Fluency
Find the next three terms for these number patterns that have a common difference.
5 , 12 , 19, .... , .... , ....
26 , 33 , 40
Increases by 7.
Complete the next three terms for the following challenging number patterns.
3, 2, 6, 5, 15, 14,___, ___, ___
First we subtract 1, then multiply by 3, subtract 1, multiply by 3 again and so on:
42, 41, 123
State whether the following number patterns have a common difference ( + or − ), a common ratio ( × or ÷ ) or neither
a) 212, 223, 234, 245, 256, …
b) 64, 32, 16, 8, 4, …
a) common + 1
b) common ratio divide by 2
Read the following clues to work out the mystery number
I have two digits, I am divisible by 3 and 5, I am odd.
15
Find the next three terms for the following number patterns that have a common difference.
a) 3 , 8 , 13 , 18 , .... , .... , ....
b) 75, 69, 63, 57 , .... , .... , ....
a) 23 , 28 , 33 (increasing by 5)
b) 51, 45, 39 ( decreasing by 6)
Complete the next three terms for the following challenging number patterns.
a) 101, 103, 106, 110, ___, ___, ___
b) 162, 54, 108, 36, 72 , ___, ___, ___
a) 115 , 121 , 128 ( first we add 2, then 3, then 4 and so on)
b) 24 , 48 , 16 ( first we divide by 3, then multiply 2 and repeat).
Find the sum of the following number sequences:
a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
I have two digits, the sum of my digits is 12, I am a multiple of 5.
The product of my digits are 35.
75
Find the next three terms for the following number patterns that have a common ratio.
a) 1215 , 405 , 135, .... , .... , ....
b) 256, 128, 64, 32, .... , .... , ....
a) 45 , 15, 5 (divided by 3)
b) 16 , 8 , 4 ( divided by 2)
When making human pyramids, there is one less person on each row above, and it is complete when there is a row of only one person on the top.
Write down a number pattern for a human pyramid with 10 students on the bottom row. How many people are needed to make this pyramid?
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55 people are needed
Find the sum for each of the following number sequences.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
55
Read the following clues to work out the mystery number.
I have three digits, I am divisible by 5, I am odd.
The product of my digits is 15 . The sum of my digits is less than 10 .
I am less than 12 × 12
135
Find the missing numbers in each of the following number patterns.
a) 62 , 56 , ___ , 44 , 38, ___ , ___
b) 14 , 42, ___ , ___ , 126, ___ , 182
a) 50 , 32 , 26 ( decreasing by 6)
b) 70 , 98 , 154 ( increasing by 28)
The table below represents a seating plan with specific seat numbers for a section of a grandstand at a soccer ground. It continues upwards for another 20 rows.
Row 4 25 26 27 28 29 30 31 32
Row 3 17 18 19 20 21 22 23 24
Row 2 9 10 11 12 13 14 15 16
Row 1 1 2 3 4 5 6 7 8
a) What is the number of the seat directly above seat number 31 ?
b) What is the number of the seat on the left-hand edge of row 8 ?
a) As each row is added, we add 8 to the seat number, so above seat 31 is seat 39.
b) For each row on the left hand side, the seat
number is 8 × n − 7, where n is the row number.
For n = 8, the seat number is 8 × 8 − 7 = 57.
Jemima writes down the following number sequence: 7, 7, 7, 7, 7, 7, 7, …
Her friend Peta declares that this is not really a number pattern. Jemima defends her number pattern, Stating that it is most definitely a number pattern as it has a common difference and also has a common ratio. What are the common difference and the common ratio for the number sequence above? Is Jemima correct or not?
Jemima is correct. The common difference is zero and the common ratio is 1.
I have three digits. The sum of my digits is 12 .
My digits are all even. My digits are all different.
I am divisible by 4 . The sum of my units and tens digits equals my hundreds digit.
642
Generate the next three terms for the following number sequences and give an appropriate name to the sequence
a) 1, 8, 27, 64, 125,___, ___, ___
b) 1, 1, 2, 3, 5, 8, 13,___, ___, ___
a) 216 , 343 , 512 ( cubic numbers )
b) 21 , 34 , 55 ( add the previous two numbers together)
Find the next five numbers in the following number pattern.
1, 4, 9, 1, 6, 2, 5, 3, 6, 4, 9, 6, 4, 8, 1, ___, ___, ___, ___, ___
This sequence is actually the list of the first nine
square numbers with all the digits separated by
commas. The next two square numbers are 100 and 121,
so the next five terms are 1, 0, 0, 1, 2.
There are a certain number of people in a room and they must all shake one
another’s hand. How many handshakes will there be if there are:
a) 3 people in the room?
b) 5 people in the room?
a) Each person shakes hands with the other two
people, so we have 3 × 2 = 6. This counts
every handshake twice, so we divide by 2 to
get 3 handshakes.
b) Each person shakes hands with the other four
people, so we have 5 × 4 = 20. This counts
every handshake twice, so we divide by 2 to
get 10 handshakes
I have three digits. I am odd and divisible by 5 and 9 .
The product of my digits is 180. The sum of my digits is less than 20 .
I am greater than 302
945