# Math Program

As with all of our materials, our online mathematics courses were created as a comprehensive package that includes lesson material, assessments, interactive activities, videos, and tools to track student progress. All of our mathematics courses align to the Ontario curriculum and cover every expectation, while putting the content in a Christ-centred worldview.

## Course Details

Elementary courses do not require a prerequisite and enrollment is typically based on the age of the student. If you have any questions on what grade best suits your family’s needs, reach out to our guidance department for support.

**Aligned Curriculum Document**: Mathematics (2020)

**Developed By**: D2L and Christian Virtual School

**Development Date**: September 2020

**Required Resources**: See below.

## Course Outlines

**Unit 1: Representing Numbers**

In the Representing Numbers unit, students learn to read and write numbers up to 10,000, show an understanding of place value up to 10,000, represent, compare, and order numbers up to 10,000. They also round four-digit numbers in real-life situations.

**Unit 2: Geometry**

In the Geometry unit, students draw lines of symmetry on 2D shapes, and identify, compare, and classify quadrilaterals. They learn how to identify various angles. Students identify, perform, and describe reflections and learn to create patterns using reflections.

**Unit 3: Addition and Subtraction**

In the Addition and Subtraction unit, students add and subtract four-digit numbers using partial sums and partial differences, as well as add and subtract four-digit numbers vertically.

**Unit 4: Multiplication and Division**

In the Multiplication and Division unit, students multiply ad multiply and divide numbers from 1 to 10. They multiply and divide by 10, 100, and 1000 using mental strategies and multiply and divide using a variety of tools. Students solve vertical multiplication equations, divide two-digit and three-digit by one-digit numbers. Students describe relationships using multiplication, and explore multiplication and unit rates. They also solve problems involving more than one operation.

**Unit 5: Patterning and Algebra**

In the Patterning and Algebra unit, students create and extend patterns, analyze terms and term numbers, create number patterns, and predict terms in a pattern. Students also determine the relationship between multiplication and division, find the missing number in a multiplication problem, and identify the commutative and distributive properties.

**Unit 6: Fractions and Decimal Numbers**

In the Fractions and Decimal Numbers unit, students represent fractions, identify the fraction of a group, compare and order fractions, show equivalent fractions, and count by halves, thirds, fourths, and tenths. Students also read and write decimal numbers, show place values from 0.1 to 10,000, represent, compare, and order decimal numbers up to tenths, count forward, add and subtract decimal numbers, and explore the relationship between fractions and decimal numbers.

**Unit 7: Coding**

In the Coding unit, students learn how to write and execute code to draw shapes. They learn the concepts of variables and nested events. Students learn how to debug code with nested events.

**Unit 8: Data**

In the Data unit, students collect data by conducting a survey and collect and organize data in charts, tables, and graphs. They learn how to create an infographic to represent data. Students read, interpret, and draw conclusions on data, demonstrate an understanding of the median, describe and compare sets of data, and explore probability and probability experiments.

**Unit 9: Measurement**

In the Measurement unit, students estimate, measure, and record mass. Students investigate grams and kilograms, capacity, millilitres and litres, and volume. They also compare mass and capacity. Students determine elapsed time and solve problems involving years, decades, and centuries.

**Unit 10: Financial Literacy**

In the Financial Literacy unit students identify different methods of payment and learn how to estimate and calculate cost using addition. They calculate the change for a cash purchase. Students explore spending, saving, earning, investing, and donating while exploring the concept of good purchases.

**Unit 1: Numbers up to 100 000**

In the Numbers Up to 100,000 unit, students learn to read and write numbers up to 10,000, explore place value up to 100,000, and represent numbers up to 100,000. Students also compare and order whole numbers and solve problems up to 100,000.

**Unit 2: Multiplication and Division **

In the Multiplication and Division unit, students solve addition and subtraction problems, multiply two-digit numbers, and solve multiplication whole numbers by 0.1 and 0.01 mentally. Students also investigate relationships involving whole number rates, divide with concrete materials and algorithms, and divide three-digit whole numbers with standard algorithms. Students also find the missing number in addition, subtraction, multiplication, and division equations.

**Unit 3: Geometry**

In the Geometry unit, students identify acute, right, obtuse, and straight angles, and measure and construct angles up to 180°. Students identify and classify triangles from their angle and side properties, and they construct triangles. Students identify and construct two-dimensional congruent shapes and draw objects from different views. Furthermore, students plot and read coordinates on a Cartesian plane and identify, describe, and perform transformations on a grid.

**Unit 4: Working with Decimal Numbers**

In the Working with Decimal Numbers unit, students explore place value of decimal numbers and represent, compare, and order decimal numbers. Students round decimal numbers to the nearest tenth. Students show equivalent decimal numbers, and add and subtract decimal numbers.

