Section 3
Problem Solving
Exemplars
Reason Logically
Level A
Teacher’s Notes
Strategy:
Level A
Reason Logically
Ordering
Resources:
A worksheet for each child
Previous
Knowledge
Children understand what “heavier” means
Compare two objects and see if children can tell which is heavier.
Compare three objects with clear differences of weight and see if
children can put them in order.
Compare unseen objects e.g. an elephant and a mouse
and see if children understand the concept of “heavier”.
Children can write the number of the objects for both
parts if they have not yet mastered writing letters.
Extension: Questions
If a fork weighs 3 cubes, how many cubes do you think
a cup weighs?
If a jotter weighs 8 beads, how many beads do you think a book weighs?
Ordering
Name: …………………………………………
Look at these pictures.
1
2
3
4
5
6
1. Write the number or name in order – heaviest first.
2. Write the number or name in order – lightest first.
Teacher’s Notes
Strategy:
Level A
Reason Logically
What can I buy?
Resources:
Problem can be put on display board or
children can use the worksheet.
Previous
Knowledge:
Addition to 50 (involving carrying figure)
Subtraction within 50 (decomposition)
If a child has difficulty point out:
a) Price of chocolate and what would be left out of 50p.
b) The fact that there is no change.
Solution:
Tablet costs 30p
Extension:
Last sentence of problem could read:
“How much is the tablet if when he buys it he has 2p change left?”
The amount of change can vary.
What can I buy?
Name: …………………………………………….
Scott has 50p to spend.
50p
A lollipop costs 20p and chocolate costs 25p.
If Scott buys chocolate, he cannot buy tablet, but if he buys a
lollipop he can buy tablet.
How much is the tablet if he buys it, he has no change?
tablet
lollipop
20p
chocolate
25p
tablet?
Reason Logically
Level B
Teacher’s Notes
Strategy:
Level B
Reason Logically
Sort it Out
Resources:
Worksheet
Previous
Knowledge:
Nil
Discuss the meaning of consecutive with the children.
Solution:
4
1
2
There are other solutions.
3
5
Sort it Out
Name: …………………………………………………
Read carefully:
2 is consecutive to 1 and 3
3 is consecutive to 2 and 4
On the houses below, arrange the number 1 to 5 so that no two
consecutive numbers are joined by a line.
Teacher’s Notes
Strategy:
Level B
Reason Logically
Weigh It Up
Resources:
Worksheet, pencil
Previous
Knowledge:
Experience of 2 pan balance
Solution:
Weigh It Up
Name: …………………………………………………………
Put these pictures in order. One picture is still to be finished.
Draw the rest of the unfinished picture to show the balance when three
weights are used.
Write down how you found your answer
Key:
parcel is this shape
weight is this shape
Reason Logically
Level C
Teacher’s Notes
Strategy:
Level C
Reason Logically
Arrange the Counters
Resources:
Worksheet, coloured counters in 4 colours
Previous
Knowledge:
Quarters
Solution:
Arrange the Counters
Name: ………………………………………..
Here are 8 counters
¼ are red
¼ are blue
¼ are yellow
¼ are white
Use coloured counters to show these fractions.
There must not be 2 counters of the same colour next to each other
on the lines.
Teacher’s Notes
Strategy:
Level C
Reason Logically
Search for a Number
Resources:
Worksheet
Previous
Knowledge:
Multiplication and division by 2 - 9
Solution:
1. 73
4. 51
2. 70
5. 18
3. 32
6. 15
Search for a Number
Name: ………………………………….
These children want you to find their numbers.
Ben: My number is inside the circle and inside the triangle. It is not
inside the square. It is greater than 20.
Jill: My number is inside all three shapes. It can be divided by 5
without a remainder. It is greater than fifty.
Tony: My number is not in the circle and not in the square but it is
in the triangle. It is an even number and can be divided exactly by 8.
Sula: My number is in the circle but not in the triangle and not in
the square. It is an odd number.
