TGHS Maths
Level 2 Mathematical Studies
This course is a “light” level 2 course. It is NOT an alternative course. It is intended for students who are not confident with algebra, but who want some experience of Level 2 Mathematics. Some of these students may come from a Level 1 Numeracy course, but will have gained one or two Achievement Standards at Level 1 (as well as the 10 Numeracy Credits).
The course is taught at Achieved level, although some students will gain Merit. It is largely an internally assessed course, although there is an option for most students to sit the Probability External. Students who achieve this standard often go on to take Level 3 Statistics.
Term 1
Networks
This is the first standard covered on this course in Year 12. Since some students will be lacking confidence at this point, it is worthwhile spending a reasonable amount of time ensuring that they meet with some success at the start.
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Resources |
Time Scale (approx.) |
Definitions (Arcs/Vertices/Regions) |
TD: Ex. 15.01 p. 228 |
2 lessons |
Traversability
Networks and Circuits |
TD: Ex. 15.02 p. 234 and 15.03 p. 237 TD: Ex 16.01 p. 246-247 |
3 lessons |
Shortest Route (ONE algorithm only) |
TD: Ex. 16.02 p. 250 |
2 lessons |
Minimum Spanning Tree (ONE algorithm only) |
Worksheet: Muddy City (good introduction) PPT: Waitakeres to use as example High Speed Broadband in the Waitakeres TD: Ex. 16.03 p. 259 |
3 lessons |
Network from Two-Way Table Combining the Techniques |
7 lessons |
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Preparation for Practice |
1 lesson + 1 lesson feedback |
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Practice Assessment |
2 lessons + 1 lesson feedback |
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Real Assessment |
2 lessons |
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| Re-assessment | Milk Collection (2) | |
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Total: |
24 lessons (about 5 weeks) |
Text Book Reference:
TD = Theta Dimensions. Note: We DO NOT have a class set of these text books.
* It appears easier to right-click and save these ppts.
Other resources:
Networks review A resource for those doing a reassessment.
Simulations
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Resources |
Time Scale (approx.) |
Introduction to Simulations |
Internet access Lesson: 1 Introduction to Simulations Lemonade Stand Game |
1 lesson |
Random Numbers |
Dice Spreadsheet |
1 lesson |
Simulating a Dice on a Spreadsheet |
Spreadsheet |
1 lesson |
Devices, Events, Trials and Outcomes |
Dice |
1 lesson |
Designing a Simulation |
Dice |
1 lesson |
Simulations in Excel |
Spreadsheet |
1 – 2 lessons |
Writing a Simulation |
Spreadsheet |
1 lesson |
Probabilities as decimals/fractions |
Spreadsheet |
2 lessons |
Writing a Report |
Spreadsheet Lesson: 10 A sample assessment |
4 lessons |
Practice Assessment |
2 lessons + 1 lesson feedback |
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Real Assessment |
2 lessons |
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Total: |
19 lessons (about 4 weeks) |
Either Excel OR google sheets can be used. (Note: The google sheets equivalent of F9 (force recalculation) is ctrl+R.). In the assessment it is permitted for the teacher to assist with spreadsheet related questions, IF the student describes what they want the spreadsheet to do.
This series of lessons is designed to be “supported self-study”, but students who have not used a spreadsheet before will need more support (especially in lesson 6).
Students should be encouraged to submit their assessment as a PRINTED word (or google) document.
Starting Simulations A simple win/lose example, to be done first with dice and then on a spreadsheet.
Starting Simulations Answers Model Achieved response to above.
More Simulations A range of other simulations.
Experiments
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Resources |
Time Scale (approx.) |
Reminder of PPDAC cycle Introduction to Experiments |
2 lessons
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Problem, Plan and Data |
In the Plan, emphasis should be placed on mangaing variations (ie keeping the conditions the same, both for each measurement and between samples - eg making sure that the level of exercise is the same). In Data, the emphasis should be on keeping the data paired.
Students plan and perform an experiment to see if exercise increases heartrate. |
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Analysis & Conclusion |
Document: section 3. This document introduces the scatterplot with the y=x line. It describes the mechanics of drawing the plot in Excel.
Document: section 4. This looks at describing the scatterplots.
Document: Section 5. This describes the mechanics of drawing a boxplot to describe the size of any shift.
The students can then repeat this exercise with the other 3 data files, and then complete the analysis for their heartrate data.
The conclusion is a restatement of the findings in the analysis.
Model Answer (1) The heartrate problem - at merit Model Answer (2) Throwing a hockey ball - at merit |
5 lessons |
Practice Assessment |
It is possible to do this standard with no practice, as the heartrate experiment can be seen as that. Model Answer (1) At merit.