**Unit 5: Fractions**

In the Fractions unit, students represent proper and improper fractions, represent mixed numbers, convert improper fractions and mixed numbers, and show equivalent fractions. Students also compare proper and improper fractions and compare and order fractions and mixed numbers. Furthermore, students explore equivalent fractions and decimal numbers and investigate the relationship between fractions and decimal numbers. Students add and subtract fractions with like denominators. They multiply and divide whole numbers by fractions.

**Unit 6: Patterning and Algebra**

In this unit, students identify, extend, and create geometric and numeric patterns, and build models from a table to show numeric patterns. Students make tables of values by adding or subtracting a rule in words and make a table of values for a pattern generated by multiplying or dividing. Students also make predictions related to growing and shrinking geometric and numeric patterns. Students extend and create repeating patterns using translation and explore patterns among whole numbers and decimals. Students explore equivalent relationships and evaluate algebraic expressions. They solve inequalities with whole numbers.

**Unit 7: Coding**

Students learn about conditional students and practice coding using them and other control structures. Students solve problems involving code, and read and alter code involving various control structures.

**Unit 8: Data**

In the Data unit, students explore samples of larger populations, collect and record data, organize data in charts, tables and graphs, as well as read, interpret, and draw conclusions from data. Students create infographics to represent data. Students calculate the mean, median, and mode and use them to describe data and compare sets of data. To investigate probability, students explore possible outcomes in a probability experiment, represent probability using fractions, and perform a probability experiment.

**Unit 9: Measurement**

In the measurement unit, students estimate and measure the perimeter of polygons, find unknown side lengths, estimate and measure the area of polygons, and create 2D shapes with the same perimeter or area. Students learn how to calculate the area of triangles and parallelograms. Students solve problems by converting metres into centimetres, and converting kilometres into metres. Furthermore, students investigate measuring the mass of an object using the appropriate unit.

**Unit 10: Financial Literacy**

In this unit, students describe how money can be transferred and estimate and calculate the cost of different transactions. Students learn how to design a budget and explore the concepts of credit and debt. Students learn how to use unit rates to find the best value and learn about tax and its applications.

**Unit 1: Numbers**

In the Numbers unit, students read and write numbers up to 1,000,000, understand, represent, compare, and order numbers, and solve word problems up to 1,000,000. Students identify prime and composite numbers and find the prime factors for composite numbers. Students also understand place value and represent, compare, and order decimal numbers.

**Unit 2: Geometry**

In the Geometry unit, students sort and classify quadrilaterals, sort and construct polygons, and classify, measure, and construct angles. They learn how to find unknown angles. Students build 3D models using drawings and sketch isometric perspectives and different views. Furthermore, students plot and read points on a Cartesian plane.

**Unit 3: Operations**

In the Operations unit, students multiply and divide four-digit numbers by two-digit numbers, add and subtract decimal numbers to thousandths, and multiply and divide decimal numbers by whole numbers using concrete materials and algorithms.

**Unit 4: Fractions, Percentages, Ratios, and Unit Rates**

In the Fractions, Percentages, Ratios, and Unit Rates unit, students represent fractions, compare fractions and mixed numbers using tools and fraction notation, and order fractions and mixed numbers. Students add and subtract fractions and multiply and divide whole numbers by proper fractions. They solve problems involving rations and learn how to calculate the percentage of a whole numbers. Students learn about the relationships among percentages, decimals, and fractions and explore the concept of unit rates.

**Unit 5: Data Management and Probability**

In the Data Management and Probability unit, students learn about discrete and continuous data, collect and organize data, select appropriate graphs, use technology, and determine how well a set of data represents a population. They learn how to create an infographic to represent data. Furthermore, students express theoretical probability as a fraction/ decimal/ percentage, represent probability on a range of 0 to 1, and predict the outcome of a probability experiment.

**Unit 6: Algebra**

In algebra, students learn to add monomials. They solve equations and problems involving one, two, and three variables. Students solve, verify, and graph inequalities.

**Unit 7: Patterning**

In the Patterning unit, students identify various repeating, growing, and shrinking patterns. They extend, create, translate, and represent patterns. Students use algebraic representations of pattern rules to solve problems. They use patterns to illustrate the relationship between whole and decimal numbers.

**Unit 8: Coding**

Students use various control structures to write efficient code. They solve problems using efficient code and debug and correct errors in coding to make it more efficient.

**Unit 9: Measurement**

In the Measurement unit, students estimate, measure, and record length, area, mass, and capacity. Students convert metric units and find the areas of quadrilaterals and polygons. Students estimate and calculate the surface area of a rectangular prism and a triangular prism.

**Unit 10: Financial Literacy**

In this unit, students compare different methods of payments and learn the different types of financial goals. Students identify factors that affect how reaching these financial goals may occur. Students describe how financial resources can be distributed and learn the concept of interest.

