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Maths flow diagrams

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```Tuesday 31:03:2020
**Please make sure to use your Term 2 Maths workbook for all the work that follows.**
Number Patterns
1. Using flow diagrams
When working with number patterns you have an input value, rule and an output value. When we have
the input value, we work from left to right to find our output number. We do this by using the rule in the
middle.
Rule
When we have our output number, we work from right to left and do the inverse (opposite) operation (of
the rule) to find our input number. Eg: 16 &divide; 2 x 5
1
When we have both our input and output numbers, we work backwards to find out what our rule is. We
need to check that our rule works for all our numbers before we can decide we have the right one.
X4
?
Complete the following activity in your Maths Term 2 workbook. The date and heading is below for you to
use. All you need to do is write down the missing answers or the missing rule. Do not redraw the flow
diagram.
31:03:2020
Textbook pg 256 and 257 ex. 137 no. 1a, b, 2a, b, 3.
_______________________________________________________________________________________
Once that has been completed, do not rule off but put a new heading. For this activity you will need to
write the full rule only. Do not re draw the flow diagram.
Textbook pg 258 and 259 ex 138 no 1 and 2.
_______________________________________________________________________________________
Rule off once completed.
_______________________________________________________________________________________
2
Wednesday 1:04:2020
2. Using tables
We can also use tables to record patterns. It works the same way as a flow diagram, just presented
differently. You still start with the input value, apply the rule which will give you the output value. If you
are given the output value, you do the inverse (opposite) operation to find the input value.
For the table below:
The input is 2
the rule is x6
therefore the output will be 12.
Rule : &times; 6
Input
2
3
4
5
6
7
8
9
10
Output
12
18
24
30
36
42
48
54
60
ACTIVITY
Redraw the following tables into your workbook (term 2) and fill in the missing input/output or rules. You
may use colour for the missing values/rules.
1:04:2020
Using tables activity.
_______________________________________________________________________________________
Rule : &times; 4 + 1
Input
2
3
6
7
9
11
8
10
5
7
12
21
26
34
38
40
18
29
Output
Rule : + 12 - 3
Input
Output
3
Rule : x 6 - 3
Input
6
Output
8
9
12
15
10
21
7
63
Rule : + 25 - 15
Input
8
10
14
4
6
8
19
21
26
32
45
63
20
76
Output
Rule : - 3 x 2
Input
Output
16
32
46
18
Rule :
Input
1
2
3
4
9
7
6
10
12
Output
5
9
13
17
37
29
25
41
49
Rule off once completed.
_______________________________________________________________________________________
4
Thursday 2:04:2020
3. Number sequences – Part 1
Number sequences are another was to represent flow diagrams and tables. This time we give the
numbers in a sequence without a rule. You will need to determine what the rule is and complete the
pattern.
Example:
3; 6; 9; 12; ___; ___; ___; ___
We will need to find what the pattern is in order for the sequence to be completed. In this case the rule is
+3. Now we can fill in the missing numbers 15; 18; 21; 24.
That was an easy one. What happens if you can’t see the pattern straight away? In that case, rewrite the
sequence given on your whiteboard with ‘bunny hops’ between each number. It now becomes a trial and
error game to work it out.
Example:
9 ; 15 ; 21 ;
+6
+6
+6
27 ; ___ ; ___ ; ___
+6
ACTIVITY
2:04:2020
Number sequences Textbook pg 260 ex 139 no. 1 &amp; 2
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5
Friday 3:04:2020
4. Number sequences – Part 2
Yesterday’s number sequences were simple, they only involved one operation. However, sequences could
be any operational sign (+ ; - ; x ; &divide;) or a combination of them. This means that the rule could be as simple
as + or x or it could be a bit more difficult and be a – and x together (- 3 x 4)
How do you then work out the rule? By rewriting the sequence on your white board, putting in bunny
hops and seeing which operation or combination of operations work. This may involve a few tries to get
the combination. Remember that the rule has to work for all the numbers given, not just for the first few.
Example:
2 ; 5 ;
11 ; 23 ; ___ ; ___
+3
+3
x3-1 x3–1
x4–3 x4–3
x2+1 x2+1 x2+1
So we know that +3 doesn’t work. Try again.
This doesn’t work either. Try again.
Nope, this doesn’t work either. Try again.
This rule works so we can now apply it and fill in the
missing values of the sequence.
Sequences could also go backwards, starting at a high number and working down to a lower number.
These could also be one operation or a combination of operations.
ACTIVITY
3:04:2020
Number sequences
______________________________________________________________________________________
Copy the following sequences in your workbook and complete. Use your whiteboard to help you figure
out the rules.
a) 501 ; 602 ; 703 ; ____ ; ____ ; ____
e) 2 ; 4 ; 8 ; 16 ; ____ ; ____ ; ____
b) 980 ; 975 ; 970 ; ____ ; ____ ; ____
f) 1 ; 3 ; 6 ; 10 ; ____ ; ____ ; ____
c) 1 ; 13 ; 23 ; 31 ; ____ ; ____ ; ____
g) 1 ; 7 ; 19 ; 43 ; ____ ; ____ ; ____
d) 100 ; 81 ; 64 ; 49 ; ____ ; ____ ; ____
h) 4 ; 7 ; 13 ; 25 ; ____ ; ____ ; ____
Rule off once complete.
______________________________________________________________________________________
MEMO’S FOR THIS WEEKS WORK WILL BE SENT IN WEEK 2
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