## Mathematics

Students at Collegiate Hall build their math skill in a four key areas:

1. Students will build their fluency and flexibility with basic math facts.

2. Students will develop a love for solving challenging and interesting problems.

3. Students will gain a strong conceptual understanding of foundational math concepts, including equations, functions, and graphs.

4. Students will develop a growing ability to create, understand, and critique mathematical theorems and their proofs.

## 4th Grade

Collegiate Hall students will develop a wide range of skills and strategies for solving a variety of problems. The standards place an emphasis on multiplication and division with whole numbers solving problems involving addition and subtraction of fractions and decimals by finding common multiples and factors.

**Big Questions Tackled:**

- What does value mean?
- What are the properties of multiplication and division?
- Why would you choose to represent data in certain types of graphs?

**Topics Covered:**

- Place Value
- Multiplying
- Dividing
- Patterns
- Factors, multiples, prime, composite
- Write numeric expression
- Solve for variables
- Find Area and Perimeter and volume
- Compare fractions
- Add/Subtract/Multiply fractions
- Compare decimals
- Add/Subtract decimals
- Calculate change of time
- Convert Measurements
- Use data to solve problems
- Create Line plots
- Measuring/Properties of angles
- Classify quadrilaterals

## 4th Grade Arithmetic

Math Skills is designed to supplement students experience in Ms. Melin’s 4^{th} Grade Math Class. Students in math skills will receive personalized and differentiated instruction: every day students will practice their math facts using an engaging computer program (Reflex Math… they can play at home too!), be provided with extra support on previously misunderstood objectives, receive accelerated instruction where appropriate, and have the opportunity to learn in a small group setting.

**Enduring Understandings:**

- Addition, subtraction, multiplication, and division with all numbers between 0 and 12.
- There is no one way to solve a math problem, and for each problem different strategies can be used to arrive at an answer (for example, drawing a picture, using an array, creating an equation, etc.)
- The world is filled with numbers, and interacting with and manipulating non-whole numbers – fractions, decimals, and percentages – translates directly to real world situations outside of the classroom.

**Topics Covered:**

- Understanding Numbers
- The Big Four Operations (+, -, x, ÷)
- Applied Number Sense
- Fractions
- Partial Numbers
- Geometry

## 5th Grade

Collegiate Hall students will be able to explore the language and patterns of math in 5^{th} grade with more critical thinking. They will understand the relationships between decimals, fractions, and the base 10 system in order to problem solve more independently.

**Big Questions Tackled:**

- What patterns occur in our number system?
- What can affect the relationship between two numbers?
- How does multiplying fractions relate to the real world?
- What are the properties of 2 dimensional figures?

**Topics Covered:**

- Place Value
- Inequalities
- Multiplication
- Division
- Compare decimals
- Add/Subtract/Multiply Divide decimals
- Compare fractions
- Add/Subtract/Multiply divide fractions
- Compare fractions and decimals
- Identify patterns
- Converting from base 10 to exponent
- Multiplying/Dividing exponents
- Solve using Order of operations
- Solve for variables
- Identify commutative/associative/distributive properties
- Plot points in 4 quadrants on coordinate plane
- Analyze data with decimal/fraction increments
- measure/compare angles
- Properties of triangles
- Properties of 2 dimensional figures
- Perimeter, area, volume, surface area
- Probability, percent, ratios

## 6th Grade

The focus in 6^{th} grade mathematics is on engaging with harder and more open-ended math tasks and problems. These develop more mature mathematical mindsets focused on reasoning, pattern-finding, and communication rather than mere computation. While doing so, students will develop a conceptual understanding of equations and expressions which form the mathematical language of describing patterns.

**Enduring Understandings:**

- Mathematical patterns can be represented many different ways such as equations, tables, graphs, words, or pictures.
- Equations are like a balanced scale, and can be solved by thinking of the unknown as an unknown weight.
- When letters are used in equations, they either represent an unknown number or a number that changes.

**Topics Covered:**

- Ratios and Proportions
- Primes, divisibility and factors
- Negative Numbers
- Equivalent Expressions (variables)
- Solving equations (unknowns)
- Area, Surface area, and Volume
- Statistics and Probability

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