**Drills, Core Curriculum**

**, and Problem Solving through**

**Cooperative Work Groups,**influences our students to learn skills that are necessary for their future success. By Strengthening Confidence, Developing Strategical Thinking and Cooperative Teamwork through their math learning, Spirit of Math is teaching our students how to learn effectively, how to face challenges creatively and efficiently, and how to work cooperatively with others.

### KINDERGARTEN

Our balanced approach integrates the four elements of our program: Drills, Problem Solving, the Core Curriculum and Co-operative

Group work.

But the Spirit of Math program is much more than just math. We are using mathematics as a way to teach students how to learn, how to face challenges and how to work with others.

Here’s what we cover in Kindergarten:

#### DRILLS

- Regrouping: Making groups of tens (up to 10 and 20)
- Skip Counting
- Addition (1×1)

#### PROBLEM SOLVING

- An introduction to various word problems that develop logical thinking, spatial sense, and the language of mathematics. Topics include “lineups” (ordering objects/people), money, math riddles, tangrams, and 3D puzzles.

#### CORE CURRICULUM

- Regrouping: Making groups of 10 (adding to 8 one- and two- digit numbers)
- Strings: Adding and subtracting strings of numbers using various strategies
- Multiplication by 2, 5, and 10
- Patterning
- Symmetry
- Money
- Time
- Cartesian Geometry

#### ASSESSMENT

Grades are available online and parents receive three report cards each year. Our students will demonstrate their understanding through:

- Assignment of the Year (15 equations)
- Mini Wizards Problem Set
- Change it Up

### GRADE 1

Our balanced approach integrates the four elements of our program: Drills, Problem Solving, the Core Curriculum and Co-operative

Group work.

But the Spirit of Math program is much more than just math. We are using mathematics as a way to teach students how to learn, how to face challenges and how to work with others.

Here’s what we cover in Grade One:

#### DRILLS

- Regrouping: Making Tens (pairs of one-digit numbers)
- Addition (1×1 and 2×1)
- Super Speed Addition (1×1)
- Integer Addition (1×1)
- Multiplication (1×1)
- Division (1×1)

#### PROBLEM SOLVING

- Tangrams (geometric puzzles)
- Counting Shapes (e.g. How many triangles of all sizes are in this diagram?)
- Cuts and Pieces (finding the number of pieces based on parallel cuts of an object, and vice versa)
- “All but” problems (e.g. If there are 5 cats and all but 3 fell asleep, how many are asleep?)
- Date problems (e.g. What is today if 3 days after yesterday was Tuesday?)
- Venn Diagrams (introduction to sets)
- Alphametrics (introductory code-breaking)
- Pathways (finding the number of “paths” on a grid)
- Magic Squares (solving arrays of numbers where each row and column sum to the same number)
- Spirit of Math Contest (annual nation-wide contest)

#### CORE CURRICULUM: Number Theory

- Regrouping: Making groups of ten (adding 4 to 8 one- and two-digit numbers)
- Integers (adding positives and negatives)
- One-digit multiplication
- Fractions (labelling, adding/subtracting with like denominators)

#### COOPERATIVE GROUP WORK

- Working in groups of 3 to 4 students to solve the POW (Problem of the Week)
- Comparing and discussing homework solutions

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

Grades are available online and parents receive three report cards each year. Our students will demonstrate their understanding through:

- Three Unit Tests (at Lessons 9, 13 and 33)
- Final Comprehensive Exam
- Independent Assignments
- Assignment of the Year (25 equations)
- Wee Wizards problem set
- Problem Poster Project
- Mighty Mathematicians research project

### GRADE 2

#### DRILLS

- Addition (2×1 and 2×2)
- Super Speed Addition (1×1)
- Integer Addition (1×1 and 2×1)
- Multiplication (1×1 and 2×1)
- Long Multiplication (2×2)
- Division (1×1 and 2×1)

#### PROBLEM SOLVING

- Consecutive number problems (e.g. finding the number of pages read in a book given the first and last pages read)
- Heads & Legs (e.g. given the number of heads and legs counted, how many of a particular two-legged or four-legged animal are there?)
- Venn Diagrams (extension from grade 1, including the “neither” category)
- Before & After/Date Problems (e.g. what is 3 days before 2 days after Sunday?)
- “Handshakes” problems (e.g. If 15 people all shook hands with each other, how many handshakes is that?)
- Alphamath (introductory code-breaking)
- Sum of a Series (e.g. find the sum of all positive integers from 1 to 20)
- Chords/Lines and Regions (dividing up a circle using straight lines (chords) to yield a maximum number of regions and extracting pattern based on the number of chords used)
- Rate Problems (e.g. If I can eat 3 apples in 15 minutes and you can eat 6 apples in 15 minutes, how many apples can we eat together in 10 minutes?)
- Spirit of Math Contest (annual nation-wide contest)

