# Grade Four Math Curriculum

# Grade Four Math Curriculum

## Introduction

The beginning of Junior School, Grade 4 is the year of sports and camps and more complex syllabus. Children transit to more definitive number sense and are introduced with different concepts including geometry, graphs, logical reasoning. The information provided in this page are identical to the Official Grade four Math Curriculum established by the Ministry of Education.

#### Table of Contents

## 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 4 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 10000, using appropriate tools and strategies, and describe various ways they are used in everyday life.
- compare and order whole numbers up to and including 10000, in various contexts.
- round whole numbers to the nearest ten, hundred, or thousand, in various contexts.

**2.Fractions and Decimals,**

- represent fractions from halves to tenths using drawings, tools, and standard fractional notation, and explain the meanings of the denominator and the numerator.
- use drawings and models to represent, compare, and order fractions representing the individual portions that result from two different fair-share scenarios involving any combination of 2, 3, 4, 5, 6, 8, and 10 sharers.
- count to 10 by halves, thirds, fourths, fifths, sixths, eighths, and tenths, with and without the use of tools.
- read, represent, compare, and order decimal tenths, in various contexts.
- round decimal numbers to the nearest whole number, in various contexts.
- describe relationships and show equivalences among fractions and decimal tenths, 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 addition, subtraction, multiplication, and division, to solve problems involving whole numbers, including those requiring more than one operation, and check calculations.

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

- recall and demonstrate multiplication facts for 1 × 1 to 10 × 10, and related division facts.

**3. Mental Math **

- use mental math strategies to multiply whole numbers by 10, 100, and 1000, divide whole numbers by 10, and add and subtract decimal tenths, and explain the strategies used.

**4. Addition and Subtraction**

- represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 10000 and of decimal tenths, using appropriate tools and strategies, including algorithms.

**5. Multiplication and Division**

- represent and solve problems involving the multiplication of two- or three-digit whole numbers by one-digit whole numbers and by 10, 100, and 1000, using appropriate tools, including arrays.
- represent and solve problems involving the division of two- or three-digit whole numbers by one-digit whole numbers, expressing any remainder as a fraction when appropriate, using appropriate tools, including arrays.
- represent the relationship between the repeated addition of a unit fraction and the multiplication of that unit fraction by a whole number, using tools, drawings, and standard fractional notation.
- show simple multiplicative relationships involving whole-number rates, 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 repeating and growing patterns, including patterns found in real-life contexts.
- create and translate repeating and growing patterns using various representations, including tables of values and graphs.
- determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating and growing patterns.
- create and describe patterns to illustrate relationships among whole numbers and decimal tenths.

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

**2. Variables**

- identify and use symbols as variables in expressions and equations.

**2. Equalities and Inequalities**

- solve equations that involve whole numbers up to 50 in various contexts and verify solutions.
- solve inequalities that involve addition and subtraction of whole numbers up to 20 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 code, including code that involves sequential, concurrent, repeating, and nested events.
- read and alter existing code, including code that involves sequential, concurrent, repeating, and nested 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, 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 qualitative and quantitative data and describe situations where each would be used.
- collect data from different primary and secondary sources to answer questions of interest that involve comparing two or more sets of data and organize the data in frequency tables and stem-and-leaf plots.

**2. Data Visualization**

- select from among a variety of graphs, including multiple-bar 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 frequency tables, stem-and-leaf plots, and multiple-bar graphs, and incorporating any other relevant information that helps to tell a story about the data.

**3. Data Analysis **

- determine the mean and the median and identify the mode(s), if any, for various data sets involving whole numbers, and explain what each of these measures indicates about the data.
- analyse different sets of data presented in various ways, including in stem-and-leaf plots and multiple-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”, “unlikely”, “equally likely”, “likely”, and “certain”, to describe the likelihood of events happening, represent this likelihood on a probability line, and use it to make predictions and informed decisions.
- make and test predictions about the likelihood that the mean, median, and mode(s) of a data set will be the same for data collected from different populations.

### 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**

- identify geometric properties of rectangles, including the number of right angles, parallel and perpendicular sides, and lines of symmetry.

**2. Location and Movement**

- plot and read coordinates in the first quadrant of a Cartesian plane and describe the translations that move a point from one coordinate to another.
- describe and perform translations and reflections 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**

- explain the relationships between grams and kilograms as metric units of mass, and between litres and millilitres as metric units of capacity and use benchmarks for these units to estimate mass and capacity.
- use metric prefixes to describe the relative size of different metric units, and choose appropriate units and tools to measure length, mass, and capacity.

**2. Time**

- solve problems involving elapsed time by applying the relationships between different units of time.

** 3. Angles**

- identify angles and classify them as right, straight, acute, or obtuse.

** 4. Area**

- use the row and column structure of an array to measure the areas of rectangles and to show that the area of any rectangle can be found by multiplying its side lengths.
- apply the formula for the area of a rectangle to find the unknown measurement when given two of the three.
- use square centimetres (cm
^{2}) and square metres (m^{2}) to estimate, measure, and compare the areas of various two-dimensional shapes, including those with curved sides.

### Financial Literacy

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

**1. Money Concepts**

- identify various methods of payment that can be used to purchase goods and services.
- estimate and calculate the cost of transactions involving multiple items priced in whole-dollar amounts, not including sales tax, and the amount of change needed when payment is made in cash, using mental math.

** 2. Financial Management**

- explain the concepts of spending, saving, earning, investing, and donating, and identify key factors to consider when making basic decisions related to each.
- explain the relationship between spending and saving and describe how spending and saving behaviors may differ from one person to another.

** 3. Consumer and Civic Awareness**

- describe some ways of determining whether something is reasonably priced and therefore a good purchase.

** **

## 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

The followings are among the most common challenges students face in grade 4:

- Fractions and decimals
- Mixed operations
- Variables and equations
- Data analysis
- Data analysis
- Probability

## 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:

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