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District Overview The mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Grade 6 Description The Grade 6 Mathematics course will provide students with the information and tools necessary to be active in their learning of the basics of algebra. Students will learn algebraic skills, problem solving skills, geometry concepts, and what rational numbers are. Students will also strive to develop an importance for algebra by studying its relation to real world applications. These topics will prepare them for 7 th grade math and beyond.Grade 6 Units:

Topic 1: Use Positive Rational Numbers Topic 2: Integers and Rational Numbers Topic 3: Numeric and Algebraic Expressions Topic 4: Represent and Solve Equations and Inequalities Topic 5: Understand and Use Ratio and Rate Topic 6: Understand and Use Percent Topic 7: Solve Area, Surface Area, and Volume Problems Topic 8: Display, Describe, and Summarize Data

Subject: Mathematics Grade: 6 Suggested Timeline: 24 class periods

Unit Title: Topic 1: Use Positive Rational Numbers

Unit Overview/Essential Understanding: Algorithms can be used to add, subtract, and multiply decimal numbers. An algorithm can be used to divide whole numbers and decimals fluently. Visual models, such as area models and number lines, can be used to multiply fractions. The product of two fractions can be found by multiplying the numerators and then the denominators. Multiplying mixed numbers is an extension of multiplying fractions. Many real-world problem situations can be represented with a mathematical model, but that model may not represent a real-world

situation exactly. Visual models, such as number lines and area models, and equations can be used to represent and solve problems that involve division

of fractions. Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction. Visual models, such as number lines and area models, can be used to represent and solve problems that involve division of a fraction by

a fraction. Dividing by a fraction is equivalent to multiplying by the fraction’s reciprocal. The quotient of mixed numbers can be found by writing the mixed numbers as fractions and multiplying the dividend by the divisor’s

reciprocal. Multistep problems require students to carefully plan the steps they follow to find the solution.

Unit Objectives: At the end of this module, students will be able to independently use their learning to:

add, subtract and multiply decimals with precision add, subtract and multiply decimals to solve real word problems use place value structure to divide whole numbers and decimals divide decimals and whole numbers to solve real world problems use models to multiply fractions multiply the numerators and then the denominators to find the product of two fractions multiply mixed numbers use models to divide with fractions use equations to divide with fractions Use models and algorithms to divide fractions by fractions divide with mixed numbers

estimate the quotient of mixed numbers solve multistep problems with fractions and decimals

Focus Standards Addressed in this Unit: CC.2.1.6.E.2 – Identify and choose appropriate processes to compute fluently with multi-digit numbersCC.2.1.6.E.1 – Apply and extend previous understandings of multiplication and division to divide fractions by fractionsImportant Standards Addressed in this Unit:N/AMisconceptions:

Where to place the decimal when multiplying decimal numbers together. When the divisor is multiplied by a power of 10, to make it a whole number, the dividend must be multiplied by the same power of 10. To find the reciprocal of a whole number, the whole number must be turned to a fraction with 1 as the denominator. When multiplying fractions, the reciprocal of the divisor must be found first even when it is a whole number.

Concepts/Content: Ratios Proportions Percent Number Theory Concepts and

Operations

Competencies/Skills: Interpret and compute quotients

of fractions Solve Problems and compute

fluently with whole numbers and decimals

Description of Activities: Solve and Discuss It/Explain It Teacher Modeled examples Guided practice Individual practice

Assessments:Summative Assessments:

Mid-topic Assessment Mid-topic Performance Task End of topic Assessment End of topic Performance Assessment

Formative Assessments: Lesson Quizzes Online Homework (Math XL)

Interdisciplinary Connections: STEM Activity – “Improve Your School” 3-Act Math – “Stocking Up”

Additional Resources: www.ixl.com Pearson, enVisionmath2.0


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Unit Title: Topic 2: Integers and Rational Numbers

