Sixth Grade Math Curriculum Map Quarter Unit Unit Focus Common Core Math Vocabulary Standards Number system fluency Number system fluency

Transcription

1 Quarter Unit Unit Focus Common Core Math Stards Vocabulary 1 Number system fluency Long division (6.NS.2) Factors Multiples Percents Decimals Fractions 1 Number system fluency Operations with decimals: add, subtract, multiply divide (6.NS.3) Factors Multiples Percents Decimals Fractions 1 Number system fluency Review GCF LCM Prime Factorization (6.NS.4) Factors Multiples Fractions Prime factorization 1 Number system fluency Review Add/Subtract Fractions 5.NF.1. 5.NF.2. Factors Multiples Percents Decimals Fractions Prime factorization

2 Sum Difference Numerator Denominator 1 Number system fluency Multiplying Dividing Fractions (6.NS.1) Factors Multiples Percents Decimals Fractions Prime factorization Sum Difference Numerator Denominator Reciprocal Quotient Product Multiplicative Inverse 1 Number system fluency Ratios Unit Rates Percent of a Number (6.RP.1) (6.RP.2) (6.RP.3) Factors Multiples Percents Decimals Fractions Prime factorization Ratio Unit Rate

3 2 Rate, Ratio, Proportional Reasoning Using a number line (6.NS.7) (6.NS.7a) (6.NS.7b) Inequality Neutral 2 Rate, Ratio, Proportional Reasoning Absolute Value (6.NS.7) (6.NS.7c) (6.NS.7d) Identity Property Absolute Value 2 Rate, Ratio, Proportional Reasoning Numbers Add/Subtract (6.NS.5) 2 Rate, Ratio, Proportional Reasoning Multiply Divide Numbers (6.NS.5) 2 Rate, Ratio, Proportional Reasoning Graphing Points on Coordinate Plane (6.NS.8) (6.G.3) Coordinate Plane

4 2 Rate, Ratio, Proportional Reasoning Number Line/Coordinate Plane (Reflections) (6.NS.6) (6.NS.6a) (6.NS.6b) (6.NS.6c) Coordinate Plane Y-Axis X-Axis Origin Cartesian Plane Rate, Ratio, Proportional Reasoning Rate, Ratio, Proportional Reasoning Expressions Exponents (6.EE.1) Scientific Notation Exponents Exponential Notation Order Of Operations (6.EE.2c) Order of Operations Exponents Exponential Notation Properties of Operations (6.NS.4) (6.EE.3) Equation Inequality Solution Variable Equivalent Equivalent expressions Properties Coefficient

5 Constant Identity Property Associative Property Commutative Property Distributive Property Order of Operations Expression 3 Expressions Expression Equations: Solving Equations by Adding, Subtracting, Multiplying (6.EE.2a-b) Equation Inequality Solution Variable Equivalent Equivalent expressions Properties Coefficient Constant Identity Property Associative Property Commutative Property Distributive Property Order of Operations Expression 3 Expressions Equivalent Expression, One-Variable Equations (6.EE.4-9) Equation

6 Inequalities Inequality Solution Variable Equivalent Equivalent expressions Properties Coefficient Constant Identity Property Associative Property Commutative Property Distributive Property Order of Operations Expression 3 Expressions Geometry: Area, Surface Area, Volume of Rectangular Prism 3D Figures Review Coordinate Plane (6.G 1-4) Equation Inequality Solution Variable Equivalent Equivalent expressions Properties Coefficient Constant Identity Property Associative Property Commutative Property Distributive Property

7 Order of Operations Expression Y-Axis X-Axis Coordinate Plane Cartesian Plane 4 Statistics Probability Statistical Variability Distribution of Data (Range, Mean, Median Mode) (6.SP.1-3) Box whisker plot Quartiles Median Extremes Range Interquartile range Histograms Box plots Mean Mode 4 Statistics Probability Display, Summarize Describe Numerical Data (6.SP.4-5) Box whisker plot Quartiles Median Extremes Range Interquartile range Histograms Box plots Mean Mode

8 Unit: Number System Fluency Quarter: 1 Stard Learning Target Focused Mathematical Practice (6.NS.2) Fluently divide multi-digit numbers using the stard algorithm (6.NS.3) Fluently add, subtract, multiply, divide multi-digit decimals using the stard algorithm for each operation (6.NS.4) Find the greatest common factor of two whole numbers less than or equal to 100 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 with a common factor as a multiple of a sum of two whole number with no common factor. (5.NF.1) Add subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way I can fluently divide single multi-digit numbers. I can add, subtract, multiply divide decimals. I can find the GCF LCM of two numbers less than or equal to 100. I can add subtract fractions with unlike denominators including mixed numbers. 1) Make sense of problems 2) Reason abstractly quantitatively 4) Model with mathematics 5) Use appropriate tools strategically 7) Look for make use of structure. 5)Use appropriate tools strategically 5)Use appropriate tools strategically

9 as to produce an equivalent sum or difference of fractions with like denominators. 5)Use appropriate tools strategically (5.NF.2) Solve word problems involving addition subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions number sense of fractions to estimate mentally assess the reasonableness of answers. (6.NS.1) Interpret compute quotients of fractions solve word problems involving division of fractions by fractions. (6.RP.1) Underst the concept of a ratio use ratio language to describe a ratio relationship between two quantities (6.RP.2) Underst the concept of a unit rate a/b associated with a ratio a:b with b not equal to zero use rate language in the context of a ratio relationship (6.RP.3) Use ratio rate reasoning to solve real world mathematical problems I can solve word problems involving addition subtraction of fractions including unlike denominators by using benchmark fractions mental math. I can apply extend previous understing of multiplication division to divide fractions by fractions. I can underst ratio concepts use ratio reasoning to solve problems. 5)Use appropriate tools strategically 6) Attend to precision 8) Look for express regularity in repeated reasoning

