TFCMATHS 91F : Foundation Mathematics 1


2024 Semester Two (1245) (15 POINTS)

Course Prescription

This mathematics course aims to promote an understanding of number skills, including an introduction to algebra. Students will learn how to use simple technology and develop their problem solving abilities.

Course Overview

This course focuses on the development of mathematical skills and the understanding of underpinning mathematical concepts. There is a need to build the confidence of students new to tertiary education who may have had variable learning experiences with mathematics, as well as to prepare them for future studies in mathematical sciences. In particular, we aim to set a mathematical platform that includes these key themes:

Number Sense which includes working with accepted mathematical conventions and notations;

Proportional processing with fractions, ratio, percentages, and how these are applied across various settings;

Measurement themes including Lengths, areas (formulated, surface and approximate) and volumes;

Algebraic manipulative skills around simplifying, expanding and factorizing;

Solving types of equations

Experiences in interpreting and solving problems using any, or combinations of, the above.

Successful completion of this course will meet the University of Auckland numeracy entry requirement. Further, completion of this course with at least a C+ grade will provide students with entry to TFC MATHS 92F (in the following year).

Course Requirements

Restriction: MATHS 91P, 92F

Capabilities Developed in this Course

Capability 1: People and Place
Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking
Capability 6: Communication
Capability 7: Collaboration
Capability 8: Ethics and Professionalism

Learning Outcomes

By the end of this course, students will be able to:
  1. Answer questions involving mathematical situations that require problem-solving strategies, including the key numeracy strategies with additive, multiplicative and proportional backgrounds. (Capability 3, 4, 5, 6 and 7)
  2. Apply order of operations ideas, including integers, fractions and substitution in formulae. (Capability 3 and 5)
  3. Perform algebraic manipulations with formulae, including transposition, and be able to solve linear, quadratic and exponential equations in mathematical situations and other models or contexts. (Capability 3, 4, 5 and 6)
  4. Use straightforward graphs to model linear rates and other situations. (Capability 3, 4, 5 and 6)
  5. Solve problems involving time and rate calculations, with Pythagoras’ Theorem, (Capability 3, 4 and 5)
  6. Apply the metric system to problems with standard two-dimensional shapes (perimeters, areas) and standard three-dimensional shapes (surface area and volumes) and the trapezoidal rule. (Capability 4, 5 and 6)
  7. Use a calculator proficiently and with large and small numbers including fractions and decimals, in mathematical and other situations, so that reasonable answers are obtained. (Capability 3, 4, 5 and 6)
  8. Apply their learning of mathematics critically and actively contribute to group collaborative activities and discussions in order to provide group solution(s) to several tasks. (Capability 1, 3, 4, 5, 6, 7 and 8)


Assessment Type Percentage Classification
Canvas quizzes (best 8 of 10) 10% Individual Coursework
Assignments (3 written) 12% Individual Coursework
Team or collaborative project tasks (2) 8% Group & Individual Coursework
Tests - Chapter, Mid Semester, Final 70% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8
Canvas quizzes (best 8 of 10)
Assignments (3 written)
Team or collaborative project tasks (2)
Tests - Chapter, Mid Semester, Final
Students must achieve a minimum mark of at least 35% on the final test in order to pass the course. 


Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at

Whanaungatanga and manaakitanga are fundamental principles of our Tuākana Mathematics programme which provides support for Māori and Pasifika students who are taking mathematics courses. The Tuākana Maths programme consists of workshops and drop-in times, and provides a space where Māori and Pasifika students are able to work alongside our Tuākana tutors and other Māori and Pasifika students who are studying mathematics.

Key Topics

  1. Fundamentals, including Multiplicative ideas, Integers, Coordinates, Areas;
  2. Introductory Number Sense, including Scientific notation, Set notation, Logarithm rules;
  3. Making sense of Proportion, including Fractions, Ratios, Percentage calculations and situations;
  4. A sense of Measurement, including Conversions, Limits, Perimeter, Area (using formulae, surface and approximate), and Volumes of standard and special solids;
  5. Introduction to Algebra, including notation, simplifying and expanding expressions, and factorizing;
  6. Equations, including Linear, Quadratic, and Exponential solutions, Transposition, Inequalities, and Simultaneous systems.

Special Requirements

  • Expect full attendance and participation in lectures.
  • Each aspect of course work is compulsory.
  • The Mid-Semester Test will run either in the evening outside of normal hours, or across two class sessions, usually held in the sixth week of semester, according to availability of venues. Any updates will be shown in the schedule provided in Week One.

Workload Expectations

This course is a standard 15-point course and students are expected to spend 10 hours per week involved in each 15-point course that they are enrolled in. For each week of this course, you can expect 5 hours of lectures, including a tutorial or assessment, plus 2 hours of reading thinking, and doing homework of the content, and 3 hours of work on assignments, e-quizzes and/or test preparation.

Delivery Mode

Campus Experience

  • Tertiary Foundation Certificate students are expected to attend and participate on Campus and are therefore not remote students. 
  • Attendance is required at scheduled activities, including classes and tutorials (such as, Group Work Collaborative tasks which receive credit for components of the course).
  • Lectures will be available as recordings. Other learning activities, including tutorials, will not be available as recordings. The course will not include live online events including tutorials. 
  • Attendance on campus is required for the tests and the Group Work Collaborations. The Quizzes may be submitted electronically on Canvas - the best eight out of ten will count toward the final mark. 
  • The activities for the course are scheduled as a standard weekly timetable delivery. 

Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

  • Course books (usually Part A and Part B) distributed in Weeks One and Six respectively;
  • Standard scientific calculator (available in UBS);
  • Ruler for measuring and graphing;
  • Squared paper for graphing;

Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

Past tests and their solutions will be provided on Canvas in Week Two and in Week Seven.

Including all the rules of logarithms on the Test Formulae sheet;

Acknowledging that our classes are mixed ability groupings, so people work at different paces and have different learning backgrounds.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.


The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter


Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:54 a.m.