### Teachers Notes

Probably the most powerful thing a student learns in mathematics lesson is that they often already have all the tools they need. With this activity students need to reason with eachother using those skills to match the properties of the quadratic with the graph. In doing so they should realise that they do have the skills they need and by use of logical deduction they can reduce what appears to be a group of different pieces of knowledge in to one. The suggestion is not that the activity magically makes students more efficient but simply that it is an opportuntiy to help them realise that they can be. The practical group aspect of the activity is also appealing to students. All this combined can make for an engaging and productive activity that acts as an important reminder both of what students are capable of and of quadratic functions before the next stages of the syllabus on this topic are covered.

### How

The following is some practical advice about how the activity might be run.

#### Resources provided

There are three separate worksheets for this activity. The activity is repeated three times with less information given each time. These can be printed, copied and given to students to cut out or laminated and cut out in advance (the latter has a good 'resusable' advanatge to make the initial time spent worth while)

• Resources needed
• Possibly scissors and glue depending on any final product desired (see 'records' below)
• Space - clear tables and room for students to share sets of cards

#### Time needs

This depends on the class in question, but can probaly be done in 45 minutes. It can be extended by asking students to create some kind of record of their general conclusions.

#### Starting and finishing

This is simple to begin. The teacher might need to introduce the idea clearly and explain that the cards should go in to groups of 5.

Teachers may want to consider carefully how they group students for this task with all the associated possibilities. It could also be done individually if you have lots of copies of the cards or elected to do it using computers.

I think that it is important that students take the time to try and articulate their conclusions either for themselves or for the class.

#### Records

In practice students are often keen to create a poster of the groups of 5 and this is easily done. Its worth considering though that this will be difficult to keep. One solution might be to ask all groups to contribute to a collective poster that could then be displayed in the class. Better yet, the teacher/students could take photographs of the results that are easily kept as a record of the activity.

As mentioned above, it is good to take the time to try and articulate general conclusions. This could be done by individuals or the class could work on one together. A written record of this could be advantageous as a reminder.

### What

• This activity generally brings out lots of reasoning skills. This is where group composition can be important, but it is great when students start to reason amongst themselves.
• There is often confusion over where and when x=0. From my experience students can find it counter intuitive that x=0 all along the y-axis and vice-versa. It may be worth taking a moment to dwell on that.
• The issue of quadratics that cant be factorised should come up and provides an excellent opportunity to explore 'classes' of quadratics.
• This may, in turn, lead to discussion of quadratics with no real roots!

### More

This is the first in a trio of activities investigating quadratic functions. They can be done in sequence or independently. Much depends on the class in question and the time available. Below are links to the other two activities,