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Grade 9 Mathematics enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. In Grade 9 Mathematics, students will reason mathematically and communicate their thinking as they solve multi-step problems.

### UNIT ONE

Rational Numbers

Essential Question: What are the differences between different types of numbers?

• In this unit, students will learn how to relate rational numbers to decimals, fractions, and integers. Students will also learn how to evaluate expressions involving rational numbers.

### UNIT TWO

Powers and Polynomials

Essential Question: How do we represent polynomials in different forms using exponents?

• In this unit, students will learn how to represent polynomials geometrically, simplify polynomial expressions using exponents and other mathematical principles, add and subtract polynomials, multiply polynomials by monomials.

### UNIT THREE

Linear Relations

Essential Question: Why do we learn about lines (word problem related)?

• In this unit, students will learn how to describe properties of linear relations, recognize whether a relation is linear or nonlinear from a table of values, a graph, an algebraic expression, or a written description. Students will also learn to create different representations of linear and nonlinear relations.

### UNIT FOUR

Linear EquationsEssential Question: How do we solve linear equations using variety of strategies?

• In this unit, students will solve linear equations using a variety of strategies. Students will rearrange linear equations and formulas and find the point of intersection of two linear relations using a graph.

### UNIT FIVE

Analytic Geometry

Essential Question: Where do we use geometry in everyday life?

• In this unit, students will find the slope of a line, find the equation of a line and find the equations of parallel and perpendicular lines.

### UNIT SIX

Investigating Relationships

Essential Question: How do we describe relationships between data?

• In this unit, students will use a scatter plot to analyze data and draw a line or curve of best fit. Students will find the equation of the line of best fit and find trends or patterns in the data and make conjectures. Students will also use graphs to describe situations like displacement over time.

### UNIT SEVEN

Properties of 2-D Figures

Essential Question: How do we investigate and create different polygons?

• In this unit, students will investigate and apply the properties of interior and exterior angles of polygons. Students will investigate and apply the properties of the diagonals of polygons and line segments created using the midpoints of sides of polygons. Students will create and test conjectures, and give supporting examples or counterexamples.

### UNIT EIGHT

Measurement

Essential Question: How is optimization related to various 2-D measurements?

• In this unit, students will learn how to find the area, surface area, and the volume of various shapes, such as trapezoids, prisms, pyramids, cylinders, cones, and spheres. Students will also learn how to optimize area and volume.