Course Overview
FIRST SEMESTER
Unit 1: Making Relevant Connections with Geometry
Expected Dates: Beginning of School Year to Early September Students in 7th grade will recognize and apply facts involving supplementary, complementary, vertical, and adjacent angles in word problems and illustrations. Students will solve for unknown angle measures in multi-step problems. Students will investigate circles. Students will show a mastery of the proportional relationships between radius, diameter and circumference of a circle. Students will apply their knowledge of area, circumference, and volume to real life scenarios. Also in real-life scenarios, students will identify and demonstrate their knowledge of surface area being the composite area of the faces of a three-dimensional figure and apply the proper formula. Students will be able express the shape resulting from slicing three-dimensional figures perpendicular to their bases, parallel to their bases, and at an angle. The students will represent proportional relationships and scale drawings of geometric figures within real-world contexts. Unit 2: Investigating Data and Probability Expected Dates: September to Mid-October In this unit, students will begin an exploration of probability and chance processes. Students will develop probability models to find the likelihood of simple events and make predictions using simulations' information. Students will compare theoretical and experimental probabilities of events and explain discrepancies. They will distinguish proportional relationships from other relationships when comparing and contrasting the probability models and sampling to produce and support valid inferences. Students will deepen their understanding of ratios to investigate proportional relationships to solve real-world problems using a variety of strategies. In 6th grade students were able to build a solid foundation in numeracy to apply that foundational knowledge and apply part whole strategies in context. In 7th grade students continue to deepen their knowledge of these strategies by exploring and developing probability models using simple events. Students investigate and learn the probability of a chance event is a number between 0 and 1. They develop a probability model and use it to find probabilities of events. Unit 3: Investigating Linear Expressions, Equations, and Inequalities in One Variable Expected Dates: Late October to Mid-November In this unit, students will explore incorporate patterning and algebraic reasoning to create, interpret, solve, and graph linear equations and inequalities in one variable. The equations and inequalities include those with rational coefficients, variables on both sides and whose solutions require the use of the distributive property and combining of like terms. Students will interpret expressions with multiple factors and/or terms and manipulate linear and literal equations expressed in various forms. Unit 4: Modeling Linear Relationships & Functions Expected Dates: Late November to Early February In this unit, students will distinguish proportional relationships from other relationships. They will use proportional reasoning to explain why the slope is the same between any two points in a similar triangle. Students will analyze the connections between proportional and nonproportional lines and equations and be able to relate their graphs to their solution sets in the coordinate plane. They will apply functional and graphical reasoning to identify whether or not functions are linear or nonlinear. Students will also interpret, write, graph, and solve linear functions in different forms, depending upon the given context. Students will extend their proportional reasoning as they use similar triangles to explain slope. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. |
SECOND SEMESTER
Unit 8Unit 4 Continued: Modeling Linear Relationships & Functions
Expected Dates: Late November to Early February In this unit, students will distinguish proportional relationships from other relationships. They will use proportional reasoning to explain why the slope is the same between any two points in a similar triangle. Students will analyze the connections between proportional and nonproportional lines and equations and be able to relate their graphs to their solution sets in the coordinate plane. They will apply functional and graphical reasoning to identify whether or not functions are linear or nonlinear. Students will also interpret, write, graph, and solve linear functions in different forms, depending upon the given context. Students will extend their proportional reasoning as they use similar triangles to explain slope. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. Unit 5: Investigating Data & Statistical Reasoning Expected Dates: Mid-February to Early March In this unit, students will extend the study of linear relationships by exploring models and tables. They will apply their functional and graphical reasoning to model relationships between quantities and describe the rate of change. The study of statistics expands from more simplistic samples and collections in sixth and seventh grade, to bivariate data, which can be graphed and a line of best fit determined. They will also make predictions and answer statistical questions based on data distributions. Unit 6: Real-Life Phenomena Explored Through Systems of Linear Equations Expected Dates: March In this unit, students will explore incorporate patterning and algebraic reasoning to create, interpret, solve, and graph linear equations and inequalities in one variable. The equations and inequalities include those with rational coefficients, variables on both sides and whose solutions require the use of the distributive property and combining of like terms. Students will interpret expressions with multiple factors and/or terms and manipulate linear and literal equations expressed in various forms. Unit 7: Irrationals, Integer Exponents and Scientific Notation Expected Dates: April to Early May In this unit, students will solve problems involving irrational numbers, radical and integer exponents, and scientific notation. Students will extend their knowledge of numerical reasoning and real numbers to include irrational numbers, develop an understanding of the properties of exponents, and perform operations with numbers expressed in scientific notation. Unit 8: Exploring Geometric Relationships Expected Dates: May to End of School Year In this unit, students will solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena. Students will extend their work with numerical reasoning (rational and irrational numbers) and apply geometric and spatial reasoning to interpret and solve problems involving the Pythagorean Theorem. Students will work with right triangles and investigate proofs of the Pythagorean Theorem and its converse. They will also extend their knowledge of volume from previous grades to explain real phenomena involving cones, cylinders, and spheres. |