**Grade 5 GT Mathematics**In Grade 5 G/T Mathematics, instructional time should focus on five 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; (4) reasoning about geometric figures; and (5) developing understanding of statistical thinking

**.**In G/T Math instruction, the standards are blended so that students apply their learning to real world situations. Students will engage in the application of mathematics by integrating standards from the following domains:

**Ratios & Proportional Relationships (6.RP)**

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 rate.

**Number Systems (6.NS/7.NS)**- Note: Standards 6.NS.A.1-6.NS.B.4 will be taught in Grade 4 GT this year (2014-15). Beginning with the 2015-16 school year, these will no longer be part of Grade 5 GT Mathematics.

Throughout this unit, 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.

Also during this unit, students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers.

**Expressions & Equations (6.EE/7.EE)**

In this unit, 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 3

*x*=

*y*) to describe relationships between quantities.

Students use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Students will understand and use properties of operations to generate equivalent expressions. Students use and solve real-life mathematical problems using numerical and algebraic expressions and equations. Also, students will use variables to represent quantities in a real-world or mathematical problem to construct and solve simple equations and inequalities in one and two step. In gaining the understanding of solving the one and two-step equations and inequalities, students will reason about the quantity of their solutions.

**Geometry (6.G/7.G)**

Students 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, student discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface 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 by drawing polygons in the coordinate plane.

Students also continue their work with area, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in later grades, they reason about relationships among informal geometric constructions. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.

**Statistics & Probability (6.SP)**

Note: Standards 6.SP.A.1-6.SP.B.5 will be taught in Grade 4 GT this year (2014-15). Beginning with the 2015-16 school year, these will no longer be part of Grade 5 GT Mathematics.

Building on and reinforcing their understanding of number, 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. 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 build on the knowledge and experiences in data analysis developed in earlier grades. They develop a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center and spread, and terms such as cluster, peak, gap, symmetry, skew, and outlier. They begin to use histograms and box plots to represent and analyze data distributions. As in earlier grades, students view statistical reasoning as a four-step investigative process:

- Formulate questions that can be answered with data
- Design and use a plan to collect relevant data
- Analyze the data with appropriate methods
- Interpret results and draw valid conclusions from the data that relate to the questions posed.

Such investigations involve making sense of practical problems by turning them into statistical investigations; moving from context to abstraction and back to context; repeating the process of statistical reasoning in a variety of contexts.