unit 1 : rates, ratios and · pdf fileunit 1 : rates, ratios and proportions time frame: 21...

Math Unit 1 Overview

MATH

Grade 6

Unit 1 : Rates, Ratios and Proportions

Time Frame: 21 days

Key Vocabulary: column, row, factor puzzle,

factors, product, multiple, rate table, unit rate,

ratio, rate, constant rate, unit rate, every, each,

per, scrambled rate table, unit price, coordinate

plane, x-axis, y-axis, ordered pair, coordinates, x-

coordinate, y-coordinate, unit rate triangle,

speed, distance, time, linked rate table ratio

table, basic ratio, equivalent ratios, proportion,

solving a proportion, , greatest common factor,

scale

Essential Questions:

What is ratio and ratio reasoning?

How does a ratio help us to compare quantities?

How does multiplication and division help us to understand ratios concepts and apply it to

problem solving?

Big Ideas:

Multiplication and Rates

Special Rate Situations and Graphing

Solve Problems with Ratio and Proportion

Identify, Solve and Write proportion Situations

Suggested Mentor Texts:

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Common Core State Standards Teaching Points/Lesson Activity Description Assessment

Mathematical Content

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

6.RP.2 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.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.EE.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.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.

Mathematical Practices

CC.K-12.MP.1 Make sense of problems and

Relate factor puzzles to four numbers in the multiplication table

Learn strategies for solving factor puzzles

Learn a quick practice routine

Solve and make factor puzzles

Understand rate situations as involving a constant increase

Distinguish multiplication situations from non-multiplication

situations

Make a table to show a rate situation for many multiples of the

situation

Understand rate tales as columns of the multiplication table

Understand unit rate and totals made from rates

Understand unit rate language

Understand how a rate table is related to equal-groups

multiplication

Decide if a constant rate is reasonable for a given situation

Identify rate tables and make up rate situations

Find the unit rate and use it to make a rate table

Make drawings to show a unit rate situation

Determine missing values in a rate table

Solve unit pricing problems

Graph a rate table in the coordinate plane

Initial Assessment –

Form A pre-test

Formative

Assessments–Quick

quizzes

Lesson 1: page 8

Lesson 2: page 16

Lesson 3: page 26

Lesson 4: page 32

Lesson 5: page 38

(Quick Quiz 1)

Lesson 6: page 50

Lesson 7: page 58

(Quick Quiz 2)

Lesson 8: page 64

Lesson 9: page 72

Lesson 10: page 80

Lesson 11: page 90

(Quick Quiz 3)

Lesson 12: page 98

Lesson 13: page 104

Lesson 14: page 108

(Quick Quiz 4)

http://www.corestandards.org/Math/Content/6/RP/A/1/



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

http://www.corestandards.org/Math/Content/6/EE/C/9/

persevere in solving them

CC.K-12.MP.2 Reason abstractly and

quantitatively

CC.K-12.MP.3 Construct viable arguments and

critique the reasoning of others

CC.K-12.MP.4 Model with mathematics

CC.K-12.MP.5 Use appropriate tools

CC.K-12.MP.6 Attend to precision

CC.K-12.MP.7 Look for and make use of

structure

CC.K-12.MP.8 Look for and express regularity in

repeated reasoning

Solve constant speed problems

Fill in missing values in a rate table

Graph a rate table in the coordinate plane

Given a graph, make a rate table

Understand that a ratio table is made from two related rate tables

Make drawings to show ratios

Use ratio language and the 2:3 written from

Understand basic ratios and equivalent ratios

Recognize ratio and non-ratio tables

Understand that a proportion is made up of two equal ratios

Solve a proportion problem by solving a factor puzzle

Tell the assumptions that must be stated to make a situation a

proportion problem

Understand that a factor puzzle can have the rows or columns

switched and still represent a proportion

Solve numeric proportion problems

Create proportion problems for numeric proportions

Understand that proportions can involve large numbers

Differentiate proportion from non-proportion problems

Solve proportion problems containing greater numbers

Understand and solve proportions that use a basic ratio

Use the greatest common factor to find a basic ratio

Math Writing Prompts

End of Unit

Assessment – Form

A assessment

Performance Task if

created.

