Short-Term Planning Grid for Mathematics
Year 6
Fractions
Addition and subtraction
Multiplication and division
Y6 Block 8
Planning grid
Days 1 - 2
Block 8
Algebra
OVERVIEW – WHAT CHILDREN WILL LEARN
Objectives you will cover, partially or fully
Explore sequences, such as triangle, perfect or happy numbers or the Fibonacci sequence. Use properties of
numbers sequences, patterns and relationships to solve problems. Include continuing the sequence, predicting
patterns and finding and testing general rules. You could link this to creating and using conversion graphs.
Prime numbers are important in that they don’t create a sequence, but have specific properties. Review
multiples, which create an infinite sequence, and factors, which are a limited set of numbers. You could link
multiples to simple formulae; if pens are 25p each then c pens will always be a multiple of 25.
8) Use simple formulae
9) Generate and describe linear number sequences
Oral/Mental Objective
and Activity
Objectives/Success
criteria
Introduction/
demonstration/
modelling
Activities set
Differentiation / Use of
other adults
Learning review
opportunities
Resources
[email protected]
ITPs: Number grid, 20 Cards; Area
Spreadsheet : Increasing Number grid, Sequences
Matchsticks or multilink to produce visual shape sequences
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Activity ideas
Triangular numbers
Make triangular numbers with multilink cubes up to the 8 th number (36 cubes).
Investigate the statement: 'Every square number is the sum of two triangular numbers’.
Happy numbers
To find out whether a number is happy you square each of its digits. Next add the answers and repeat.
If you end up with 1 the number is happy!
For instance, is 19 a happy number?
12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1 This means that 19 is a happy number.
The happy numbers up to 100 are:
1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100 but don’t tell the children!
Display
Groups or pairs of children create A3 posters explaining about a certain type of number, for
instance primes, multiples or perfect numbers. Their aim is to make a poster that children in
Year 4 could understand, which has relevant images and a small amount of useful text. The
text must take up between 20% and 30% of the total space, and there must be between 4
and 6 images. Also make posters for tests of divisibility and use these to help when working
with factors and prime numbers.
Developing sequences
Most children will be able to find the next terms in a simple sequence. Look at sequences
based on addition, subtraction, multiplication and division, getting children to start sequences
of their own choice in groups, and then pass the sequence to another group who can
continue the sequence.
More complex sequences will be interesting for some children, but don’t limit this only to
children that you expect to find it easy.
Possible sequences are:
2, 6, 12, 20, 30, 42....
The number added each time increases by 2.
2, 8, 23, 47, 80, 122, 173.... The number added each time increases by 9.
Can this work with other operations?
What’s the formula
Calculators
The cost of c pens at 15 pence each is 15c pence. What does this mean? Does it matter
Use the constant function on a calculator to explore sequences.
how many pens there are? Does it matter what the price is?
Press 5 + 3 = = = or 5 + 3 + + = = =. Most calculators will add 3 repeatedly when you do this, with the first
Use classroom objects to make more formulae, such as: There are 6 pots of pencils.
one starting at 5. Use this function to create sequences. Ask children to explore starting from different
There are e pencils in each pot. What would the formula be? Put out pots of pencils
numbers, repeatedly subtracting, creating numbers that are a multiple of 5 plus 1, numbers that would give
labelled with the formula.
a remainder of 4 when divided by 6 and so on.
Drawing sequences
Conversion graphs
Take a simple visual sequence, such as
Create graphs showing multiples (e.g. 15 times table, counting in steps of 0.3 or £1.20 etc.), other simple conversions
the first one. Draw the next two terms in
(currency exchange rates), sequences (e.g. start at 5 and count in 2s) and more complex ideas such as triangular
this sequence. How many small squares would there be in
numbers, square numbers or primes.
the 10th picture? Now go back and make a small change to
Use the straight line graphs created from some of the sequences to check multiplication and division facts or to work
the second pattern. What difference does this make to the sequence? Write
out prices for a number of items at £1.20 each. Compare this to the formula where the cost of 1 ice cream is 120i in
numbers for each item in the sequence and see how these change, possibly
pence or 1.2i in £.
showing them on a number line to have a clear image of the differences.
Discuss the interesting shapes made by graphs that don’t produce straight lines, or that don’t start from the origin (0,0)
More ideas
Explore and compare the square number sequence and the triangle number sequence

Investigate the differences between terms of the sequence of square numbers 1, 4, 9, 16, ... and triangle numbers 1, 3, 6, 10…… Describe the pattern and use it to continue the sequence.
Recognise and use sequences, patterns and relationships involving numbers and shapes to solve problems such as: Which numbers are ‘Happy ‘or’ Perfect’ numbers. Is my age, house number,
phone number…… happy?
The first two numbers in the 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, _ , _ This may involve work on the Fibonacci sequence. Details of Happy and Perfect numbers and the Fibonacci sequence can be found on the internet.
How can you use factors to calculate 35 × 14?
Describe the relationship between terms in this sequence: 2, 3, 8, 63...
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Make the ITP '20 cards' generate this sequence of numbers: 1, 3, 7, 13...
