Math curriculum for Grades 1-8

Students work with numbers up to 50 and begin to develop an understanding of the ways we use numbers. They are also introduced to the idea of fractions, through the context of sharing things equally.

Students begin to look at how patterns can be used to make predictions. They also begin to work on the idea that in a number sentence (for example, 2 + 2 = 4) both sides must be equal to each other. These ideas are foundational to algebra work in later grades. Students will begin to write code to order a sequence of steps. They will also be introduced to mathematical modelling to analyze and create solutions for real-life situations, such as creating a seating arrangement for a class event.

Students begin to develop their understanding about data by setting out to answer a question of interest (for example, “What type of animals do my classmates like?”). They organize this data into categories, and then display this information in a graph or table that will support them in drawing conclusions.

Students develop their spatial sense as they compare the length, mass and capacity of different objects as well as learn how calendars are organized to describe time. They also learn specific language to describe different shapes.

Students learn to recognize Canadian coins and bills and compare their values.

Students learn about positive motivation, and how to use self talk strategies such as “I’ve done this before so I know I can do it again” as encouragement that they can do it or to encourage peers when counting.

Students work with numbers up to 200. They develop and apply their growing understanding of numbers in various ways, such as solving problems with addition and subtraction. They continue to build understanding of fractions through the context of sharing things equally.

Students continue to learn about patterns and how to extend patterns made with shapes or numbers. They also learn about equality by adjusting pairs of addition and subtraction statements to make them equal. Students will develop code to move multiple objects from 1 location on a grid to another. They will also use mathematical modelling to analyze and create solutions for real-life situations, such as planning a nutritious breakfast program that most Grade 2 students would enjoy.

Students continue to develop their understanding of data as they learn ways to collect, organize, display and interpret more complicated data. They will learn about the likelihood of events happening and how they can use that information to make informed decisions, (for example, “If it is likely to rain tomorrow, then I should wear rain boots”).

Students continue to develop their spatial sense as they learn to visualize what different shapes look like when they are turned around or taken apart. They learn to recognize and describe more complex shapes and create simple maps of familiar places. Tools such as rulers will be used to accurately measure the lengths of objects, and timers and clocks are used to measure how much time has passed.

Students build on their understanding that money has value and identify different ways to represent the same amount of money. For example, how different combinations of coins can add up to $1, and how different combinations of loonies, toonies and bills can add up to $100.

Students practise critical and creative thinking. For example as students are learning to break down different denominations of money, they use and select different tools and strategies such as:

• making lists of different combinations
• drawing pictures of different groupings
• using coin manipulatives to represent money amounts in different ways

Students work with numbers up to 1,000 and learn how to break down numbers in different ways. For example, the number 225 can be described as 200 + 20 + 5 or 2 hundreds, 2 tens, and 5 ones. Students learn that fractions can be represented in more than 1 way — for example, one-half can be thought of as 2 one-fourths. Multiplication is introduced as an area of rows and columns, and students are expected to know multiplication facts of × 2, × 5 and × 10, and related division facts.

Students learn to identify and describe what repeats in a pattern, such as when a specific event happens every Monday, or when a number sequence goes up by 2 each time. Students begin to identify multiplication and division equations that are equal, such as 3 × 4 and 6 × 2. Students will write code to perform a repeating operation, such as a repeating “add 3”, beginning at 0, to make a number pattern. They will also use mathematical modelling to analyze and create possible solutions for real-life situations, such as planning a community vegetable garden.

Students continue to develop their understanding of data. They learn more ways to collect, organize and display data. They start to use scales on their graphs and begin to use averages to make comparisons of data.

Students continue to develop their spatial sense as they recognize and describe 3-dimensional objects and imagine what these objects would look like if they were taken apart or flipped around. Students continue to measure length and are introduced to measuring the weight and capacity of objects. They learn about how to measure area of 2D shapes and how to tell time on both digital and analog clocks.

Students continue to develop their understanding of money by calculating the change required for simple transactions involving whole-dollar amounts.

Students identify and learn to manage emotions that they may feel such as pride, confusion, fear and excitement when faced with a new challenge to solve, such creating and executing code that represents a math situation.

