## Introduction

Around the time children reach the second grade, their thinking and problem-solving skills begin to take off. They start to explore specific activities that interest them and learn skills like tying their own shoelaces, making them feel more independent and confident. This is also the age at which children influence each other easily. In the meantime, understanding of mathematical concepts becomes even more critical for students. The information provided in this page are identical to the Official Grade Two Math Curriculum established by the Ministry of Education. ## Overall and Specific Expectations

The overall expectations are divided in five main categories each of which contains several subcategories. Every subcategory lists specific expectations for grade 2 in more detail.

### 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. Whole numbers

• read, represent, compose, and decompose whole numbers up to and including 200, using a variety of tools and strategies, and describe various ways they are used in everyday life.
• compare and order whole numbers up to and including 200, in various contexts.
• estimate the number of objects in collections of up to 200 and verify their estimates by counting.
• count to 200, including by 20s, 25s, and 50s, using a variety of tools and strategies.
• describe what makes a number even or odd.

2. Fractions

• use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 10 items among 2, 3, 4, and 6 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts.
• recognize that one third and two sixths of the same whole are equal, in fair-sharing 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 addition and subtraction, and the relationships between addition and multiplication and between subtraction and division, to solve problems and check calculations.

2. Math Facts

• recall and demonstrate addition facts for numbers up to 20, and related subtraction facts.

3. Mental Math

• use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 50, and explain the strategies used.

• use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 100.

5. Multiplication and Division

• represent multiplication as repeated equal groups, including groups of one half and one fourth, and solve related problems, using various tools and drawings.
• represent division of up to 12 items as the equal sharing of a quantity, and solve related problems, using various tools and drawings.

### 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 a variety of patterns involving geometric designs, including patterns found in real-life contexts.
• create and translate patterns using various representations, including shapes and numbers.
• determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns represented with shapes and numbers.
• create and describe patterns to illustrate relationships among whole numbers up to 100.

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

• identify when symbols are being used as variables and describe how they are being used.

2. Equalities and Inequalities

• identify and use equivalent relationships for whole numbers up to 100, in various contexts.

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 code, including code that involves sequential and concurrent events.
• read and alter existing code, including code that involves sequential and concurrent events, and describe how changes to the code affect the outcomes.

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, analyze and use data to make convincing arguments and informed decisions, in various contexts drawn from real life. They will

1. Data Collection and Organization

• sort sets of data about people or things according to two attributes, using tables and logic diagrams, including Venn and Carroll diagrams.
• collect data through observations, experiments, and interviews to answer questions of interest that focus on a single piece of information; record the data using methods of their choice; and organize the data in tally tables.

2. Data Visualization

• display sets of data, using one-to-one correspondence, in concrete graphs, pictographs, line plots, and bar graphs with proper sources, titles, and labels.

3. Data Analysis

• identify the mode(s), if any, for various data sets presented in concrete graphs, pictographs, line plots, bar graphs, and tables, and explain what this measure indicates about the data.
• analyse different sets of data presented in various ways, including in logic diagrams, line plots, and bar graphs, by asking and answering questions about the data 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 mathematical language, including the terms “impossible”, “possible”, and “certain”, to describe the likelihood of complementary events happening, and use that likelihood to make predictions and informed decisions.
• make and test predictions about the likelihood that the mode(s) of a data set from one population will be the same for data collected from a different population.

### Financial Literacy

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

1. Money Concepts

• identify different ways of representing the same amount of money up to Canadian 200¢ using various combinations of coins, and up to \$200 using various combinations of \$1 and \$2 coins and \$5, \$10, \$20, \$50, and \$100 bills.

## List of Skills

More than 280 math skills are considered in the math curriculum for grade 2 most of which are common to grade 1. Please, use the detailed list of skills in the old LG for grade 2.

## 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.

1. 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.
2. 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.
3. 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

The followings are among the most common challenges students face in grade 2:

1. Mixed operations
2. Fractions
3. Divisions
4. Data analysis
5. Symmetry
6. Measurement
7. Graphs

## What We Can Offer

Students have different goals and expectations according to their background, knowledge, or experience. This data along with the result of assessment session help us to design a unique plan for each student. There are different kinds of helps that we offer students in Genius Math:

1. To review and practice their class notes and handouts
2. To be helped with their homework, quizzes, and tests
3. To improve their math skills in general
4. To level up (e.g., moving from B- to B+)
5. To get A+
6. To learn topics beyond curriculum
7. To prepare for math competitions
See Our Lessons & Pricing!
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