Transcript Slide 1

Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
PLT Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Finding connections between different words.
(Which PLT skills?)
- Accurately find the nth term of a sequence from
picture patterns. (Grade C)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
BRAIN IN GEAR
Self
Manager
Team
Worker
Which ones are you using?
TASK
Work out what the missing words in red are.
36 I in a Y
36 Inches in a Yard
0 R in a M
0 Runs in a Maiden
4 D to make a PC
4 Digits to make a Pin Code
EXTENSION
Develop your own Mathematical letter puzzles as above.
Creative
Thinker
Effective
Participator
PLT Skills
Independent
Enquirer
Reflective
Learner
STARTER
Self
Manager
Team
Worker
Which ones are you using?
TASK
1)
2) Factorise:
64
8et + 12t
= 8 and -8
= 4t(2e + 3)
5) Find the LCM of
4 and 6
3) Expand:
-6(3x - 5)
= -18x + 30
6) Find the HCF of
21 and 35
=7
= 12
EXTENSION
Expand and simplify:
x
x
(x + 7)(x + 9) = x2 + 63 + 7x + 9x
= x2 + 16x+ 63
x
x
4
4) g divided by g
= g-5
7) Write 42 as a
product of
prime factors
= 2x3x7
9
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills Nth term from picture patterns Which ones are you using?
EXAMPLES
1) The diagram shows a pattern of
matches building up.
7
4
+3
squares building up.
13
10
+3
2) The diagram shows a pattern of
+3
(a) Work out the nth term for the pattern of matches
3n + 1
(b) How many matches will the 100th pattern have?
Substitute 100 into the nth term above
3 x 100 + 1 = 301
3
5
7
+2
+2
(a) How many squares will there be in the nth pattern?
2n + 1
(b) What is the largest pattern number you can
make with 187 squares?
Make the nth term equal to 187 and solve
2n + 1 = 187
-1
2n
÷2
n
-1
= 186
÷2
= 93
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills Nth term from picture patterns Which ones are you using?
TASK (GRADE C)
1) A pattern of squares is built up from
matchsticks as shown.
2)
A pattern of triangles is built up from matchsticks.
Appropriate diagram
(a) Draw the fifth set of triangles in this pattern.
(b) How many matchsticks are needed for the nth
(a) Draw the fourth diagram. Appropriate diagram
2n + 1
(b) How many squares are there in the nth diagram?4n - 3 set of triangles?
(c) How many squares are there in the 25th diagram? 97 (c) How many matchsticks are needed to make
the 60th set of triangles? 121
(d) With 200 squares, which is the biggest diagram that
(d) If there are only 100 matchsticks, which is the
could be made? 50th
largest set of triangles that could be made? 49th
3) A conference centre had tables each of which could sit 4)Regular pentagons of side length 1 cm are joined
six people. When put together, the tables could seat
people as shown.
together to make a pattern as shown. Copy this
pattern and write down the perimeter of each shape.
(a) How many people could be seated at four tables? 18
(b) How many people could be seated at n tables put
together in this way? 4n + 2
(c) At a conference, 50 people wished to use the tables
in this way. How many tables would they need? 12
(a) What is the perimeter of patterns like this made from
(i) 6 pentagons (ii) n pentagons (iii) 50 pentagons?
20cm
(3n+2)cm
152cm
(b) What is the largest number of pentagons that can be
put together like this to have a perimeter less than 1000
cm? 332
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills Nth term from picture patterns Which ones are you using?
EXTENSION (GRADE C)
n
Picking a large value of
n gives an answer of
zero on a calculator, so
eventually the whole
area will be covered.
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills Nth term from picture patterns Which ones are you using?
MINI-PLENARY
A pattern is formed from squares.
1
5
3
(a) Draw Pattern 4. (1 mark)
7
(b) Find the number of squares in Pattern 6. (1 mark)
2n - 1
2 x 6 - 1 = 11
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
DISCOVERY
Self
Manager
Team
Worker
Which ones are you using?
LINK BACK TO OBJECTIVES
- Accurately find the nth term of a
sequence from picture patterns.
What grade
are we
working at?
PLENARY ACTIVITY
GCSE GRADE C EXAM QUESTION
Consecutive patterns are put together.
(a) The numbers of counters in the combined
patterns form the sequence: 4, 9, 16, …
How many counters will be in the next combined pattern in the sequence?
25
(b) What type of numbers are 4, 9, 16, … ?
Square numbers
(c) How many counters will be in the combined pattern formed by patterns 9 and 10?
10 x 10
100
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about finding
the nth term of a sequence from picture patterns. It can be a skill or a
reflection, or something else that might be prominent in your brain.
Where are we
in our
journey?
What grade
are we
working at?
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I don’t
understand
I nearly
understand
www.mistrymaths.co.uk
I fully
understand
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
WWW (What Went Well)
EBI (Even Better If)
On your post it
notes…
Think about how you
can improve your
work.
www.mistrymaths.co.uk