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)

Always aim high!LESSON OBJECTIVES

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PLT SkillsWhich ones are you

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AUTHORWhere are we in

our journey?

Real life cross/curricular

links?www.mistrymaths.co.uk

BRAIN IN GEAR

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Work out what the missing words in red are.

TASK

EXTENSION

Develop your own Mathematical letter puzzles as above.

36 I in a Y

0 R in a M

4 D to make a PC

36 Inches in a Yard

0 Runs in a Maiden

4 Digits to make a Pin Code

STARTER

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EXTENSION

TASK

Expand and simplify:

1) 2) 3) 4)

Factorise:8et + 12t

5)

64 g divided by g

Find the LCM of 4 and 6

6)

4 9Expand: -6(3x - 5)

Find the HCF of 21 and 35

7) Write 42 as a product of prime factors

= 8 and -8 = 4t(2e + 3) = -18x + 30 = g-5

= 12 = 7= 2 x 3 x 7

x x

x

x

x2= + 63 + 7x

x2= + 16x+ 63(x + 7)(x + 9) + 9x

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PLT SkillsWhich ones are you

using?Nth term from picture patternsEXAMPLES1) 2)

(a) Work out the nth term for the pattern of matches

(b) How many matches will the 100th pattern have?

4 7 10 13

The diagram shows a pattern of matches building up.

+3 +3 +3

3n+ 1

Substitute 100 into the nth term above

3 x 100 + 1 = 301

The diagram shows a pattern of squares building up.

(a) How many squares will there be in the nth pattern?

(b) What is the largest pattern number you can make with 187 squares?

3 5 7

+2 +2

2n+ 1

Make the nth term equal to 187 and solve 2n + 1 = 187

- 1 - 1

2n = 186÷ 2 ÷ 2

n = 93

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PLT SkillsWhich ones are you

using?TASK (GRADE C)

Nth term from picture patterns

A pattern of squares is built up from matchsticks as shown.

(a) Draw the fourth diagram.(b) How many squares are there in the nth diagram?(c) How many squares are there in the 25th diagram?(d) With 200 squares, which is the biggest diagram that could be made?

1) 2) A pattern of triangles is built up from matchsticks.

(a) Draw the fifth set of triangles in this pattern.(b) How many matchsticks are needed for the nth set of triangles?(c) How many matchsticks are needed to make the 60th set of triangles?(d) If there are only 100 matchsticks, which is the largest set of triangles that could be made?

3) 4)A conference centre had tables each of which could sit six people. When put together, the tables could seat people as shown.

(a) How many people could be seated at four tables?(b) How many people could be seated at n tables put together in this way?(c) At a conference, 50 people wished to use the tables in this way. How many tables would they need?

Regular pentagons of side length 1 cm are joined together to make a pattern as shown. Copy this pattern and write down the perimeter of each shape.

(a) What is the perimeter of patterns like this made from (i) 6 pentagons (ii) n pentagons (iii) 50 pentagons?

(b) What is the largest number of pentagons that can be put together like this to have a perimeter less than 1000 cm?

4n - 3Appropriate diagram

97

50th

Appropriate diagram

2n + 1

121

49th

18

4n + 2

12

20cm (3n+2)cm 152cm

332

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PLT SkillsWhich ones are you

using?EXTENSION (GRADE C)

Nth term from picture patterns

n

Picking a large value of n gives an answer of zero on a calculator, so eventually the whole area will be covered.

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MINI-PLENARY

Nth term from picture patterns

A pattern is formed from squares.

(a) Draw Pattern 4. (1 mark)

(b) Find the number of squares in Pattern 6. (1 mark)

1 3 5

7

2n - 1

2 x 6 - 1=11

DISCOVERY

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LINK BACK TO OBJECTIVES

- Accurately find the nth term of a sequence from picture patterns.

What grade are we

working at?

PLENARY ACTIVITYGCSE GRADE C EXAM QUESTION

Consecutive patterns are put together.

(a) The numbers of counters in the combinedpatterns form the sequence: 4, 9, 16, …How many counters will be in the next combined pattern in the sequence?

(b) What type of numbers are 4, 9, 16, … ?

(c) How many counters will be in the combined pattern formed by patterns 9 and 10?

25

Square numbers

10 x 10 100

Draw your brain

What have you learnt?

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.

What grade are we

working at?

Where are we in our

journey?

.

How well do you understand the task?

I don’t understand

I nearly understand

I fully understand

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Enterprise Skills Which ones are you using?

SELF ASSESSMENT

Plenary Activity

www.mistrymaths.co.uk

SELF ASSESSMENT

Plenary Activity

On your post it notes…

Think about how you can improve your

work.

WWW (What Went Well)

EBI (Even Better If)

Creative Entrepreneur

Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise Skills Which ones are you using?

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