Download Generate Expressions from Patterns * Learning Outcomes

1
Generate Expressions from Patterns –
Learning Outcomes
 Use tables to represent a repeating-pattern situation.
 Generalise and explain patterns in words and numbers.
 Write arithmetic expressions for particular terms in a
sequence.
2
Use Tables to Represent Patterns
 A pattern is an ordered list of numbers, objects, or
diagrams that is predictable.
 The order of the pattern is important, making it different
to a set.
 e.g. {M, A, R, Y} is not the same pattern as {A, R, M, Y}.
 is a repeating pattern.
 The repeat happens every four tiles.
 We can predict the next shapes by continuing the
pattern.
3
Use Tables to Represent Patterns
 What shape is the:
i.
14th object?
ii.
19th object?
iii.
24th object?
iv. 28th object?
 Is there any way to predict the pattern besides going
through each object?
 If we number them, can we tell by the last digit?
 Can we tell by if the number is even or odd?
 If you double the number, will it give the same shape?
4
Use Tables to Represent Patterns
 Represent the pattern in a table instead of a line.
 Make the table as long as the pattern (or two/three
times as long).
Number
Object
Number
Object
Number
1
5
9
2
6
10
3
7
11
4
8
12
Object
5
Explain Patterns in Words and Numbers
 With a table, we can see how the pattern continues.
Number
Object
Number
Object
Number
1
5
9
2
6
10
3
7
11
4
8
12
Object
 Each row has the same shape – but how do we define
the rows?
 The purple squares are on 4, 8, 12, …- multiples of 4!
 The green circles always come before purple squares, so
they must be one less than a multiple of 4.
6
Explain Patterns in Words and Numbers
Number
Object
Number
Object
Number
1
5
9
2
6
10
3
7
11
4
8
12
 Purple squares – multiple of 4,
 Green circles – one less than multiple of 4,
 Red triangles – two less than multiple of 4.
 Blue diamonds – three less than multiple of 4.
Object
7
Explain Patterns in Words and Numbers
 For large numbers, how do you know which shape fits?
 Divide the number by 4 and check the remainder.
 Purple squares – divide evenly.
 Green circles – x.75 (i.e. remainder 3)
 Red triangle – x.50 (i.e. remainder 2)
 Blue diamond – x.25 (i.e. remainder 1)
8
Write Arithmetic Expressions
 Consider the sequence:
 3, 9, 15, 21, 27, …
 Imagine each number in a box in sequence:
3
Box
#1
9
Box
#2
15
Box
#3
1. Draw out the next three boxes.
2. What number is in box #10?
3. What box contains the number 75?
4. What number is in box n?
21
Box
#4
27
Box
#5
9
Write Arithmetic Expressions
3
9
15
21
27
Box
Box
Box
Box
Box
#1
#2
#3
#4
#5
 The number in box #1 is called the start term, a.
 The difference between boxes is called the common
difference, d.
 The number in box #n is called the nth term, Tn. (e.g. box
#5 contains the 5th term, T5, box #25 contains the 25th
term, T25).
10
Write Arithmetic Expressions
 Write the first five terms of the following sequences:
1. start term = 2, common difference = 5
2. start term = 5, common difference = 2
3. start term = 18, common difference = -2
 Describe in words how to find the nth term of each of
these sequences.
 Write an expression in terms of n to describe the nth term
of these sequences.
11
Write Arithmetic Expressions
 Write the first four terms of each of the following
sequences:
1. 𝑇𝑛 = 5𝑛 + 1
2. 𝑇𝑛 = 2𝑛 + 4
3. 𝑇𝑛 = 9 4 − 2𝑛
 Write down the start term and the common difference
for each of the sequences above.