Introduction to algorithms

An algorithm is a set of steps used to complete a specific task. Although this word is often used in relation to technology, it can have a wider application in everyday use. For example, an algorithm for preparing to go home at the end of a school day would involve packing up, clearing desks, and so on. The following video (2:30) provides an excellent overview of algorithms.

Number guessing game

• The teacher chooses a secret number between 1 and 100 and writes it on the board before covering it over to conceal the number.
• Students have 7 guesses to discover the number.
• The teacher can only give "Yes" or "No" answers.
• Reminders are written on the board to narrow down the options (e.g., if a students asked "Is it odd?" and the answer was "No", the teacher would write "Even" on the board.
• Guesses are tallied up on the board and the answer is revealed after the seventh guess unless guessed earlier.
• The game is played again with a student running the game.

The next stage with this activity is to contrast good guesses such as "Is it lower than 50?" with random guesses such as "Is it 87?"  This can then be used as an introduction to algorithms where the aim is to narrow down the options. This is also a good way to introduce the word 'strategy'. A useful website for playing this game is https://toytheater.com/hundreds-chart/. On this site you can eliminate the numbers which have been ruled out using different colours. For example, the mystery number was 14 and the yellow shading was in response to the question, "Is it bigger than 50?". The blue shading was in response to the question, "Is it even?"

Create an algorithm to solve the number guessing game. The algorithm should use only seven steps. The algorithm should reveal the secret number every time.

Number generation activity

• Students choose a number between 1 and 100 and write it in a box in the middle of a sheet of paper (e.g., "25")
• Students think of different ways to get this number and write them all over the page (e.g., 10 + 15; 5 x 5, 20 + 5, 30 - 5, 10 + 10 + 2 + 3, and so on).

Algorithms and pseudocode

Pseudocode is an informal description of steps using natural language intended for human understanding rather than machine execution. It uses elements similar to coding but without adhering to the strict syntax rules of any specific programming language.The following video (4:58) explains algorithms using a counting example and pseudocode.

Branching

In algorithms and coding, branching is when a single branch is subdivided into two or more branches. Branching is used to make decisions and follow different paths of code based on conditions. Terminology for branching includes "if/else", "if/then", and even "yes/no". The following screenshot uses yes and no to show how to safely cross a road.

(Screenshot from https://players.brightcove.net/2750693524001/default_default/index.html?videoId=6385325199112)

Word search activity

Create an algorithm to solve word searches using pseudocode

• This challenge is open ended as there is a whole range of appropriate ways to address this.
• The main criteria is that each child's algorithm is logical and sequential.

Tessellation activity This activity is based on the video below

• Each student will need a piece of A4 paper and scissors.
• Ask students to fold their paper into half, then quarters and then eighths (i.e., fold in half and then half again and then half again).
• Cut out a random shape with four straight sides.
• As children to try fitting the 8 pieces together so that they tessellate.
• [There is a trick to this which is written in the dot point below the video so that students can't see it until you scroll down. They might figure it out for themselves but it is recommended that you don't spoil the surprise so encourage some experimentation first.]

The following video (5:00) provides a good overview of tessellation and then goes into a lot of detail about angles to show how tessellations work.

• The trick is to rotate each piece by 180 degrees which is the same as turning it upside down. This also means that there are only two orientations.
• Each grouping of two pieces is then translated (i.e., moved or slid) over to join up as shown in the following screenshot.

Moderated self-assessment

Discussions with students around the key components of conceptual topics and how they fit together can generate insights into student achievement.

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