Unit Overview/Essential Understanding: Integers are counting numbers, their opposites, and zero. Integers can be compared, ordered, and used to describe real-world contexts. Each rational number can be associated with a unique point on the number line. A number to the right of another on the number line is the greater number The absolute value of a number can be described as the number’s distance from zero on the number line. A coordinate plane is formed by a horizontal number line, the x-axis, and a vertical number line, the y-axis, that intersect at a point called

the origin. An ordered pair (x, y) locates a point on the coordinate plane. Many real-world problem situations can be represented with a mathematical model, but that model may not represent a real-word

situation exactly The distance between two points on a coordinate plane with the same first coordinate or the same second coordinate can be found by

adding or subtracting the absolute values of the coordinates that differ. The coordinates of the vertices of a polygon on the coordinate plane can be used to find the lengths of the sides of the polygon and its

perimeter.Unit Objectives: At the end of this module, students will be able to independently use their learning to:

identify opposites of integers compare and order integers use integers to represent real-world quantities and explain the meaning of zero in each context plot rational numbers on a number line compare and order rational numbers use rational numbers to represent real-word quantities use absolute value to represent a number’s distance from zero interpret absolute value in real-world situations identify and graph points with rational coordinates on the coordinate plane reflect points with rational coordinates across both axes use mathematical modeling to represent a problem situation and to propose a situation test and verify the appropriateness of their math models explain why the results from their mathematical models may not align exactly with the problem situation use absolute value to find the distance between two points that lie on the same horizontal or vertical line on a coordinate plane solve real-world and mathematical problems involving distances on the coordinate plane

find side length of polygons on the coordinate plane find the perimeter of polygons on the coordinate plane

Focus Standards Addressed in this Unit: CC.2.1.6.E.4 – Apply and extend previous understandings of numbers to the system of rational numbersCC.2.3.6.A.1 – Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volumeImportant Standards Addressed in this Unit:N/A

Misconceptions: Numbers that are not preceded by a sign are presumed to be positive. Because negative numbers increase from right to left, students may place mixed numbers to the right of the whole number rather than

the left. Students may confuse the account balances with their absolute values. Students may think that they can find the distance between any two coordinates by adding or subtracting the absolute values of

coordinates.Concepts/Content:

Integers Rational numbers Area Surface Area Volume

Competencies/Skills: Use positive and negative

numbers to represent .quantities in real-word contexts

Plot integers and other rational numbers on a number line and on a coordinate graph

Interpret the opposite and absolute value of an integer as its distance from zero on a number line

Compare and order rational numbers



Mid-topic Assessment

Mid-topic Performance Task End of topic Assessment End of topic Performance Assessment


Interdisciplinary Connections: STEM Activity – “Improve Your School” 3-Act Math – “The Ultimate Throw”


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Unit Title: Topic 3: Numeric and Algebraic Expressions

Unit Overview/Essential Understanding: A whole number exponent can be used to represent repeated multiplication of a number. Any number can be written as its prime factorization. The greatest common factor (GCF) is the greatest factor that two or more numbers have in common. The least common multiple (LCM) is the smallest multiple that two or more non-zero numbers have in common. There is an agreed-upon order in which operations are carried out in a numerical expression. Algebraic expressions use variables to describe situations in which some of the information is not known. Parts of expressions can be described using words such as term, coefficient, product, and factor. The value of an algebraic expression can be found by replacing the variables with given numbers and doing the calculation that results. Many real-world problem situations can be represented with a mathematical model, but that model may not represent a real-world

situation exactly. The Distributive Property and other properties of operations are used to identify and write equivalent expressions. Algebraic expressions can be simplified using the properties of operations to combine like terms and generate equivalent expressions.