#### CORE CURRICULUM: Number Theory

- Regrouping: Making groups of ten (adding 4 to 8 one- and two-digit positive and negative numbers)
- Integers (adding positives and negatives)
- Primes, composites, factors, and perfect squares
- Rationals (fractional distances on a number line)

#### COOPERATIVE GROUP WORK

- Working in groups of 3 to 4 students to solve the POW (Problem of the Week)
- Comparing and discussing homework solutions

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

Grades are available online and parents receive three report cards each year. Our students will demonstrate their understanding through:

- Three Unit Tests (at Lessons 5, 13, 23 and 33)
- Final Comprehensive Exam
- Independent Assignments (Black & Orange Gumdrops, January Thaw)
- Assignment of the Year (creating 50 different equations equaling any number from 1-100 using only 4 digits)
- Wise Wizards problem set
- Problem Poster Project
- Mighty Mathematicians research project

### GRADE 3

Our balanced approach integrates the four elements of our program: Drills, Problem Solving, the Core Curriculum and Co-operative Group Work.

But the Spirit of Math program is much more than just math. We are using mathematics as a way to teach students how to learn, how to face challenges and how to work with others.

Here’s what we cover in Grade Three:

#### DRILLS

- Addition (2×2 and 3×2)
- Integer Addition (2×1 and 2×2)
- Multiplication (2×1 and 3×1)
- Division (2×1 and 3×1)
- Long Multiplication (3×2 with decimals)
- Long Division (2×1 and 3×2)
- Perfect Squares to 25
^{2} - Fraction-Decimal Equivalents (half, thirds, fourths, fifths, ninths, and tenths)

#### PROBLEM SOLVING

- Date problems (extending from grades 1 and 2, solving using equations instead of number lines)
- “All but” problems (e.g. If there are 5 cats and all but 3 fell asleep, how many are asleep?)
- Interval problems (extending from Cuts & Pieces problems – e.g. Eight flowers are each planted in a row 40 centimetres apart. How far apart is the first flower and the last flower?)
- Venn Diagrams (with 3 circles)
- Averages (calculating average based on a data set, calculating an increase in average, comparing averages)
- Pathways with 2 grids
- Spirit of Math Contest (annual nation-wide contest)
- CNML Contest (Canadian National Mathematics League)

#### CORE CURRICULUM: Number Theory

- Regrouping: Making groups of ten (adding 8 to 10 two-digit positive and negative numbers)
- Relocation with multiplication and division
- Primes, composites, and factors
- Fractions (mixed and improper fractions, reducing by prime factoring, comparing and ordering fractions with different numerators and denominators, fractions with zero, i.e. undefined and indeterminate)

#### COOPERATIVE GROUP WORK

- Working in groups of 3 to 4 students to solve the POW (Problem of the Week)
- Comparing and discussing homework solutions

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Five Unit Tests (at Lessons 5, 11, 20, 25 and 33)
- Final Comprehensive Exam
- Independent Assignments (Tricks or Treats, Jettsie & Joanie, Little Spirit)
- Assignment of the Year (creating 75 different equations equaling any number from 1-100 using only 4 digits)
- Wise Wizards 2 problem set
- Problem Poster Project
- Famous Mathematicians research project

### GRADE 4

Our balanced approach integrates the four elements of our program: Drills, Problem Solving, the Core Curriculum and Co-operative Group work.

Here’s what we cover in Grade Four:

#### DRILLS

- Integer Addition (2×2)
- Multiplication (3×1)
- Division (2×1 and 3×1)
- Long Multiplication (3×2 with decimals)
- Long Division (4×2 with decimals)
- Perfect Squares to 25
^{2}

#### PROBLEM SOLVING

- Consecutive number problems (extending from grade 2, incorporating consecutive odd/even numbers)
- “Handshakes” problems (e.g. If 15 people all shook hands with each other, how many handshakes is that?)
- Probability (calculating mathematical probability)
- Heads & legs (e.g. given the number of heads and legs counted, how many of a particular two-legged or four-legged animal are there?)
- Arrangements of Letters in a Word (finding the number of different ways the letters in a given word can be arranged; introduction to combinatorics)
- Counting pathways using factorials
- Rate Problems (extending from grade 2)
- Least Common Multiple (e.g. Mrs. Cherry bakes a pie every 42 minutes, and Mr. Pickle makes a sandwich every 28 minutes. If they both serve their first dish at 9 a.m., when will they next serve a dish at the same time?
- Spirit of Math Contest (annual nation-wide contest)
- CNML Contest (Canadian National Mathematics League)

