Act out the Situation
Level A
Teacher’s Notes
Strategy:
Level A
Act out the Situation
Tallest and Smallest
1st Problem
Who is the tallest in the group?
Who is the smallest in the group?
2nd Problem
Who is the tallest in the class?
Who is the smallest in the class?
This is done in groups. Use the knowledge from the group
answers to do Problem 2.
Teacher’s Notes
Strategy:
Level A
Act out the Situation
Let’s Go Shopping
Resources:
Worksheet for each child
Previous
Knowledge:
Addition and subtraction within 10
Solution:
1.
teddy 8p + ball 2p = 10p
rabbit 7p + cart 3p = 10p
2.
teddy 8p + ball 2p = 10p
rabbit 7p + ball 2p =
and 1p left
9p
rabbit 7p + cart 3p = 10p
cart 3p + duck 5p =
and 2p left 8p
cart 3p + ball 2p =
and 5p left 5p
duck 5p + ball 2p =
and 3p left 7p
duck 5p + duck 5p = 10p
3.
duck and ball and a cart
5p + 2p + 3p 10p
Extension:
The child could list the combinations of things he could
buy for 10p and still have some money left.
Solution as shown in 2
Let’s Go Shopping
Name: …………………………………………….
teddy 8p
cart 3p
ball 2p
rabbit 7p
duck 5p
Put 10 (1 pences) in your purse.
1.
What 2 things can you buy for 10p and have no change left?
I can buy a ………………………………..and a ……………………………………………
2.
Can you buy another two things for 10p? ……………………………
What are they?
I can buy a …………………………………….. and a ……………………………………..
3.
Can you buy 3 things for 10p? ……………………………………………….
What are they?
I can buy a ………………………………………and a …………………………………….
and a …………………………………………………..
Teacher’s Notes
Strategy:
Level A
Act out the Situation
Around the Table
Resources:
2 red, 2 blue and 2 green counters per child
A card to act as a table for each child.
1 problem sheet per group.
Previous
Knowledge:
Solution:
An understanding of “opposite” and
“next to”
Around the Table
Name: ………………………………………….
There are six children to sit at the table.
Two are wearing red jumpers; two blue jumpers and the other
two are wearing green jumpers.
Children wearing the same colour jumpers cannot sit next to
each other or opposite each other.
Can you find where they will sit?
Use your counters and card to help you.
Show your answer by drawing it and colouring the circles.
Act out the Situation
Level B
Teacher’s Notes
Strategy:
Level B
Act out the Situation
Hoops
Resources:
The children themselves, 3 hoops (3 colours)
Previous
Knowledge:
Nil
1.
Ask all 3 members of the group to stand in the hoops.
Jasmine
2.
3.
4.
Duncan
Laura
How many ways can the pupils arrange themselves in
the 3 hoops?
How can we remember who’s been where?
When Jasmine is in the red hoop, how many ways can
Duncan and Laura be arranged in the other hoops?
Encourage systematic recording:J
J
D
D
L
L
Solution:
6 arrangements
JDL
JLD
DJL
DLJ
LJD
LDJ
D
L
J
L
J
D
L
D
L
J
D
J
Teacher’s Notes
Strategy:
Level B
Act out the Situation
Line Up
Resources:
The children
Previous
Knowledge:
Nil
1.
Choose a group of four girls and three boys.
2.
Ask the group to line up with no two boys together and
no two girls together.
3.
Ask if it is possible to stand in a ring with two boys together
and no two girls together.
Extension:
1.
Discuss with the group the numbers of girls and boys
needed to make a line with no two boys together and no
two girls together.
2.
Discuss the numbers of girls and boys needed to make a
ring with no two boys together and no two girls together.
Solution:
Line:
Numbers of boys and girls must be consecutive numbers.
Circle: Numbers of boys and girls must be equal.
Teacher’s Notes
Strategy:
Level B
Act out the Situation
Counters
Resources:
Worksheet, counters
Previous
Knowledge:
Addition to 10
Solution:
6 counters – 5 spaces
6 counters/6 spaces
7 counters/6 spaces
7 counters/7 spaces
8 counters/7 spaces
8 counters/8 spaces
Counters
Name: ……………………………………………………
a)
Put 6 counter in a line.
How many spaces are there between them?
6
Arrange the counters so that there are
b)
spaces.
Put 7 counters in a line.