Use the greatest common factor to find a basic ratio

Differentiate proportion from non-proportion problems

Solve problems that use a basic ratio

Use greatest common factor to solve proportion problems with

greater numbers

Solve, explain and edit proportion problems

Apply mathematical concepts and skills in meaningful contexts

Reinforce the common core mathematical content standards and

mathematical practices with a variety of problem-solving situations


MATH

Grade 6

Unit 2 : Area of Polygons

Time Frame: 13 days

Key Vocabulary: perimeter, area, square unit,

base, height, square inch, square foot, square

centimeter, right angle, perpendicular, height,

base, related rectangle, right angle, height,

parallelogram, rhombus, base, perpendicular,

related rectangle, related parallelogram, acute

triangle, obtuse triangle, parallelogram, area

base, height, vertex, dimensions, trapezoid,

complex figures, pentagon, hexagon, octagon,

polygon, regular polygon, ordered pairs, regular

polygon, coordinates, tessellations


What are different strategies for finding the area of regular and irregular shapes?

What are the different strategies for finding volume of rectangular prisms?

Why is it important to know more than one strategy to find area?

Big Ideas:

Units of Area

Area of any Right Triangle

Area of any Parallelogram

Area of any Triangle

Select the Needed Measurements

Area of any Trapezoid

Area of a Complex Figure

Area of any Regular Polygon

Graph Polygons in the Coordinate Plane

Focus on Mathematical Practices


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6.G.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.

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 and mathematical problems.

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

6.EE.3 Apply the properties of operations to generate equivalent expressions.

6.EE.6 Use variables to represent numbers and write

Use formulas to solve problems involving perimeter and area

Express measurements using exponents

Derive formulas for the area of a right triangle


Derive formulas for the area of a parallelogram using a rectangle


Find the area of any triangle

Identify the height of any triangle

Recognize that the area of a triangle is always one-half the area of

a parallelogram with the same height and base


Select or infer the dimensions needed to find the area and

perimeter of triangles and parallelograms


Form A pre-test

Formative

Assessments–Quick

quizzes

Lesson 1: page 128

Lesson 2: page 136

Lesson 3: page 146

Lesson 4: page 154

Lesson 5: page 162

(Quick Quiz 1)

Lesson 6: page 170

Lesson 7: page 178

Lesson 8: page 184

Lesson 9: page 194

http://www.corestandards.org/Math/Content/6/G/A/1/


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



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.





quantitatively







structure


repeated reasoning

Solve real-world problems

Derive the formula for the area of a trapezoid


Decompose complex figures into simpler figures

Solve problems involving perimeter and area

Decompose regular polygons into triangles

Solve problems involving perimeter and area

Draw polygons in the coordinate plane

Use coordinates to determine the side lengths of polygons

Solve real world problems


Reinforce the common core standards and mathematical practices

with a variety of problem-solving situations

(Quick Quiz 2)


End of Unit

Assessment – Form

A assessment

Performance Task if

created.


MATH

Grade 6

Unit 3 : Operations with Whole Number,

Fractions and Decimals

Time Frame: 23 days

Key Vocabulary: dividend, divisor, quotient,

remainder, ungrouping, numerator, denominator,

equivalent fractions, simplifying, unsimplifying,

common factor, common denominator, least

common multiple, reciprocal


How do operations illustrate the relationships between numbers?

How do we solve real world problems involving fractions and decimals?

How does knowing the relationship between divisors and quotients help me be a better

mathematician?

Big Ideas:

Multiplication and Division of Whole Numbers and Decimals

Relating, Composing, and Decomposing Decimals and Fractions

Multiplying Fractions and Dividing with Fractions and Whole Numbers

Dividing a Fraction by a Fraction


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6.NS.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.

