6 Weeks Unit Unit Focus and Learning Targets CC Math Standards 1 Division of Fluently divide multi-digit numbers using the standard algorithm. 6.NS.2 multi-digit numbers I can divide multi-digit numbers with speed and accuracy. I can use estimation and know if my answer makes sense. Vocabulary dividend, division notation, /, divisor, quotient, remainder, multi-digit, algorithm 1 Computation with decimals Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm. The use of estimation strategies supports student understanding of decimal operations. I can estimate with decimals. I can use estimation to determine the reasonableness of my answers. I can add and subtract multi-digit decimals with speed and accuracy. I can multiply and divide multi-digit decimals with speed and accuracy. 6.NS.3 addend, sum, minuend, subtrahend, difference, factor, product, divisor, dividend, quotient, remainder, estimation, reasonableness, algorithm 1 Factors and multiples 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. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2). 6.NS.4 Distributive Property, factor, greatest common factor (GCF), least common multiple (LCM), multiple, prime factorization I can identify the factors of two whole numbers less than or equal to 100 and determine the Greatest Common Factor. I can identify the multiples of two whole numbers less than or equal to 12 and determine the Least Common Multiple. I can use the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor. I can use the Distributive Property to express the sum of two whole numbers. 1
I can use prime factorization to determine the LCM and GCF of given numbers. 1 Fractions Interpret and compute quotients of fractions divided by fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 6.NS.1 quotient, reciprocal, inverse operation, equation I can compute quotients of fractions divided by fractions. I can interpret the meaning of quotients of fractions. I can solve real-world problems involving the division of fractions by fractions by using models and equations to represent the problem. 2 Integers and Absolute value Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperatures above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write -30 = 30 to describe the size of the debt in dollars. 6.NS.5 6.NS.7c +,, integer, negative, positive, opposite, rational, rational numbers, zero, magnitude, absolute value,,,,, magnitude I can identify an integer and its opposite on a number line. I can explain positive and negative numbers. I can use integers to represent quantities in real world situations. I can identify the absolute value of rational numbers. 2
2 Integers on a Number Line Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(- 3) = 3, and that 0 is its own opposite. Interpret statements of inequality as statements about the relative position of two numbers on a number line. Students use inequalities to express the relationship between two rational numbers, understanding that the value of numbers is smaller moving to the left on a number line. 6.NS.6a 6.NS.7a 6.NS.7b 6.NS.7d (x, y), coordinate plane, ordered pair, point, opposite, quadrant, x-axis, y- axis, origin, x, -x, absolute value, >, <,,, rational numbers, inequalities increase, decrease Write, interpret, and explain statements of order for rational numbers in real-world contexts. Understand ordering of rational numbers, that numbers get progressively smaller the further to the left you go on a number line. Distinguish comparisons of absolute value from statements about order. As the negative number moves to the left of a number line, the number decreases. However, the absolute value of a number is the distance from zero. I can recognize opposite signs of numbers as locations on opposite sides of 0 on the number line. I can describe the absolute value of a rational number as the distance from 0 on the number line. I can interpret absolute value as the magnitude of the number from 0 in a real world situation. I can use coordinates and absolute values to find distances between points. I can explain how numbers on a number line increase and decrease. I can reason that a double negative, e.g., -(-2) is the opposite of that number. I can explain statements of order for rational numbers in a 3
real world situation. I can distinguish comparisons of absolute value from statements about order. 2 Integers on the coordinate plane Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on all quadrants on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in all four quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6.NS.6c 6.NS.6b 6.NS.8 +,, coordinate plane, ordered pair, x-axis, y-axis, axes, origin, quadrants,(x, y), point, reflection, absolute value, distance, points, origin, coordinate Solve real-world problems involving graphing in all four quadrants on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first or same second coordinate. Understand that a line segment on a coordinate plane I can find and position integers and other rational numbers on a horizontal or vertical number line diagram. I can recognize the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located. I can reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y-axis [(x,y) and (-x,y)]. I can reason that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x-axis [(x,y) and (-x,y). I can demonstrate, using a coordinate plane, that if two ordered pairs only differ by the signs, the points are reflections across one or both axes. I can solve real-world problems by graphing points in all four quadrants of a coordinate plane. 4