How many spaces are there between them?
Arrange 7 counters so that there are
c)
7
spaces.
Now put 8 counters in a line.
How many spaces are there between them?
Arrange 8 counters so that there are
8
spaces.
Act out the Situation
Level C
Teacher’s Notes
Strategy:
Level C
Act out the Situation
Who’s “It”?
Resources: Worksheet for each child
Previous
Knowledge: Counting in a circle
Children may begin to solve the problem by acting out the
situation simply guessing who was first. Working backwards
will probably occur to them later, or using a diagram might help.
Solution:
Start at Mark and keep counting on thirteen, crossing out the
names you reach. The result will be that Lisa will be left in at the end.
Therefore leave Jane last who is opposite Lisa start at David.
Who’s “It”?
Name: ………………………………………
Eight children gather to play ‘Hide-and Seek’. To decide who is to do
the seeking and finding, they stand in a circle singing a number
rhyme with thirteen words. Counting clockwise, this meant that
every thirteenth children was ‘out’. The last child left was Jane.
Where did the count start?
Ian
David and Kirsty
Jane and Kerry
Lisa
Mark
Tariq
There are a few ways of working out this problem. Try with a group
of eight children from your class.
Teacher’s Notes
Strategy:
Level C
Act out the Situation
Cover the Square
Resources:
Worksheet
Previous
Knowledge:
Must distinguish between columns and also
understand diagonals.
Solution:
B
R
R
R
B
B
R
B
R
Cover the Square
Name: …………………………………………….
Use 5 red counters and 4 blue ones.
Place them on the square so that each column and row has 2
red and 2 blue
You must not have 3 counters of the same colour in any row,
column or diagonal.
Act out the Situation
Level D
Teacher’s Notes
Strategy:
Level D
Act out the Situation
Weighing
Resources:
Previous
Knowledge:
Boxes for each group of children containing
five items of differing weights. A balance
for comparing weights.
Nil
The items in each box have to be ordered by weight.
The children do this by comparing relative weights.
A balance may be used if appropriate. Do not use weights
or a calibrated scale.
After the task has been completed a teacher-led lesson
compares the results and methods used.
Teacher’s Notes
Strategy:
Level D
Act out the Situation
Hop and Slide
Resources:
Previous
Knowledge:
Pegs and pegboards or squared paper
with counters (two colours).
Nil
Before the lesson you need to place five chairs in a row
at the front of, and facing, the class. Select two boys and
two girls to occupy four of the five seats.
“The four people sitting in front of you are frogs!
The problem they have is to move so that the boy frogs
change places with the girl frogs. These frogs can only
Move in the following ways: They can slide along an empty chair;
 They can jump over one frog into an empty chair”
Contd.
Teacher’s Notes
Level D
Hop and Slide (contd.)
When there have been several attempts at the problem you
may decide to stop the action and seek ideas from the rest
of the class. Continue with action and discussion until the
problem has been solved.
“Did anyone notice how many moves it took”?
The challenge is to exchange places in as few moves as possible.
Let the frogs have another go at doing it – the rest of you
count the number of moves. Keep a note of the slides and jumps.
An alternative approach is to ask the children to direct the ‘frogs’.
Recording the moves on the board using ‘s’ and ‘j’ will help
develop the idea of using shorthand notation; in order
to distinguish between the girls and boys you could
use different colours.
At any one time you can change the focus of action
from the class to groups or pairs. Give the children suitable
materials to try out the activity themselves.
Remind them to keep a record of their slides and jumps.
Try: 1 girl and 1 boy (and 3 chairs)
3 girls and 3 boys (and 7 chairs)
4 girls and 4 boys (and 9 chairs)
Solution:
Contd.
Teacher’s Notes
Level D
Hop and Slide (contd.)
Solution:
The following table shows the underlying patterns
(for teacher’s reference only).
Number of frogs of each
colour
1
2
3
4
Number of ‘jumps’ over
the frogs
1
2
3
4
Number of ‘slides’ to
adjacent squares
2
4
6
8
Total number of moves
needed
3
8
15
24
Teacher’s Notes
Strategy:
Level D
Act out the Situation
Hop to It!
Resources:
Usual classroom equipment.
Counters or similar to represent stepping
stones.
Previous
Knowledge:
Little more than addition of whole numbers
and systematic organisation.
