Reasoning and explaining
Year 5 Autumn 6
Solve mathematical puzzles
Previous learning
Core for Year 5
Extension
Understand and read these words:
Understand, read and begin to write these words:
Understand, read and write these words:
problem, puzzle, solution, method, explain how you know,
give your reasons, …
pattern, relationship, rule, …
problem, puzzle, solution, method, justify, explain how you
know, give your reasons, … general statement, …
pattern, relationship, rule, …
problem, puzzle, solution, method, justify, explain how you
know, give your reasons, … general statement, …
pattern, relationship, rule, formula, substitute, …
Solve mathematical puzzles and problems, e.g.
Solve mathematical puzzles and problems, e.g.
Solve mathematical puzzles and problems, e.g.
• Find three consecutive numbers which add up to 48.
What other numbers up to 50 can you make by adding
three consecutive numbers?
• Find:
two consecutive numbers with a product of 182;
three consecutive numbers with a total of 333.
• Which number(s) between 20 and 40 have:
• Put the numbers 1 to 9 in the circles so that the difference
between each pair of joined numbers is odd.
• Choose any four numbers from the grid. Add them up.
Find as many ways as possible of making 1000.
the most factors
the least factors
an odd number of factors?
• Give an example of a two-digit number with:
exactly two factors (e.g. 17)
exactly three factors (e.g. 49)
exactly four factors (e.g. 10)
exactly five factors (e.g. 16)
exactly ten factors (e.g. 48)
more than ten factors (e.g. 84)
• Complete this addition table.
+
55
100
15
• Complete this addition table.
40
+
75
95
• I think of a number between 1 and 10.
I multiply it by 5, then add 1, and get 26.
What is my number?
© 1 | Year 5 | Autumn TS6 | Reasoning and explaining
99
120
27
• Complete this multiplication table.
100
146
150
• I think of a number.
I divide it by 4, then subtract 5, and get 11.
What is my number?
• I think of a number, square it and add 4..
The answer is 40.
What is my number?
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Explain methods and reasoning orally
Previous learning
Core for Year 5
Extension
Describe and explain methods, reasoning and solutions to
puzzles and problems, orally and in writing, with diagrams.
Describe and explain methods, reasoning and solutions to
puzzles and problems, orally and in writing, with diagrams.
Describe and explain methods, reasoning and solutions to
puzzles and problems, orally and in writing, with diagrams.
For example, explain orally or write that:
For example, explain orally or write that:
For example, explain orally or write that:
• 17 + 23
Add 17 and 3 to get 20, then 20 more to get 40.
• 7003 – 6994
6994 + 6 = 7000, add 3 more is 7003,
so the answer is 6 + 3 = 9.
• 42 × 15
• 15 × 12 is 15 × 4 × 3 = 60 × 3 = 180.
• 400 × 80 is equivalent to 4000 × 8 = 32 000.
• 65 – 28
65 – 30 is 35, but then add back 2 to make 37.
42 × 10 = 420
42 × 5 = 210
42 × 15 = 630
half of 42 × 10
the sum of 420 and 210
Make general statements about odd and even numbers, including their sums and differences
Previous learning
Core for Year 5
Extension
Identify properties of odd and even numbers and make
general statements, e.g.
Make general statements about odd and even numbers
including their sums and differences, e.g.
Give examples to match a true statement, e.g.
• The last digit of an even number is 0, 2, 4, 6 or 8.
• The sum of:
• Any odd number is one more than an even number.
• The last digit of an odd number is 1, 3, 5, 7 or 9.
odd + odd = even
two odd numbers is even;
• Every other number is an odd number.
• Every other number is an even number.
• The numbers on each side of an odd number are both
even.
• The numbers on each side of an even number are both
odd.
• Any odd number is one more than an even number and
one less than the next even number.
• Any even number is one more than an odd number and
one less than the next odd number.
• The rule for the sequence of even numbers is:
‘Start at 0, and keep adding 2.’
• The rule for the sequence of odd numbers is:
‘Start at 1, and keep adding 2.’
© 2 | Year 5 | Autumn TS6 | Reasoning and explaining
two even numbers is even;
one odd and one even
number is odd.
For example: 23, which is an odd number, is 1 more than
22, which is an even number.
even + even = even
• Any even number can be written as the sum of two odd
numbers.
even + odd = odd
For example: 16 is an even number, and 16 = 13 + 3,
which are both odd numbers.
• Multiples of 4 are always even.
• The difference between:
two odd numbers is even;
two even numbers is even;
one odd and one even number is odd.
For example: 12 is a multiple of 4, and 12 is even.
• The sum of:
three odd numbers is odd;
three even numbers is even;
two odd and one even numbers is even;
two even and one odd numbers is odd.
• The product of:
two odd numbers is odd;
two even numbers is even;
one odd and one even number is even.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999