Through this past year, I’ve had the privilege of teaching both 10th grade geometry and 8th grade numeracy, which gave me a good variety of ages and curriculum to work with and learn about. Teachers at UPCS have curricular autonomy, so the curriculum I based much of my teaching off of followed along with what my two mentor teachers worked with in the past.

Geometry

Unit 1 – Polygons

I started my takeover with teaching all about polygons, tying in previously from a lot of the class’s work with triangles and angles, building that into shapes with greater than three sides. Students discovered a lot of what made a polygon a polygon and learned how to solve problems with polygons.

Unit 2 – Transversals

We then took our expanded knowledge of shapes and angles and put some extra logical thinking to it with introducing proofs through transversals. Students discovered whether or not angles created from a transversal would be congruent, supplementary, or neither through interactive discovery lessons, then were put to the task of proving these relationships using only postulates and teaching their peers about their proofs.

Unit 3 – Quadrilaterals and Coordinate Proofs

Using what we knew about transversals and angle pair relationships, we applied this to a coordinate grid and learned about characteristics of certain quadrilaterals and what we needed to know to prove different types of quadrilaterals. Students then put all this together by creating a blueprint for a house and proving the shapes of each room on the coordinate grid.

Unit 4 – Transformations

Students learned about how to transform a figure on a coordinate grid through translations, reflections, rotations and dilations. Utilizing isometric transformations, students created their own Tetris game and described the transformations that each piece took.

Unit 5 – Area and Polynomials

Students learned about multiplying and factoring polynomials in the context of finding area for buildings that have an unknown size. Students were provided puzzle-type questions to discover how to find the dimensions given an area and utilized problem-solving skills to find areas given the dimensions.

Unit 6 – 3D Shapes – Volume and Surface Area

This unit built up from 2D to 3D, applying a lot of what was learned and extending it into a third dimension. Students became the experts on their own shapes and taught each other about them at the beginning of the unit, then learned how to apply their knowledge to deeper-thinking real-world problems.

Unit 7 – Circles

Pi week! Students learned all about understanding circles, from the area and circumference equations to arcs, inscribed angles, and sectors.

Unit 8 – Linear Equations

By this point, we began some algebra review to make sure that the students felt freshened up in their skills before MCAS. Here, students learned how to make scatterplots and predict using a line of best fit and learned how to create linear equations given real-world scenarios.

Unit 9 – Systems of Equations and Inequalities

Students learned about solving systems graphically and algebraically through different contexts including cards, businesses, transportation, and grocery shopping.

Numeracy

Unit 1 – “Lazy Man Graphing”

By this point in the year, students had a good grasp of graphing using a table. Here, we tried building the understanding of the y-intercept and slope and how they work on a graph through plotting the intercept, moving one point through the slope, then drawing a line between them.

Unit 2 – Solutions to equations

In order to build algebraic understanding up for systems of equations, we went over how to tell if a coordinate point satisfied an equation by plugging in the x value and seeing if the resulting y value was the same as the point.

Unit 3 – Solving Systems of Equations by Graphing

Students put their graphing knowledge to work by graphing different scenarios of real-world contexts together to find when two graphs met. Students looked at purchasing from different companies, charging a phone and headphones, selling skateboards, and phone payment plans to see this.

Unit 4 – Rearranging Standard Form Equations to Slope-Intercept Form, Finding x and y intercepts

Many systems are written in standard form, but they make graphing fairly tricky. Here, students learned how to rearrange the equations so that y was isolated and the slope and intercept were found. Students then learned how to plug in 0 for either x or y to find the opposite intercept, then plot the intercepts and draw the line between them.

Unit 5 – Solving Systems of Equations by Substitution

Students know a lot of skills build around solving for systems of equations, but now we get to put them all together by solving algebraically for a system. Students worked in different contexts to find the solution by substituting one equation into the other and solving, then representing that in different ways, either through graphs or tables. Students became experts on some problems at the start of the unit, then taught their peers about their process and which company they suggested buying from. From there, contextual practice built up into solving more complex systems algebraically.