Students work with numbers up to 10,000 and are introduced to decimals. They learn how decimal numbers are used in real-life, such as taking a person’s temperature on a thermometer and when making and recording precise measurements. Students will begin to divide 2- and 3-digit whole numbers by a 1-digit whole number and are expected to know multiplication facts from 1 × 1 to 10 × 10. They also begin to solve problems that require more than 1 operation with whole numbers.

Students continue to build their knowledge of patterning as they begin to classify patterns as repeating or growing. They also begin to determine the values that make algebraic statements true. For example, if n + 3 = 10, then n must be 7. Students learn to write and read code to create geometric designs. They use the modelling process to analyze and create solutions for real-life situations, such as how to design a schoolyard to appeal to the student body at a school.

Developing an understanding of data continues as students collect, organize and display 2 or more data sets using frequency tables and multiple-bar graphs. Students learn how to create an infographic, so that they can tell a story about data.

Students learn the characteristics and properties of a rectangle and learn how to determine the area of a rectangle. They learn about the relationships between the various units in the metric system which is the measurement system used throughout Canada and most of the world.

Students learn that there are different ways to pay for goods and services. Students also learn some ways to determine whether an item is good value for the price.

To learn about positive motivation, educators encourage students to use a variety of tools and strategies, adjusting as they go in order to reach a solution.

Students continue to work with numbers up to 100,000. Students are introduced to percentages and continue to build their understanding of decimals and fractions and begin adding and subtracting fractions with the same denominator. Students are expected to know multiplication facts from 0 × 0 to 12 × 12. They also solve problems involving more than 1 operation with whole and decimal numbers.

Students continue to classify patterns as repeating, growing and shrinking. Students begin to write and solve algebraic equations involving whole numbers, such as 3 + x = 24 − 5. Students apply their understanding of multiplication and ratios to create and execute code for patterns that grow. They use the process of mathematical modelling to solve problems drawn from real-life, such as maximizing the seating capacity in a venue.

Students learn about the importance of using various sampling techniques to get “good” data. They create infographics and learn how to identify when graphs are misleading. Students begin to use experiments to understand the concept of probability.

The development of spatial sense continues as students study the triangle. Students learn the characteristics and properties of different kinds of triangles, including their angles and measurements. Work continues in understanding and using the metric system to measure length, area, mass and capacity, and to convert from larger units to smaller ones.

Students learn about different ways to transfer money between people and organizations, such as e-transfers and cheques. They calculate the total cost and change required for cash transactions involving items priced in dollars and cents, using mental math and other strategies. Students learn how to determine the best value for an item – for example, 5 apples for $1.00 versus 3 apples for 75 cents. Students prepare basic budgets and learn about the concepts of credit and debt.

Students continue to develop healthy relationship skills and practise how to have positive interactions when engaging with others about mathematical ideas.

In addition to working with numbers up to 1 million, students are introduced to integers, such as −2, −1, 0, 1, 2. They learn the divisibility rules of 2, 3, 4, 5, 6, 8, 9, and 10. For example, a number is divisible by 5 if it ends in a 5 or 0. Expanding operational skills include dividing a whole number by a fraction or a mixed number, such as 2½. Students also solve problems that involve more than 1 operation and the use of whole numbers, decimals and fractions.

Students continue to work with patterns and start to identify patterns that grow at a constant rate. For example, if someone drives 100 kilometres per hour, the distance travelled increases by 100 kilometres for each hour. They solve algebraic expressions involving whole numbers and decimal tenths, and algebraic equations involving multiple terms, such as 2x + 3x = 5. Students use code to solve problems that involve optimization, such as finding the maximum area for a given perimeter. They also use the process of mathematical modelling to solve problems drawn from real-life, such as planning a nutritionally balanced and cost-effective lunch program.

Students learn to distinguish between discrete data, such as the number of students, and continuous data, such as the amount of precipitation in centimetres. They learn how to display these different types of data, with graphs that show change over time, including broken-line graphs. Students also learn different ways to describe probability. For example, there is a 1 in 4 chance of winning a prize at the school fun fair, or there is a 40% chance of rain tomorrow.

Developing spatial sense continues with an emphasis on 4-sided shapes. Students learn the characteristics and properties of different kinds of 4-sided shapes and how to find their areas. They also build 3-dimensional structures and learn how to calculate surface area. Students learn to convert from one unit to another in the metric system. They also focus on extending their ability to measure angles with protractors and learn to use angle properties to solve for unknown angle measures.