Encourage the children to act out the situation at their desks
using counters or similar to represent stepping stones.
Alternatively use sheets or card laid out on the classroom floor.
At the end of the lesson discuss ways of listing the jumps and
how to list in a systematic way.
Solutions:
1.
(s,l)
2.
There are five ways with three stepping stones.
(s,s,s,s,s) (l,s,s) (s,l,s) (s,s,l) and (l,l).
3.
No. of stones
0
1
2
3
4
5
6
7
8
9
No. of ways
1
2
3
5
8 13 21 34 55 89
4.
Adding consecutive numbers gives the next number.
5.
89.
6.
The sequence is called the Fibonacci sequence.
Hop to It!
Name: ………………………………………….
Freddy frog wishes to cross a river. He does not like getting his
feet wet so he is going to use stepping stones.
He can jump two gaps with a long
hop.
With a short hop he can only jump
one gap.
To cross where there are two
stepping stones, he can either do
three short hops, which can be
written down (s, s, s)……………….
…….or he can make a long hop
followed by a short hop, which can
be written down (l,s).
1.
There is another way for Freddy to cross the river.
Write it down.
2. On the way home he sees another crossing place where there
are three stepping stones.
How many different ways can he cross the river at this point?
List all the ways.
Hop to It! (contd.)
Name:……………………………………………..
3. Now try to find how many different ways there are of crossing
the river for different numbers of stepping stones. Record your
results in a table.
Number of stepping stones
0
Number of different ways of crossing
1
1
2
3
4. Find a rule that links each of the numbers in the bottom row of
the table.
5. How many different ways will there be to cross the river at a
point where there are nine stepping stones?
6. Find out the name of the sequence of numbers in the bottom row
of the table.
4
Act out the Situation
Level E
Teacher’s Notes
Strategy:
Level E
Act out the Situation
Change the Triangle
Resources:
Pencil and paper. Counters.
Previous
Knowledge:
Nil
Children could work in pairs. Teacher explanation, possibly getting
class to demonstrate the answer to question 1.
Children’s response to Q3 will vary with ability, some can
demonstrate with counters where more able children would supply
a diagrammatic answer. The objectives of this series of questions
are:
a) Trial and improvement practice.
b) Communicating via diagrams.
Solutions: Diagrammatic solutions on separate sheet.
Number of counters
1
3
6
10 15 21 28 36 45 55
Number of moves
0
1
2
3
5
7
The rule is “Divide by 3, ignoring the remainder.”
9
12 15 18
Teacher’s Notes
Level E
Change the Triangle (contd.)
Diagrammatic Solutions:
Contd.
Teacher’s Notes
Level E
Change the Triangle
Diagrammatic Solutions.
(contd.)
28 counters
36 counters
Contd.
Teacher’s Notes
Level E
Change the Triangle
Diagrammatic Solutions:
45 counters
(contd.)
Change the Triangle
Name:
…………………………………………………………………………..
A triangle made with 10 counters can be changed from
this
to this
by moving only 3 counters.
1. Show how this can be done. (If having difficulty try triangles
with 3 counters then 6 counters first).
2. Make a triangle with 15 counters. Show how to turn (invert)
this triangle in as few moves as possible.
3. Show how to invert other triangles of 21, 28 etc. counters in
the smallest number of moves possible and make a table of
your results.
Number of counters
Number of moves
3
6
10
3
15
21
4. Have you noticed anything when making your moves or making
your table?
Explain what you have noticed.
Teacher’s Notes
Strategy:
Level E
Act out the Situation
Take to Win
Resources:
A pile of coins, counters etc.
Previous
Knowledge:
Nil
Emphasise that it is a strategy to win that the child is trying
to get. Once they have that, he or she will win all the time.
Solution:
The player who wishes to win must
leave 5 for his opponent to take from.
No matter what he takes you win.
He takes
1
you take
3
He must lift last one
He takes
2
you take
2
He must lift last one
He takes
3
you take
1
He must lift last one
Extension:
You can take up to 4 at a time.
Now what is your strategy to win?
Take to Win
Name: ………………………………………
This is a game for two players.
Start with a pile of counters, or coins, or matchsticks.
Rules:
1. Each player plays in turn and must lift 1, 2, or 3 coins from the
pile.
2. The player forced to remove the last coin loses the game.
Play the game with your friends and see if you can determine a
winning strategy.