Gibbs Course Descriptions and Math Pathways

The focus of this small group Mathematics Intervention class is to improve foundational skills and concepts required for developing mathematical fluency. Students meet with a mathematics teacher in small groups to work on skill fluency, to prepare for upcoming assessments and assignments, and to develop communication skills within mathematics.

Students are identified for this level of support if they are performing on or below grade level AND scoring Partially Meeting Expectations on the Mathematics MCAS. In addition, students may be recommended for this class based on various local mathematics assessments, IEP testing results, and/or a demonstration of overall low foundational mathematics skills. Recommendations from the students’ prior mathematics teacher will also be considered for this level of support. All of the lessons are aligned to the 2017 Massachusetts Curriculum Framework for Mathematics of both content and practice.

In grade 6, instructional time focuses on four critical areas: (1) connecting ratio and rate to whole number multiplication and division, and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

Students in Math 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in grade 7 by drawing polygons in the coordinate plane.

All students will engage in mathematical practices such as reasoning abstractly and quantitatively, looking for and expressing regularity in repeated reasoning, and looking for and making use of structure.

Students that are bypassing Math 6 will be enrolled in Math 7A. The opportunity is meant for students that display evidence of mastery of the content of Math 6 as well as the reasoning of Math 6. Students in this course will engage in the same material as that of Math 7 in addition to Math 8 topics that will prepare students for Algebra I, such as solving multi-step linear equations, solving systems of linear equations, and statistics and probability. In Math 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.

All students will engage in mathematical practices such as reasoning abstractly and quantitatively, looking for and expressing regularity in repeated reasoning, and looking for and making use of structure.