# Grade Seven Math Curriculum

# Grade Seven Math Curriculum

## Introduction

Beginning of Intermediate School and on the brink of their teenage years, Grade 7 helps children discover their true personality. This is also the year in which academic competition starts to rise and directions towards future careers begin to be mapped. Strengthening of mathematical concepts in this grade also becomes imperative. Moving from the world of basic decimals and fractions, Grade 7 further explores the number system and proportional relationships and introduces the concepts of transformations and congruence.

#### 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 7 in more detail.

### Number

**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**

- represent and compare whole numbers up to and including one billion, including in expanded form using powers of ten, and describe various ways they are used in everyday life.
- identify and represent perfect squares, and determine their square roots, in various contexts.
- read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers to thousandths, in various contexts.

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

- use equivalent fractions to simplify fractions, when appropriate, in various contexts.
- generate fractions and decimal numbers between any two quantities.
- round decimal numbers to the nearest tenth, hundredth, or whole number, as applicable, in various contexts.
- convert between fractions, decimal numbers, and percents, 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 and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations.

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

- understand and recall commonly used percents, fractions, and decimal equivalents.

**3. Mental Math **

- use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used.

**4. Addition and Subtraction**

- use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of integers.
- add and subtract fractions, including by creating equivalent fractions, in various contexts.

**5. Multiplication and Division**

- determine the greatest common factor for a variety of whole numbers up to 144 and the lowest common multiple for two and three whole numbers.
- evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts.
- multiply and divide fractions by fractions, using tools in various contexts.
- multiply and divide decimal numbers by decimal numbers, in various contexts.
- identify proportional and non-proportional situations and apply proportional reasoning to solve problems.

### 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 compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing patterns on the basis of their constant rates and initial values.
- create and translate repeating, growing, and shrinking patterns involving whole numbers and decimal numbers using various representations, including algebraic expressions and equations for linear growing patterns.
- determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns involving whole numbers and decimal numbers, 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 integers.

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

**2. Equalities and Inequalities**

- solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions.
- solve inequalities that involve multiple terms and whole numbers 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**

- Students will solve problems and create computational representations of mathematical situations using coding concepts and skills. They will
- read and alter existing code, including code that involves events influenced by a defined count and/or sub-program 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 **

- explain why percentages are used to represent the distribution of a variable for a population or sample in large sets of data and provide examples.
- collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages.

**2. Data Visualization**

- select from among a variety of graphs, including circle 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 and circle graphs, and incorporating any other relevant information that helps to tell a story about the data.

**3. Data Analysis **

- determine the impact of adding or removing data from a data set on a measure of central tendency and describe how these changes alter the shape and distribution of the data.
- analyse different sets of data presented in various ways, including in circle 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**

- describe the difference between independent and dependent events, and explain how their probabilities differ, providing examples.
- determine and compare the theoretical and experimental probabilities of two independent events happening and of two dependent 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**

- describe and classify cylinders, pyramids, and prisms according to their geometric properties, including plane and rotational symmetry.
- draw top, front, and side views, as well as perspective views, of objects and physical spaces, using appropriate scales.

**2. Location and Movement**

- perform dilations and describe the similarity between the image and the original shape.
- describe and perform translations, reflections, and rotations on a Cartesian plane, 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**

- describe the differences and similarities between volume and capacity and apply the relationship between millilitres (mL) and cubic centimetres (cm
^{3}) to solve problems. - solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another.

- describe the differences and similarities between volume and capacity and apply the relationship between millilitres (mL) and cubic centimetres (cm

** 2. Circles**

- use the relationships between the radius, diameter, and circumference of a circle to explain the formula for finding the circumference and to solve related problems.
- construct circles when given the radius, diameter, or circumference.
- show the relationships between the radius, diameter, and area of a circle, and use these relationships to explain the formula for measuring the area of a circle and to solve related problems.

** 3. Volume and Surface Area**

- represent cylinders as nets and determine their surface area by adding the areas of their parts.
- show that the volume of a prism or cylinder can be determined by multiplying the area of its base by its height and apply this relationship to find the area of the base, volume, and height of prisms and cylinders when given two of the three measurements.

### Financial Literacy

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

**1. Money Concepts**

- identify and compare exchange rates and convert foreign currencies to Canadian dollars and vice versa.

** 2.Financial Management**

- identify and describe various reliable sources of information that can help with planning for and reaching a financial goal.
- create, track, and adjust sample budgets designed to meet longer-term financial goals for various scenarios.
- identify various societal and personal factors that may influence financial decision making and describe the effects that each might have.

** 3.Consumer and Civic Awareness **

- explain how interest rates can impact savings, investments, and the cost of borrowing to pay for goods and services over time.
- compare interest rates and fees for different accounts and loans offered by various financial institutions and determine the best option for different scenarios.

** **

## List of Skills

More than 340 math skills are considered in the math curriculum for grade 7 many of which are common to grade 6. Please, use the detailed list of skills in the old LG for grade 7.

## 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 7:

- Fractions and decimals
- Mixed operations
- Variables and equations as well as inequalities
- Data analysis
- Mixed transformations and impacts on geometric shapes
- Area and volume
- 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 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