Download EM unit notes - Hamilton Trust

Reasoning and explaining
Year 5 Summer 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, …
pattern, relationship, rule, general statement, …
problem, puzzle, solution, method, justify, explain how you
know, give your reasons, …
pattern, relationship, rule, formula, general statement, …
Explain reasoning and methods to solve problems such as:
Explain reasoning and methods to solve problems such as:
Explain reasoning and methods to solve problems such as:
• You can use each of the digits 1, 2, 3 and 4 once and any
operation to make the answer 6.
• Write down any two-digit number, e.g. 36.
Reverse the digits and write down the number: 63.
Find the difference between the two numbers: 63 – 36 = 27.
• Put 2 or 3 in each box.
12 = F + F + F + F + F
Put 2 or 5 in each box.
13 = F + F + F + F + F
Put 3 or 4 in each box.
17 = F + F + F + F + F
Put 4 or 5 in each box.
22 = F + F + F + F + F
(3 × 4) ÷ (2 × 1)
What other numbers from 1 to 20 can you make using
each of the digits 1, 2, 3 and 4 once and any operation?
• 72 cubes can be arranged to make a 2 × 3 × 12 cuboid.
What other cuboids can you make with 72 cubes?
Explain how you worked out your cuboids.
Do the same thing with some other two-digit numbers.
What do you notice?
• The dots on opposite faces of a dice add up to 7.
Imagine rolling two dice.
five white, four blue, five white, four blue…
• Complete this multiplication table.
×
5
40
3
15
30
15
36
40
Explain how you worked it out.
• A line of counters is set out in a pattern:
What colour is the 65th counter?
What position in the line is the 17th blue counter?
The score is the total number of dots you can see on the
tops and at the sides.
Which numbers are face down to score 30?
Explain how you worked out your answer.
• Nasreen bought some 20p stamps and some 10p stamps.
She bought three times as many 10p stamps as 20p
stamps. She spent £2 altogether.
How many 20p stamps did she buy? How many 10p
stamps?
• Jack has some goats and chickens.
He has 15 goats and chickens altogether.
They have 34 feet between them.
How many goats does Jack have? How many chickens?
• Peter has 37 CDs. He puts all of them in piles.
Some piles have 4 CDs in them.
Some piles have 3 CDs in them.
How many piles of 3 CDs are there?
How many piles of 4 CDs?
• Take £1 worth of coins: four 1p, three 2p, four 5p, three
10p and two 20p. Find all the different ways of using the
coins to pay 50p exactly.
© 1 | Year 5 | Summer TS6 | Reasoning and explaining
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:
• 102 + 245
245 plus 100 is 345, and 2 more is 347.
• 109 ÷ 21
21, 42, 63, 84, 105.
21 × 5 = 105, plus 4 more is 109, so the answer is 5 r 4.
• 17.5% of £30 000
• 500 – 180
Take away 200 from 500, that’s 300, add 20 is 320.
• 23 × 5
20 × 5 is 100, and 3 × 5 is 15, so altogether it’s 115.
• 50 ÷ 4
Half of 50 is 25, and half of 15 is 12.5.
•
1
of 424
8
Half of 424 is 212, half of 212 is 106, and half of 106 is 53,
so one eighth of 424 is 53.
• 387 ÷ 9
10%
5%
2.5%
17.5%
= £3000
= £1500
= £ 750
= £5250
387 ÷ 3 = 129
129 ÷ 3 = 43
Make general statements about patterns and relationships
Previous learning
Core for Year 5
Extension
Make general statements about patterns or relationships, e.g.
Make general statements about patterns or relationships, e.g.
Make general statements about patterns or relationships, e.g.
• Write the missing amounts in this sequence.
The same amount is added each time.
• Here is a number sequence.
• Describe the rule for this sequence:
£2.65
£2.75
…
£2.85
…
£3.15
Describe the rule for the sequence.
• Write the numbers missing from these sequences.
11
13
14
0 1 1 2 3 5 8 13 F F
Describe the rule for the sequence.
Write the next two numbers in the sequence.
• Draw the next pattern for each sequence.
Describe each rule.
1, 3, 6, 10, 15, 21, … (triangular numbers)
Investigate this statement: ‘Every square number can be
made by adding two consecutive triangular numbers.’
• Fill in the missing numbers in these sequences.
Describe each rule.
10, 25, F, F, 80, …
15
1, 4, F, F, 25, 36, F, …
F, F, –61, –42, –23, …
33
42
• Here is a repeating pattern of shapes.
Each shape is numbered.
• Here is a sequence made from squares and circles.
Describe each sequence.
The pattern continues in the same way.
Write the numbers of the next two stars in the pattern.
Complete this sentence.
Shape number 37 will be a circle because ...
© 2 | Year 5 | Summer TS6 | Reasoning and explaining
Draw the next two patterns in the sequence.
How many squares will there be in pattern 10?
How many circles?
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999