Additional Materials
Materials Required
Estimated Time Needed
(Times are approximate and will depend on the needs of the students.)
Draw students' attention to the questions you have written.
In trials, teachers found keeping groups small helped more students play an active role.
You have two tasks during small-group work: to note different student approaches to the task, and to support student problem solving.
Note different student approaches to the task.
Notice how students work on finding the quadratic function for the number of whole tiles.
Notice also whether and when students introduce algebra. If they do use algebra, note the different formulations of the functions they produce, including incorrect versions, for use in whole-class discussion. You can use this information to focus the whole-class plenary discussion towards the end of the lesson.
Support student problem solving.
Try not to make suggestions that move students towards a particular approach to this task. Instead, ask questions to help students clarify their thinking.
If several students in the class are struggling with the same issue, you could write a relevant question on the board.
You might also ask a student who has performed well on one part of the task to help a student struggling with that part of the task. The following questions and prompts have been found the most helpful in trials:
You may find that some students do not work systematically when drawing tabletops and organizing their data.
Students may justify their formulas by drawing another example to see if the generalization fits a new case, reasoning inductively. Some stronger explanations are shown in the Sample Responses to Discuss.
These are three of the common problem-solving approaches taken by students in trials.
This analysis task will give students an opportunity to evaluate a variety of alternative approaches to the task without providing a complete solution strategy.
Identify one or two of these approaches to discuss in the plenary discussion.
Note similarities and differences between the sample approaches and those the students took in small-group work.
The intention is for you to focus on getting students to understand the methods of working out the answers, rather than either numerical or algebraic solutions. Focus your discussion on parts of the two small-group tasks students found difficult.
Below, we have given details of some discussions that emerged in trial lessons.