New Brunswick · Grade 11
Foundations of Mathematics 110
New Brunswick’s Grade 11 math course, from Logical Reasoning to Number.
- Units
- 4
- Lessons
- 10
- Skills
- 28
- Provincial exam
- None
- Official curriculum
- New Brunswick Department of Education and Early Childhood Development
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 5 skills
Logical Reasoning
Making and proving conjectures
Making conjectures by inductive reasoning
I can gather evidence from examples and state a conjecture.
Official code: LR1
Proving conjectures deductively
I can prove a conjecture is always true using deductive reasoning.
Official code: LR1
Finding the error in a false proof
I can find the invalid step in a flawed proof.
Official code: LR1
Puzzles and games: numerical reasoning
Finding a strategy in a number puzzle or game
I can find and test a strategy to win a number game.
Official code: LR2
Justifying a puzzle solution
I can justify why a puzzle strategy always works.
Official code: LR2
The official wording · 5 outcomes
- LR1
- Analyze and prove conjectures using logical reasoning
- LR1
- prove conjectures using logical reasoning, to solve problems
- LR1
- Analyze and prove conjectures using logical reasoning
- LR2
- Analyze puzzles and games that involve numerical reasoning, using problem-solving strategies
- LR2
- puzzles and games that involve numerical reasoning, using problem-solving strategies
Key ideas
Inductive reasoning moves from specific observed cases to a general conjecture.
Working backward from a winning position reveals the moves that force a win.
A conjecture is a plausible statement, not yet proven — more examples strengthen belief but never prove it.
Looking for a numerical pattern (multiples, remainders) often exposes the key positions.
A single counterexample disproves a conjecture.
Watch out for
- Believing that checking many examples proves a conjecture true.
- Treating each game as luck rather than looking for a repeatable strategy.
- Ignoring a case that breaks the pattern instead of treating it as a counterexample.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 9 skills
Geometry
Deriving proofs of angle and triangle properties
Proving angle relationships
I can prove why two angles are equal or supplementary.
Official code: G1
Proving triangle properties
I can prove the triangle angle-sum and related triangle properties.
Official code: G1
Structuring a formal geometric proof
I can lay out a multi-step geometric proof with statements and reasons.
Official code: G1
Solving angle and triangle problems
Solving angle problems
I can find unknown angles using angle relationships.
Official code: G2
Solving triangle problems
I can find unknowns in triangles using triangle properties.
Official code: G2
Multi-step angle and triangle problems in context
I can solve real problems that combine several angle and triangle properties.
Official code: G2
The sine law and cosine law
Solving triangles with the sine law
I can solve a triangle using the sine law.
Official code: G3
Solving triangles with the cosine law
I can solve a triangle using the cosine law.
Official code: G3
The ambiguous case of the sine law
I can decide how many triangles are possible in the ambiguous (SSA) case.
Official code: G3
The official wording · 9 outcomes
- G1
- Derive proofs that involve the properties of angles
- G1
- Derive proofs that involve the properties of angles and triangles
- G1
- Derive proofs that involve the properties of angles and triangles
- G2
- Solve problems that involve the properties of angles
- G2
- properties of angles and triangles
- G2
- Solve problems that involve the properties of angles and triangles
- G3
- Solve problems that involve the cosine law and the sine law
- G3
- problems that involve the cosine law and the sine law
- G3
- the cosine law and the sine law, including the ambiguous case
Key ideas
Vertically opposite angles are equal because each is supplementary to the same angle.
Set unknown angles equal or supplementary based on the relationship, then solve.
The sine law relates each side to the sine of its opposite angle: a/sin A = b/sin B = c/sin C.
Corresponding and alternate angles at parallel lines are equal by the parallel-line postulate.
Parallel-line pairs give equations linking several unknown angles.
Watch out for
- Measuring angles with a protractor and calling it a proof.
- Treating co-interior angles as equal rather than supplementary.
- Pairing a side with the wrong (non-opposite) angle.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 7 skills
Relations and Functions
Systems of linear inequalities
Graphing a single linear inequality
I can graph a linear inequality and shade the correct region.
Official code: RF1
Solving a system of linear inequalities
I can find the region that satisfies a whole system of inequalities.
Official code: RF1
Modelling a real situation with inequalities
I can turn a real constraint problem into a system of inequalities and read its region.
Official code: RF1
Characteristics of quadratic functions
Vertex and axis of symmetry
I can find the vertex and axis of symmetry of a parabola.
Official code: RF2
Intercepts and roots
I can find the intercepts of a quadratic and relate them to its graph.
Official code: RF2
Domain and range
I can state the domain and range of a quadratic function.
Official code: RF2
Modelling with quadratic functions
I can use a quadratic model to answer a real question.
