AST_Using a target game to practise mental computation involving addition of whole numbers
In this game, you will learn to
improve on your mental computational skills on addition
use problem solving skills, such as guess and check and logic, to find a strategy to win
SLS Page 1: Target Game: How to play the game?
Credits: This game was originally conceptualised by Theresa Heng using physical number cards. It was developed into an interactive game by Lawrence Wee, Lead Specialist from Educational Technology Division.
This is an interactive game to be played by two players. It is designed to help students practise their mental computation on additionsof whole numbers. Students can play it at home with a family member if it is assigned as homework.
In class, this maths app can be played on iPad or mobile phone. Teachers can assign students to work in groups to challenge one another. Students can collaborate as a group and work out a stretegy to win.
The objective of the game is to be the first player to reach the target sum when the two players take turns adding the running sum of the number cards chosen. Students to discover the strategy to be a sure winner regardless of being the 1st Player or 2nd Player.
Teachers can use this maths app to reward students in the class who have already completed their work. Teachers can also modify the activity to tie in with their own SLS lesson LOs related to addition of numbers.
There are 3 challenges with increasing level of difficulty. Students may initially win through trial and error after one or two games in each challenge. At the end of the game, there will be some key questions posted to get students to think of the strategy to be a sure winner.
This interactive game may appear to be very simple and only meant for Lower Primary students, but it can also be suitable for Upper Primary students if the task assigned to them is to be of different target to reach with different number of cards given.
Here's how to play the Target Game for Challenge 1:
Number of Players: 2
Material(s): Only the interactive Game board, no pen, paper or calculator is allowed for calculation.
Objectives of Challenge 1:
The winner is the first player to reach the target sum of 20.
Rules:
1. This is an addition game for two players; Player Red and Player Blue to decide who to start the game.
2. Players take turns to click on any one of their own number cards with no limitto the number of times the same card has been chosen. The card will automatically be placed on the blank space in the centre row, from left to right.
3. Players will add quietly the sum of the cards that appear in the centre row through *mental calculation. For example if the two cards chosen by the two players are 5 and 1, then the sum will be 6.
4. Game continues with players taking turns to add the running sum of the chosen number cards. For example, if the next 2 cards are 3 and 1, then the total will be 6 + 3 + 1= 10
5. The first player to reach the target sum of 20 wins the game!
(*Players can decide to show or hide the score if they agree.)
Refere to the pictures below to understand the functions of the different buttons before you start to play.
Challenge 1: Target 20 with Cards 1 to 5
Let students enjoy the game through trial and error to win. They have to keep a record to investigate the number chosen by each play for each move. Does first Player always win/lose?
Game No.
1st Player's Number Chosen
2nd Player's Number Chosen
1st Player's Number Chosen
2nd Player's Number Chosen
1st Player's Number Chosen
2nd Player's Number Chosen
1st Player's Number Chosen
2nd Player's Number Chosen
1
2
3
4
After playing Challenge 1, if students discover the strategy to win, let them apply the strategy for Challenge 2 and Challenge 3 as the level of difficulty increases.
Question: Is 1st player always the winner?
Answer: Not necessary, both 1st or 2nd player can win the game if you know the strategy to win.
Strategy to Win:
To be a sure winner, players need to work towards the target sum by selecting the correct card that adds to that total.
To calculate the target sum:
Challenge 1
To reach the Target Sum of 20, here is the formula: T - (H + L)
where Target Sum, T = 20, Highest Number Card, H = 5, Lowest Number Card, L = 5
Let's work backwards to discover:
Before reaching 20, Target Sum to achieve = 20 - (5 + 1) = 14
Before reaching 14, Target Sum to achieve = 14 - (5 +1) = 8
Before reaching 8, Target Sum to achieve = 8 - (5 +1) = 2
Hence to be a sure winner, players need to achieve the running total of 2, 8 or 14 when during their turn to choose a number card.
Explanation:
Target Sum to achieve = 20 - Highest Number - Lowest Number
You need to achieve the target sum, 14 whereby your opponent's next move will only reach maximum of summing total as 19 so that your last move will reach the goal of target sum 20.
For example:
14 + 5 (Opponent's number) = 19 then your last move is 1 to reach 20
or 14 + 4 (Opponent's number) = 18 then your last move is 2 to reach 20
or 14 + 3 (Opponent's number) = 17 then your last move is 3 to reach 20
or 14 + 2 (Opponent's number) = 16 then your last move is 4 to reach 20
or 14 + 1 (Opponent's number) = 15 then your last move is 5 to reach 20
Are you ready for Challenge 1?
1. Remember to click reset to start a new game.
2. Select Challenge 1 and the colour cards to be 1st player to start the game.
3. All number cards can be chosen more than once.
Please take turns to be the first player when playing with your family member.
Record the number chosen by each player until the target sum of 20 is reached for the 4 games in the table below.
How many games did you win?
Is the winner always the 1st player? What do you think?
Game No.
1st Player's Number Chosen
2nd Player's Number Chosen
1st Player's Number Chosen
2nd Player's Number Chosen
1st Player's Number Chosen
2nd Player's Number Chosen
1st Player's Number Chosen
2nd Player's Number Chosen
1
2
3
4
Out of the 4 games, I won _________ times.
What do you notice about the running sum of the winner's last move?
Let's fill in the following blanks to understand how to win the game.
Let's study the the following number equations, A + B + C = 20
Case 1: If B = 1, C = 5, then A + 1 + 5 = 20, so A is
Case 2: + 2 + 4 = 20
Case 3: + 3 + 3 = 20
Case 4: + 4 + 2 = 20
Case 5: + 5 + 1 = 20
Are all your answers the same? How is this answer related to the Target Game?
About
About This card game designed to help understand how to always be the first person to reach 20 by allowing students to develop their own thinking about the rules of reaching twenty.
Let assume end in the last number, say 20 Start is the beginning number say 0 largest card number is say, n = 11 for both RED and BLUE players.
The hint is to always win, you need to reach (end-start) - n -1 , which is 8 so that whatever the next move by the opponent ranging from 1 to 11, you can place your next card to reach end =20!
Another example is Let assume end in the last number, say 20 Start is the beginning number say 0 largest card number is say, n = 5 for both RED and BLUE players. So the AI step is = end - i*(n+1), so stepAI[0] = 20 -0*(5+1) = 20 stepAI[1] = 20-1*(5+1) = 14 stepAI[2] = 20-2*(5+1) = 8 stepAI[3] = 20-3*(5+1) = 2 so to win, try to land on 2, followed by 8, followed by 14 and lastly to win 20! enjoy!
Game play can be made more challenging by varying target end number from default 20 to 40 for example. start number from default of 0 to 10 for example number of cards available to players, default is 11 odd numbers card only for player 1 or 2 even numbers cards only for player 1 or 2
Interesting Fact This app is created to support playing of adding up in creative and challenging ways.
Acknowledgement This physical card game was originally shown to me and conceptualized by Theresa Heng.
My sincere gratitude for the tireless contributions of Francisco Esquembre, Fu-Kwun Hwang, Wolfgang Christian, Félix Jesús García Clemente, Anne Cox, Andrew Duffy, Todd Timberlake and many more in the Open Source Physics community.