# Grade Six Math Curriculum

# Grade Six Math Curriculum

## Introduction

#### Table of Contents

## Overall and Specific Expectations

### Numbers

**A. Number Sense **Students will demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life. They will

**1. Rational numbers**

- read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life.
- read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines.
- compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts.

**2. Fractions and Decimals,and Percents**

- read, represent, compare, and order decimal numbers up to thousandths, in various contexts.
- round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts.
- describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts.

**B.Operations**:

Students will use knowledge of numbers and operations to solve mathematical problems encountered in everyday life. They will

**1.Properties and Relationships**

- use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations.

**2. ****Math Facts**

- understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and 10.

**3. Mental Math **

- use mental math strategies to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50%, and explain the strategies used.

**4. Addition and Subtraction**

- represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms.
- add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts.

**5. Multiplication and Division**

- represent composite numbers as a product of their prime factors, including through the use of factor trees.
- represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms.
- represent and solve problems involving the division of three-digit whole numbers by decimal tenths, using appropriate tools, strategies, and algorithms, and expressing remainders as appropriate.
- multiply whole numbers by proper fractions, using appropriate tools and strategies.
- divide whole numbers by proper fractions, using appropriate tools and strategies.
- represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies.
- solve problems involving ratios, including percents and rates, using appropriate tools and strategies.

### Algebra

**A. Patterns and Relationships **Students will identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts. They will

**1. Patterns **

- identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and specify which growing patterns are linear.
- create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations.
- determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns.
- create and describe patterns to illustrate relationships among whole numbers and decimal numbers.

**B. Equations and Inequalities**Students will demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts. They will

**1. Variables and Expressions**

- add monomials with a degree of 1 that involve whole numbers, using tools.
- evaluate algebraic expressions that involve whole numbers and decimal tenths.

**2. Equalities and Inequalities**

- solve equations that involve multiple terms and whole numbers in various contexts and verify solutions.
- solve inequalities that involve two operations and whole numbers up to 100 and verify and graph the solutions.

**C. Coding**Students will solve problems and create computational representations of mathematical situations using coding concepts and skills. They will

**1. Coding Skills**

- solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves conditional statements and other control structures.
- read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code.

**D. Mathematical Modelling**Students will apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

### Data

**A. Data Literacy **Students will manage, analyse, and use data to make convincing arguments and informed decisions, in various contexts drawn from real life. They will

**1. Data Collection and Organization **

- describe the difference between discrete and continuous data and provide examples of each.
- collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals.

**2. Data Visualization**

- select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs.
- create an infographic about a data set, representing the data in appropriate ways, including in tables, histograms, and broken-line graphs, and incorporating any other relevant information that helps to tell a story about the data.

**3. Data Analysis **

- determine the range as a measure of spread and the measures of central tendency for various data sets and use this information to compare two or more data sets.
- analyse different sets of data presented in various ways, including in histograms and broken- line graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions.

**B. Probability**Students will describe the likelihood that events will happen and use that information to make predictions. They will

**1. Probability**

- use fractions, decimals, and percents to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions.
- determine and compare the theoretical and experimental probabilities of two independent events happening.

### Spatial Sense

**A. Geometric and Spatial Reasoning **Students will describe and represent shape, location, and movement by applying geometric properties and spatial relationships to navigate the world around them. They will

**1. Geometric Reasoning**

- create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry.
- construct three-dimensional objects when given their top, front, and side views.
- draw top, front, and side views of objects, and match drawings with objects.

**2. Location and Movement**

- plot and read coordinates in all four quadrants of a Cartesian plane and describe the translations that move a point from one coordinate to another.
- describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations.

**B. Measurement**Students will compare, estimate, and determine measurements in various contexts. They will

**1. The Metric System**

- measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa.

** 2. Angles**

- use a protractor to measure and construct angles up to 360° and state the relationship between angles that are measured clockwise and those that are measured counterclockwise.
- use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures.

** 3.Area and Surface Area**

- determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas.
- create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas.
- determine the surface areas of prisms and pyramids by calculating the areas of their two- dimensional faces and adding them together.

### Financial Literacy

**A. Money and Finances **Students will demonstrate an understanding of the value of Canadian currency. They will

**1. Money Concepts**

- describe the advantages and disadvantages of various methods of payment that can be used to purchase goods and services.

** 2.Financial Management**

- identify different types of financial goals, including earning and saving goals, and outline some key steps in achieving them.
- identify and describe various factors that may help or interfere with reaching financial goals.

** 3.Consumer and Civic Awareness**

- explain the concept of interest rates and identify types of interest rates and fees associated with different accounts and loans offered by various banks and other financial institutions.
- describe trading, lending, borrowing, and donating as different ways to distribute financial and other resources among individuals and organizations.

** **

## List of Skills

## Evaluation

Objective evaluation is believed to be one of the most essential parts of teaching mathematics. In Genius Math, we use different tools and methods to evaluate the mathematical knowledge of students and their progress. Our evaluation process consists of three stages: before teaching sessions, during teaching sessions and after teaching sessions.

**Initial Assessment Test**

Before starting our teaching sessions, we administrate an assessment test to obtain some insights on the strengths and weaknesses of students and their previous math knowledge. This key information helps us to come up with a special plan for every single student.**Standard Problems**

During teaching sessions, we use a combination of different resources providing standard problems that are designed by famous mathematicians all over the world to improve the problem-solving skills of students. Among those resources are Math Kangaroo Contests, CEMC (University of Waterloo), AMC (American Mathematics Competitions), and even IMO (International Mathematics Olympiad), the latter might be considered for those who want to tackle more challenging problems or prepare for math olympiads. We use these problems to design homework, quizzes, and tests for our students based on their grades, needs and goals. As a matter of fact, such problems can be used to unveil the depth of students’ mathematical understanding.**Final Assessment Test**When teaching sessions are over, students are asked to take another assessment test aiming to show their real progress in mathematics.

## Most Common Challenging Topics

- Fractions and decimals
- Mixed operations
- Prime factorization
- Data analysis
- Mixed transformations in coordinate plane
- Angle and area
- Probability

## What We Can Offer

- To review and practice their class notes and handouts
- To be helped with their homework, quizzes, and tests
- To improve their math skills in general
- To level up (e.g., moving from B- to B+)
- To get A+
- To learn topics beyond curriculum
- To prepare for math competitions