I can calculate distances between two points with the same first coordinate or the same second coordinate using absolute value. 2 Algebraic Expressions Write, read, and evaluate expressions in which letters represent numbers. Write algebraic expressions from written expressions. Identify parts of an expression using mathematical terms. Evaluate expressions at given values of their variables. I can translate written phrases into algebraic expressions. I can translate algebraic expressions into written phrases. I can identify parts of an expression using mathematical terms. I can evaluate expressions given specific values for variables. I can evaluate algebraic expressions that arise from realworld problems. 6.EE.2a 6.EE.2b 6.EE.2c Coefficient, evaluate, algebraic expression, variable, sum, term, product, factor, quotient, order of operations 2 Expressions with Exponents Write and evaluate numerical expressions using whole number exponents. Evaluate expressions at given values of their variables including those involving whole number exponents. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. 6.EE.1 6.EE.2c 6.EE.6 Coefficient, evaluate, algebraic expression, written expression, exponent, power, base, superscript, ^, formula I can write numerical expressions involving whole number exponents. I can solve problems that include exponents. I can apply order of operation rules for expressions that include whole number exponents. I can use variables to represent numbers. Write expressions for real-world and mathematical problems. 5
3 Equality of Expressions Identify when two expressions are equivalent (when the two expressions name the same number regardless of the value substituted into them). Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.4 6.EE.3 Distributive Property, associative property, commutative property, multiplicative identity property, reciprocal, inverse, like terms I can combine like terms to find equivalent expressions. I can determine if two expressions are equivalent. I can prove that two expressions are equivalent no matter what number is substituted for the variable. I can create equivalent expressions using the properties of operations. I can apply properties of operations to create equivalent expressions. 3 Equations and Inequalities Values that Make the Equation and Inequality True Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. I can determine which value makes an equation true. I can determine which values make an inequality true. I can substitute a variable with a given variable in an equation to determine if the value is the solution. I can substitute a variable with a given value in an equality to determine if the value is a solution. 6.EE.5 Variable, inequality, equation, substitution, value, solution set 6
3 Equations Using Variables Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. 6.EE.6 Variables, expressions I can use variables to represent numbers in equations and inequalities. Understand that a variable can represent one number or a set of numbers. Write equations and inequalities for real-world and mathematical problems. 3 Solving one step equations for nonnegative numbers Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. I can solve one-step equations using all four operations with non-negative rational numbers. I can model solutions for equations of the form x + p = q and px =q with manipulatives, diagrams or story contexts. I can write and solve problems that represent real-world mathematical problems that involve non-negative rational numbers. 3 Inequalities Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Recognize that a constraint or a condition in an inequality refers to the boundary defined in the solution set. I can write an inequality to represent a set of solutions for real-world and mathematical problems. 6.EE.7 6.EE.8 Non-negative, rational, equations, inverse operations, Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, reciprocal, Additive Identity Property, Commutative Property of Addition, Commutative Property of Multiplication Infinity, infinitely, finite, inequality, constraint, condition, solution set, Multiplication Property of Equality, Multiplicative Identity Property, number line, Subtraction Property of Equality 7
3 Dependent and Independent variables I can recognize that inequalities of the form x > c and x < c have an infinite number of solutions. I can graph solutions to inequalities on a number line. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. I can describe how the change in the independent variable affects the dependent variable. I can use variables to represent two quantities that change in relationship to one another. I can identify the relationship between a table, graph, and equation. I can compare the data in a graph, a table, and an equation and determine when they represent the same real-world problem. I can recognize when quantitative relationships between dependent and independent variables are linear. I can organize and display data using tables and graphs. 6.EE.9 Coordinate plane, coordinates, value, x- axis, y-axis, x- coordinate, y- coordinate, dependent, independent, ordered pair, origin, quantitative, table, graph, equation 4 Ratios and Unit Rates Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the relationship between parts and wholes. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. 6.RP.1 6.RP.2 Ratio, terms of the ratio, part, whole Equivalent ratio, @, rate, unit rate, ratio, per, convert, conversion I can write a ratio to describe the relationship between two quantities. 8
I can explain the relationship between ratios, fractions, and division. Write a ratio in the form of a:b, a/b, a to b where b is not equal to 0. I can solve mathematical problems involving simple unit conversions. I can calculate unit rates given certain quantities. 4 Ratio tables and tape diagrams Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.RP.3a Equivalent ratios, tape diagrams, double number lines, equations, value, quantities, quadrants, proportion, proportional I can identify equivalent ratios. I can make and use a table of equivalent ratios to solve problems. I can find the missing value from a table of equivalent ratios. I can plot the values from a ratio table on a coordinate plane. I can use tables to compare ratios. I can use tape diagrams to solve ratio problems. 4 Real world ratio and unit rate Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 6.RP.3b Constant, equivalent ratios, tape diagrams, double number lines, equations, rate, unit rate 9