Erin: My number is even. It is inside the square. It can be divided
exactly by 9, 3, and 2. It is less than 40.
Ali: My number is not in any of the shapes. It is less than 20, but
more than 10. It can be divided exactly by 5.
Teacher’s Notes
Strategy:
Level C
Reason Logically
MacDonald Family
Resources:
Worksheet
Previous
Knowledge:
Nil
Solution:
The least number is four.
2 boys and 2 girls
MacDonald Family
Name: …………………………………………………….
What is the smallest possible number of children in the MacDonald
family, if each child has, at least, one brother and at least one
sister.
Teacher’s Notes
Strategy:
Level C
Reason Logically
Code Cracker
Resources:
Worksheet
Previous
Knowledge:
Addition to 15
Solution:
Code Cracker
Name: …………………………………….
Task 1
Below are the names of 5 drinks all written in code.
The same symbol always stands for the same letter.
Hint: One of the drinks is coffee and one is tea.
Crack the code and find the drinks.
Task 2
Below are the names of 5 sports all written in code.
The symbols in this case stand for different letters than those
in Task 1.
Hint: David Beckham is famous for one of these sports.
Crack the code and find the sports.
Contd.
Code Cracker
(contd.)
Name: …………………………………………………..
Task 3
Use the CODEX system to decode these messages:
a)
J
WJOA
b)
TWRA
JK
c)
JYGAKUJDCUJFYK
HFJYD
PL
PCUIAPCUJSK
NCGFRVJUA
CVA
SFWFRV
AXSJUJYD
Use the CODEX system to code these messages. You supply the
missing answers:
d)
My name is?
e)
My hobby is?
f)
My favourite pop group is?
TASK 4
PCOA
LFRV
FEY
SFHAX
CYH
KFPA
SFHAH PAKKCDAK
Code Cracker
Name: …………………………………………………..
You are now going to read and write secret messages.
In CODEX the code letter C stands for the real letter A,
The code letter T stands for B, the code letter S stands for
C and so on.
Codex you will notice that the all code letters are on the outer
ring and the real letters are on the inner ring.
2 letters are missing from the CODEX code letters – they
are J and Z.
Let J stand for I and Z stand for Z itself.
For
example
Code
letters
Real Letters
PCUIK
JK
NRY
MATHS
IS
FUN
Code Cracker
Name: ………………………………………….
This means
5
+
4
=
What are these sums?
Use the code to make up some of your own.
9
Reason Logically
Level D
Teacher’s Notes
Strategy:
Level D
Reason Logically
Eliminate!
Resources:
Worksheet
Previous
Knowledge:
Nil
This lesson teaches the child to use information contained in
a problem to eliminate all but the correct answer from a given
set of possibles.
Pass out the worksheet and instruct the children to complete it.
Once the children have completed the worksheet, the results
Should be discussed with the class. Allow the children to
analyse each clue in the detective problem and explain how it
can be used to eliminate a suspect. By itself, the first clue will
not eliminate a suspect since being ‘registered at a hotel’ does
not necessarily indicate that he spent the night.
Ask the children which clue they used first to solve the second
problem. There may be some discussion of the exact order,
however there will probably be agreement on the use of clues b, c,
and e, before a and d. The choice of the first clue is important.
Children should learn to read all the statements first and then
determine which one is easiest to use and/or which one will
eliminate the most choices.
Solutions: Q1. Harry Carry
Q2.
8706
Eliminate!
Name: ………………………………………
Ace Detective Thistle Bines of the
Glasgow Murder Squad is investigating
a murder at the Old Granada Hotel.
Five men are being held as suspects.
“Giant” Gerry Green. He is 250cm tall, weighs 140kg, and loves
his dear mother so much that he has never spent a night away from
home.
Harry Carry. He is a 200kg Sumo wrestler.
“Hi” Peter Grey. He is a small man only 130cm tall; he hates high
places because of a fear of falling.
