The opportunity to teach both a numeracy and an integrated math class allowed me to have two very different math experiences. Because the numeracy class was generally less tied to a certain curriculum timeline than the integrated math class, I felt more free to have my students work on multi-day projects that required a high level of problem solving. In my integrated math class, I tried to focus more on making math relevant to my students’ lives to engage them in the curriculum. Fortunately, linear equations, which we spent the entire first half of the year learning, are highly applicable to patterns in everyday life, so creating activities around them proved to be fun and rewarding. 

Numeracy

Unit 1 – Integer Rules
We began the year by exploring positive and negative integers using hot/cold cubes. Students worked in expert groups to discover their given integer rule and then presented their findings to the class.

Unit 2 – Combining Like Terms
After more practice with positive and negative integers, we then segued into simplifying expressions that contained different terms. Students used Algeblocks to represent like and unlike terms and saw that they could only combine like terms.

Unit 3 – Distributive Property
From there, students began simplifying expressions by using their knowledge of the distributive property, positive/negative integer rules, and combining like terms. As a summative assessment, students created and presented original projects to show their understanding of the distributive property. Projects included raps, posters, graphic novels, and “Dear Confused” letters.

Unit 4 – Fraction Operations
After taking a pretest to assess their understanding of fraction operations, students then worked through an individualized series of fraction stations to learn the different operations. Upon finishing the fraction stations, students used their new knowledge to solve the riddle of Diophantus’s age and created mathematical tombstones for his “graveyard.”

Unit 5 – Solving Equations and Systems of Equations Algebraically
For the next few weeks, students worked to solve equations that eventually included distribution and fractions. They then applied this knowledge to solve real-world systems of equations scenarios and even created some scenarios themselves.

Unit 6 – Exponent Rules and Scientific Notation
We then transitioned to learning how to simplify equations using different exponent rules. In pairs, students discovered one exponent rule and then planned and implemented a lesson in which they each taught their rule to half the class. Students also played card games that asked them to recognize equivalent exponential expressions. Building off the exponent rules, students then figured out how to write numbers in scientific notation and simplify expressions that used scientific notation to represent real-life scenarios.

Integrated Math

When I took over my integrated math class at the beginning of November, my students were working to interpret slope and y-intercept from real-world scenarios. Students had been focusing on linear equations since the beginning of the school year and our study of them extended until mid-March.

Unit 1 – Linear equations
Within the broad topic of linear equations, we explored the following concepts:

• Finding slope and y-intercept from a table, equation, and graph
• Using slope and y-intercept to write a linear equation
• Distinguishing between proportional relationships and other linear relationships
• Interpreting the slope of proportional relationships as the unit rate
• Finding the solution to a system of equations using a table and graph
• Interpreting the solution to a system of equations in a real-world context
• Determining how many solutions a system has by looking at the equations
• Graphing lines from an equation

For most of the linear equations unit, students first encountered a concept by analyzing a real-world scenario and then worked on more skills-based practice. In November, students compared the rates of a robber and the policeman who was chasing him and used that data to create tables and graphs. From there, they found the slope and y-intercept and wrote linear equations. To practice working with unit rate and proportional relationships, students compared the price of papusas from different restaurants in Worcester and the amount of sugar in different sizes and brands of sodas. When studying systems of equations, groups of students analyzed different real-world scenarios to determine which company, product, or talent was the better business choice and then created commercials to advertise their findings.

Unit 2 – Square Roots and Rational Numbers
In this quick unit, students got reacquainted with the idea of a square number and learned that taking the square root is the inverse of squaring a number. After familiarizing themselves with perfect squares and their integer square roots, they realized that the square roots of non-perfect squares were irrational and could be estimated using the square roots of perfect squares.

Unit 3- Pythagorean Theorem
Students discovered the Pythagorean Theorem for themselves by finding the relationship between the area of the three squares that can be made using each side of a right triangle. From there, they used the formula to find the lengths of the hypotenuse and legs of a right triangle, as well as to determine whether or not a triangle is a right triangle. 

Unit 4 – Transformations
Students first encountered transformations by looking at Ms. Pac-man’s movements in a video game, and then went on to graphing transformed shapes on a coordinate plane. After defining translations, reflections, rotations, and dilations based on their graphs, students practiced working with each transformation through station work. They then transitioned from working with one transformation at a time to working with sequences of transformations, writing multi-step directions for their classmates to follow to get from the pre-image to the image. To conclude the unit, students used transformations to create art on a coordinate grid.

Additional Topics
As MCAS approached, we quickly explored transversals, volume, and line of best fit. After MCAS, we looked at each of these topics in more depth.