Math

Unit 1: Rates, Ratios and Proportions (Aug-Sept)

In this unit, 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. By analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates.

Unit 2: Areas of Polygons (Sept)

In this unit, students build upon their learning in earlier grades of finding areas of rectangles as they derive the formula of a triangle, a parallelogram, and a trapezoid by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. They will also draw polygons on the coordinate plane and use those coordinates to find the length of a side.

Unit 3: Operations with Whole Numbers, Fractions and Decimals (Oct-Nov)

In this unit, students compute with multi-digit numbers and perform arithmetic operations, including those involving fractions, decimals, and whole numbers. Students create connections among strategies that evolve into the proficient and fluent (efficient, accurate, appropriate and flexible) use of standard algorithms. They will also apply and extend their understanding of multiplication and division to divide fractions by fractions and connect meaning to real world problems.

Unit 4: Surface Area of Prisms and Pyramids (Nov-Dec)

In this unit, students further their skills in identifying and analyzing three-dimensional figures. They also build on what they learned previously to compose and decompose plane shapes to form a net and develop ways to find the surface area of solid figures. At this grade level, surface area is limited to faces that are triangles and rectangles.

Unit 5: Expressions and Equations (and Inequalities) (Dec-Jan)

In this unit, students develop an understanding 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.

Unit 6: Volume of a Regular Prism (Feb)

In this unit, students explore volume of rectangular prisms with fractional edge lengths. They discover that a rectangular prism can have a volume that is less than one cubic unit. They use their knowledge of equations to apply formulas V = lwh and A = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Unit 7: Ratios and Rates with Fractions, Decimals and Percents (Feb-Mar)

In this unit, students build on concepts of rates, ratios, and proportion introduced earlier in the year. Students will apply their skills of multiplication and division of fractions to find unit rates for ratios and to use these rates to solve problems. This work includes part to whole ratios, percents (finding percent of any number and converting between forms of a number (ie. fraction, decimal, percent), and measurement conversions to solve real world problems.

Unit 8: Rational Numbers and the Coordinate Plane (Mar-Apr)

In this unit, students extend their previous understandings of numbers 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. Students then apply their understanding of the coordinate plane to graph polygons and find vertical or horizontal distances between points.

Unit 9: Analyzing Statistics (Apr-May)

In this unit, students build on the knowledge and experiences in data analysis learned in earlier grades to develop a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center. They begin to use dot plots, histograms, and box plots to represent and analyze data distributions for quantitative data, and examine the multiple representations of the same data set.

Unit 10: Pulling the Learning Together (May)

In this culminating unit, students have the opportunity to apply grade level content in problem solving situations. The essence of this unit is flexibility, in order to differentiate and address the needs of students. Students engage in real world problems that require perseverance and communicate their thinking by constructing viable arguments and critiquing the reasoning of others. Instructional ideas can be found in the “Resources for Pulling the Learning Together” document in the Resources tab.