Mathematics and the NCEA realignment Part two

1. Mathematics and the NCEA realignmentPart two Webinar facilitated by Angela Jones and Anne Lawrence

2. Mathematics and the NCEA realignment • AS 1.4 • Feedback on the standard and the task • Assessment decisions • AS 1.5 • Next steps

3. Introductions Mathematics and NCEA realignment Angela Jones Senior adviser Secondary Outcomes Team Ministry of Education angela.jones@minedu.govt.nz Anne Lawrence Adviser in Numeracy, Mathematics & Statistics Massey University College of Education a.lawrence@massey.ac.nz

4. The standard How well does the SOLO taxonomy reflect the A, M, E criteria for achievement standard 1.4? The taxi task and the schedule How effective is the taxi task at eliciting different levels of student thinking? What other kind of tasks could be used to assess Achievement standard 1.4? What about portfolios? Meeting the standard What evidence is required? Feedback on 1.4 Achievement standard 1.4

5. What does the standard say? Applying linear algebra - using a range of methods in solving problems, demonstrating knowledge of algebraic concepts; solutions which would usually require only one or two steps. Relational thinking - one or more of logical sequence of steps; connecting different concepts; demonstrating understanding; forming and using a model, and relating findings to a context, or communicating thinking using appropriate mathematical statements.  Extended abstract thinking - one or more of demonstrating understanding of abstract concepts; developing a chain of logical reasoning; forming a generalisation, and using correct mathematical statements, or communicating mathematical insight.

6. Student work - is there evidence for A, M or E?

7. What have we learnt about levels of thinking? Students at achieve are: At merit, students are: At excellence, students are:

8. AS 1.5 Apply measurement in solving problems A: Apply measurement in solving problems. M: Apply measurement in solving problems, using relational thinking. E: Apply measurement in solving problems, using extended abstract thinking. These achievement objectives are related to this standard: • convert between metric units, using decimals • deduce and use formulae to find the perimeters and areas of polygons, and volumes of prisms • find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders • apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures • calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

9. AS 1.5 Apply measurement in solving problems Solving problems - using a range of methods solving problems, demonstrating knowledge of concepts, solutions usually require only one or two steps. Relational thinking - one or more of a logical sequence of steps; connecting different concepts and representations; demonstrating understanding of concepts; forming and using a model, and relating findings to a context, or communicating thinking using appropriate mathematical statements. Extended abstract thinking - one or more of devising a strategy to investigate or solve a problem; identifying relevant concepts in context; developing a chain of logical reasoning; forming a generalisation, and using correct mathematical statements, or communicating mathematical insight.

10. AS 1.5 Apply measurement in solving problems Measurement includes the use of standard international metric units for length, area, capacity, mass, temperature, and time. Derivedmeasures include density, speed and other rates such as unit cost or fuel consumption. Students will be expected to be familiar with methods related to: • perimeter • area and surface area • volume • metric units.

11. Task 1.5A Garden sculpture • This assessment requires you to design a garden which has a stone sculpture in it, and provide various measurement calculations for the owner of the garden. • You will be assessed on your depth of understanding and application of measurement. It is important you communicate your thinking and your solutions clearly and relate your findings to the context.

12. Sculpture design The sculpture must contain at least two different 3-dimensional geometric solids, for example, a sphere, rectangular prism, pyramid, cylinder, cone, or hemisphere. Examples could look like: The entire sculpture must fit neatly into a shipping crate which is a cuboid shape and has internal base measurements which are 55 cm long and 0.6 m wide. The crate will look like: • Garden Design The base of the sculpture is to be surrounded by a paved area which is 50cm wide. A small fence is to be placed around the outer edge of this paved area. Possible sketches of the garden from above could look like:

13. Design your sculpture. Draw and label a diagram of the shape of the sculpture, and list appropriate measurements, using a common unit (either mm, cm, or m). Show all calculations and list all dimensions with units for each of these pieces of information required by the owner: • The length of the surrounding fence • The area of the paved surround • The volume of each of the pieces making up your sculpture, and give a total volume The local quarry provides stone in rectangular prisms of any size. Each separate 3-dimensional shape in your sculpture will be carved out of a new rectangular block. Calculate the minimum volume of stone in cubic metres (m3) from which each shape of your sculpture could be carved. You must state clearly the dimensions of each of the rectangular prisms you will need to use. The sculpture is to be transported in a shipping crate which is a cuboid shape and has internal base measurements which are 55 cm long and 0.6 m wide. Give a rule for the volume, in cubic metres, for the minimum volume needed for any sculpture which fits the given base measurements.

14. Example of achieve for 1.5 A sample sculpture might consist of a sphere of radius 0.2m placed on the top of a prism of height 0.1m and square base side length 0.4. Perimeter = 4 x 0.9 = 3.6m Area = 0.92 – 0.42 = 0.65 m2 Vsphere = 4/3()(0.2)(0.2)(0.2) = 0.0335 m3 Vcuboid = (0.4)(0.4)(0.1) = 0.016m3 Correct calculations for at least two of these methods could be expected • Length of fence • Area of paving • A component shape volume with appropriate units, for example, area is mm2, cm2 or m2 must be supplied in at least two calculations and a clear identification as to what is being calculated

15. Example of merit for 1.5 For total volume • Vsphere = 4/3()(0.2)(0.2)(0.2) = 0.0335 m3 • Vcuboid = (0.5)(0.5)(0.1) = 0.025 m3 • Total volume of sculpture = 0.0585 m3 Given the selected sculpture elements meet the stated requirements and the calculations follow some logical sequence of steps with appropriate units stated in most solutions.

16. Example of excellence for 1.5 A general rule could be Volume (m3)= 0.55 x 0.6 x h Where h is the height of the total sculpture. and Evidence of insight could be: However, it would depend on the relative sizes of the separate shapes. It is possible, for example, that two shapes could sit “side by side” in the box rather than “on top” of each other. In this case the height of the box will be the height of the tallest shape sitting on the base of the box. Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against criteria in the AS.

17. Process from here Online forum: • How does this work? Homework: • Trial the task, • Mark student work - keep notes about judgements but leave student work unmarked (raw) • Select student work to cover a range of grades • Submit raw student scripts

18. Next steps • Trial the task • Mark • Select and submit student scripts • Participate in online forum