Alternatively: Practice assessment and resources |
3 lessons |
Real Assessment |
The assessment has two different experiments. It is groupwork, with half of the groups working one task, and half on the other.
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5 lessons |
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Total: |
15 lessons (about 3 weeks) |
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Resources |
Time Scale (approx.) |
Right Angle Triangles Revision of the work from last year
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Booklet made up from the trigonometry sections of 10Ticks |
5 lessons |
Area of Triangle
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Theta Dimensions Ex. 11.04 p. 169 |
1 lesson |
Sine Rule Labelling sides/angles Finding sides Finding angles Applications
When tackling applications, students should draw a diagram, showing the triangle which they are using. |
Theta Dimensions Ex. 12.02 p. 178 Theta Dimensions Ex. 12.04 p. 180 Theta Dimensions Ex. 12.05 p. 181
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5 lessons |
Cos Rule Finding sides Finding angles Applications
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Theta Dimensions Ex. 13.02 p. 190 Theta Dimensions Ex. 13.04 p. 193 Theta Dimensions Ex. 13.06 p. 196 |
5 lessons |
Circular Measure Length of arc Area of sector
Only need the examples which are in degrees. Area of sector may need some more examples writing. |
Theta Dimensions Ex. 14.02 p. 209 Q3, 4a, 6b, 10b, 11. Theta Dimensions Ex. 14.04 p. 215 Q1b and Ex. 14.05 p. 216 Q1, 2.
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3 lessons |
Assessment Preparation Mixed Trig Examples Surveying questions |
Theta Dimensions Ex. 13.07 p. 200 Worksheet: Paddocks Worksheet: Paddocks (2) Answers. Also allows production of more worksheets. |
4 lessons |
Assessment Practice Real
A formula resource will be provided |
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5 lessons |
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Total: |
28 lessons (about 6 weeks) |
Questionnaires (Note: these documents need to be slightly rewritten. They have references to extra copies of the documentation which is not required, and no longer provided. The length of the assessment also requires discussion).
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Resources |
Time Scale (approx.) |
Assessment requirements Questionnare design |
Students need to have a good understanding of the requirments of the assessment, as it relates to the desin process. In particular, they should know that they need to produce: 1) a draft questionnaire which is put to a desk review 2) a re-drafted questionnaire which is put to a Pilot Survey and 3) a final questionnaire.
Document: Design a Questionnaire Lessons 1
The student instructions are included in the first document.
At the end of these lessons, students should complete this quick quiz: quiz |
2 lessons |
Writing the Introduction |
Document: Design a Questionnaire Lessons 3-4
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2 lessons |
Screening Questions Demographic Data |
Screening questions ensure that the sample is from the target population. Demographic questions enable the sample to be split into subgroups.
Document: Design a Questionnaire Lesson 5-6
The outcome should be that the students have an outline questionnaire, with a header (logo, attribution, confidentiality statement, and screening/demographic questions), but NOT the main body of questions. |
2 lesson |
Question types |
Students need to show a basic undersatnding of the different types of question available. As well as the role of screening/demographic questions, the very least that would be expected is an understanding of open/closed questions. This is a major requirment for Merit.
Document: Design a Questionnaire Lessons 7-8
Then students should complete the quiz here
THEN: students continue with their hairdresser questionnaire.
"Write the main body of the questions, making sure that you use three different question types, and that you can explain why you are using them." |
2 lessons |
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Real Assessment |
Portfolio style assessment |
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Total: |
13 lessons (about 3 weeks) |
Probability
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Resources |
Time Scale (approx.) |
Two Way Tables |
Two way table booklet |
3 lessons |
Relative Risk |
Nulake EAS 2.12 p24-27 |
2 lessons |
And Rule and Or Rule |
10Ticks L7-8 P1 p17-18 |
3 lessons |
Describing the Normal Distribution |
Teacher notes: Normal Distribution Lesson 1 |
1 lesson |
Approximate Areas (68%, 95%, 99%) |
Teacher notes: Normal Distribution Lessons 2-3 |
5 lessons |
Inverse Normal |
Th: p361-364 or Th2: p434-436 |
2 lessons |
Finding the mean and s.d using inverse normal (Excellence) |
Nulake EAS 2.12 p48 |
1 lesson |
End of Unit Assessment |
Nulake EAS 2.12 p49-55 |
2 lessons |
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Total: |
19 lessons (about 4 weeks) |
Text Book Reference: Th = Theta (Edition 1 'sky tower')
Th2= Theta (2nd edition 'climber')
