
• Represent and interpret sequences, patterns and
relationships involving numbers and shapes;
suggest and test hypotheses; construct and use
simple expressions and formulae in words then
symbols (e.g. the cost of c pens at 15 pence each is
15c pence)
I can describe and explain sequences, patterns and
relationships
Assessment for Learning
Describe the relationship between terms in this
sequence:
2, 3, 8, 63, ...
Make the ITP ‘20 cards’ generate this sequence of
numbers:
1, 3, 7, 13, ...
I can suggest hypotheses and test them
I can write and use simple expressions in words and
formulae
Explain why a square number always has an odd
number of factors.
The first two numbers in this sequence are 2.1 and
2.2. The sequence then follows the rule: 'to get the
next number, add the two previous numbers'. What are
the missing numbers?
2.1, 2.2, 4.3, 6.5,

Express missing number problems algebraically.
Find pairs of numbers that satisfy an equation with
two unknowns. Enumerate possibilities of
combinations of two variables.
I can use letters to represent unknowns.
I can solve number puzzles using Algebra
• Recognise that prime numbers have only two
factors and identify prime numbers less than 100;
find the prime factors of two-digit numbers; identify
common multiples and common factors of
numbers.
I can work out which numbers less than 100 are
prime numbers
I can identify common multiples and common
factors
The perimeter of a rectangle is 2 × (l + b), where l is
the length and b is the breadth of the rectangle.
What is the perimeter if l = 8 cm and b = 5 cm?
The number of bean sticks needed for a row which is
m metres long is 2m + 1. How many bean sticks do
you need for a row which is 60 metres long?
Can you tell me a prime number? And another?
What do these two numbers have in common?
Millie and Ryan play a number game.
Is it under 20? No
Is it under 25? Yes
Is it odd? Yes
Is it a prime number? Yes
What is the number?
What are the common multiples of 12 and 4?
What are the common factors for 24 and 16? (relate to
equivalent fractions)
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Redbridge Version 2014
Objectives Unit 1

Use knowledge of multiplication facts to derive
quickly squares of numbers to 12 × 12 and the
corresponding squares of multiples of 10.
Assessment for Learning
Is it always, sometimes or never true that a square
number has an even number of factors.
I can say the squares of numbers to 12 × 12 and
work out the squares of multiples of 10.
• Use approximations, inverse operations and tests of
divisibility to estimate and check results
I can estimate and check the calculations that I do
Roughly, what will the answer to this calculation be?
How do you know that this calculation is probably
right? Could you check it a different way?
Should the answer be odd or even? How do you
know?
• Describe, identify and visualise parallel and
perpendicular edges or faces; use these properties
to classify 2-D shapes and 3-D solids; compare and
classify geometric shapes based on their properties
and sizes and find unknown angles in any triangles,
quadrilaterals and regular polygons
Look at this cube. How many edges are parallel to this
one? How many edges are perpendicular to this one?
I can compare and classify 2-D shapes including
with perpendicular or parallel sides.
Which of these shapes has two pairs of parallel sides?
• Make and draw shapes with increasing accuracy
and apply knowledge of their properties
How would you check if two lines are parallel?
Perpendicular?
Tell me some facts about parallelograms.
Draw two straight lines from point A to divide the
shaded shape into a square and two triangles.
I can make and draw 2D shapes accurately using
given dimensions and angles accurately.
Use your ruler and set-square to draw a 5 cm by
7 cm rectangle.
Investigate the minimum number of flaps that you
would need to put on the edges of a net of the cube in
order to secure each edge of the cube.
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Redbridge Version 2014
Year 6 Block B: Securing number facts, understanding shapes
Unit 2
Objectives Unit 2
Assessment for Learning
•
How could you organise the information to help you?
Tabulate systematically the information in a
problem or puzzle; identify and record the
steps or calculations needed to solve it,
using symbols where appropriate; interpret
solutions in the original context and check
their accuracy
How many triangles can you see in this diagram?
I can use a table to help me solve a problem
I can identify and record what I need to do to
solve the problem, checking my answer
How can you make sure that you have counted them
makes sense and is accurate
all?
•