write expressions using whole number exponents to represent real-world and mathematical problems evaluate expressions with whole number exponents find the prime factorization of a whole number find the greatest common factor (GCF) and the least common multiple (LCM) of two whole numbers use the GCF and the distributive property to add use the GCF and LCM to solve problems evaluate expressions using the order of operations insert grouping symbols in a numerical expression to affect the value of the expression write an algebraic expression to model a pattern write an algebraic expression from a word phrase use precise mathematical language when identifying parts of an expression evaluate algebraic expressions, including those with whole numbers, decimals, and fractions use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their math models

explain why the result from their mathematical models may no align exactly to the problem situation write equivalent algebraic expressions identify equivalent algebraic expressions justify whether two expressions are equivalent use properties of operations to simplify algebraic expressions by combining like terms

Focus Standards Addressed in this Unit: CC.2.2.6.B.1 – Apply and extend previous understandings of arithmetic to algebraic expressionsCC.2.1.6.E.3 – Develop and/or apply number theory concepts to find common factors and multiplesCC.2.2.6.B.2 – Understand the process of solving a one-variable equation or inequality and apply the real-world and mathematical problemsImportant Standards Addressed in this Unit:N/A

Misconceptions: The exponent tells you the number of times the base is a factor, not the number of times it is multiplied When completing an order of operations problem, multiplication and division are done together from left to right. Parts of an algebraic expression are not always written in the same order. You can create equivalent expressions with Commutative, Associative, and Distributive properties.

Concepts/Content: Algebraic Expressions Number Theory Concepts and

Operations

Competencies/Skills: Write, identify and evaluate

numerical expressions involving exponents

Write, read and evaluate algebraic expressions

Apply the properties of operations to generate equivalent expressions

Solve problems and compute fluently with whole numbers and decimals

Find common multiples and factors including greatest common factor and least common multiple

Use the distributive property to express a sum of two numbers.


Assessments:

Summative Assessments: Mid-topic Assessment Mid-topic Performance Task End of topic Assessment End of topic Performance Assessment


Interdisciplinary Connections: STEM Activity – “Design a Bridge” 3-Act Math – “The Field Trip”


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Subject: Mathematics Grade: 6 Suggested Timeline: 27 Class Periods

Unit Title: Topic 4: Represent and Solve Equations and Inequalities

Unit Overview/Essential Understanding: A solution of an equation is a value for the variable that makes the equation true. An equation is true when the expressions or numbers on both sides of the equal sign have the same value. The same number can be added to, subtracted from, or multiplied on both sides of an equation and equality is maintained. Dividing on both sides of an equation by the same non-zero number also maintains equality. A problem situation can be represented by an equation with a variable. An equation can be solved by using the inverse operation and a property of equality. A multiplication or division problem situation can be represented by an equation with a variable. Inverse relationships and properties of equality can be used to solve equations with fractions, mixed numbers and decimals. An inequality is a mathematical sentence that contains the inequality symbol < (is less than), > (is greater than), ≤ (is less than or equal

to), ≥ (is greater than or equal to), or ≠ (is not equal to). An inequality describes a situation that has an infinite number of numerical possibilities. Many real-world problem situations can be represented with a mathematical model, but that model may not represent a real-world

situation exactly. Variables can be used to represent quantities that change in relationship to one another. The dependent variable changes in response to the independent variable. Patterns can be used to identify the relationship between quantities and write an equation that describes the relationship. Tables, graphs, and equations can be used to analyze the relationship between dependent and independent variables.


identify equations and variables use substitution to find solutions to equations use the properties of equality to keep both sides of an equation equal identify which properties or equality are used to write equivalent expressions write one-variable addition and subtraction equations use inverse relationships and properties of equality to solve one-step addition and subtraction equations write one-variable multiplication and division equations use inverse relationships and properties of equality to solve one-step multiplication and division equations write and solve equations that involve fractions, decimals, and mixed numbers understand the symbols required to write an inequality

write inequalities to describe mathematical or real-world situations describe solutions to an inequality represent solutions to an inequality on a number line use mathematical modeling to represent a problem situation and to propose a solution identify dependent variables identify independent variables analyze the relationships between variables by using tables write equations to represent the relationships between variables analyze the relationship between dependent and independent variables using tables, graphs, and equations

