East Saint Louis District 189 Math Curriculum Grade 6 Web viewEast Saint Louis District 189 Math Curriculum ... to understand squares and square roots of numbers as well ... Louis

East Saint Louis District 189 Math Curriculum Grade 6

Sequence of Grade 6 Modules Aligned with the Standards Module 1: Positive Numbers and the Number Line 13 Days Module 2: Negative Numbers and the Number Line 8 Days Module 3: Multiplying and Dividing Fractions and Decimals 16 Days Module 4: Ratio 11 Days Module 5: Rates 10 days Module 6: Percent 12 Days Module 7: Algebraic Expressions 16 Days Module 8: Equations and Inequalities 13 Days Module 9: The Coordinate Plane 10 Days Module 10: Area of Polygons 13 Days Module 11: Circumference and Area of a Circle 13 Days Module 12: Surface Area and Volume of Solids 13 Days Module 13: Introduction to Statistics 9 Days Module 14: Measures of Central Tendencies Extension of Module 14: Statistics (7th grade book)

15 Days 9 Days

Summary of YearSixth grade mathematics is about (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; and (4)developing understanding of statistical thinking.

Key Areas of Focus for Grade 6: Ratios and proportional reasoning; early expressions and equations

Required Fluency: 6.NS.2 Multi digit division‐ 6.NS.3 Multi digit decimal operations‐

Adapted from Math In Focus. Page 1


CCSS Major Emphasis ClustersRatios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Apply and extend previous understandings of numbers to the system of rational numbers.

Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one variable equations and inequalities.‐ Represent and analyze quantitative relationships between dependent and independent variables.

Rationale for Module Sequence in Grade 6In Module 1, students will represent numbers in many different ways. They will use a number line to compare positive numbers, including fractions and decimals. Students will learn the difference between composite and prime numbers in order to use the Fundamental Theorem of Arithmetic to find the unique prime factorization of numbers. Students will apply this knowledge to find the greatest common factor and least common multiple by using tree diagrams, ladder diagrams or factor lists. Students will use geometric models to understand squares and square roots of numbers as well as cubes and cube roots. Students will apply their knowledge of exponents to using the order of operations to evaluate expressions.

Negative numbers is the focus of Module 2. Students will begin by using a number line to compare and order negative and positive numbers by visualizing the numbers’ position. Students will apply their knowledge of negative numbers to real world situations such as temperature. Absolute value will be taught using the number line to help students visualize a distance from zero. Students will also use absolute value skills to prepare them for performing operations on positive and negative numbers. Students will finish this module by using absolute value to interpret real-world situations.

In Module 3, students will learn how to divide fractions and to multiply and to divide decimals. Students will use bar models to understand and model division. Students will continue the use of bar models by drawing and revising models to aid in solving multi-step real-world problems.



Students will extend concepts learned with fractions to ratios in Module 4. Students will write equivalent ratios and ratios in simplest form. They will use comparison models and the unitary method to solve ratio problems. The bar model will also serve as the basis for solving problems with three quantities. Additionally, the students will deepen their understanding by solving problems involving two related sets of ratios and ratios that change.

Module 5 will extend the student’s knowledge of ratios to the concept of rate. They will move beyond the basic rate problems from Grade 5 into unit rates, rates that vary over time and average rates. Bar models will help students visualize more complex rate problems. Students will use word problems and tables to develop the d = s·t formula. Since average speed problems are used in business, science and other applications, students begin to develop that understanding in this module by finding the average speed by dividing the total distance by the total time.

Bar models will be used extensively in Module 6 as students visualize percent problems and solve them using the unitary method and more traditional models. Students will understand that percent means “per hundred” or “out of 100” in order to write fractions for percents with a denominator of 100. Grade 6 will be using new notation and terminology to connect with previously learned concepts. Students will start the module by writing equivalent fractions, decimals and percents. Bar models will be used to find the percent given a part and the whole, find a part given its percent and the whole and find the whole given a part and its percent. This work continues as students use bar models and the unitary method to find percent increase and percent decrease to solve real-world application problems.

Students will learn how to write algebraic expressions to represent situations in the world around them in Module 7. Students will start by learning to use variables to represent unknown quantities. They will learn the terminology for correctly identifying the terms in expressions. Students will evaluate algebraic expressions and simplify, expand and factor expressions as well. Students must be able to recognize equivalent expressions and solve real world problems using algebraic expressions. Bar models will continue to be the visual model used throughout this module to help students connect to abstract concepts.

