Problem solving
Year 6 Summer 11
Solve logic problems
Previous learning
Core for Year 6
Extension
Use, read and begin to write these words:
Use, read and write these words:
Use, read and write these words:
problem, solve, solution, method, explain, give a reason, show
your working, … possibilities, work systematically, list, table, …
problem, solve, solution, method, explain, give a reason, show
your working, … possibilities, work systematically, list, table, …
problem, solve, solution, method, explain, give a reason, show
your working, … possibilities, work systematically, list, table, …
Use reasoning skills to solve logic problems, e.g.
Use reasoning skills to solve logic problems, e.g.
Use reasoning skills to solve logic problems, e.g.
• Ruth has six children: Annie, Beth, Charlie, David, Ellie
and Fred. What is the age of each child?
Clues:
The sum of Annie’s and Beth’s ages is 8.
The sum of Beth’s and Charlie’s ages is 10.
Beth and David are twins.
Ellie is twice as old as Annie.
Fred is the oldest by 2 years.
The sum of all their ages is 40.
• I have three different coloured boxes.
Inside each box is a multilink cube and a counter, which
are a different colour from each other and from the box.
There is one blue cube, one blue counter, one red cube,
one red counter, one yellow cube and one yellow counter.
Which coloured box contains which coloured cube and
which coloured counter?
Clue:
The red multilink cube and the yellow counter are not in the
blue box.
• Four athletes are running in a marathon.
When the first athlete crosses the finishing line, the third
athlete still has 6 km to run.
The fourth athlete is 4 km from the second athlete.
The third athlete is 1 km nearer to the fourth athlete than he
is to the second athlete.
How far is the fourth athlete from the finishing line?
• Harry, Holly, Sandip and Zoe are friends.
Each likes two vegetables from this list:
peas, carrots, broccoli and cabbage.
Each vegetable is liked by only two children.
Which two vegetables does each friend like?
Clues:
Zoe and Sandip don’t like carrots.
Zoe likes cabbage and Sandip likes broccoli.
Harry and Sandip like peas.
• Each shape stands for a different number.
The totals of each row and column are shown.
What number does each shape stand for?
▲
„
z
▲
„
z
z
„
▲
„
z
„
z
▲
z
▲
25
20
• Amy, Beth, Charlie and David each have a different shape.
Who has which shape and what is its colour?
Clues:
One of the shapes is a cube.
One of the shapes is red.
David's shape is a cone. The cone is not blue.
Amy's shape is yellow. It is not the sphere.
Charlie's shape is not the green cylinder.
• It is a Tuesday.
Zoe, Holly and Ram are skating at the ice rink.
The ice rink opens every day of the week.
Zoe goes skating every third day.
Holly goes skating every fourth day.
Ram goes skating every fifth day.
What day of the week will it be when they are all together
at the ice rink again?
9
Find the remaining totals.
© 1 | Year 6 | Summer TS11 | Problem solving
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Solve visual puzzles
Previous learning
Core for Year 6
Extension
Use reasoning skills to solve visual puzzles, e.g.
Use reasoning skills to solve visual puzzles, e.g.
Use reasoning skills to solve visual puzzles, e.g.
• You need 6 drinking straws each the same length. Cut two
of them in half. You now have 8 straws, 4 long and 4 short.
• How many different triangles can you see in this diagram?
• Emily colours 3 squares on this 4 by 4 grid.
The squares touch edge to edge.
You can make 2 squares from the 8 straws like this.
Arrange your 8 straws to make 3 squares, all the same
size. Draw a diagram to show your solution.
• Using straight cuts, show how to divide a square into 6
smaller squares.
• A rectangular library area is screened off into four smaller
rectangular areas. The areas of three of the smaller areas
are 12, 18 and 30 square metres.
12 m2
18 m2
• Take three shapes like this.
30 m2
Use the three shapes to make a symmetrical shape.
How many different symmetrical shapes can you make
using the three shapes.
What is the area of the whole library?
• This pattern is made from 16 matchsticks.
How many of your shapes have only one line of symmetry?
How many have two lines of symmetry?
• This 4 by 4 grid is divided into two identical parts.
Each part has the same area and the same shape.
Take away just four matches to leave exactly four
equilateral triangles.
Explore ways of dividing a 4 by 4 grid into two parts with
equal areas but different shapes.
© 2 | Year 6 | Summer TS11 | Problem solving
• Imagine you have some squared paper on the table in front
of you. Imagine colouring an L-shape on the paper. It is
just one square wide.
How many edges does it have?
How many vertices does it have?
What sort of polygon is it?
Now imagine colouring a T-shape on your paper.
How many edges does it have?
How many vertices does it have?
What sort of polygon is it?
In how many different ways can Emily colour three of the
16 squares?
• A newspaper is made up of a number of double sheets,
with a single sheet placed in the middle.
When the paper is taken apart, page number 26 and page
number 37 are on the same sheet of paper.