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

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

6.NS.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.





quantitatively




Review meanings of place value

Review multidigit division with whole numbers

Use appropriate strategies to estimate and adjust multipliers in

division problems

Review subtraction and regrouping strategies

Observe patterns in multiplication by 0.1 and 0.01

Multiply by a decimal

Observe patterns in division by 0.1 and 0.01

Divide by a decimal divisor

Identify whether a situation requires multiplication or division

Understand how the size of the multiplier affects the size of the

product

Place the decimal points in products and quotients

Compare fractions and decimals

Add and subtract fractions, mixed numbers and decimals

Write equivalent fractions and decimals

Add, subtract, and compare fractions and decimals with different

unit fractions or different numbers of decimal places

Find common denominators when the denominators have not

common factors and are not multiples

Discuss different strategies for finding a common denominator

Write equations to solve real world problems involving fractions


Form A pre-test

Formative

Assessments–Quick

quizzes

Lesson 1: page 218

Lesson 2: page 226

Lesson 3: page 236

Lesson 4: page 246

Lesson 5: page 254

(Quick Quiz 1)

Lesson 6: page 264

Lesson 7: page 272

Lesson 8: page 278

Lesson 9: page 286

(Quick Quiz 2)

Lesson 10: page 297

Lesson 11: page 306

Lesson 12: page 314

(Quick Quiz 3)

Lesson 13: page 322

Lesson 14: page 330

http://www.corestandards.org/Math/Content/6/NS/A/1/

http://www.corestandards.org/Math/Content/6/NS/B/2/






structure


repeated reasoning

and decimals

Multiply fractions and whole numbers

Multiply fractions

Multiply mixed numbers

Divide fractions and whole numbers

Identify problems as multiplication or division situations

Practice multiplying and dividing with fractions in a variety of

problem situations

Relate division to finding an unknown factor in a multiplication

problem

Divide fractions by dividing numerators and dividing denominators

Understand the idea of dividing by unsimplifying

Connect dividing by unsimplifying to multiplying by the reciprocal

Practice dividing with fractions

Understand that numbers change in predictable ways when

multiplied and divided by fractions less than 1 and fractions greater

than 1

Understand and apply decimal and fraction operations




Lesson 15: page 338

Lesson 17: page 352

(Quick Quiz 4)


End of Unit

Assessment – Form

A assessment

Performance Task if

created.


MATH

Grade 6

Unit 4 : Surface Area of Prisms and

Pyramids

Time Frame: 10 days

Key Vocabulary: face, lateral face, edge, vertex

(vertices), base, congruent, prism, rectangular

prism, net, surface area, cube, pyramid, face,

edge, slant height


What are the different strategies for finding surface area of prisms?

Why is it important to know more than one strategy to find area?

Big Ideas:

Nets and Surface Area of Prisms

Nets and Surface of Pyramids


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6.G.1 Find the area of right triangles, other

triangles, special quadrilaterals, and polygons by

composing into rectangles or decomposing into

Use nets to model rectangular prisms

Explore the surface area of rectangular prisms

Use nets to model nonrectangular prisms


Form A pre-test

Formative

Assessments–Quick


triangles and other shapes; apply these

techniques in the context of solving real-world

and mathematical problems.

6.G.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.

6.EE.2 Write, read, and evaluate expressions in

which letters stand for numbers.

6.EE.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.





quantitatively







structure


Explore the surface area of nonrectangular prisms

Find the surface area of prisms

Solve real world problems involving surface area of prisms

Use nets to model pyramids

Find the surface area of pyramids

Solve real world problems involving surface area of pyramids




quizzes

Lesson 1: page 374

Lesson 2: page 384

Lesson 3: page 390

(Quick Quiz 1)

Lesson 4: page 398

Lesson 5: page 404

(Quick Quiz 2)


End of Unit

Assessment – Form

A assessment

Performance Task if

created.



repeated reasoning


MATH

Grade 6

Unit 5: Expressions and Equations

Time Frame: 24 days

Key Vocabulary: algebraic expression, evaluate

an expression, expression, numerical expression,

order of operations, term, variable, base,

exponent, power, equivalent expressions,

associative property of addition, commutative

property of addition, coefficient, like terms,

associative property of multiplication,

commutative property of multiplication, simplify,

distributive property, greatest common factor,

double number line, dependent variable,

independent variable, inequality, solution of an

equality, solution, solve, inverse operations,

multiplication inverse


How are real world situations expressed and recorded in mathematics?

