Dicey Operations
In these addition and subtraction games, you'll need to think strategically to get closest to the target.
Dicey operations printable sheet
Dicey operations scoring sheet
If you know how to add and subtract, you may enjoy these challenges.
How close can you get to the target?
Click on the purple cog to select from the available challenges.
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?
And when you're ready for multiplication and division challenges, you might like to look at More Dicey Operations...
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.
Here are two examples of games you could play:
Game 1Image
| Game 2Image
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There are two parts to this game, whether you choose Game 1 or Game 2, or a version of your choice. The first part involves an element of chance and the second part involves careful reasoning.
Find a partner and a 1-6 dice, or preferably a 0-9 dice if you have one.
Each player will need to draw an addition or subtraction grid that matches the game they've chosen. (Alternatively, there is a printable scoring sheet linked at the top of this page.)
Part 1
Throw the dice. Each player decides where to place that number in their own grid. Continue until all the cells are filled.
Whoever has the result closer to 1000 wins.
Part 2
This time, seeing the numbers thrown in part 1, each player decides where to place them on their own grid (as in the interactivity above).
Again, whoever has the result closer to 1000 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 1000 after each round. First to 5000 loses.
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why play these games?
These games are thought provoking and very engaging. They encourage discussion of place value, mental calculations and estimation, alongside valuable strategic mathematical thinking.
Possible approach
Use the interactivity to introduce the task - you could initially suggest that they place the numbers randomly and find the total, and then introduce the idea of aiming for a particular target. Then, working in pairs, set them the challenge of getting as close to the target as possible, and when the class is ready, bring them together to compare their solutions.
Now give everyone, ideally in pairs, time to work on several examples of the problem. Whether working at computers/laptops or with paper and pencil, set students the challenge of trying to hit their target in fewer than three attempts. Encourage students to justify their strategies to their partners.
Once they have had chance to play several rounds, bring everyone together to discuss their thinking. How are they deciding where to place the numbers?
You can encourage students to work on problems of varying levels of difficulty by selecting the appropriate settings using the purple cog.
Key questions
Why are some cells more significant than others?
What might you try first? Why?
What are effective strategies for placing the numbers?
Possible support
Some pupils may benefit from having a go at Nice or Nasty, which focuses on place value, before trying these challenges.
If students are not working at a computer, and are collecting all the numbers before deciding where to place them, you could provide them with number cards that they can move around to consider different options.
Choose the easiest scoring system or allow calculators for checking the more difficult version.
Allow pairs of students to play against other pairs, so that they can support each other.
Possible extension
Cryptarithms offers an engaging follow-up challenge.
More Dicey Operations challenges students to get as close to a target as possible using multiplication and division.
You may also wish to move students on to Countdown and Countdown Fractions.
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