What is the page number of the back page of the paper?
• Imagine a cereal packet standing on the kitchen table and
that you have some quick drying paint.
Paint the front of the packet red.
Now paint the back red.
Paint the top and bottom of the packet red and the other
two faces blue.
Now study the packet carefully.
How many edges has the packet altogether?
How many of these edges are where a red face meets a
blue face?
How many edges are where a red face meets another red
face?
How many edges are where a blue face meets another
blue face?
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Solve mathematical puzzles
Previous learning
Core for Year 6
Extension
Solve mathematical puzzles, e.g.
Solve mathematical puzzles, e.g.
Solve mathematical puzzles, e.g.
• Mrs Bassett bought some chickens and ducks.
She spent exactly £50.
Chickens cost £5.50 each and ducks cost £7.50 each.
How many ducks and how many chickens did she buy?
• Use the numbers 1 to 9.
• Use the numbers 1 to 9.
• Take ten cards numbered 0 to 9.
Each time use all ten cards.
Arrange the cards to make:
– five numbers that are multiples of 3
– five numbers that are multiples of 7
– five prime numbers.
• 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?
Write them in order.
• Choc bars cost 26p each. Fruit bars cost 18p each.
Anil spent exactly £5 on a mixture of choc bars and fruit
bars. How many of each did he buy?
• Tammy’s age this year is a multiple of 8.
Next year it will be a multiple of 7.
How old is Tammy?
• The sum of two numbers is 5.
The difference between the numbers is 0.5.
What are the numbers?
© 3 | Year 6 | Summer TS11 | Problem solving
Put one number in each square of the grid so that each of
the rows, columns and diagonals add up to the same
number.
Put one number in each square of the grid so that no two
of the rows, columns or diagonals add up to the same
number.
• A group of friends share equally the cost of a £24 meal.
If the number of friends in the group were doubled, each of
them would pay £2 less.
How many friends are there in the group?
• The fossil of an argentinosaurus is 37 metres long.
Its tail is twice as long as its head, and its body is 2 metres
longer than half its head.
How long is the head, body and tail of the fossil of the
argentinosaurus?
• Two families go to the cinema.
The Smith family buy tickets for one adult and four children
and pay £19.
The Jones family buy tickets for two adults and two
children and pay £17.
What is the cost of one child's ticket?
• 572 is a three-digit number.
The sum of the digits is 5 + 7 + 2 = 12.
What is the smallest three-digit number you can find with a
digit sum of 23?
How many different three-digit numbers can you find
altogether with a digit sum of 23?
• Descending numbers are whole numbers such that each
digit is different and smaller than the one before.
• Last year Dan’s age was a square number.
Next year it will be a cube number.
How old is Dan?
• The product of two numbers is 999.
The difference between them is 10.
What are the two numbers?
• Use each of the digits 1 to 6.
Put one digit in each box.
FFFF × FF
What is the smallest product you can make?
What is the biggest product you can make?
92 is a two-digit descending number.
863 is a three-digit descending number.
9754 is a four-digit descending number.
How many three-digit descending numbers are there?
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Explain methods and reasoning orally and in writing
Previous learning
Core for Year 6
Extension
Describe and explain methods of working out calculations,
orally and in writing.
Describe and explain methods of working out calculations,
orally and in writing.
Describe and explain methods of working out calculations,
orally and in writing.
For example, explain orally or write that:
For example, explain orally or write that:
For example, explain orally or write that:
• 7003 – 6994
6994 + 6 = 7000, add 3 more is 7003,
so the answer is 6 + 3 = 9.
• 42 × 15
• 17.5% of £30 000
• 24 × 4
Double 24 is 48, and double 48 is 96.
• 400 × 80 is equivalent to 4000 × 8 = 32 000.
• 87 ÷ 2
Half of 80 is 40, and half of 7 is 3.5, so it’s 43.5.
42 × 10 = 420
42 × 5 = 210
42 × 15 = 630
half of 42 × 10
the sum of 420 and 210
• 15 × 12 is 15 × 4 × 3 = 60 × 3 = 180.
•
1
20
of 400
One tenth of 400 is 40, so one twentieth of 400 is 20.
Explain reasoning and solutions to the puzzles and problems
on the previous three pages, orally and in writing, using lists,
tables or diagrams as appropriate.
© 4 | Year 6 | Summer TS11 | Problem solving
Explain reasoning and solutions to the puzzles and problems
on the previous three pages, orally and in writing, using lists,
tables or diagrams as appropriate.
• 387 ÷ 9
10%
5%
2.5%
17.5%
= £3000
= £1500
= £ 750
= £5250
387 ÷ 3 = 129
129 ÷ 3 = 43
• 49 × 30
50 × 30 = 1500, subtract 30 is 1470.
Explain reasoning and solutions to the puzzles and problems
on the previous three pages, orally and in writing, using lists,
tables or diagrams as appropriate.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999