How are mathematical expressions, equations, and inequalities used to represent and

solve real-world and mathematical problems?

How are expressions manipulated to suit various purposes and help solve problems?

Big Ideas:

Writing, Interpreting and Analyzing Expressions

Equivalent Expressions

Representing and Describing Quantitative Relationships

Solving Equations and Inequalities


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



6.EE.3

Apply the properties of operations to generate

equivalent expressions.

6.EE.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).

6.EE.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.






in a specified set.

6.EE.B.7

Solve real-world and mathematical problems by

writing and solving equations of the form x + p =

Understand the meanings of variable, expression, and term

Use the Order of Operations to simplify numerical expressions

Evaluate algebraic expressions for given values of the variables

Interpret whole number exponents as indicating repeated

multiplication

Write and simplify numerical expressions involving exponents

Evaluate algebraic expressions involving exponents

Use expressions with exponents to represent figures

Translate between algebraic expressions and words

Analyze algebraic expressions by applying the order of operations

Draw diagrams that represent the structure of algebraic

expressions

Identify and write expressions for dot diagrams

Make dot diagrams to match algebraic expressions

Analyze and evaluate algebraic expressions

Write expressions for areas of complex figures

Write expressions for surface areas of rectangular prisms based

on their nets

Understand the meaning of equivalent expressions

Write and recognize equivalent expressions

Connect real world situations, models and expressions


Form A pre-test

Formative

Assessments–Quick

quizzes

Lesson 1: page 422

Lesson 2: page 432

Lesson 3: page 442

Lesson 4: page 452

Lesson 5: page 459

(Quick Quiz 1)

Lesson 6: page 474

Lesson 7: page 488

Lesson 8: page 500

Lesson 9: page 510

(Quick Quiz 2)

Lesson 10: page 520

Lesson 11: page 532

Lesson 12: page 542

Lesson 13: page 550

(Quick Quiz 3)

Lesson 14: page 562






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 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.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.












6.NS.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

Understand and apply the commutative and associative properties

of addition and multiplication

Simplify expressions by combining like terms

Identify coefficients of terms

Understand and apply the distributive property

Use the properties of arithmetic to identify and write equivalent

expressions

Simplify and evaluate expressions

Use properties to write and recognize equivalent expressions

Write expressions for real world situations

Recognize quantities that vary together

Define variables for quantities

Use tables, diagrams, and equations to represent relationships

between quantities that vary together

Investigate how the rate of motion relates to tables, graphs, and

equations relating time and distance

Use different representations to find or estimate distances traveled

in given amounts of time

Make a table and a graph based on an equation

Relate equations, graphs and tables for constant-change situations

Write and relate cost equations to situations

Make tables to identify the company that offers the lowest price for

different numbers of items

Find solutions of inequalities

Lesson 15: page 572

Lesson 16: page 582

Lesson 17: page 594


End of Unit

Assessment – Form

A assessment

Performance Task if

created.





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.





quantitatively







structure


repeated reasoning

Graph one-variable inequalities

Write and graph inequalities that represent real world situations

Determine whether a given value is a solution of an equation or

inequality

Solve equations by reasoning about which value of the variable will

make the sides equal

Model and solve addition and subtraction equations

Model and solve multiplication and division equations





MATH

Grade 6

Unit 6: Volume of Rectangular Prisms

Time Frame: 8 days

Key Vocabulary: volume, unit cube, centimeter

cube, inch cube, cubic unit, cubic centimeter,

cubic inch


What are the different strategies for finding volume of rectangular prisms?

Big Ideas:

Writing, Interpreting and Analyzing Expressions

Equivalent Expressions

Representing and Describing Quantitative Relationships

Solving Equations and Inequalities


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Review the meaning of volume and how it is different from surface

area


Form A pre-test

Formative







in a specified set.