The advantages and disadvantages of using different methods of payment for goods and services are explored. Students investigate different types of financial goals, identify and describe factors that could affect these goals, and outline steps to achieve them. Students explain the concept of interest rates and identify interest rates and fees offered by banks and other financial institutions. They also learn how trading, lending, borrowing and donating are different ways to distribute resources.

Students continue to deepen their sense of self by connecting what they are learning to real life situations. For example, they might track different things, such as the number of steps they take each day, minutes of screen time or physical activity and how they feel afterwards. They could then prepare graphs and data visualization tools information for analysis, reflection and learning.

Working with numbers up to 1 billion, students learn the term “rational numbers”, and how to identify them. They are expected to know multiplication facts from 0 × 0 to 12 × 12. Students begin to generate factors (for example, factors of 6 are 1 and 6, 2 and 3), multiples (such as multiples of 6 are 6, 12, 24, and so on) and add and subtract fractions by creating equivalent fractions. Students explore problems that require addition and subtraction of integers (for example, determine the overall score or change in temperature).

Students connect their understanding of whole-number patterns to patterns involving decimals. They continue to solve equations that involve multiple terms, whole numbers, and decimal numbers, such as 2x + 5 = 3x − 1. Students write code to simulate mathematical situations, such as rotating a shape or doubling its size. They also use mathematical modelling to provide insight into real-life situations, such as remodelling a room with a set budget.

Students learn how to use circle graphs to represent data. They begin to develop a critical eye for analyzing data by examining graphs that may be misleading. Students also determine the differences between the probability of independent events versus dependent events. For example, how does the probability differ if 2 marbles are drawn from a bag with or without putting them back before drawing again.

Students continue to develop spatial sense as they study the circle. Students learn to measure various aspects of circles, such as circumference, diameter, radius and area. They use these and other measurements to find the surface area and volume of cylinders and other 3-dimensional objects. Students also learn how to dilate - enlarge and shrink - a shape.

Students begin to learn that international currencies have different values compared to Canadian dollars and understand how exchange rates work. They develop an awareness of how to plan for and reach financial goals. Students build their knowledge of how interest rates can affect savings and investments. They also learn about the cost of borrowing and compare interest rates and fees for different types of accounts and loans to become more informed consumers.

Students learn how to cope with stress and manage complex challenges. For example, they might break down a task into smaller portions, make a plan and take it one step at a time.

Students use scientific notation such as 5.46 × 106 to understand, represent and compare very large and small numbers more easily, which is often required in Science curriculum. Students use fractions, decimals and percentages interchangeably and should be able to recall square numbers to 144 and their square roots. Students solve problems that involve proportions (for example, determining the percentage increase or decrease in the attendance of a show) and whole numbers, fractions, decimals, integers and exponents.

Students continue to develop their understanding of patterns, including those that involve integers. They use algebraic notation, such as, s = d/t, to represent the relationship between speed, distance and time. They solve algebraic equations involving multiple terms, integers and decimal numbers. Students write code to create a line or curve that falls between the greatest number of data points. They also use mathematical modelling for real-life situations, such as making predictions about future fundraisers based on the funds raised from past fundraisers.

Students continue to build their data skills. They analyze data that is presented in more complex ways, such as in scatter plots, that show the relationship between 2 variables. In addition, students continue to increase their understanding of probability by comparing the outcomes of more complex experiments.

Students continue to develop spatial sense as they study right-angle triangles. They learn that if 2 side lengths are known, then the length of the third can be figured out without measuring it, using the Pythagorean Theorem. Students learn how to calculate unknown angles by applying the angle properties of intersecting and parallel lines. Students also build their understanding of very large units such as a terabyte and very small units like a nanosecond that are used in current technologies.

Students learn to create a plan to reach financial goals and identify ways to maintain balanced budgets. Students compare different ways that consumers can get value for their money when spending, such as using reward programs or taking advantage of sales. Students investigate the concepts of simple and compound interest using technology, (for example, a spreadsheet program or online loan calculator) and explain how interest affects long-term financial planning.

Students continue to build healthy relationship skills as they interact with their classmates to solve mathematical problems. They may use protocols to promote respectful interactions, such as listening to different perspectives, building on one another’s thinking, agreeing or disagreeing with reason and practising wait time.