Dicey Addition
1 out of 3
In these addition games, you'll need to think strategically to get closest to the target.
Problem
Dicey Addition printable sheet
Have a go at the interactivity below.
How close can you get to the target?
How are you deciding where to put the digits?
Can you come up with a strategy for deciding where to place the digits so that you get as close as possible to the target in your first attempt?
If you are working away from a computer, you could treat this as a game for two people, or play in two teams of two.
There are two parts to this game. The first part involves an element of chance and the second part involves careful reasoning.
Find a partner and a 1-6 dice, or a 0-9 dice if you have one.
Each player will need to draw this addition grid:
Part 1
Throw the dice once. Each player decides where to place that number in their own grid. Throw the dice again, continuing until all the cells are filled.
Whoever has the result closer to 100 wins.
Part 2
Now list all the numbers you threw in part 1. On a new grid, each player decides where to place those numbers on their own grid.
Can you get closer to the target than you did before?
Again, whoever has the result closer to 100 wins.
There are two possible scoring systems for each part of the game:
- A point for a win. The first person to reach 10 wins the game.
- Each player keeps a running total of their 'penalty points', the difference between their result and 100 after each round. First to 500 loses.
You can vary the target to make it easier or more difficult.
Student Solutions
We received this solution from the Math Magicians Club at South Walney Junior School:
We placed the 9,8,7,6 in the units column because if we had 9,8,7,6 in the tens column then it would equal more than 100 by a larger difference.
If we had 5,4,3,2,1, you are more likely to reach 100 if you put these into the tens column.
If we rolled a high number at the start it is quite safe to place this into the tens column and then if you roll a high number again, it is best to place that number in the units.
Thank you Math Magicians. We would be interested to hear from anyone else who had some ideas about this challenge.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why play this game?
This game is thought provoking and very engaging. It encourages discussion of place value, mental calculations and estimation, alongside valuable strategic mathematical thinking.
Possible approach
This game is a simpler version of Dicey Operations in Line.
It can be played with 1-6 die but ideally would be played with a decahedral 0-9 dice or a spinner (an interactive 10-sided spinner is available here).
Invite volunteers (perhaps working in teams of two) to play the game on the board and explain the rules to them and the rest of the class.
When the game is over confirm who has won and explain the scoring system.
Working in teams of two, set learners off on playing the game. Depending on your aims for the lesson, offer the simple or more complicated scoring system.
When appropriate, encourage learners to vary the targets.
Encourage learners to justify their strategies to their partners, and draw their ideas together at the end of the lesson.
Key questions
How are you trying to get close to 100?
How are you deciding where to place the numbers?
How do you decide which targets are appropriate?
Possible extension
When working on the second version of the game whereby the four numbers are thrown before deciding where to place them, encourage learners to justify and prove that their arrangement is as close to 100 as possible.
You may wish to move learners on to Dicey Operations in Line. A slightly different version of this game, Dicey Operations, involves the same mathematics using the column method of addition and subtraction.
Possible support
Simplify the calculations by using fewer cells in each game.
Perhaps provide learners with number cards that they can move around the grid to consider different options.
Pupils who find estimation difficult could use calculators to check their estimates.
Choose the easiest scoring system or allow calculators for scoring the more difficult version.
Allow pairs to play against other pairs, so that partners can support each other.