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Mathematics Matters Lesson Accounts 25 - 'Mystery Type' Geometry Cards

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 May 2008 by ncetm_administrator
Updated on 16 June 2008 by ncetm_administrator

Mathematics Matters Lesson Accounts
A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

Lesson Account 25 - 'Mystery Type' Geometry Cards

Written by Julie Pattison
Organisation North Yorkshire LA
Age/Ability Range Students had previously covered work on various areas of geometry. In this lesson, the teacher was using a set of ‘mystery type’ cards (but with only one unique solution).

How was the session/task introduced?
Students were in groups of three or four and cards were dealt out. They could read their own cards but couldn’t show them to the others. They were told very little else except that the starting point could be found on one of the cards.

How was the session/task sustained?
The task itself involved pupils creating a ‘map’ of distances and bearings between different towns. They were then asked to find other unknown distances and / or bearings. Each card had a fact and question on it which were not necessarily related.

How was the session/task concluded?
Different groups had used different approaches and the strengths and limitations were discussed.(See also what mathematics was learnt).

Students who had ‘stuck’ to the instructions to keep to the cards themselves reported how much harder it was than those who had ‘cheated’ and shared them.

What were the critical moments?
Groups understanding the task
Collecting together the key facts
Finding the key fact to unpicking the problem
Deciding on the mathematics to use and being confident of their choice.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
The teacher had intended the pupils to use and apply the sine and cosine rule to solve the task but the focus of the lesson was on problem solving so he allowed groups to solve this using any method. This led to an interesting debate at the end where pupils compared sine and cosine approach and scale drawing. Class conclusion was that although the scale drawing approach was quicker the sine and cosine approach was more accurate and mathematical. It also brought up the issue of how scaling up to actual sizes magnified errors in measurement.

How was that mathematics learnt?
Pupils learned through a combination of discussion and researching through exercise and text books. The teacher was used as a sounding board and asked questions to challenge pupil approaches but left all decisions up to the pupils (apart from a little reassurance to the less confident groups).

Other memorable outcomes
It was interesting that the teacher had underestimated the learning that had taken place and was worried that the students who chose scale drawing had not made progress. This led to a discussion on what progress was and a clarity in content driven versus skills driven learning objectives.

Problem solving card sort task aimed at sine and cosine rule. Resources created by Julie Pattison (available on North Yorkshire County Council maths section of website).

Click here to download the sheets to accompany this resource (PDF format).


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Strategies for investigation and problem solving
Builds on the knowledge learners already have
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Uses rich, collaborative tasks

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05 November 2009 20:27
I tried this task with a Y9 level 6 class. I had just taught bearings and thought that this would be a nice task for them to complete by solving it using scale drawing. Unfortunately it was far too difficult and not possible as Towns B & D have no direct information to place them, you have to draw them on tracing paper and then move them along until the distance between them is correct on the bearing of 175 degrees. I was annoyed to find that the bearing of B from A was written as 90 degrees (not 090 degrees) and the other questions and angles were not bearing related. This is probably an excellent activity for a class studying cosine rule.... but don't use it to support the learning of bearings.
By tessadams
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