Focus Standards Addressed in this Unit: CC.2.2.6.B.1 – Apply and extend previous understandings of arithmetic to algebraic expressionsCC.2.2.6.B.2 – Understand the process of solving a one-variable equation or inequality and apply the real-world and mathematical problemsCC.2.2.6.B.3 – Represent and analyze quantitative relationships between dependent and independent variablesImportant Standards Addressed in this Unit:N/A

Misconceptions: The exponent tells you the number of times the base is a factor, not the number of times it is multiplied When completing an order of operations problem, multiplication and division are done together from left to right. Parts of an algebraic expression are not always written in the same order. You can create equivalent expressions with Commutative, Associative, and Distributive properties.

Concepts/Content: Algebraic Expressions Algebraic Equations

Competencies/Skills: Write, identify and evaluate

numerical expressions involving exponents



Represent and analyze quantitative relationships between independent and dependent variables

Solve and interpret one variable


equations or inequalities in real world mathematical problems

Assessments:



Interdisciplinary Connections: STEM Activity – “Design a Bridge” 3-Act Math – “Checking a Bag”


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Subject: Mathematics Grade: 6 Suggested Timeline: 25 periods

Unit Title: Topic 5: Understand and Use Ratio and Rate

Unit Overview/Essential Understanding: Ratios can be used to describe the relationship between two quantities where for every x units of one quantity, there are y units of

another quantity. Equivalent ratios can be found by multiplying or dividing both terms by the same nonzero number. Ratio tables can be used to compare ratios and solve problems. Equivalent ratios can be represented in a table, and the pairs of values can be potted on a coordinate plane. A rate is a special type of ratio that compares two quantities with different units of measure. A unit rate is a special rate that compares a quantity to one unit of another quantity. Rates are easily compared when they are expressed as unit rates. Unit rates, including unit prices, can be used to solve problems. Many real-world situations can be represented with a mathematical model, but that model may not represent a real-world situation

exactly. Unit rates and conversion factors can be used to convert customary units of measure. Unit rates and conversion factors can be used to convert metric units of measure. Unit rates and conversion factors can be used to convert between customary and metric units of measure.


use ratios to describe the relationship between two quantities use bar diagrams and double number line diagrams to model ratio relationships use multiplication and division to find equivalent ratios solve problems by finding equivalent ratios use ratio tables to compare ratios compare ratios to solve problems represent equivalent ratios on graphs use ratio tables and graphs to solve problems use rates to describe ratios in which the terms have different units use rates and unit rates to solve problems use ratio reasoning to compare rates and solve problems use unit rates to solve problems involving constant speed use unit rates to solve problems involving unit price

solve unit rate problems using an equation use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their math models explain why the results from their mathematical models may not align exactly to the problem situation use ratio reasoning and conversion factors to convert customary units of measure

Focus Standards Addressed in this Unit: CC.2.1.6.D.1 – Understand ratio concepts and use ratio reasoning to solve problems

Important Standards Addressed in this Unit:N/A

Misconceptions: Students may get confused when three or more quantities are described. Students may thing two ratios are not equivalent when you cannot multiply the terms of one ratio by a whole number to get the other

ratio. Students may have trouble figuring out with rate to use to solve a problem. Example: 12mi per gallon or 1 gallon per 12 mi

Concepts/Content: Ratio Proportions Percent

Competencies/Skills: Represent ratio relationships in

various forms Determine unit rates in context Interpret and compute quotients

of fraction Solve problems using ratio and

rate reasoning Convert measurement units using

equivalent ratios


Assessments:


Formative Assessments: Lesson Quizzes

Online Homework (Math XL)Interdisciplinary Connections:

STEM Activity – “Get into Gear” 3-Act Math – “Get in Line”


