Topic outline

  • General

    Our first booklet comprised of Assessment Rich tasks and an outline of how we used these in the classroom.

    The natural progression was to develop these tasks in line with the Assessing Pupil Progress (APP) guidelines. We continue to be convinced that rich tasks form a vital part of our classroom practice and in addition provide valuable evidence for assessing students.

    In this booklet introduce 7 new tasks that can be incorporated into schemes of work for the purpose of periodic, formative assessment. These tasks are suitable for Key Stage 3 students of any ability. Each task is accompanied by a level ladder which can be used for peer and self assessment, as well as teacher assessment. These also allow students to be aware of ways in which they can improve their work, in order to progress to the next level.

    Each task will include:

    · an introduction to the activity

    · the resources that have been used

    · reflections which include ideas of how to support and extend learning

    · students’ responses which will include levelled work

  • Topic 1

    Impress me with the Statistics you know

    This was a very simple task that involved little preparation, but whose outcomes were an effective tool for APP. In a previous lesson I collected data on gender, shoe size, height and eye colour. Using this I then introduced the task by asking the students to impress me with all the Statistics they knew. I did this with a mixed ability Year 7 group over 3 x 1hr lessons; students were put into same level pairs/small groups and asked to design a poster demonstrating their statistical knowledge.

    Resources: Power point presentation (see slides), copy of data sheet (included), level ladder (included), paper/sugar paper, colouring pens/pencils, scissors, glue, protractor, compass, calculator.

    Reflections: The aim of the activity is to encourage independent and collaborative learning. During each lesson I did not help students with how to do any of the statistical calculations/graphs etc, I did however encourage them to help each other and also guided them to where they may find out how to, for example, draw a pie chart.

    At the end of each lesson students were given a level ladder and asked to decide what level they felt they were working at now, they were then asked to write down what they needed to do to in order improve/extend their work and move up a level.

  • Topic 2

    Alpha Totals

    This is an investigation which was given to all our year 7 pupils as a one week extended homework task. The task links to an Algebra module completed in class and is designed to encourage pupils to think about sequences and nth term.

    Resources: Task sheet, level ladder, a variety of number squares, 10 x 10, 9 x 9 etc

    Reflections: This task was adapted from the ‘T – totals’ GCSE coursework task.

    Responses: I have included a selection of student work ranging from level 3 to level 5

  • Topic 3

    Billiards

    This was an investigation which was given to all of our Year 8 pupils as a two week extended homework task. The task is to investigate patterns (finishing pocket, number of bounces etc.) found on billiard tables of various sizes, where the table has four pockets and the ball always rebounds at 90°.

    The investigation was introduced in a Maths lesson and further details were available on our school VLE. The level descriptors, in this case, were used as a marking aid for teachers, rather than for pupils to assess their own work. Pupils were given a level and then feedback on strengths/areas for improvement in the form of ‘2 stars and a wish’.

    This would work equally well as a classwork task over several lessons. Pupils could then use the level ladders to assess their own work and to identify ways to extend their own work.

    Resources: Task sheet (attached). Level ladder. Centimetre squared paper, rulers. ICT access if pupils are to use the online resource which plots the path of the ball on tables of various sizes – although pupils can easily draw out the paths themselves on centimetre squared paper.

    Reflections: There is an interactive version of this task on the Subtangent website (link on pupil sheet). This could be given to pupils, or withheld to make the task easier/more difficult as desired.

    A writing frame was produced for the very weakest pupils to encourage them to investigate logically, to record their results carefully and to explain any patterns that they found (attached).

    Responses: I have included photos of a selection of student work ranging from level 3 to level 8.

  • Topic 4

    Smarties

    Pupils are given a selection of Smarties e.g. a tube, a box, a fun size box etc...

    A good start is to ask pupils about the ‘Maths of a Smartie’ and see what ideas they come up with.

    Suggestions include making tables of the different colours, average colours, comparing small with big, how long it takes to suck a Smartie until it disappears, how many calories in one Smartie, value for money....

    The style of this task is very investigational and the students are left to get on to see what they produce.

