Gateway’s middle school math program develops flexible and confident mathematical thinkers. We encourage learning through investigation, discovery, and problem-solving. Mathematics is taught through a combination of direct instruction, practice, and investigations in small groups. Gateway’s curriculum gives the solid foundation needed to succeed in middle school and to prepare for high school. Gateway middle school teachers work with students at their level, providing differentiated curriculum and online enrichment.
All sixth graders participate in Course 1 of College Preparatory Mathematics. In this class students learn the foundations of collaborative practice, productive discussion, and iterative inquiry to derive the meaning of mathematical procedures. Discovering how to learn in this way is viewed with equal importance to the content covered. Students in sixth grade study statistics as they collect, organize, and display data in multiple ways, analyze data using measures of central tendency, and represent data sets using various methods. They learn to construct and deconstruct numbers and operations by representing and comparing quantities using manipulatives, diagrams, and number expressions. For example, students learn how to use rectangular arrays to represent multi-digit multiplication. In addition, students represent integers on number lines and with manipulatives. They make sense of multiple representations of portions (decimal, fraction, percent) and convert from one form to the other. Students recognize ratios in tables and graphs and solve corresponding problems. They use ratios to describe relationships with similar plane figures and other situations. They also use models and standard algorithms for computations with fractions and decimals. Students explore beginning Pre-Algebra concepts such as simplifying variable expressions by combining like terms, using the Distributive Property, evaluating variable expressions and solving simple equations and inequalities. They also solve distance, rate, and time problems as well as solve percent problems including those with discounts, interest, and tips. Geometry is integrated into all areas of math investigations and students can compute area, surface area, and volume of rectangular solids and represent solids using nets.
In Course 2 students develop more strategies in collaborative mathematical practice and productive dialogue. They debate around mathematical ideas, and continue iterative inquiry to derive the meaning of more complex procedures. Learning in this way continues to be viewed with equal importance to the content covered. Course 2 develops students’ abstract thinking which is required for more algebraic representations. Students complete operations with integers and rational numbers, including use of the Order of Operations. They use diagrams and equal ratios to represent part-whole relationships. Percentages and scale factors are used to determine percent increase or decrease, discounts, and markups. Pre-Algebra skills are developed through investigation of how variable expressions represent quantities in contextual problems. Additionally, students learn to simplify variable expressions by combining like terms and using the Distributive Property. Students solve linear equations, including those with fractional coefficients, and those with no solutions or infinitely many solutions. They solve and graph one-variable inequalities. An extensive exploration of probability includes comparing experimental and theoretical probabilities, distinguishing between dependent and independent events, and calculating the probability of compound independent events. Students also represent probabilities of multiple events using area models, tree diagrams, and systemic lists. Study of statistics is continued through designing, conducting, and analyzing surveys. In addition, students collect, compare, and describe the distribution of data. Distance, rate, and time problems continue from Course 1 with increasing complexity. Proportional thinking is emphasized, as are ratios and the calculation of unit rates. Students extend their understanding of geometry through recognizing and using the properties of similar figures and scale factors to solve problems. They describe angles, angle pairs, and their measures. Students deepen their ability to compute area and perimeter of standard and compound shapes, as well as compute the volume of a variety of solids.
Students in Course 3 explore algebraic concepts by using problem-solving strategies such as: questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments that justify their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas. This course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. They learn to represent a linear function with a graph, table, rule, and context. They solve systems of equations by using tables and graphs. In addition, students symbolically manipulate expressions to solve problems including those with fractional coefficients, and solve contextual word problems using multiple strategies. They describe various geometric transformations on a coordinate grid. Their study of statistics continues from previous years as they represent data using scatterplots and describe associations, collect and analyze data, and make predictions based on the trend of the data. Students compare ratios and calculate unit rates and slope ratios. They analyze the slope of a line graphically, numerically, and contextually. Students recognize and solve problems involving proportional relationships. They graph and analyze non-linear functions. Connections between Algebra and Geometry are explored as students use the properties of similar figures to solve problems, and use the Pythagorean Theorem to solve problems in two and three dimensions. In addition, students use the relationships between angles created by parallel lines with transversals and the Triangle Angle Sum Theorem to solve problems. Students use square roots and cube roots as well as represent and simplify expressions using positive and negative exponents, use standard and scientific notation, and perform operations with numbers represented in scientific notation.
Core Connections Integrated I is the first course in a sequence of college preparatory mathematics courses that continues through Calculus. Because this is a high school equivalent course, we expect students who participate in this class to be motivated, exhibit excellent work habits, seek challenges, and to maintain a grade of at least 85%. The course is well-balanced among procedural fluency, deep conceptual understanding, problem solving, and adaptive reasoning. Integrated Math I develops fluency with solving linear equations, inequalities, and systems, and extends these skills to non linear functions. Students learn to represent and solve quadratic and exponential functions through use of graphs, tables, equations, and contexts. They use multiple techniques such as factoring, distributing, multiplying polynomials, and expanding exponential expressions to solve problems symbolically. Students analyze the slope of a line multiple ways, including: graphically, numerically, contextually (as a rate of change), and algebraically. They solve equations and inequalities using a variety of strategies. In addition, students solve systems of equations and inequalities with two variables both graphically and algebraically. They explore the relationship between Algebra and Geometry by use of rigid transformations and symmetry to demonstrate congruence. They develop triangle congruence theorems, and use coordinates to prove geometric theorems. Students explore geometric constructions (with compass and straightedge) as well as simple geometric proofs. They recognize representations of arithmetic and geometric sequences, including use of tables, graphs, and explicit or recursive formulas. Students learn statistical analysis of two-variable data: this includes determining regression lines, correlation coefficients, and creating residual plots.