Skip counting day 1 Skip counting by what

Skip counting- day 1 Skip counting by what numbers will result in landing on 100?

Some observations • Thinking about numbers less than 10 we see that counting by 2, 4, 5 will land us on 100 • We realize that there are 2 parts to skip counting • How much we skip count by • How MANY times we have to do it to land on a number

2 parts to skip counting • Skip count by 3’s: 3 6 12 9 15 21 18 24 33 27 36 30 39 Notice that the first time you “count” you land on 3 and 1 x 3 =3 second time you “count” you land on 6 and 2 x 3=6 … 10 th time you count you land on 30 and 10 x 3 =30

2 parts to skip counting • Skip count by 6’s: 6 12 18 24 30 36 42 48 Notice that the first time you “count” you land on 6 and 1 x 6 =6 second time you “count” you land on 12 and 2 x 6=12 … 5 th time you count you land on 30 and 5 x 6 =30

So what numbers can we skip count by and land on 30? • Of course by 1’s and by 30 • Well, by 2’s and 3’s- if we count by 2’s 15 times we land on 30 and by 3’s 10 times we land on 30 • So that gets us thinking… what if we skip counted by 15 or by 10? 15+15=30 and 10+10+10=30 so we can add 15 and 10 to the list. • By sixes worked- count by 6, five times and if we count by 5, six times… that works Is that all or do we check all numbers less than 30? ?

Observations • The numbers that work appear to come in pairs, and are paired depending on how much to skip count by & how many times to do it • Since 2 is the smallest either of these can be, we see we just need to consider up to half the value of the number, but in fact we can do better than that….

• Suppose both the number you skip counted by and how many times you did it were the same - that helps us find the value of what you need to check up to • So could we get 30 by taking some number times itself? Well, no. . But 5 x 6 comes close. So 6 is the largest we need check.

Skip counting and landing on 36? • Is there a number that times itself is 36? Yes- 6 x 6 =36. We just need to check up to 6. • Skip count by 1’s- yes, so by 36 works • Skip count by 2’s- yes, 18 times, so 18 works! • Skip count by 3’s- yes, 12 times, so 12 works • Skip count by 4’s, yes, 9 times, so 9 works • Skip count by 5’s, no • Skip count by 6’s, yes- 6 times Done

The formal math terms When we skip count by a number A and land on the number M then we say that A is a factor of M (think part) M is a multiple of A (think to grow) So 36 is a multiple of 3 and 3 is a factor of 36 but 36 is NOT a factor of 3 nor is 3 a multiple of 36

• Factors come in pairs, and sometimes may be the same value 3 x 12= 36 and so 3 & 12 are factors of 36 6 x 6 =36 so 6 is a factor of 36 • In skip counting, factors are how much you skip count by and how many times you do it

So. . by what numbers can you skip count by and land on 100? • By what numbers do you have to skip count by to make sure you get them all? • The numbers that work are the factors of 100 and will come in pairs • 100 is a multiple of the numbers that work