    They can display their findings in the format of a poster.

    What Maths is involved? Sorting, Planning, Concluding, Explaining , Scale drawing, Displaying and interpreting data, Graphs and charts, Scatter diagrams, Averages skills, Fractions and percentages, Surface area and volume of 3D shapes (including an elliptical spheroid), Value for money / Proportion, Probability and expectation

    Resources: A selection of Smarties and containers, Materials for display

    Reflection: Make sure that the pupils have explained all their findings on their poster with step by step workings.

    How do they know that they are correct?

    How could they extend this?

    Possible extension: A few pupils decided to investigate elliptical spheroids and find the volume and surface area. Pupils could then work out percentage changes.

    This task can also be extended to different chocolate bars etc...

    Possible support: The basic bars and charts using the different colours are great for support work and also finding simple averages.

  • Topic 5

    Zoo

    The first part of this task is to find the largest area with a perimeter of 100m. Most students start by looking at different rectangles by changing the dimensions, some may need an example to start. Once they have found the shapes with the largest area, they can design their Zoo taking in to consideration the factors given. Students should be encouraged to think about what else a Zoo needs other than just animals. They can then look at routes around their Zoo and estimate timings if you were to walk around it.

    Resources: For weaker students the perimeter could be reduced to 20m, and they could consider this first, and then try out their solution for a larger perimeter. Students could be given a blank table to help organise their results. Giving students a set area to design their Zoo works well – A4 5mm square paper or A3 1cm square paper worked well. The nrich problem; Largest Product http://nrich.maths.org/1785 could also be used as an introduction to this task.

    Reflections: For the most able students this task could be used to introduce Pythagoras and/or Trigonometry. However for the majority of students the task could be used to assess their knowledge of area and perimeter, while using it as a teaching opportunity for accurate drawings and construction. Students could then construct different polygons to count or calculate the areas.

  • Topic 6

    Two piece tangram

    This is an investigation which was given to all our year 7 pupils as a one week extended homework task. The task links to a SSM module completed in class and is designed to encourage pupils to thing about the properties of shapes.

    Resources: Task sheet, level ladder, individual pieces of squared paper; I used origami paper to make it easier.

    Reflections: There are a number of similar tasks available; many of you will have seen the 3 piece tangram. We also used an extension task, attached.

    Responses: I have included a selection of student work ranging from level 3 to level 5

  • Topic 7

    Consecutive numbers

    Pupils take a look at a sequence on consecutive numbers add apply different operations in between and see if they can spot any patterns in their results.

    They are then to extend the problem by asking ‘what if…?’

    This task offers opportunities to work together when sharing results and making decisions as to which consecutive numbers to look at next.

    What Maths is involved? Mental arithmetic with all four operations, Positive and negative numbers, Recognising and describing links, Working systematically, Generalising, Visualising, Algebra skills, Mathematical reasoning and proof

    Resources: There is a PowerPoint that could be useful as support. Calculators could be offered when the pupils extend their ideas

    Key questions

    Do you think you've found all the possibilities?

    Tell me about your answers.

    Do you notice anything about your answers?

    Can you explain why these things always happen?

    Possible extension: I have found that all the students who have been involved in this investigation have got very excited as various observations are made, patterns seen and questions asked. The most enjoyable times for me have been hearing ten year olds using their own form of algebra and coming to some powerful [for them] realisations about why every one has a 0, −2 and −4.

    The problem has also been the starting point for some pupils to be able to ask "I wonder what would happen if ...?" And in this case it's been:

    ... we used more consecutive numbers each time?

    ... we had a starting point in the negative numbers?

    ... we took consecutive to mean going up in 2s?

    ... we were allowed to use fractions or decimals in between the whole numbers?

    For the very able: These pupils would be encouraged to work on proofs. Then there is the useful mathematical idea of making comparisons - say between using 4 consecutive numbers and 6 consecutive numbers. They could also examine other properties of the answers for any set of 4 consecutive numbers so as to get a generalisation established.

    Possible support: On the odd occasions that pupils needed support I have found that putting a number of pupils together to work as a sharing group is all that has been necessary.