“Curly” Boots. His nickname is a result of his totally bald head.
Henry “The Claw” Brown. He lost both of his hands in an accident.
1. Use the following clues to help Detective Bines solve this crime:
a) The killer was registered at the hotel.
b) Before he died, the victim said the killer had served time in
prison with him.
c) Brown hair from the killer was found in the victim’s hand.
d) The killer escaped by diving from the third floor balcony into the
river running by the hotel, and then swimming away.
e) Smudges were found on the glass table top indicating that the
killer wore gloves.
Contd.
Eliminate!
(contd.)
Name: ……………………………………………………
2. Find the number described by the clues below.
Circle the correct number.
a)
It is divisible by 4
b)
It is larger than 8641
c)
It is an even number
d)
The sum of the digits is 21
e)
It is less than 9756
9078
6552
8948
9884
9341
9714
3242
8643
10341
1874
Which clue(s)
should you use
first
……………………..
5483
9096
9462
What does
this
eliminate?
……………………
8832
2359
8706
8814
Teacher’s Notes
Strategy:
Level D
Reason Logically
Best Clues
Resources:
Worksheet
Previous
Knowledge:
Children should have done
Worksheet ELIMINATE
During discussion with the class, re-emphasise the choice of
the first clue to be used. A statement is chosen first
because it;
1)
2)
is the easiest one to use, or
will eliminate the most possibilities.
Solution:
1) Since the blue marble was picked, can the other marble
be red? No. Explain: A red marble would be mean Box 2
has the correct line which contradicts clue (d).
What is the correct lid for Box 2? Black.
2)
Can Box Y contain the red and black marbles? No.
Explain: If so, then Box X would have red marbles.
This contradicts clue (d). What are the correct lids for
Boxes, A,B,C?
Box
Correct Lid
X
Y
Z
Red-Black
Red
Black
Best Clues
Name: ……………………………………………..
Study the clues that are given below and explain how they can tell
exactly which marbles are in each box.
X
Y
Red Lid
a)
b)
c)
d)
e)
Black Lid
Z
Red-Black
Lid
One box contains 2 red marbles.
One box contains 2 black marbles.
One box contains 1 red and 1 black marble.
None of the lids is on its correct box.
Jason reached into the box with the red-black lid and pulled out
a black marble.
1. Since a black marble was picked, can the other marble be
red?………………………………….Explain……………………………………………………………
………………………………………………………………………………………………..
What is the correct lid for box 2 ……………………………………………
2. Can box Y contain red and black marbles? ……………………………..
Explain………………………………………………………………………………………………
What are the correct lids for boxes X,Y and Z?
Box
X
Y
Z
Correct Lid
Teacher’s Notes
Strategy:
Level D
Reason Logically
More Best Clues
Resources:
Worksheet
Previous
Knowledge:
Children should have completed
Worksheet BEST CLUES
During discussion with the class, re-emphasise the choice of the
first clue to be used. A statement is chosen because it;
1) is the easiest one to use, or
2) will eliminate the most possibilities
Solutions:
Q1 Winner is circled.
Game
1
2
3
4
5
6
Home
Team
Dons
Gers
Jags
Dons
Jags
Gers
Visitors
Gers
Dons
Dons
Jags
Gers
Jags
Team
Won
Lost
Q2
Dons
1
3
9371
Jags
3
1
Gers
2
2
More Best Clues
Name: …………………………………………
1. Three teams in the Motherwell Football League played each
other at home and away. Find the win – loss record for the six
games shown in the schedule below, if:
a) The Dons never defeated the Jags.
b) The Gers never lost a home game.
c) The Gers lost 2 games.
Game
1
2
3
4
5
6
Home Team
Dons
Gers
Jags
Dons
Jags
Gers
Visitors
Gers
Dons
Dons
Jags
Gers
Jags
Jags
Gers
Team
Dons
Won
Lost
Contd.
More Best Clues (contd.)
