## Countdown

Here is a chance to play a version of the classic Countdown Game.

The challenge is to use the numbers available and the four standard operations (addition, subtraction, multiplication and division) to hit the target.

Start by choosing any six cards. The top row always contains the numbers 25, 50, 75 and 100, and the bottom row contains the numbers 1 to 10. Alternatively you could click on "Quickstart". Then click on "Generate new target" and the computer will choose a target.

You can only use each card once in your solution, and it is always possible to find a solution.

#### Why play this game?

Countdown offers a motivating context in which to practise calculation strategies.  There is usually more than one way of hitting the target, which offers an opportunity for rich discussion on the merits of alternative methods. It encourages learners to estimate and to 'tinker' with solutions as they get closer to the target number.  ('Tinkering' is one of the mathematical habits of mind referred to by Al Cuoco et al.)

#### Possible approach

Demonstrate the game to the class.

If the students have access to computers or tablets they can work in pairs on various examples. The Settings menu offers students the possibility of working at different challenge levels:

• level 1 can always be done using two cards
• level 2 can always be done using three cards
• level 3 can always be done using four cards
• level 4 can always be done using five cards
• level 5 can always be done using all the cards.

If students don't have access to computers or tablets you could generate several examples and write them on the board for students to have a go at with their partner using pencil and paper.

Once students have successfully completed some challenges, bring the class together to share strategies and discuss the advantages of different methods.  It may be worthwhile to collect strategies on a 'working wall' so the whole group can look back and see which prove useful time and time again.

Finally, set aside some time for students to have a few more goes to put into practice the strategies they have discussed. Students may want to challenge themselves to always find the solution using the minimum number of cards.

If they come across a particularly difficult example you could share it with the rest of the class by using the "Replay code" which can be entered in the Settings menu (access using the purple cog in the top right). If no-one finds a solution, you can leave the challenge on the wall as a 'simmering' activity for a few days so that members of the class can come back to it in their own time.

Countdown is one of the most popular resources on NRICH, so you may like to discuss your experiences of using this activity in your classroom on Twitter, using the hashtag #NRICHcountdown.

#### Key questions

How could you get close to the target?
How could you use rounding and estimation to help?

#### Possible support

Suggest that students work on the level 1 and 2 problems initially. You could also use the "Replay code" facility to share accessible examples (e.g. 25,7,4,9,3,5,125) before letting students loose on randomly generated examples.

#### Possible extension

Countdown Fractions offers a much more challenging version of the game.

Some of your students might be interested in this blog post, written by Nick Berry, which describes some questions he asked himself about the traditional Countdown game, and how he used coding to help answer them. We used some of the optimisation ideas from the article in the development of the new Countdown game.