Simplifying doughnut
Can you match up these equivalent algebraic expressions?
Problem
This activity is designed to be tackled in pairs or small groups, but can also be completed individually. For more information on how this can be done in groups, take a look at the teachers' resources.
These printable domino cards can be put together to make four 'doughnuts' of four dominoes. The ends of dominoes which join together need to be algebraically equivalent.
For example, a doughnut could look like this:
Have a go at making the four doughnuts. What do you notice?
Once you've made four doughnuts, you might like to try using the same set of cards to make two large doughnuts instead, with eight dominoes in each doughnut.
Is it possible to make one very large doughnut, using all sixteen cards? And if it is possible, is there more than one way of doing this? How many can you find?
Teachers' Resources
Why do this problem?
This problem provides an opportunity for students to work together collaboratively to simplify algebraic expressions in an engaging context.
Possible approach
This activity can be done in a very structured way in groups of four (or five, including an observer). The cards can be handed out randomly - four dominoes to each group member - and the group can work together in silence, with learners handing one of their cards to another learner based on their observations of each other's needs. An observer can make sure the team obeys the rules, as well as making a note of times that members of the team responded to the needs of others.
Observers can also give a hint if no progress is being made. This hint should be to point to one of the expressions and to say something along the lines of, "Think about how many dominoes have an end that is equivalent to this expression."
As teams finish, ask them to discuss what they have learnt about working together. Use observers to feed into the discussions. Then spend some time discussing as a class how they might work more effectively in future.
Key questions
As this task is designed to be carried out in silence, the use of key questions is inappropriate during the task but can inform discussion of team behaviours when the task is complete.
- Can you give any good examples of when someone noticed what you needed and tried to help?
Possible support
Some learners might find it easier to work in a less structured way with these dominoes. For example, being able to move the dominoes all freely around and being encouraged to write on the dominoes to keep track of the equivalent algebraic expressions will make this task more accessible for some students.
Possible extension
The dominoes can also be arranged into some larger doughnuts. Ask the team to create these shapes.
Learners could also work on making their own algebraic dominoes. What makes a good set of dominoes for this activity? What would they change/keep the same about the features of the set of dominoes in the problem?