Name: ………………………………………………………..
2. Study the clues. Eliminate all but the correct number.
9135
5731
5241
2537
8361
3715
1693
1935
7591
5263
5313
9731
3175
3174
9371
7621
1469
a) The sum of the first and last digit is equal to the sum of the two
middle digits.
b) The four digits in the number are all different.
c) The hundreds digit is small than the thousands digit and the ten
digit.
d) All of the digits are odd.
e) The units digit is the smallest natural number.
Reason Logically
Level E
Teacher’s Notes
Strategy:
Level E
Reason Logically
Brain Teasers
Resources:
Worksheets 1 and 2
Previous
Knowledge:
Square numbers
1. Issue Worksheet 1 instructing the children to complete it,
paying close attention to any hints given.
2. After the children have completed the problems discuss the
strategies used, allowing the children time to explain their
reasons for choosing a particular clue with which to begin
the elimination process.
3. In problem 1, children may use the clue divisibility by five to
develop a list of solutions since the multiples of five are
familiar and easy to write. You may point out that the
multiples of nine would be a better choice as the list would
be shorter. When using the third clue, elimination can be
used to narrow the list of numbers to be squared.
4. As the list of possible solutions contains only numbers with 5
in the units, the whole numbers chosen to be squared must
also contain 5 in the units.
5. In problems 2 and 4 a table is given in order that the children
fill in the blanks as they read the clues. Constructing tables
as organisers should be discussed.
Follow-up work, Worksheet 2.
Contd.
Teacher’s Notes – Level E
Brain Teasers – Worksheet 1 (contd.)
Solutions:
1.
(i)
(ii)
b, d, e.
List the multiples of 5 between 200 and 400 which
are odd. Check if divisible by 9 and not a
square number. Note that if the sum of the digits
equals nine then the number is divisible by nine.
(iii)
315 is the number.
2.
Colour
Picture
Country
3.
Red
Tower
France
White
Fountain
Germany
Blue
Flower
Denmark
Green
Castle
England
Make a list of multiples of 5 that are odd.
Check division by 3 and 4 for a remainder of 1.
4. (a)
Name
Debbie
Lisa
Erin
(b)
Hat
Erin
Debbie
Lisa
Gloves
Lisa
Erin
Debbie
No, if so she would have to wear Erin’s hat.
Brain Teasers
Worksheet 1
Name………………………………………………………………
1.
Who am I?
Clues:
a) I am not even.
b) I am greater than 200
c) I am not a square number
d) I am divisible by 5.
e) I am less than 400
f) I am divisible by 9
2.
Linda received four stamps from England, Denmark, France and
Germany for her collection. The stamps are not marked so she
does not know which stamp came from each country.
A fellow stamp collector gave her the following clues:-
The French stamp is red
The English stamp has a picture of a castle.
The white stamp has a picture of a fountain.
The flower is on the blue stamp
The Danish stamp is not white.
The tower is not on the green stamp.
Use the clues and complete the table below.
Colour
Picture
Country
Contd.
Brain Teasers
Worksheet 1 (contd.)
Name………………………………………………………………
3. Farmer Murray was on his way to market
when a case of eggs fell off the back of his lorry.
Looking at the mess on the road a passer-by asked
how many eggs were in the case.
“When I counted in twos there was one left over,
when I counted in threes or fours there was one
left over, but when I counted in fives there were
no eggs left over”, said farmer Murray.
If farmer Murray had less than 100 eggs in the
case what are the possible numbers of eggs
he could have had?
4. Lisa, Erin, and Debbie left school together.
In their rush to leave, they mixed up their hats and gloves.
Each one wore someone else’s hat and the gloves that belonged
to yet another. If Debbie wore Erin’s hat, work out whose
hat and gloves each girl wore.
a)
Name
Debbie
Lisa
Erin
Hat
Erin
b) Can Lisa be wearing Debbie’s gloves?