Module 8 will begin with students deepening their understanding of the = to mean that two expressions have the same value. This will require multiple presentations and examples using a balanced scale in order to take this leap into abstraction. Students will use inverse operations to solve equations and begins to establish a strong base of using the properties of equality for further work in algebra. Students will then use an unbalanced balance scale to deepen their understanding of < and >. Students will evaluate inequality expressions and are introduced to the symbols ≤ and ≥ expanding their conceptions of comparing two quantities. This module will introduce students to the term linear equation and that it can be represented by the graph of a line. Students will use number lines to represent solutions to inequalities. Students will also learn that the representations of solutions of rays and lines indicate infinite solutions including fractions, mixed numbers and decimals as solutions. Bar models will be used to solve real world application problems.



Students will identify and plot points on the coordinate plane and calculate the lengths of line segments, including the sides of polygons in Module 9. Students will identify quadrants and be able to reflect points across an axis. Students will identify polygons from plotting points and then extend their work to locate unknown vertices when given the coordinates of two or more vertices. Absolute value will be used to calculate distance on the coordinate plane and students will solve problems involving the lengths of sides of polygons (even when the grid interval is greater than 1). Students will also calculate the perimeter of a polygon and locate a point in the interior of a polygon when give the distance from the side of the polygon. Students are introduced to linear graphs as a tool for representing the relationship between 2 variables. This knowledge will be used to solve application problems for real world situations.

Students will derive the formulas for area of triangles, parallelograms, trapezoids and regular polygons in Module 10. Then they will use the formula to find areas and unknown dimensions of these figures. Students will work on precise language by learning that the terms length and width apply to rectangles and do not apply to other polygons. Students will use a variety of types of triangles to identify the height of the triangle. Hands on activities will help as students move from concrete examples of the area of parallelograms and trapezoids to the formula for area of these figures. Students will recognize that the formula for the area of a triangle is the basis for deriving other area formulas. Polygons can be divided into identical triangles by drawing the segments from one vertex to another through the center. Students can find the area by using the length of one side of the polygon and the height of one of the triangles. Students will end this module by finding the area of composite figures.

Extending their work from plane figures to solids occurs in Module 12. Students will relate their nets and use nets to find surface area. Extensive use of hands-on activities will help students relate pictorial and concrete models to the abstract formulas. Students will draw prisms using isometric dot paper to reinforce the concrete-pictorial connection. Students will use formulas and algebraic thinking to solve surface area and volume problems modeling real-life situations.

In Module 13, students will collect, organize and tabulate data. They will display data using dot plots and histogram and analyze the distribution of the data. Students will use tally charts and frequency tables to organize data. Students will analyze distribution by observing the shape of dot plots. Students will use the terms symmetrical and skewed to describe the curve of data. Students will understand the importance of the scale along the vertical and horizontal axis when constructing a histogram. Students should compare histograms of the same data by looking at 4-intervals vs. 8 intervals and understand that the appearance of the graph may change but the data distribution does not. Students will learn about the difference between a histogram and a bar graph.



Students will learn to find the mean, median and mode of a data set and how to solve real world problems in Module 14. Students will also be able to identify a missing data item, given the mean and the rest of the values. Students also learn to compute weighted averages. Students will extend their work from Module 13 by relating the mean, median and mode to the distribution of a data set.

Students will further extend their work from Modules 13 and 14 by identifying measures of variation. They will divide a data set into quartiles and identify the interquartile range. Students will use this information to draw and interpret stem and leaf plots and box plots. (Resources for this extension will be found in the Grade 7 Math In Focus Book B sections 9.1-9.3).

Alignment Chart

Module and ApproximateNumber of Instructional Days

Common Core Learning Standards Addressed in Grade 6 Modules5

Suggested Text Book Resources

Number Talks and Instructional Strategies

Performance Based Tasks/Assessmentswww.illustrativemathematics.orgSEE APPENDIX FOR PRINTED COPY

Module 1:Positive Numbers and the Number Line(13 days)

MP. 1MP. 2MP. 3MP.4

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.B.4 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).

Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.C.6 Understand a rational number as a point on

Vocabulary:*Base (of an exponent)*Common Factor*Common Multiple*Composite Number*Cube (of a number)*Cube Root*Exponent*Factor (of a number)*Greatest Common Factor*Inequality

Factors and Common Factors6.NS.B.4 Multiples and Common Multiples6.NS.B.4


http://www.illustrativemathematics.org/illustrations/256


http://www.corestandards.org/Math/Content/6/NS/C/6

http://www.illustrativemathematics.org/


the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.

6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.

*Least Common Multiple*Mulitple*Number Line*Numerical Expression*Perfect Cube*Perfect Square*Positive Number*Prime Factor*Prime Number*Square (of a number)*Square Root*Whole Number

Fractions on the Number Line6.NS.C.7.a Integers on the Number Line 26.NS.C.7.a

Distance to School6.EE.A.2 Rectangle Perimeter 16.EE.A.2 The Djinni’s Offer6.EE.A.1

Module 2:Negative Numbers on the Number Line (8 days)

MP. 4MP. 7


6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature 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.

6.NS.C.6 Understand a rational number as a point on

Vocabulary:*Absolute Value*Negative Number*Opposite

It's Warmer in Miami6.NS.C.5 Mile High6.NS.C.5








http://www.corestandards.org/Math/Content/6/NS/C/7/a


the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6a 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.

6.NS.C.7 Understand ordering and absolute value of rational numbers.

6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

6.NS.C.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.

6.NS.C.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value 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.C.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars

Above and below sea level6.NS.C.7 Jumping Flea6.NS.C.7 Integers on the Number Line 26.NS.C.7.a Fractions on the Number Line6.NS.C.7.a Comparing Temperatures 6.NS.C.7.b






http://www.corestandards.org/Math/Content/6/NS/C/7/d

http://www.corestandards.org/Math/Content/6/NS/C/7/c

http://www.corestandards.org/Math/Content/6/NS/C/7


represents a debt greater than 30 dollars.

Module 3:Multiplying and Dividing Fractions and Decimals(16 days including 2 days for cumulative review)

MP.3MP. 4MP. 7MP. 8

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?


6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

Vocabulary:*Improper Fraction*Mixed Number*Reciprocals

Traffic Jam6.NS.A.1 Running to School, Variation 26.NS.A.1 Making Hot Cocoa, Variation 16.NS.A.1 Making Hot Cocoa, Variation 26.NS.A.1 How many _______ are in ?6.NS.A.1 How Many Containers in One Cup / Cups in One Container? 6.NS.A.1 Drinking Juice, Variation 26.NS.A.1 Drinking Juice, Variation 36.NS.A.1 Baking Cookies6.NS.A.1

Interpreting a Division Computation6.NS.B.2 Setting Goals6.NS.B.2 Buying Gas6.NS.B.3 Gifts from Grandma, Variation 36.NS.B.3 Jayden’s Snacks6.NS.B.3 Movie tickets6.NS.B.3 Reasoning about Multiplication and Division and Place Value,



















6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Part 16.NS.B.3 Reasoning about Multiplication and Division and Place Value, Part 26.NS.B.3

Module 4:Ratio (11 days)

MP.1MP. 4MP. 7MP. 8

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.RP.A.3 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.

6.RP.A.3a 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.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Vocabulary:*Equivalent Ratio*Ratio*Simplest form (of a ratio)*Term (of a ratio)

Games at Recess6.RP.A.1 The Escalator, Assessment Variation6.RP.A.1, 6.RP.A.2

Voting for Three,Variation 26.RP.A.3Voting for Three,Variation 36.RP.A.3 Running at a Constant Speed, Assessment Variation6.RP.A.2, 6.RP.A.3 Security Camera6.RP.A.3 Mixing Concrete6.RP.A.3 Jim and Jesse's Money6.RP.A.3 Kendall's Vase - Tax6.RP.A.3 Friends Meeting on Bicycles6.RP.A.3, 6.RP.A.3.b Converting Square Units6.RP.A.3 Currency Exchange6.RP.A.3 Dana's House6.RP.A.3

Module 5:Rates (10 days)

Apply and extend previous understandings of multiplication and

Vocabulary:*Average Speed*Rate*Speed

Traffic Jam6.NS.A.1 Video Game Credits6.NS.A.1























MP. 1MP. 2MP.6

division to divide fractions by fractions.

6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.


6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.