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, 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 edge lengths in the context

of solving real-world and mathematical problems.










quantitatively

Express volume using an exponent

Solve real world problems involving volume and surface area

Determine the volume of rectangular prisms with edge lengths less

than 1 unit

Find the volume of prisms with fractional edge lengths by packing

them with cubes of appropriate unit fraction edge lengths

Compose a rectangular prism with fraction edge lengths by layers

Write an expression for the volume of a rectangular prism with

whole-number or mixed-number dimensions

Practice finding volume of prisms with fractional edge lengths

Solve real world problems involving volume

Understand how the variables of the volume formula are related

Write and solve equations to solve real world problems



with variety of problem-solving situations

Assessments–Quick

quizzes

Lesson 1: page 616

Lesson 2: page 626

Lesson 3: page 638

Lesson 4: page 644

Lesson 5: page 652


End of Unit

Assessment – Form

A assessment

Performance Task if

created.









structure


repeated reasoning


MATH

Grade 6

Unit 7: Ratios and Rates with Fractions,

Decimals and Percents

Time Frame: 20 days

Key Vocabulary: compare ratios, unit rate

strategy, cross-multiplication, tape diagram,

multiplicative comparison, percent, liquid volume,

bar graph, circle graph


How does a ratio help us to compare quantities?

Why is it useful to know different forms of representing relationships between quantities?

Big Ideas:

Ratios, Fractions, Unit Rates, and Cross-Multiplying

Ratios with Tape Diagrams and Equations

Percent

Relate Different Measurement Units


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Use tables of equivalent ratios to compare ratios


Form A pre-test

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

6.RP.2 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.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.






in a specified set.

6.EE.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.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

Graph ratios and use graphs to compare ratios

Use unit rates to describe ratios and to compare ratios

Use the unit rate strategy to solve proportion problems

Make horizontal ratio tables

Write ratios in fraction notation

Compare and contrast fractions and ratios

Use the cross-multiplication method for solving a proportion

Understand why the cross-multiplication method works

Use tape diagrams to solve proportions

Compare solving proportions with tape diagrams to other methods

Solve problems involving part-to-part ratios and part-to-whole

ratios

Describe ratios using multiplicative comparisons

Describe ratios using equations

Use and discuss a variety of methods that can be used to solve

proportion problems

Recognize problems that are not proportion problems

Understand the meaning of percent

Find equivalent fractions, decimals, and percents

Learn methods for calculating a percent of a number

Find percent of a number

Find the whole from a percent and a portion

Formative

Assessments–Quick

quizzes

Lesson 1: page 672

Lesson 2: page 684

Lesson 3: page 692

Lesson 4: page 698

(Quick Quiz 1)

Lesson 5: page 706

Lesson 6: page 714

Lesson 7: page 720

(Quick Quiz 2)

Lesson 8: page 730

Lesson 9: page 740

Lesson 10: page 750

Lesson 11: page 756

(Quick Quiz 3)

Lesson 12: page 766

Lesson 13: page 776

(Quick Quiz 4)


End of Unit




distance and time.
















quantitatively







structure


repeated reasoning

Calculate the percent one number is of another

Use percents to make comparisons

Practice solving percent problems

Learn methods for converting units of length

Convert units of length in order to calculate area

Convert units of liquid volume, mass and weight within the same

measurement system




Assessment – Form

A assessment

Performance Task if

created.



MATH

Grade 6

Unit 8: Analyzing Statistics

Time Frame: 19 days

Key Vocabulary: numerical data, dot plot,

histogram, interval, leveling out, fair share, mean,

leveling data, unleveling data, median,

symmetric, range, quartiles, first quartile, third

quartile, box plot, interquartile range, mean

absolute deviation, cluster, peak, gap, outlier


Why is it important to summarize and display numerical data?

What are measures of center and how are they helpful in describing data?

What are measures of variation and how are they helpful in describing data?