#### CORE CURRICULUM: Number Theory

- Regrouping: Making groups of ten (adding various two- and three-digit positive and negative numbers)
- Positive and negative integers (integral distance)
- Relocation with multiplication and division
- Prime numbers and prime factoring
- Tests of Divisibility
- Geometry (points, lines, angles, and polygons)

#### COOPERATIVE GROUP WORK

- Working in groups of 3 to 4 students to solve the POW (Problem of the Week)
- Comparing and discussing homework solutions

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

- Group research and presentation

#### ASSESSMENT

- Five Unit Tests (at Lessons 5, 12, 18, 25 and 37)
- Final Comprehensive Exam
- Independent Assignments (Grade Four Problem Sets, These Will Haunt You)
- Assignment of the Year (creating 100 different equations equaling all numbers from 1-100 using only 4 digits)
- Wise Wizards 3 problem set
- Problem Poster Project
- Famous Mathematicians research project

### GRADE 5

Our balanced approach integrates the four elements of our program: Drills, Problem Solving, the Core Curriculum and Co-operative Group Work.

Here’s what we cover in Grade Five:

#### DRILLS

- Multiplication (3×1 – 80 questions)
- Division (3×1 – 80 questions)
- Integer Addition (3×3 – 80 questions)

#### PROBLEM SOLVING

- Weekly PODs (Problem of the Day) – group problem-solving in a variety of topics
- Independent problem set assignments

#### CORE CURRICULUM: Number Theory

- Grade 5 is the foundational year where students learn a variety of core topics in great depth. The grades 1-4 curriculum build up to the grade 5 year, and grades 6 onward build upon the grade 5 year

- Relocation Property
- Signed Numbers
- Order of Operations
- Factors, Multiples, and Primes
- Number Sets

#### COOPERATIVE GROUP WORK

- Working in groups of 3 to 4 students to solve the POD (Problem of the Day)
- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Four Unit Tests (at Lessons 6, 12, 21, and 35)
- Final Comprehensive Exam
- Independent Assignments (Mastermind, Fifty Mix) with corresponding tests
- Assignment of the Year (creating 100 different equations equaling all numbers from 1-100 using only 4 digits and keeping digits in order)

### GRADE 6

Here’s what we cover in Grade Six:

#### DRILLS

- Long Multiplication (up to 5 digits, with decimals
- Perfect Squares (up to 60
^{2}) - Fraction-Decimal Expansions (half to twelfths)
- Oral Percent Drills

#### PROBLEM SOLVING

- Major independent problem set assignments

#### CORE CURRICULUM: Number Theory

- Rationals (adding and subtracting using LCMs, multiplying and dividing using prime factoring, distances on a number line, ordering rationals)
- Ratio, Rate, Percent, and Proportion (solving and simplifying ratios, rate proportion and percent problem solving, percent-decimal-fraction conversions)
- Geometry (points, lines, angles, angle theorems, classification of triangles, Pythagorean theorem, similar and congruenttriangles, polygons, circle geometry)

#### COOPERATIVE GROUP WORK

- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively problem solve
- Developing critical thinking and decision-making skills

#### ASSESSMENT

Grades are available online and parents receive three report cards

Our students will demonstrate their understanding through:

- Six Unit Tests (at Lessons 17, 23, 25, 30, 35, and 36)
- Final Comprehensive Exam
- Independent Assignments (Brain Bogglers I & II, Mind Benders) with corresponding tests

### GRADE 7

Our balanced approach integrates the four elements of our program: Drills, Problem Solving, the Core Curriculum and Co-operative Group Work.

Here’s what we cover in Grade Seven:

#### DRILLS

- Rational Addition: practice adding rationals of different numerators and denominators

#### PROBLEM SOLVING

- Math Challenge Assignments: seven different problem sets assigned throughout the year covering a variety of challenging types of problems

#### CORE CURRICULUM:**In-depth focus on problem solving**

- Counting Shapes (e.g. How many rectangles of all sizes are in a given diagram?)
- Arrangements of Letters in a Word (calculating combinations with factorials)
- Pathways (grids, non-grids, and word formations)
- Pascal’s Triangle (patterns and combinatorics)
- Patterns (sequences and series)
- Patterns involving Prime Factoring
- Measurement (triangle geometry, Heron’s Formula, Pick’s Rule, area and perimeter of polygons, metric conversions)
- Venn Diagrams (introducing set notation)
- Number Bases (including performing operations in different number bases)
- Angles on a Clock (finding the angle between the minute hand and the hour hand based on different times, and vice versa)

#### COOPERATIVE GROUP WORK

- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Nine Unit Tests (at Lessons 5, 7, 8, 12, 13, 17, 21, 28, and 29)
- Final Comprehensive Exam

### GRADE 8

Here’s what we cover in Grade Eight:

#### DRILLS

- Simplifying Radicals: using knowledge of prime factoring to mentally simplify radicals into mixed form

#### PROBLEM SOLVING

- Jet Set Assignments: eight different problem sets assigned throughout the year covering a variety of challenging types of problems. The aim is to improve at problem solving and to prepare for math contests.