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Unit Title: Topic 6: Understand and Use Percent

Unit Overview/Essential Understanding: A percent is a rate in which the first term is compared to 100. The percent is the number of hundredths that represent the part of the whole Fractions, decimals, and percentages are three ways to show parts of a whole A percent greater than 100 is equivalent to more than the whole. A percent less than 1 is equivalent to less than 1/100 of the whole. Equivalent fractions and compatible numbers can be used to estimate the percent of a number. Finding the percent of a whole is like finding the fractional part of a whole Models and equations can be used to find the whole amount when the percent and part are known Many real-world problems situations can be represented with a mathematical model, but that model may not represent a real-world

situation exactlyUnit Objectives: At the end of this module, students will be able to independently use their learning to:

represent the percent of a whole find the percent of a whole write equivalent values as fractions, decimals, and percentages write fractions as decimals and percentages when the denominator of the fraction is not 100 write percentages that are great than 100 write percentages that are less than 1 estimate the percent of a number use the decimal form of a percent to find the percent of a number write an equation to solve a percent problem find the whole amount when given a part and the percent use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their math models explain why the results from their mathematical models may not align exactly to the problem situation

Focus Standards Addressed in this Unit:

CC.2.1.6.D.1 – Understand ratio concepts and use ratio reasoning to solve problemsImportant Standards Addressed in this Unit:N/AMisconceptions:

Students may have difficulty writing a percent when the model does not show hundredths. If student use the “shortcut” and move the decimal two places to the right to make a percent, they need to know how percent relates

to decimals and fractions. Students may not understand the difference between ½ and ½%. Have students represent a problem with an equation before they use the calculator or they might use it incorrectly. Students may confuse the part and the whole in a percent problem.

Concepts/Content: Ratio Proportions Percent

Competencies/Skills: Represent ratio relationships in

various forms Determine unit rates in context Interpret and compute quotients

of fraction Solve problems using ratio and

rate reasoning Convert measurement units using

equivalent ratios


Assessments:



Interdisciplinary Connections: STEM Activity – “Engineering to Prevent Extinction” 3-Act Math – “Ace the Test”



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Unit Title: Topic 7: Solve Area, Surface Area, and Volume ProblemsUnit Overview/Essential Understanding:

The formula for the area of a parallelogram, A=bh, can be derived from the formula of area of a rectangle. The formula for the area of a triangle, A = ½bh, can be derived from the formula for the area of a parallelogram. The areas of trapezoids and kites can be found by decomposing the trapezoids and kites into shapes for which the area formulas are

known. A solid figure can be classified based on the number of bases, the shape of the base(s), and the shape of the other faces. A net can be used to represent a polyhedron. Many real-world problem situations can be represented with a mathematical model, but that model may not represent a real-world

situation. The surface area of a prism is the sum of the area of its faces. The surface area of a pyramid is the sum of the area of its faces. Unit cubes or formulas can be used to find the volume of rectangular prisms and cubes.


use a formula to find the areas of parallelograms and rhombuses find the base or height of a parallelogram or rhombus when the area and the height or base are known find the area of triangles, including right triangles find the corresponding base or height or a triangle find the area of trapezoids find the area of kites find the areas of polygons by composing and decomposing shapes, including polygons on the coordinate plane classify sold shapes identify solid figures from nets draw nets of solid figures use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of math models explain why the results from mathematical models may not align exactly to the problem situation find the surface area of rectangular prisms, including cubes find the surface area of triangular prisms find the surface areas of square and triangular pyramids use cubes and a formula to find the volume of a rectangular prism or a cube with fractional edge lengths

Focus Standards Addressed in this Unit: CC.2.3.6.A.1 – Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volumeCC.2.2.6.B.1 – Apply and extend previous understandings of arithmetic to algebraic expressionsCC.2.1.6.E.4 – Apply and extend previous understandings of numbers to the system of rational numbersCC.2.2.6.B.2 – Understand the process of solving a one-variable equation or inequality and apply to real-world and mathematical problemsImportant Standards Addressed in this Unit:N/AMisconceptions:

Students may confuse the height and side of a parallelogram and rhombuses. Students may confuse the height and side of a triangle. Students may mistake the left and right sides of the kite as having the same area. Students may have difficulty distinguishing the difference between prisms and pyramids. When finding volume, students may only find the number of cubes in the bottom layer of the figure.

