## Math Curriculum

### Into Math:

Into Math uses an approach focused on a growth mindset for students and real feedback from teachers to drive growth for each and every learner. It prepares students to tackle any problem, supported by a teacher who has the tools and instructional techniques needed to ensure success. Every lesson begins with rigor right from the start. Independent learning tasks encourage students to practice productive perseverance by jumping into a new challenge or working collaboratively to solve problems while teachers guide and differentiate instruction.

In Grade 6, instructional time should focus 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.

1. Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
2. Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
3. Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
4. Building on and reinforcing their understanding of numbers, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.
5. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students in Grade 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.

### Cooperative Problem Solving:

Twice a month, students will work in groups to solve challenging math problems. Students will work on collaboration, questioning, and presentation skills in addition to developing critical thinking skills.

### Problem of the Day:

Students are given a daily word problem that is repeated practice of previously learned material. Problem of the day helps students build automaticity in math, through continuous practice. Students use a math rubric to self-assess their work and the work of their peers.

## English Language Arts Curriculum

To build a foundation for college and career readiness, students must read widely and deeply from among a broad range of high-quality, increasingly challenging literary and informational texts. Through extensive reading of stories, dramas, poems, and myths from diverse cultures and different time periods, students gain literary and cultural knowledge as well as familiarity with various text structures and elements. By reading texts in history/social studies, science, and other disciplines, students build a foundation of knowledge in these fields that will also give them the background to be better readers in all content areas.

### Into Literature:

Into Literature provides sixth with appropriately rigorous and high quality texts which students have the option to read or follow along with audio. The questions and tasks support close reading and critical analysis. The materials support knowledge building as well as attending to growing vocabulary and independence in literacy skills.

### Fountas & Pinnell:

The Fountas & Pinnell Benchmark Assessment Systems are accurate and reliable tools PS 86 teachers use to identify the instructional and independent reading levels of students. This assessment tool is also used to document student progress through one-on-one formative and summative assessments

### Writing:

Students will learn about the writing process as they publish writing pieces throughout the year to prepare them for Performance-Based Assessments (PBAs). Sixth graders will be exposed to various writing genres, narrative fiction, non-fiction, poetry, and opinion writing.