6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate

*Unit Rate Running to School, Variation 26.NS.A.1

Making Hot Cocoa, Variation 16.NS.A.1 Making Hot Cocoa, Variation 26.NS.A.1 How many _______ are in?6.NS.A.1 How Many Containers in One Cup / Cups in One Container? 6.NS.A.1 Drinking Juice, Variation 26.NS.A.1 Drinking Juice, Variation 36.NS.A.1

Interpreting a Division Computation6.NS.B.2

Converting Square Units6.RP.A.3 Currency Exchange6.RP.A.3 Dana's House6.RP.A.3 Data Transfer 6.RP.A.3.b

Friends Meeting on Bicycles6.RP.A.3, 6.RP.A.3.b Games at Recess6.RP.A.1 Jim and Jesse's Money6.RP.A.3 Kendall's Vase - Tax6.RP.A.3 Mangos for Sale6.RP.A.2




















http://www.corestandards.org/Math/Content/6/RP/A/2


language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1


6.RP.A.3b 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.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Mixing Concrete6.RP.A.3 Price per pound and pounds per dollar6.RP.A.2 Running at a Constant Speed6.RP.A.3, 6.RP.A.3.b Running at a Constant Speed, Assessment Variation6.RP.A.2, 6.RP.A.3 Security Camera6.RP.A.3 The Escalator, Assessment Variation6.RP.A.1, 6.RP.A.2 Voting for Three, Variation 16.RP.A.3 Voting for Three, Variation 26.RP.A.3 Voting for Three, Variation 36.RP.A.3

Module 6:Percent(12 days)

MP.3MP.4MP.7MP.8



6.RP.A.3c 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.

Vocabulary:*Base (of a percent)*Commission*Discount*Interest*Interest Rate*Markup*Percent*Sales Tax

Voting for Three Variation 16.RP.A.3 Voting for Three Variation 26.RP.A.3 Voting for Three,Variation36.RP.A.3 Shirt Sale6.RP.A.3.c Running at a Constant Speed6.RP.A.3, 6.RP.A.3.b Running at a Constant Speed, Assessment Variation6.RP.A.2, 6.RP.A.3 Security Camera6.RP.A.3 Mixing Concrete6.RP.A.3
























Overlapping Squares6.RP.A.3.c Jim and Jesse's Money6.RP.A.3 Kendall's Vase - Tax6.RP.A.3 Friends Meeting on Bicycles6.RP.A.3, 6.RP.A.3.b Converting Square Units6.RP.A.3 Currency Exchange6.RP.A.3 Dana's House6.RP.A.3

Module 7:Algebraic Expressions(16 days including 2 days for cumulative review)

MP.3MP.4MP.6MP.7


6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

6.EE.A.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. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from

Vocabulary:*Algebraic Expression*Coefficient*Equivalent Expression*Evaluate*Expand*Factor*Like Terms*Simplify*Substitute*Terms (of an expression)*Variable

Distance to School6.EE.A.2 Rectangle Perimeter 16.EE.A.2 Anna in D.C.6.RP.A.3.c, 6.EE.A.3, 6.EE.B.7, 7.RP.A.3, 7.EE.B.3 Rectangle Perimeter 26.EE.A.4Equivalent Expressions6.EE.A.4 Firefighter Allocation6.EE.B.6, 6.EE.B.7 Pennies to heaven6.EE.B.6, 6.NS.B.3, 6.RP.A.3, 8.EE.A.3, 8.EE.A.4, 8.F.A.1












formulas used in real-world problems. 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). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

6.EE.A.3 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.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Reason about and solve one-variable equations and inequalities.

6.EE.B.6 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

Pennies to heaven6.EE.B.6, 6.NS.B.3, 6.RP.A.3, 8.EE.A.3, 8.EE.A.4, 8.F.A.1 Firefighter Allocation6.EE.B.6, 6.EE.B.7



Module 8:Equations and Inequalities(13 days)

MP.4MP.6MP.7MP.8


C6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 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). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

Reason about and solve one-variable equations and inequalities.

6.EE.B.5 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.

6.EE.B.7 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.

6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or

Vocabulary:*Equation*Inequality*Solution*Linear Equation*Dependent Variable*Independent Variable

Log Ride6.EE.B.5

Firefighter Allocation6.EE.B.6, 6.EE.B.7

Fishing Adventures 16.EE.B.8



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.

Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.C.9 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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Chocolate Bar Sales6.EE.C.9

Module 9:The Coordinate Plane(10 days)

MP.2MP.4MP.5


6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6b Understand signs of numbers in ordered

Vocabulary:*Coordinates*Coordinate Plane*Linear Graph*Quadrants of a Coordinate Plane*x-axis*y-axis


http://www.corestandards.org/Math/Content/6/NS/C/6/b


pairs as indicating locations in 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.C.6c 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 a coordinate plane.

6.NS.C.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value 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.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.A.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 and mathematical problems.

Apply and extend previous



understandings of arithmetic to algebraic expressions. 6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 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). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

Module 10:Area of Polygons(13 days)

MP.4MP.6MP.7MP.8




6.G.A.1 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.

Vocabulary:*Base (of a triangle)*Formula*Height (of a triangle)*Regular Polygon

Base and Height6.G.A.1 Finding Areas of Polygons, Variation 16.G.A.1 Same Base and Height, Variation 16.G.A.1








6.G.A.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 and mathematical problems.

Same Base and Height, Variation 26.G.A.1

Module 12:Surface AreaAnd Volume of Solids (13 days)

MP.1MP.2MP.4MP.6


6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.



6.G.A.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, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional

Vocabulary:*Cross Section*Net*Pyramid*Surface Area

The Djinni’s Offer6.EE.A.1

Banana Bread6.G.A.2 Computing Volume Progression 16.G.A.2 Computing Volume Progression 26.G.A.2 Computing Volume Progression 36.G.A.2 Computing Volume Progression 46.G.A.2











edge lengths in the context of solving real-world and mathematical problems.

6.G.A.4 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.

Module 13:Introduction to Statistics(9 days)

MP.3MP.4MP.5

Develop understanding of statistical variability.

6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

6.SP.A.2 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.

Summarize and describe distributions.

6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5a Reporting the number of observations.

Vocabulary:*Dot Plot*Frequency*Histogram*Outlier*Range*Skewed*Symmetrical

Buttons: Statistical Questions6.SP.A.1Electoral College6.SP.B.5.d, 6.SP.A.2

Puppy Weights6.SP.A.2, 6.SP.B.4



6.SP.B.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.



Module 14:Measures of Central Tendency(13 days)

MP.1MP.2MP.4MP.5

Develop understanding of statistical variability.

6.SP.A.2 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.

6.SP.A.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.

Summarize and describe distributions.

6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5a Reporting the number of observations.

6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered

Vocabulary:*Mean*Median*Mode

Electoral College6.SP.B.5.d, 6.SP.A.2

Puppy Weights6.SP.A.2, 6.SP.B.4



Module 14 Extension:Measures of Central Tendency (Chapter 9 from 7th Grade Math In Focus Book B)(9 days + 2 additional days for cumulative review and end of year assessment)

Develop understanding of statistical variability.6.SP.A.3Recognize 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.

Summarize and describe distributions.6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.6.SP.B.5.cGiving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Use random sampling to draw inferences about a population.7.SP.A.1Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

VOCABULARY*5-point summary*biased sample*box plot*box-and-whisker plot*first quartile*interquartile range*leaf*lower quartile*mean absolute deviation*measure of variance*range*second quartile*stem*stem-and-leaf plot*third quartile*upper quartile

Resources will include the 7th Grade Math In Focus Book B sections 9.1 – 9.3

Key: Major Clusters; Supporting Clusters; Additional Clusters


http://www.corestandards.org/Math/Content/7/SP/A/1/

http://www.corestandards.org/Math/Content/6/SP/B/5/c/

http://www.corestandards.org/Math/Content/6/SP/B/4/

http://www.corestandards.org/Math/Content/6/SP/A/3/


Examples of Linking Supporting Clusters to the Major Work of the Grade Solve real-world and mathematical problems involving area, surface area and volume: In this cluster, students work on problems with

areas of triangles and volumes of right rectangular prisms, which connects to work in the Expressions and Equations domain. In addition, another standard within this cluster asks students to draw polygons in the coordinate plane, which supports other work with the coordinate plane in The Number System domain.


Documents

East Saint Louis District 189 Math Curriculum Grade 6 Web viewEast Saint Louis District 189 Math Curriculum ... to understand squares and square roots of numbers as well ... Louis