Explain why a square number always has an odd number of factors.
Children tabulate information, working systematically, to help them to solve problems and explain their conclusions. They explain their methods and reasoning,
using symbols where appropriate.
For example, they explore a problem such as: In a village where all the roads are straight, every time two streets intersect a street lamp is required. Investigate the number of street lamps required for 2
streets, 3 streets, 4 streets ... What is the minimum and maximum number of lamps needed for 5 streets? For n streets? What could you draw to help you solve this? Does your answer make sense?
How do you know you have identified the maximum number of intersections for 5 streets? Explain how making a table could help you to solve this problem.
Children are able to continue and produce sequences given a general rule, include whole and decimal numbers, negative and positive. They represent and interpret sequences, patterns and
relationships involving numbers and shapes and investigate visual sequences – involving shapes, matchsticks, and so on.
Describe a sequence to a friend, using words. How does the visual image help in explaining. Describe it using numbers. 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? Begin to use term to term rules and general rules.
Children investigate relationships and patterns in numbers. They write a formula for converting from one currency to another, researching the accurate exchange rate and using symbols to express the
relationship between the two currencies. They find the digit sum of multiples of 3 and use results to establish a rule for divisibility by 3. They explore multiples of other numbers in a similar way and
establish general rules for recognising where a number is a multiple of 2, 3, 4, 5, 6, 8 or 9.
How would you change an amount of money from pounds sterling to euros? Record it for me, using symbols.
How many squares of multiples of 10 lie between 1000 and 2000? How many lie between 1000 and 10 000?
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.
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.
In your group, consider the sum of five numbers in a straight line on the 100-square. What do you notice? Think about this problem and how to solve it. Take turns to contribute one idea for the group
to discuss.
How would you change an amount of money from pounds sterling to euros? Record it for me, using symbols. Is there a rule? ( formula)
Assessment opportunities
As they work with a wider range of sequences, look for children who use negative numbers, for example, to continue a sequence back past 0. Look for evidence of children recognising and describing
relationships and properties such as multiple, factor, square and prime.
As they investigate shapes and numbers, look for evidence of children making general statements or formulating 'rules'. When they work with number sequences that go up in steps of a regular size,
look for children who explain a rule for working out a number in the sequence, given its position, for example, the twentieth number.
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Y6 Block 8
Planning grid
Days 3 - 4
OVERVIEW – WHAT CHILDREN WILL
LEARN
Use 1/100, 1/1000, x100 and x1000 to solve
measures problems. Revise the links
between mm, cm and m, g and kg, ml and l,
and p and £.
Objectives you will cover, partially or fully
10) Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three
decimal places where appropriate
11) Use, read, write and convert between standard units, converting measurements of length, mass, volume and time
from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places
Oral/Mental Objective
and Activity
Objectives/Success
criteria
Introduction/
demonstration/
modelling
Activities set
Differentiation / Use of
other adults
Learning review
opportunities
Resources
[email protected]
ITP: Moving digits
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Activity ideas
Sort
Find one; find 1000
Children quickly write statements showing the relationships between units of measurement on
Use the ‘Estimate the weight’ sheet, with the cards cut up and placed around the room next to the
strips of paper. Groups take it in turns to sort the papers, deciding for themselves how to do this.
items to be estimated.
They then photograph the sort. Show the pictures on the IWB for children to decide what the
criteria were for the sort.
Make a table
Children create their own tables of information to show what happens when different measures are multiplied or divided by 10.
Encourage children to use staring points that are not only 1, 10 or 100.
Does it work in the same way for length, weight, capacity and money?
What is different?
What about time? Why doesn’t this work with time? (Consider months, weeks and days and not just hours and minutes).
More ideas
Children continue to solve practical problems involving estimating and measuring. For example, they suggest how to estimate the weight of one grain of rice or the thickness of one sheet of paper.
When finding the thickness of one sheet of paper, they measure the thickness of 100 sheets and then divide their answer mentally by 100.
They understand that the measurement found for the thickness of one sheet of paper is approximate. They communicate clearly how a problem was solved, explaining each step and commenting on
the accuracy of their answer.
What measurement is 10 times as big as 0.01 kg? How do you know that it is 10 times 0.01 kg?
I divide a measurement by 10, and then again by 10. The answer is 0.3 m. What measurement did I start with? How do you know?
The height of a model car is 6 centimetres. The height of the real car is 45 times the height of the model. What is the height of the real car? Give your answer in metres.
How do I write 5 metres 6 centimetres as a decimal?
Assessment opportunities
Look for evidence of children drawing on a range of mathematics to solve problems. As they consider how to estimate very small measurements, look for children drawing on their knowledge of place
value. For example, children might recognise that dividing a number by 10, 100 or 1000 is easier to calculate than dividing by other numbers, and so understand the approach of first measuring the
weight of 100 grains of rice or the thickness of 100 sheets of paper. Some children might be able to draw on their understanding of area and their calculation skills to estimate the weight of one sheet of
paper, given the description from a packet of paper of ‘80 g per m2’.
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