Represent and interpret sequences, patterns
and relationships involving numbers and
shapes; suggest and test hypotheses;
construct and use simple expressions and
formulae in words then symbols (e.g. the
cost of c pens at 15 pence each is 15c
pence)
 and  each stand for a different number.
I can describe and explain sequences,
patterns and relationships
How could you use symbols to help you to solve this
problem?
I can suggest hypotheses and test them
I can write and use simple expressions in
words and formulae
Each shape stands for a number. The numbers shown
are the totals of the line of four numbers in the row or
column. Find the remaining totals.
 = 34
+=++
What is the value of ? Now make up another problem
like this.
Express missing number problems
algebraically. Find pairs of numbers that
satisfy an equation with two unknowns.
Enumerate possibilities of combinations of
two variables.
Here are five number cards:
I can use letters to represent unknowns.
A and B stand for two different whole numbers.
I can find all possibilities
The sum of all the numbers on all five cards is 30.
What could be the values of A and B?
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Redbridge Version 2014
Objectives Unit 2
Assessment for Learning
•
How many distinct prime factors has 16? What about
17?
Recognise that prime numbers have only two
factors and identify prime numbers less than
100; find the prime factors of two-digit ;
identify common multiples and common
factors of numbers.
I can work out which numbers less than 100
are prime
I can identify common factors, common
multiples and prime numbers.
Can you give me a number with prime factors 3 and 5?
What about 2 and 3?
How could you use prime factors to help you to multiply
by 18?
Which numbers between 20 and 30 have the greatest
number of factors? Which have the least? Which have
an odd/even number of factors?
Can you find two numbers which have 3 common
factors?
•
Use approximations, inverse operations and
tests of divisibility to estimate and check
results
How do you know that 234 is divisible by 3?
I can estimate and check the result of a
calculation
I think that my answer to 3768 × 3 is wrong. How can I
tell?
Should the answer be a multiple of 4? How could you
check?
What would be the best approximation for 9.8 × 31.8?
•
Solve multi-step problems, and problems
involving fractions, decimals and
percentages; choose and use appropriate
calculation strategies at each stage,
including calculator use.
Which three prime numbers multiply to make 231?
What is the missing number in these calculations?
21.8 ×  = 294.3
(14.7 + ) × 4.8 = 164.64
I can use a calculator to solve problems with
more than one step
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Redbridge Version 2014
Objectives Unit 2
Assessment for Learning
•
What is the same about a rhombus and a kite? What is
different?
Describe, identify and visualise parallel and
perpendicular edges or faces; use these
properties to classify 2-D shapes and 3-D
solids; compare and classify geometric
shapes based on their properties and sizes
and find unknown angles in any triangles,
quadrilaterals and regular polygons
I can use the properties of parallel and
perpendicular to describe and classify 2-D
shapes and 3-D solids
Name a shape that has one pair of parallel sides, but
no pairs of perpendicular sides.
What do you notice about the opposite sides of this
parallelogram? Is it true for all parallelograms? What
about this trapezium?
By moving just one point, can you change this shape
into a kite? A rhombus? A non-isosceles trapezium?
I can compare and classify geometric shapes
based on their properties and sizes and find
unknown angles in any triangles,
quadrilaterals and regular polygons.
Which quadrilaterals have diagonals that intersect at
right angles?
If two angles in a triangle are 45º and 80º, what is the
third angle?
•
Make and draw shapes with increasing
accuracy and apply knowledge of their
properties, including nets.
I can make and draw shapes accurately
Give me instructions to get me to draw a rhombus
using my ruler and a protractor.
On the grid below, use a ruler to draw a pentagon that
has three right angles.
I can build simple 3D shapes including nets.
Make a net of a cube with each edge being 8cm.
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Redbridge Version 2014
Objectives Unit 2