#### CORE CURRICULUM

- Radicals (various operations and applications)
- Exponents (exponent rules, patterns)
- Algebra (solving and graphing equations and inequalities, linear relations)

#### COOPERATIVE GROUP WORK

- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Three Unit Tests (at Lessons 11, 22, and 28)
- Seven Problem Solving Tests based on the Jet Set Assignments (at Lessons 6, 10, 14, 18, 22, 26, and 30)
- Final Comprehensive Exam

### GRADE 9

Here’s what we cover in Grade Nine:

#### DRILLS

- There are no new drills in grade 9; however, students consolidate the skills they have acquired in previous grades through the core topics this year

#### PROBLEM SOLVING

- Cerebral Contortions: challenging weekly assignments that require students to use their previous knowledge in a problem-solving capacity, yet require a deeper level of thinking.
- The Big 100: an independent problem solving assignment intended to be a preparation for math contests the students have the option of writing

#### CORE CURRICULUM

- Review of geometry and algebra
- Solving systems of equations
- Factoring polynomials
- Absolute value
- Graphing techniques and transformations

#### COOPERATIVE GROUP WORK

- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Weekly quizzes based on the Cerebral Contortion assignments (from Lessons 4 to 21)
- Five Unit Tests (at Lessons 6, 9, 13, 26, and 32)
- Final Comprehensive Exam

### GRADE 10

Here’s what we cover in Grade Ten:

#### DRILLS

- Mental Arithmetic: Starting in grade 1, Spirit of Math students complete their class with an oral mental math question given by the teacher (when it is answered correctly, the class may be dismissed). In grade 10, students do mental arithmetic drills with the question given on paper, where they need to mentally calculate the answer and write it down.
- Radian/degree equivalents: students mentally calculate radian measurements given a degree measurement, and vice versa
- Trigonometry drills: students mentally calculate trigonometric ratios of common angles given in degrees and radians

#### PROBLEM SOLVING

- Cerebral Contortions: challenging weekly assignments that require students to use their previous knowledge in a problem-solving capacity, yet require a deeper level of thinking.
- Math Challengers: assignments based on various topics (algebra, logic, and exponents and factoring) where the focus shifts from solving the problem and arriving at the correct answer to presenting thorough, well-organized solutions
- Trigonometry contest questions: to consolidate their knowledge from the trigonometry unit this year, and to help prepare for upcoming math contests the students have the option of writing

#### Core Curriculum

- Trigonometry
- Logarithms
- Complex numbers and polar coordinates
- Conics

#### COOPERATIVE GROUP WORK

- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Weekly quizzes based on the Cerebral Contortion assignments (from Lessons 9 to 21, 27, 37)
- Three Unit Tests (at Lessons 7, 13, and 19)
- Final Comprehensive Exam

### GRADE 11

Here’s what we cover in Grade Eleven:

#### DRILLS

- Mental Arithmetic: In grade 11, students continue practicing their mental calculation skills

#### PROBLEM SOLVING

- Problem sets based on the following topics:

- Functions
- Logarithms
- Algebraic equations
- Sequences and series

- Geometry Mania: challenging problems based on a variety of concepts in 2- and 3-dimensional geometry

#### CORE CURRICULUM

- The grade 11 year focuses on Calculus. The material taught is comparable to that of a first-year university calculus course. Topics covered include:

- Limits
- Derivative rules
- 2
^{nd}and 3^{rd}degree derivatives - Derivatives of Logarithmic, Exponential & Trigonometric Functions
- Implicit Differentiation
- Partial Differentiation
- Maximum-Minimum Problems
- Rates of Change Problems
- Curve Sketching
- Integrals & Applications

#### COOPERATIVE GROUP WORK

- Comparing and discussing homework solutions to independent assignments and core work

- Strengthening communication and social skills
- Learning how to share ideas on how to collaboratively solve problems
- Developing critical thinking and decision-making skills

#### ASSESSMENT

- Tests based on problem sets (at Lessons 6, 11, 18, and 27)
- Six Unit Tests (at Lessons 8, 16, 22, 25, 31, and 37)
- Final Comprehensive Exam