**Unit 1: Read, Represent, and Compare Numbers**

In the Read, Represent, and Compare Numbers unit, students will learn to read, represent, and compare whole numbers, decimal numbers, and fractions. They will also learn about multiples and factors and how to determine them for whole numbers. Students will explore square numbers and square roots and learn how to add and subtract integers.

**Unit 2: Geometry**

In the Geometry unit, students will learn to describe and classify 3D figures, draw figures and shapes using different perspective views, and understand how shapes can be similar without being identical. They will also learn how to dilate a shape by drawing a version of the same shape that is larger or smaller but having the same proportions. In addition, students will transform shapes on a grid.

**Unit 3: Operations**

In the Operations unit, students will extend their knowledge to multiply and divide fractions and decimal numbers. They will solve multi-step problems involving both multiplication and division and start to use exponents to represent repeated multiplication.

**Unit 4: Fractions**

In the Fractions unit, students will add and subtract fractions, improper fractions, and mixed numbers, as well as learn how to simplify fractions.

**Unit 5: Proportional Relationships**

In the Proportional Relationships unit, students will learn to generate equivalencies among fractions, decimal numbers, and percentages. They will develop this skill to solve problems involving percentages of whole numbers and increasing and decreasing whole numbers by percent. In addition, students will solve problems involving unit rates.

**Unit 6: Data**

In the Data unit, students will learn ways to collect data, represent data, and convey messages using data in infographics. Students will also explore central tendency and the ways in which to determine the different types, as well as learning how to analyse data to make inferences and draw conclusions.

**Unit 7: Patterning and Algebra**

In the Patterning and Algebra unit, students will explore and compare number patterns in whole numbers and integers. They will also be introduced to algebraic expressions, monomials, and inequalities.

**Unit 8: Coding**

In the Coding unit, students will learn to read, write, alter, and debug code that is controlled by defined counts and uses sub-programs.

**Unit 9: Measurement**

In the Measurement unit, students will solve problems relating to perimeter, area, volume, capacity, and surface area. Students will also explore measurements of circles, such as their circumference and area. They will then be able to determine the surface area and volume of cylinders.

**Unit 10: Financial Literacy**

In the Financial Literacy unit, students will explore international currencies and compare their value to Canadian dollars and other currencies. They will explore how to plan for and reach a financial goal using budgeting, knowledge of the impact of interest rates, and fees associated with different types of accounts.

**Unit 1: Representing Numbers**

In the Representing Numbers unit, students learn how to represent large and small numbers including using scientific notation. Students also learn how to describe, compare, and order rational and irrational numbers.

**Unit 2: Geometry**

In the Geometry unit, students solve problems involving area, perimeter, circumference, area, volume, and angles. Students are introduced to the Pythagorean Theory as a way to find missing side lengths of right triangles. Students develop their understanding about scale drawings, transformations of shapes, and tessellation. Students also learn about large and small units of measurement.

**Unit 3: Operations**

In the Operations unit, students solve single-step, multi-step, and multi-operation problems involving rational numbers and percentages, and extend their knowledge to multiply and divide integers. Student develop mental math strategies to divide whole numbers and decimal numbers by powers of ten. In addition, students explore square numbers and square roots.

**Unit 4: Fractions**

In the Fractions unit, students extend their learning to add, subtract, divide, and multiply fractions and mixed numbers.

**Unit 5: Proportional Reasoning**

In the Proportional Reasoning unit, students solve single-step, multi-step, and multioperation problems involving fractions, decimal numbers, ratios, rates, and percentages.

**Unit 6: Data**

In the Data unit, students extend their knowledge to represent, analyse, and describe relationships about data. Students also develop their understanding of probability.

**Unit 7: Patterning and Algebra**

In the Patterning and Algebra unit, students learn to determine the general term of a pattern using algebraic expression, create their own patterns, and describe them in different ways. Student solve algebraic equations in different ways and learn about inequalities represented with algebra.

**Unit 8: Coding**

In the Coding unit, students learn to read, create, alter, and debug code that involves data analysis and use that analysis to inform decisions.

**Unit 9: Measurement**

In the Measurement unit, students solve problems involving perimeter, circumference, area, surface area, and volume of 2D and 3D shapes.

**Unit 10: Financial Literacy**

In the Financial Literacy unit, students learn how to create and maintain a balanced budget to reach a financial goal. In addition, they analyse simple and compound interest, credit cards, and reward programs that give them the best value for their money.

## Required Resources

These course are entirely online and do not require nor rely on any textbook. Students will require the following resources, however, to complete all of the activities within the courses:

- A scanner, smart phone camera, or similar device to digitize handwritten or hand-drawn work
- A smart phone camera or similar device to take pictures of student work
- A device to record audio
- A printer
- A physical binder, folder, or notebook for offline activities
- Calculator
- Protractor
- Compass
- Ruler with centimetres
- Various household items to complete offline activities