Which quadratic?
In this activity you will need to work in a group to connect different representations of quadratics.
Problem
This resource is from Underground Mathematics.
What are the key features of a quadratic and what information do you need to be able to identify these for a particular example?
This problem is designed to be tackled in a team of four, working as two pairs. One of the pairs is trying to identify the quadratic on a randomly chosen card. You can download the cards here.
Instructions
- To begin, place all of the cards on the table and spend a couple of minutes familiarising yourselves with the types of images and equations that might be chosen.
- Next, one pair takes control of the cards, moving them out of sight from the other pair. They select a card at random. The other pair can now ask up to 8 "yes/no" questions to determine the hidden quadratic. It is important that each pair confers and agrees before asking or answering each question.
- You are permitted a maximum of two guesses at the hidden function, and each guess counts as one of your 8 questions.
Some things to consider
- Did you guess the quadratic correctly? If not, what additional information did you need?
- Did you make the most of the information you were given? Could you have avoided asking any of your questions?
- Were your questions clear? Did the other pair understand what you meant? Could you have used mathematical language to improve this?
- Would you ask the same questions next time?
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.
Student Solutions
There are many different approaches to this problem. Here are the questions Emma, Tamsin, Ellie, Sophie, Isabella and Alex from Sandbach High school used to help narrow down the possible choice of quadratics.
Is it a negative quadratic shape?
A
Is the turning point on the y-axis?
Is the turning point on the x-axis?
B
Has it been translated vertically?
Has it been translated horizontally?
Though group A and B are similar questions.
They have also observed that group A and group B are very similar questions, so in fact you only need to ask one of these pairs of questions. Can you see why? How would the answers to one of the pairs of questions give you the answers to the other pair and vice versa?
From this point we still need to ask a few more questions to identify the quadratic exactly out of the 18 possibilities. Nicolette from St Stephen's School has suggested some more specific questions to end with:
More specific questions could be if the parabola has been vertically translated upwards or downwards, or if the parabola has been translated horizontally left or right.