Big Ideas:

Displaying Data

Summarizing Data, The Mean, the Median

Describing Variability in Data


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Recognize that numerical data involve variability

Display, interpret, and summarize numerical data


Form A pre-test

6.SP.1 Recognize a statistical question as one

that anticipates variability in the data related to

the question and accounts for it in the answers.

6.SP.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.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, and

box plots.

6.SP.5 Summarize numerical data sets in relation

to their context.





quantitatively







Interpret and construct a dot plot and a histogram

Understand that equal groups represent the mean

Calculate the mean

Use the mean to summarize and compare data in context

Determine the mean using a dot plot

Understand that the mean is a balance point of a dot plot

Find the median of a numerical set of data

Understand that shifting data can affect the mean and median

Choose the mean or the median as an appropriate measure

Understand that range is a measure that can be used to describe

the variability of data

Calculate the range of a set of numerical data

Calculate the first and third quartiles of a set of numerical data

Draw and interpret a box plot for a set of numerical data

Calculate the interquartile range of a set of numerical data

Understand the interquartile range is a measure that can be used

to describe the variability of data

Given a set of numerical data, calculate each value’s distance from

the mean; calculate the mean absolute deviation

Compare and interpret mean absolute deviations

Describe the shape of data

Choose an appropriate measure to describe a set of data

Collect and analyze data

Formative

Assessments–Quick

quizzes

Lesson 1: page 796

Lesson 2: page 806

(Quick Quiz 1)

Lesson 3: page 814

Lesson 4: page 820

Lesson 5: page 828

Lesson 6: page 838

(Quick Quiz 2)

Lesson 7: page 848

Lesson 8: page 858

Lesson 9: page 866

Lesson 10: page 872

Lesson 11: page 880

(Quick Quiz 3)


End of Unit

Assessment – Form

A assessment

Performance Task if

http://www.corestandards.org/Math/Content/6/SP/A/1/



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

structure


repeated reasoning




created.


MATH

Grade 6

Unit 9: Rational Numbers and the

Coordinate Plane

Time Frame: 15 days

Key Vocabulary: opposites, positive numbers,

negative numbers, origin, integers, absolute

value, ordered pair, x-coordinate, y-coordinate,

coordinate plane, x-axis, y-axis, rational number,

reflected point


How do operations illustrate the relationships between numbers?

How do we solve real world problems involving fractions and decimals?

Why are there negative numbers?

How can you write and graph positive and negative integers?

Big Ideas:

Discuss, Compare and Graph Integers

Discuss, Compare and Graph Rational Numbers


N/A

Technology:

Destination Math

Mega Math

Soar to Success

Interactive iTools



6.NS.5 Understand that positive and negative

numbers are used together to describe quantities

Identify positive and negative numbers in real world situations

Identify opposites


Form A pre-test

Formative

http://www.corestandards.org/Math/Content/6/NS/C/5/

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.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.7 Understand ordering and absolute value

of rational numbers.

6.NS.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.





quantitatively






Determine distance on a number line

Locate and plot integers on a horizontal or vertical number line

Compare and order integers using number lines and in real world

situations

Use absolute value to write opposites and compare integers

Identify quadrants of the coordinate plane

Locate and plot integers in all four quadrants of the coordinate

plane

Graph the solutions of real world problems

Locate and plot rational numbers on horizontal and vertical number

lines

Identify rational number opposites

Compare and order rational numbers using a number line

Compare and order rational numbers in real world situations

Use ordered (x, y) pairs to calculate distance in the coordinate

plane

Identify the effect on coordinates for reflections in the coordinate

plane

Graph real world situations in the coordinate plane




Assessments–Quick

quizzes

Lesson 1: page 898

Lesson 2: page 908

Lesson 3: page 920

Lesson 4: page 932

(Quick Quiz 1)

Lesson 5: page 942

Lesson 6: page950

Lesson 7: page 962

(Quick Quiz 2)


End of Unit

Assessment – Form

A assessment

Performance Task if

created.





structure


repeated reasoning

unit 1 : rates, ratios and · pdf fileunit 1 : rates, ratios and proportions time frame: 21...

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