Can you find some two-digit numbers that belong in two of the sets?
10, 15, 45, 50 all fit for multiples of 5 and Triangular numbers
Can you find some two-digit numbers that belong in three sets?
10 and 50 fit for multiples of 5; Triangular numbers and Even, but not multiples of four
What is the smallest number that belongs in all four sets?
The smallest number that belongs in all sets is 210.
42x5=210
210 is the 21st triangular number
210 is even but cannot be multiplied by 4 (210÷4= 52.5)
210 is a multiple of 3 (210÷3= 70) but not a multiple of nine (210÷9= 23.333)
How could you describe the pattern of the numbers that satisfy both Alison's and Sam's statements?
After 2x5= 10, the numbers that fit the pattern are:
30, 50, 70, 90 etc.
6x5=30
10x5=50
14x5=70
18x5=90
As you can see, the number you need to multiply by 5 goes up by 4.
How about the numbers that satisfy both Alison's and Matt's statements?
15, 30, 60, 75 etc.
These are the numbers that fit Alison's and Matt's statements. You are adding 15 to the previous number but on the 3rd time you are going to add 15 you add 30.
Can you describe patterns for other pairs of statements?
10, 15, 45, 50 etc.
Fit Alison's and Becky's statements. Every 4th and 5th triangular numbers fit both of their descriptions.