Assessment for Learning
Illustrate and name parts of circles including If the radius of a circle is 5cm. What is the diameter?
radius, diameter and circumference and
know that the diameter is twice the radius
Draw a circle with a diameter of 12cm.
I can name the parts of a circle, including
radius, diameter and circumference and
know that the diameter is twice the radius.
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Redbridge Version 2014
Year 6 Block B: Securing number facts, understanding shapes
Unit 3
Objectives Unit 3
Assessment for Learning
•
Imagine you have 25 beads. You have to make a
three-digit number on an abacus. You must use
all 25 beads for each number you make.
How many different three-digit numbers can you
make?
How can you be sure that you have counted
them all?
How will you organise the information in this
problem?
Two boys and two girls can play tennis.
Yasir said: 'I will only play if Holly plays.'
Holly said: 'I won't play if Ben is playing.'
Ben said: 'I won't play if Luke or Laura plays.'
Luke said: 'I will only play if Zoe plays.'
Zoe said: 'I don't mind who I play with.'
Which two boys and which two girls play tennis?
Tabulate systematically the information in a
problem or puzzle; identify and record the
steps or calculations needed to solve it, using
symbols where appropriate; interpret solutions
in the original context and check their
accuracy
I can use a table to help me solve a problem
I can identify and record what I need to do to
solve the problem, checking that my answer
makes sense and is accurate
•
Represent and interpret sequences, patterns
and relationships involving numbers and
shapes; suggest and test hypotheses;
construct and use simple expressions and
formulae in words then symbols (e.g. the cost
of c pens at 15 pence each is 15c pence)
Draw the next two terms in this sequence:
I can describe and explain sequences,
patterns and relationships
Describe this sequence to a friend, using words.
Describe it using numbers.
I can suggest hypotheses and test them
How many small squares would there be in the
10th picture?
I can write and use simple expressions in
words and formulae
I want to know the 100th term in the sequence.
Will I have to work out the first 99 terms to be
able to do it? Is there a quicker way? How?
How would you change an amount of money
from pounds sterling to euros? Record it for me,
using symbols.

Express missing number problems
algebraically. Find pairs of numbers that
satisfy an equation with two unknowns.
Enumerate possibilities of combinations of
two variables.
I can use letters to represent unknowns.
I can solve number puzzles using algebra
p and q each stand for whole numbers.
p + q = 1000 and p is 150 greater than q.
Work out the values of p and q.
Field A is twice as long as field B but their widths
are the same and are 7.6 metres.
If the perimeter of the small field is 23m what is
the perimeter of the entire shape containing both
fields?
11
Redbridge Version 2014
Objectives Unit 3
Assessment for Learning
•
Investigate which numbers to 30 have only one
distinct prime factor (prime numbers, squares of
prime numbers, cubes of prime numbers).
Predict what numbers to 60 will have only one
distinct prime factor when you test them.
Recognise that prime numbers have only two
factors and identify prime numbers less than
100; find the prime factors of two-digit
numbers
I can tell you all the prime numbers up to 100
and find the prime factors of other numbers

Use knowledge of multiplication facts to
derive quickly squares of numbers to 12 × 12
and the corresponding squares of multiples of
10.
Is it always, sometimes or never true that when
you square an even number, the result is
divisible by 4
I can say the squares of numbers to 12 × 12
and work out the squares of multiples of 10.
•
Use approximations, inverse operations and
tests of divisibility to estimate and check
results
I can estimate and check the result of a
calculation
Is this calculation correct? How do you know?
What inverse operation could you use to check
this result?
I multiplied two odd numbers and my answer was
186. Explain why I cannot be correct.
Should the answer be a multiple of 6? How could
you check?
This sequence of numbers goes up by 40 each
time.
40 80 120 160 200 ...
This sequence continues. Will the number 2140
be in the sequence? Explain how you know.
•
Describe, identify and visualise parallel and
perpendicular edges or faces; use these
properties to classify 2-D shapes and 3-D
solids; compare and classify geometric
shapes based on their properties and sizes
and find unknown angles in any triangles,
quadrilaterals and regular polygons
I can identify 3-D shapes with perpendicular
or parallel edges or faces
Imagine a triangular prism. How many faces
does it have? Are any of the faces parallel to
each other?
How many pairs of parallel edges has a squarebased pyramid? How many perpendicular
edges?
Look at these 3-D shapes (e.g. a cuboid,
tetrahedron, square-based pyramid and
octahedron). Show me a face that is parallel to
this one. Which face is perpendicular to this one?
What can you tell me about the faces of a
cuboid? Why are so many packing boxes made
in the shape of a cuboid?
Which of these shapes is incorrectly placed on
this Carroll diagram? Change the criteria so the
shapes are correctly sorted according to their
properties.
12
Redbridge Version 2014
Objectives Unit 3
Assessment for Learning
•
Use your ruler and protractor. Draw the net of a
regular tetrahedron with edges of 6 cm.
Make and draw shapes with increasing
accuracy and apply knowledge of their
properties including making nets.
I can make and draw shapes accurately
I can draw 2D shapes using given dimensions
and angles
I can recognise, describe and build simple 3D
shapes, including nets
Use compasses to draw a circle. Use a ruler and
protractor to draw a regular pentagon with its
vertices on the circumference of the circle.
Tell me an example of a circular object that
would have a radius of about 5 cm. What about
50 cm? 500 cm?
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