Gloves
Teacher’s Notes
Level E
Brain Teasers - Worksheet 2
Solutions:
1.
2.
Zam
Zut
Zill
Zap
Zot
Make a list of multiples of 7 that are odd. Check division
by 3 and 4 for a remainder of 1.
7
3.
Family
Dog
4.
Place
Colour
Dog
21
Brown
German
Shepherd
1
Yellow
Terrier
35
49
Mitchell
2
Purple
Setter
Simpson
Poodle
3
Green
Collie
4
Red
Poodle
Brain Teasers Worksheet 2
Name …………………………………………….
1. An archaeologist digging on a site found a set of pots used by an
ancient tribe. There were five different sized pots with the names,
Zill, Zap, Zam, Zot and Zut. After studying some scrolls which were
also found, he realised the names were not on the correct jars.
Zap
Zam
Zut
Zot
Zut
Zill
Zot
Use the clues and place the correct name on each jar shown below.
Clues:
a) A Zut is bigger than a Zot
b) A Zill is never the smallest.
c) A Zut is not the biggest.
d) Only one thing is small than a Zap.
e) A Zam is bigger than a Zill.
f) More than one thing is bigger than a Zill.
Contd.
Brain Teasers Worksheet 2
(contd.)
Name: ……………………………………………..
2. Joe has a collection of compact discs. When he puts them
in piles of two, he has one left over. He also has one left over when
he puts them in piles of 3 or piles of 4. He has none left over when
he puts them in piles of 7. What is the least number of compact
discs he can have?
3.
a)
b)
c)
d)
e)
f)
The Brown family, the Mitchell family and the
Simpson family lives in 3 houses on the same side of
Well Street.
The Browns live next to the Mitchells.
There are no children in the middle house.
The family on the right does not have a German Shepherd dog.
Kathy thinks her poodle is the best dog a person can have.
Lynn Brown and Kathy Simpson are best friends and go to the
same primary school.
The German Shepherd and the poodle are not neighbours.
From the clues determine which family lives in which house and who
has which dog.
Contd.
Brain Teasers Worksheet 2
(contd.)
Name: ……………………………………………..
4.
There was a dog show in which four places were awarded. A
poodle, collie, setter, and terrier all entered. All had collars of
different colours. There were no ties. Find which dog won
each place and the colour of his collar.
a)
b)
The poodle wore the red collar, not the green collar.
The collie received the place next to the dog with the purple
collar.
The dog with the yellow collar received first place.
The dog with the purple collar was second.
The colours of the poodle’s collar and the terrier’s collar mix to
form orange.
c)
d)
e)
Reason Logically
Level F
Santa’s Reindeer
Name …………………………………………….
Santa sends his reindeer to Scotland to deliver the Christmas
parcels.
A certain number of reindeer leave Lapland.
A third of them get lost due to bad weather, 45 give up due to
exhaustion and 315 arrive safely in Stirling.
How many reindeer left Lapland?
Who will pull Santa’s sleigh?
Name: ………………………………………………..
It is Christmas Eve, and Santa has to choose the reindeer that will
pull his sleigh around the world. This year, Santa has a special way
of selecting his reindeer.
There are 100 reindeer altogether, and each is looked after in its
own stable by its own elf. Santa asks each elf to visit the stables.
If a door is open the elf has to close it and vice versa.
To start with all the doors are closed.
 The first elf goes to all the stables and opens all the doors.
 The second elf goes only to every second stable so he closes
doors, 2,4,6,8, etc.
 The third elf visits the third stable and every third stable after
that, closing and opening doors.
 The fourth elf visits every fourth stable, the fifth elf every
fifth stable and so on, until the 100th elf visits only the last
stable.
The reindeer that Santa decides to take with him are those whose
doors are open after all the elves have visited.
Find out
Which reindeer go?
Does Rudolph who lives in stable 100 go?
Other questions
If you are given a particular stable number, how can you decide if
the reindeer in that stable will go?