# Grade Five Math Curriculum

# Grade Five Math Curriculum

## Introduction

#### Table of Contents

## Overall and Specific Expectations

### 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 100000, using appropriate tools and strategies, and describe various ways they are used in everyday life.
- compare and order whole numbers up to and including 100000, in various contexts.

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

- represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts.
- compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts.
- read, represent, compare, and order decimal numbers up to hundredths, in various contexts.
- Round decimal numbers to the nearest tenth, in various contexts.
- describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, 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 operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations.

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

- and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts.

**3. Mental Math **

- use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, 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 100000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms.
- add and subtract fractions with like denominators, in various contexts.

**5. Multiplication and Division**

- represent and solve problems involving the multiplication of two-digit whole numbers by two- digit whole numbers using the area model and using algorithms and make connections between the two methods.
- represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately.
- multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings.
- represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts.

### 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, growing, and shrinking patterns, including patterns found in real-life contexts.
- create and translate growing and shrinking 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, growing, and shrinking patterns.
- create and describe patterns to illustrate relationships among whole numbers and decimal tenths and hundredths.

**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**

- translate among words, algebraic expressions, and visual representations that describe equivalent relationships.
- evaluate algebraic expressions that involve whole numbers.

**2. Equalities and Inequalities**

- solve equations that involve whole numbers up to 100 in various contexts and verify solutions.
- solve inequalities that involve one operation and whole numbers up to 50 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 conditional statements and other control structures.
- read and alter existing code, including code that involves conditional statements and other control structures, 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 **

- explain the importance of various sampling techniques for collecting a sample of data that is representative of a population.
- collect data, using appropriate sampling techniques as needed, to answer questions of interest about a population, and organize the data in relative-frequency tables.

**2. Data Visualization**

- select from among a variety of graphs, including stacked-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 relative-frequency tables and stacked-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 decimal numbers and explain what each of these measures indicates about the data.
- analyse different sets of data presented in various ways, including in stacked-bar 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**

- use fractions to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions.
- determine and compare the theoretical and experimental probabilities of an event 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**

- sort three-dimensional objects and two-dimensional shapes according to one attribute at a time and identify the sorting rule being used.
- construct three-dimensional objects, and identify two-dimensional shapes contained within structures and objects.
- construct and describe two-dimensional shapes and three-dimensional objects that have matching halves.

**2. Location and Movement**

- describe the relative locations of objects or people, using positional language.
- give and follow directions for moving from one location to another.

**B. Measurement**Students will compare, estimate, and determine measurements in various contexts. They will

**1. Attributes **

- identify measurable attributes of two-dimensional shapes and three-dimensional objects, including length, area, mass, capacity, and angle.
- compare several everyday objects and order them according to length, area, mass, and capacity.

**2. Time**

- read the date on a calendar, and use a calendar to identify days, weeks, months, holidays, and seasons.

### Financial Literacy

**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 triangles and construct different types of triangles when given side or angle measurements.
- identify and construct congruent triangles, rectangles, and parallelograms.
- draw top, front, and side views of objects, and match drawings with objects.

**2. Location and Movement**

- plot and read coordinates in the first quadrant of a Cartesian plane using various scales and describe the translations that move a point from one coordinate to another.
- describe and perform translations, reflections, and rotations up to 180° 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**

- use appropriate metric units to estimate and measure length, area, mass, and capacity.
- solve problems that involve converting larger metric units into smaller ones and describe the base ten relationships among metric units.

** 2. Angles**

- compare angles and determine their relative size by matching them and by measuring them using appropriate non-standard units obtuse.
- explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles.

** 3. Area**

- use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram and the area of a triangle and solve related problems.
- show that two-dimensional shapes with the same area can have different perimeters and solve related problems.

## 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

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

## What We Can Offer

- 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