Concepts/Content: Area Surface Area Volume Integers Rational Numbers Algebraic Equations

Competencies/Skills: Represent and analyze

quantitative relationships between independent and dependent variables

Solve and interpret one variable equations or inequalities in real world and mathematical problems

Determine the area of triangles, quadrilaterals, irregular polygons and compound polygons

Calculate the area of a polygon on a plane given the coordinates of the vertices

Find volumes of right rectangular prisms with fractional edge lengths

Use nets to find surface area of 3-dimensional figures

Write, identify, and evaluate numerical expressions involving exponents




Use positive and negative numbers to represent quantities in real world contexts.

Plot integers and other rational numbers on a number line and on a coordinate graph.

Interpret the opposite and absolute value of an integer as its distance from zero on the number line

Compare and order rational numbers




Interdisciplinary Connections: STEM Activity – “Pack It” 3-Act Math – “That’s a Wrap”



Unit Title: Topic 8: Display, Describe, and Summarize DataUnit Overview/Essential Understanding:

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A statistical question anticipates variability in responses and can be answered by collecting and analyzing data. The mean, median, and mode are measures that can be used to describe the center of the data set. The range is a measure that can be used to describe the variability of a data set. A box plot is a good choice for displaying a distribution of numerical data values on a number line. Data values can be organized into equal intervals and displayed in a frequency table or histogram. Measures of variability, such as the mean absolute deviation (MAD) and interquartile range (IGR), describe the spread and clustering of

data in a set. Data sets may best be described using different measures of center and variability. A set of numerical data collected to answer a statistical question has a distribution that can be described by its center, spread, and

overall shape. Many real-world problem situations can be represented with a mathematical model, but that model may not represent a real-world

situation exactly.Unit Objectives: At the end of this module, students will be able to independently use their learning to:

identify statistical questions write statistical questions and display the collected data determine mean, median, mode, and range of a data set display data in a box plot interpret and analyze a box plot organize data into equal intervals and display the data in a frequency table or histogram interpret and analyze a histogram calculate the mean absolute deviation (MAD) and interquartile range (IQR) of a data set select the most appropriate measure of center and variability for a data set use measures to describe data sets describe the center, spread, and overall shape of a data set summarize numerical data sets using measures of center and related measures of variability use mathematical modeling to represent a problem situation and to propose a solution test and verify the appropriateness of their math models explain why the results from their mathematical models may not align exactly to the problem situation

Focus Standards Addressed in this Unit: CC.2.4.6.B.1 – Use a set of numerical data to develop an understanding of and recognize statistical variabilityCC.2.4.6.B.2 – Use numerical data and apply statistical properties to summarize and describe a distributionImportant Standards Addressed in this Unit:N/AMisconceptions:

Students may confuse the height and side of a parallelogram and rhombuses. Students may confuse the height and side of a triangle. Students may mistake the left and right sides of the kite as having the same area. Students may have difficulty distinguishing the difference between prisms and pyramids. When finding volume, students may only find the number of cubes in the bottom layer of the figure.

Concepts/Content: Data Distributions

Competencies/Skills: Display data in dot plots,

histograms, and box-and-whisker plots

Determine quantitative measures of center and variability

Choose the appropriate measure of center and variability for a set of data





Interdisciplinary Connections: STEM Activity – “Shake It Up” 3-Act Math – “Vocal Range”


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web view · 2017-06-21these topics will prepare them for 7th grade math and beyond. ......

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