The Outwood Grange Family of Schools

Let Me Count The Ways (teacher notes):

1. Obviously an important skill in problem solving is to be able to count the number of different outcomes than can occur from any given situation.2.It is natural for students to try to take shortcuts when counting – what we need to try to ensure is a that they use a logical method that ensures viable options aren’t missed when students take these shortcuts.3. In Problem 0 students may say there are 3 different outcomes (2 heads, 2 tails or 1 of each). This is almost correct! Because there are 2 possible outcomes (H or T) on each coin, there are actually 2x2=4 different outcomes. To work them all out get the students to imagine the coins are a 5p and 10p. We then have 4 outcomes:

Head on 5p coin Tail on 5p coin

Head on 5p coin 2 heads Head then tail

Tail on 10p coin Tail then head 2 tails

Different!Different!

The Outwood Grange Family of Schools

Let Me Count The Ways:

5. (Extension): When playing mini-cricket in the back garden a boundary scores either 3 or 4. I hate running, so try to score all my runs in boundaries, with at least one of each kind. What is the smallest score that can be achieved like this in two different ways?

For each of the following questions write down how many different outcomes there are and then produce a list of all of the outcomes: 1.Flipping 3 coins2.Rolling 2 dice3.Ordering a 2 course meal from a menu that has a choice of 3 starters and 2 main courses4.Picking 2 counters from a bag that contains 7 red counters & 3 blue counters

Problem 0:If we flip 2 coins, how many different outcomes are there? And what are they?

The Outwood Grange Family of Schools

Answers:

The Outwood Grange Family of Schools

Let Me Count The Ways:

Problem 0:If we flip 2 coins, how many different outcomes are there? And what are they? 2 outcomes on the first coin and 2 on the 2nd. So 2x2=4 (HH, HT, TH & TT)

The Outwood Grange Family of Schools

Let Me Count The Ways:

For each of the following questions write down how many different outcomes there are and then produce a list of all of the outcomes: 1.Flipping 3 coins. 2 outcomes on each coin. So 2x2x2=8 (HHH, HHT, HTH, THH, HTT, THT, TTH & TTT – try to be logical about your list of 8 solutions) 2.Rolling 2 dice. 6 outcomes on each die. So 6x6=36 (1&2, 1&3, 1&4, 1&5, etc)3.Ordering a 2 course meal from a menu that has a choice of 3 starters and 2 main courses. 3 starters & 2 mains. So 3x2=64.Picking 2 counters from a bag that contains 7 red counters & 3 blue counters. 7 reds & 3 blues. So 7x3=21 (of course, your results will look like red & red, red & blue or blue & blue, but imagine each red was numbered 1-7 & each blue 1-3)

The Outwood Grange Family of Schools

Let Me Count The Ways:

5. (Extension): When playing mini-cricket in the back garden a boundary scores either 3 or 4. I hate running, so try to score all my runs in boundaries, with at least one of each kind. What is the smallest score that can be achieved like this in two different ways?

Possible scores: 3, 4, 6, 7, 8, 9, 10, 11, 12, … 12 is the smallest one

possible in 2 different ways (three 4s or four 3s).