I can solve unit rate problems involving unit rates (including unit pricing and constant speeds). I can solve a unit rate problem by reasoning about tables of equivalent ratios, tape diagrams, double line diagrams, or equations 4 Percent Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. I can explain that percent is out of 100. I can explain how ratio and percent are related. I can find a percent of a quantity as a rate per 100 using ratios. I can solve problems involving finding the whole given a part and the percent by reasoning about tables or equivalent ratios, tape diagrams, double line diagrams, or equations. I can solve problems involving finding the whole given a part and the percent by reasoning about tables or equivalent ratios, tape diagrams, double line diagrams, and equations. 6.RP.3c Whole, part, percent, rate, equivalent ratios, tape diagrams, double number line, equation 5 Convert measurement units Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing 6.RP.3d Customary measurement, metric measurement, units, distance, volume, weight, gram, liter, meter 10
quantities I can convert units to solve real-world problems using multiplication and division in multiple ways. I can convert measurement units using ratio reasoning within customary units. I can convert measurement units using ratio reasoning within metric units. I can convert measurement units using ratio reasoning between customary and metric units. 5 Area Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. I can find the area of right triangles and other triangles. I can describe the relationships between the area of triangles and rectangles. I can find the area of quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes. I can find the area of polygons in real-world and mathematical problems. 5 Volume Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths (e.g., 3½ x 2 x 6) and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.1 6.G.2 Right triangles, quadrilaterals, polygons, composition, decomposition, rhombus, trapezoid, kite, square units Volume, rectangular prism, edge, cube, base, height, length, three-dimensional, square units, cubic units 11
I can use unit cubes to find the volume of right rectangular prisms in mathematical problems. I can use the formulas V = lwh and V = bh to find the volume of right rectangular prisms. I can find the volume of right rectangular prisms in realworld problems. 5 Polygons on a Coordinate Plane Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.3 Coordinate plane, polygon, vertex (vertices), points, sides I can draw polygons in the coordinate plane with given vertices. I can find the length of a side of a polygon when the endpoints of the side have either the same first coordinate or the same second coordinate. I can apply the techniques of finding polygon side lengths in real-world and mathematical problems. 5 Surface Area Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. I can represent three-dimensional figures using nets made up of rectangles and triangles. I can use nets to find the surface area of threedimensional figures composed of rectangles and triangles. I can apply the surface area techniques of threedimensional figures composed of rectangles and triangles in real-world and mathematical problems. I can solve real-world problems that involve finding the surface area of a rectangular prism, right triangular prism, 6.G.4 Surface area, nets, rectangles, triangles, three-dimensional, prisms, square pyramid, tetrahedron, square units, cubic units 12
right square pyramid, or right tetrahedron. 6 Measures of center and measures of variation Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.1 6.SP.2 6.SP.3 Statistics, statistical question, data, variability, variation, distribution, measures of center, spread, mean, median, range, statistical questions I can recognize the difference between a statistical and a non-statistical question. I can recognize that a statistical question will have variability in answers. I can explain how data answers statistical questions. I can write statistical questions. I can find the center of a set of data. I can describe a set of data by its spread and overall shape. I can recognize that mean and median are single numbers that represent measures of center and it summarize all values in a set of data. Know that range is a single number that is a measure of variation and it describes how values vary in the set of data. I can find the mean of a data set. I can find the median of a data set. 6 Displaying data and observing trends Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.4 6.SP.5 Box plots (box-andwhisker plots), number line, histograms, dot 13
Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability I can display numerical data on a dot plot, histogram and box plot. I can explain which type of plot (dot plot, line plot, histogram, or box plot) is the best way to display data. I can report the number of observations in a data set. I can analyze a data set and describe what attribute is being measured, how it was measured, and its units of measurement. I can find the inter-quartile range of a set of data on a graph. I can describe overall patterns and striking deviations in a set of data on a graph. I can explain how data can be affected by the context in which it was gathered. I can justify the use of a particular measure of center or measure of variability based on the shape of the data I can use a measure of center and a measure of variation to draw inferences about the shape of the data distribution I can describe overall patterns in the data and how they relate to the context of the problem. I can describe any deviations from the overall pattern and how they relate to the context of the problem. I can describe the overall shape of the set of data in terms of its symmetry plots, data set, attribute, interquartile range, lower quartile, upper quartile, maximum, minimum, deviation, symmetry, distribution, measures of center, mean, median, range, measures of variation, variability, attribute 14