10 Unit: Rate, Ratio, Proportional Reasoning Quarter: 2 (6.NS.7) Underst ordering absolute value of rational numbers. (6.NS.7a) Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram (6.NS.7b) Write, interpret, explain statements of order for rational numbers in real-world contexts (6.NS.7) Underst ordering absolute value of rational numbers. (6.NS.7c) Underst the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation (6.NS.7d) Distinguish comparisons of absolute value from statements about order (6.NS.5) Underst that positive negative numbers are used together to describe quantities having opposite directions or values; use positive I can identify the absolute value of a number. I can use the absolute value to calculate the distance between points. I can add subtract integers to describe quantities having opposite directions or values. 6)Attend to precision 6)Attend to precision 6)Attend to precision

11 negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation Sixth Grade Math Curriculum Map (6.NS.5) Underst that positive negative numbers are used together to describe quantities having opposite directions or values; use positive negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation (6.NS.8) Solve real-world mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates absolute value to find distances between points with the same first coordinate or the same second coordinate (6.G.3) 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 mathematical problems. (6.NS.6) Underst a rational number as a point on the number. Extend number line diagrams coordinate axes familiar from previous grades to I can multiply divide integers to describe quantities having opposite directions or values. I can graph points in all four quadrants of the coordinate plane. I can use coordinates to construct or find the length of a side of a polygon. I can plot identify ordered pairs on a coordinate plane. 6)Attend to precision 6)Attend to precision

12 represent points on the line in the plane with negative number coordinates. 5)Use appropriate tools strategically 6)Attend to precision (6.NS.6a) Recognize opposite signs of numbers as indicating locations on opposite sides of zero on the number line; recognize that the opposite of the opposite of a number is the number itself (6.NS.6b) Underst signs of numbers in ordered pairs as indicating locations 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. I can recognize a reflection according to the ordered pair. (6.NS.6c) Find position integers other rational numbers on a horizontal or vertical number line diagram; find position pairs of integers other rational numbers on a coordinate plane. (6.EE.1) Write evaluate numerical expressions involving whole-number exponents (6.EE.2c) Evaluate expressions at specific values of their variables. Include expressions that arise from formulas in real-world problems. I can write evaluate numerical expressions with whole-number exponents. I can evaluate expressions, including those from real-world formulas. 3) Construct viable arguments critique the reasoning of others 3)Construct viable arguments critique the reasoning of others

13 Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

14 Unit: Expressions Quarter: 3 (6.NS.4) Find the greatest common factor of two whole numbers less than or equal to 100 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 with a common factor as a multiple of a sum of two whole numbers with no common factor. (6.EE.3) Apply the properties of operations to generate equivalent expressions (6.EE.2a) Write expressions that record operations with numbers with letters sting for numbers. (6.EE.2b) Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity I can find the GCF LCM of two numbers less than or equal to 100. I can generate apply the properties of operations to solve problems. I can translate algebraic expressions into written phrases. I can identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) I can describe one or more parts of an expression as a single entity. 3)Construct viable arguments critique the reasoning of others 3)Construct viable arguments critique the reasoning of others (6.EE.4) Identify when two expression are equivalent (6.EE.5) Underst solving an equation or inequality as a process of answering a question I can identify two equivalent expressions prove they are equivalent no matter what number is substituted. I can explain how solving an equation is the process to find the value(s), if any, that make the equation true. 3)Construct viable arguments critique the reasoning of others

15 (6.EE.6) Use variables to represent numbers write expressions when solving a real world or mathematical problem (6.EE.7) Solve real-world mathematical problems by writing solving equations of the form x + p = q px = q for cases in which p, q, x are all nonnegative rational numbers. (6.EE.8) 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. (6.EE.9) Use variables to represent two quantities in a real world problem that change in relationship to one another; write an equations 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 independent variables using graphs tables, relate these to the equation. (6.G.1) Find area of right triangles, other triangles, special quadrilaterals, polygons by composing into rectangles or decomposing into triangles other shapes; apply these I can use substitution to find if a given value makes an equation or inequality true. I can solve real-world mathematical problems involving area, surface area, volume. 5)Use appropriate tools strategically

16 techniques in the context of solving real-world mathematical problems (6.G.2) Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, show the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V=lwh V=bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world mathematical problems. (6.G.3) 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 mathematical problems. Sixth Grade Math Curriculum Map (6.G.4) Represent 3-Dimensional figures using nets made up of rectangles triangles, use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world mathematical problems.

17 Unit: Statistics Probability Quarter: 4 (6.SP.1) Recognize a statistical question as one that anticipates variability in the data related to the question accounts for it in the answers. (6.SP.2) Underst that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, overall shape. (6.SP.3) 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.4) Display numerical data in plots on a number line, including dot plots, histograms, boxplots. (6.SP.5) Summarize numerical data sets in relation to their context. I can develop an understing of how data statistics vary. I can display numerical data in plots on a number line, including dot plots, histograms, boxplots. 5)Use appropriate tools strategically 6)Attend to precision 5)Use appropriate tools strategically 6)Attend to precision