Official code: RF2
The official wording · 7 outcomes
- RF1
- problems that involve systems of linear inequalities in two variables
- RF1
- Model and solve problems that involve systems of linear inequalities in two variables
- RF1
- Model and solve problems that involve systems of linear inequalities
- RF2
- characteristics of quadratic functions, including vertex, intercepts, domain and range, axis of symmetry
- RF2
- characteristics of quadratic functions, including vertex, intercepts
- RF2
- characteristics of quadratic functions, including vertex, intercepts, domain and range
- RF2
- Demonstrate an understanding of the characteristics of quadratic functions
Key ideas
The boundary line is solid for ≤ or ≥ and dashed for < or >.
The vertex is the highest or lowest point of a parabola.
Test a point (often the origin) to decide which side to shade.
The axis of symmetry is the vertical line through the vertex.
Every point in the shaded half-plane satisfies the inequality.
Watch out for
- Using a solid line for a strict inequality (< or >).
- Reading the y-intercept as the vertex.
- Shading the wrong side without testing a point.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 7 skills
Number
Renting, leasing and buying
Comparing the costs of renting, leasing and buying
I can compare the total cost of renting, leasing, and buying.
Official code: N1
Justifying a rent-lease-buy decision
I can justify a rent, lease, or buy decision using costs and benefits.
Official code: N1
Analyzing an investment portfolio
Interest rate, rate of return, and total return
I can compute the rate of return and total return of an investment.
Official code: N2
Evaluating a portfolio's performance
I can evaluate a portfolio by comparing return and risk.
Official code: N2
Diversifying a portfolio
I can explain how diversifying a portfolio changes its total return and risk.
Official code: N2
Personal budgets
Building a personal budget
I can build a personal budget and see whether it balances.
Official code: N3
Adjusting a budget to meet a goal
I can adjust a budget to reach a goal or handle a change.
Official code: N3
The official wording · 7 outcomes
- N1
- Analyze costs and benefits of renting, leasing and buying
- N1
- Analyze costs and benefits of renting, leasing and buying
- N2
- Analyze an investment portfolio in terms of interest rate, rate of return, total return
- N2
- Analyze an investment portfolio in terms of interest rate, rate of return, total return
- N2
- Analyze an investment portfolio in terms of interest rate, rate of return, total return
- N3
- Solve problems that involve personal budgets
- N3
- Solve problems that involve personal budgets
Key ideas
Total cost includes all payments plus fees, minus any resale or equity value.
Rate of return = gain divided by amount invested, as a percent.
Net (take-home) income is what is available to budget, not gross pay.
Leasing usually has lower monthly payments but no ownership at the end.
Total return combines income (interest, dividends) and change in value.
Watch out for
- Comparing only the monthly payment and ignoring total cost and ownership.
- Confusing the stated interest rate with the actual rate of return.
- Budgeting from gross pay instead of net income.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
Which course?
New Brunswick has 3 math courses for Grade 11. Here they are side by side.
- Financial and Workplace Mathematics 1104 units · 30 skillsNo provincial examWhat it coversGeometry · Number · Algebra · Statistics
- Foundations of Mathematics 110This course4 units · 28 skillsNo provincial examWhat it coversLogical Reasoning · Geometry · Relations and Functions · Number
- Pre-Calculus 1103 units · 30 skillsNo provincial examWhat it coversAlgebra and Number · Trigonometry · Relations and Functions
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows New Brunswick’s own curriculum for Foundations of Mathematics 110.
Textbooks
The course’s curriculum guide names its core resource:
“the core resources for Foundations of Mathematics 110 and 120 … (NB Foundations of Mathematics 11 Ch.8.5-8.6, or Foundations of Mathematics 12 Ch.1.5-1.6)”
- Foundations of Mathematics 11
From the course’s curriculum guide, read October 28, 2026. gnb.ca
Study it in MapleMind
MapleMind teaches Foundations of Mathematics 110 one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Foundations of Mathematics 110 organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
- 29
- Fillable fields
- 1,383
- Price
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Questions about Foundations of Mathematics 110
What is Foundations of Mathematics 110?
New Brunswick’s Grade 11 math course: 4 units and 28 skills, from Logical Reasoning to Number.
What units are in Foundations of Mathematics 110?
1. Logical Reasoning, 2. Geometry, 3. Relations and Functions and 4. Number.
Is there a provincial exam for Foundations of Mathematics 110?
No. New Brunswick gives no provincial exam for Foundations of Mathematics 110.
What textbook does Foundations of Mathematics 110 use?
The course’s curriculum guide names its core resource: Foundations of Mathematics 11.
What comes after Foundations of Mathematics 110?
Calculus 120, Financial and Workplace Mathematics 120, Foundations of Mathematics 120, Pre-Calculus 120A and Pre-Calculus 120B.
Can MapleMind help with Foundations of Mathematics 110?
Yes. MapleMind teaches every skill of Foundations of Mathematics 110, step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
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