Ratios and Proportional Relationships (6.RP) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities.  Students connect multiplication and division to ratios and rates by experiencing relative size or objects and quantities.  Students connect fractions and ratios.

1a  Understands unit rate and uses reate and ratio language to describe a ratio relationship between two quantities (6.RP.1, 6.RP.2)

The Number System (6.NS) 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 extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, most importantly 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.

2a  Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions (6.NS.1)

2b  Fluently divide multi-digit numbers using standarad algorithm (6.NS.2)

2c  Fluently add, subtract, multiply and divide multi-digit decimals using standard algorithm  (6.NS.3)

2d  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.  (6.NS.4)

2e  Understands that positive and negative numbers are used together to describe quantities having oppositedirections or values (6.NS.5)

2f  Understands a rational number as a point on the number line both horizontally and vertically (6.NS.6)

2g Understands ordering and absolute value of rational numbers (6.NS.7)

2h  Solves real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. (6NS.8)

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 use properties of operations to rewrite expressions in equivalent forms.  Students know that the solution of an equation are the values of the variables that make the equation true.  Students use properties and equality to solve one step equations.  Students construct and analyze tables and use equations to describe the relationship between quantities.

3a  Writes and evaluates numerical expressions involving whole-number exponents (6.EE.1)

3b  Read, write, and evaluate expressions in which letters stand for numbers when solving a real-world or mathematical problem. (6.EE.2, 6.EE.6)

3c  Evaluates expressions at specific values of their variables which include whole-number exponents by using conventional order. (Order of Operations) (6.EE.2)

3d  Applies the properties of operations to generate equivalent expressions. (distributive property, combining like terms) (6.EE.3)

3e  Identifies when two expressions are equivalent. (6.EE.4)

3f   Uses substitution to determine whether a given number in a specified set makes an equation or inequality true.(6.EE.5)

3g  Graphs solutions of inequalities on number line diagram (6.EE.8)

3h  Represents quantitative relationships between dependent and independent variables (6.EE.9)

Geometry (6.G)Students build on their prior learning by reasoning about relationships among shape to find area, surface area, and volume.  They decompose shapes to relate back to the rectangle, developing and justifying formulas for triangles and parallelograms.  Students use this knowledge to find surface area of prisms and pyramids.  They do this work with fractional side lengths and begin work on scale drawings and constructions by drawing in the coordinate plane.

5a  Find area by composing or decomposing into  rectangles and triangles (6.G.1)

5b  Find volume of right rectangular prisms (6.G.2)

5c  Work with the coordinate plane to find length of a side of polygons (6.G.3)

5d  Creates and uses nets representing three-dimensional figures to find
surface areas (6.G.4)

5e  Apply the geometric techniques learned to solve real-world and mathematical problems (6.G) (Mathematical practice #1)

Statistics and Probability (6.SP)Students’ understanding of number is built on and reinforced by looking at data statistically.  They come to understand that data may not have a definite center and that central tendency can be looked at with different lenses.  Median is roughly the middle value, mean is the value each data point would take on if the total were redistributed equally, and thus the data’s balance point.  The measure of variability helps summarizes data to more degree, hence students learn to describe, identify clusters, peaks, gaps, and symmetry of numerical data.

4a  Recognizes a statistical question that anticipates variability in data (6.SP.1)

4b  Describes statistical data by its center, spread, and shape (6.SP.2)

4c  Recognizes that a measure of center is a single number that summarizes the data (6.SP.3)

4d  Summarizes and describes distributions by displaying numerical data in line plots, dot plots, histograms and box plots (6.SP.4; 6.SP.5)

Mathematical Problem Solving

6a  Accurately solves grade appropriate problems.

6b  Effectively communicates problem solving steps, strategies, and solutions.