Grade Six Advanced Mathematics Curriculum...

Grade Six Advanced Mathematics Curriculum Map

Course Number: 1205010 The intention of the Curriculum Map is to provide a consistent scope and sequence for the course across the district. While the instruction and resources will be based on the needs of the students, the expectation is that every student enrolled in the course will learn the standards in each module.

Unit 1 – Module 1

The Number System - Integers

(Approximately 5 days)

Highlighted Math Practice

Florida Math Standard Students should be able to: MFAS Tasks Suggested Instructional Resources

MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from Inside Mathematics

MAFS.6.NS.3.5: 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.

Identify an integer and its opposite.

Represent real-world quantities with positive and negative integers.

Rainfall Change

Relative Decimals

Relative Fractions

Relative Integers

Go Math – Lessons 1.1

MAFS.6.NS.3.7b: 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 -7oC.

Compare and order integers

Graph integers on a number line

Absolute Altitudes

Positions of Numbers

South Pole

Submarines

Visualizing Absolute Value


MAFS.6.NS.3.7c: 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.

Find absolute value of a rational number

Interpret

Absolute Altitudes


South Pole

Submarines



Module 1 - Key Vocabulary

Absolute Value Integers Negative Numbers Positive Numbers Opposites Inequality Number Line

http://www.cpalms.org/Public/PreviewStandard/Preview/6328

http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-2-reason-abstractly-quantitatively


http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-4-model-with-mathematics


http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/55953



http://www.cpalms.org/Public/PreviewResource/PreviewAssessment/55377


http://www.cpalms.org/Public/PreviewResource/PreviewAssessment/59107













Unit 1 – Module 2

The Number System – Factors and Multiples

(Approximately 4 days )



MAFS.K.12.MP.2.1: Reason abstractly and quantitatively. Click here for video examples from Inside Mathematics

MAFS.6.NS.2.4: 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.

Find the greatest common factor of two whole numbers less than or equal to 100.

Find the least common multiple of two whole numbers less than or equal to 12.

Represent real-world quantities with positive and negative integers.

Greatest Common Factor

Least Common Multiple

Using the Distributive Property

Go Math – Lessons 2.1 & 2.2


Greatest Common Factor Least Common Multiple










Unit 1 - Module 3

The Number System – Rational Numbers




MAFS.K.12.MP.3.1: Construct viable arguments and critique the reasonableness of others. Click here for video examples from Inside Mathematics

MAFS.6.NS.3.6: MAFS.6.NS.3.6a: 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. MAFS.6.NS.3.6c: 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.

Classify whole number, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between set of numbers

Identify opposites and absolute values of rational numbers

Explaining Opposites

Graphing on Cartesian Planes

Graphing Points in the Plane

Graphing Points on the Number Line

Locating Quadrants

Point Locations

What is the Opposite

Go Math – Lessons 3.1 & 3.2

MAFS.6.NS.3.7: Understand ordering and absolute value of rational numbers. MAFS.6.NS.3.7a: 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. MAFS.6.NS.3.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -30C > -70C to express the fact that -30C is warmer than -70C. MAFS.6.NS.3.7c: 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.

Compare and order set of rational numbers arising from mathematical and real –world context.

Absolute Altitudes


South Pole

Submarines




Rational Numbers Venn Diagram Absolute Value Whole Number Integers Irrational Number


http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-3-construct-viable-arguments-critique-the-reasoning-of-others























Unit 2 – Module 4

Number Operation – Fraction




MAFS.K.12.MP.4.1:

Model with

mathematics.

MAFS.K.12.MP.5.1: Use

appropriately tools

strategically.

MAFS.6.NS.2.4 Find the greatest common factor of two whole numbers and the least common multiple of two whole numbers … Use the Distributive Property to express the sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers.

Adding fraction and mixed number

Subtraction fraction and mixed number

Multiplying fractions with whole numbers

Greatest Common Factors

Least Common Multiples

Using the Identity Property

Go Math – Lesson 4.1

MAFS.6.NS.1.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, …

Multiply fractions

Multiply mixed numbers

Divide fractions

Divide mixed numbers

Solve problems involving multiplication and division of fractions

Contextualizing Fraction Division

Fraction Division

Juicing Fractions

Models of Fraction Division

Go Math – Lesson 4.2, 4.3, 4.4


Quotient Fraction Mixed number Reciprocal Numerator Denominator















Unit 2 - Module 5

Number Operation- Decimal




MAFS.K.12.MP.4.1:

Model with

mathematics. Click here

for video examples from

Inside Mathematics

MAFS.K.12.MP.5.1:

Look for and make use

of structure. Click here


Inside Mathematics

MAFS.6.NS.2.2 Fluently divide mulit-digit numbers using the standard algorithm.

Divide by whole number

Interpret the remainder

Long Division – 1

Long Division – 2

Long Division – 3


MAFS.6.NS.2.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation

Add and subtract decimal

multiply decimals

divide decimals

solve problems involving multiplication and division of fractions and decimals

Adding Multidigit Decimals

Dividing Multidigit Decimals

Multiplying Multidigit Decimals

Subtracting Multidigit Decimals

Go Math – Lessons 5.2, 5.3, 5.4, 5.5


Quotient Repeating decimal Terminating decimal




http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-5-use-appropriate-tools-strategically










http://www.cpalms.org/Public/PreviewStandardAssessment/Preview/57021




Unit 3 - Module 6

Proportionality : Ratios and Rates




MAFS.K.12.MP.3.1:

Construct viable

arguments and

critique the

reasonableness of

others.

MAFS.K.12.MP.4.1: Model with mathematics MAFS.K.12.MP.6.1:

Attend to precision

MAFS.6.RP.1.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

represent ratios with concrete models

write ratios and find equivalent ratios

Comparing Rectangles

Comparing Time

Interpreting Ratio

Writing Ratios


MAFS.6.RP.1.2: 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.

use rates and unit rates to compare quantities Book Rates

Explaining Rates

Identifying Unit Rates

Writing Unit Rates


MAFS.6.RP.1.3: 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 MAFS.6.RP.1.3a: 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. MAFS.6.RP.1.3b: Solve unit rate problems including those involving unit pricing and constant speed

apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

Bargain Breakfast

Comparing Rates

Finding the Whole

Homework Time

Making Coffee

Measurement Conversion

Party Punch – Comparing Rates

Sara’s Hike

The Meaning of Pi

Go Math- Lesson 6.1, 6.2, 6.3


Rate Unit rate Ratio Equivalent Ratio



http://www.floridastandards.org/Standards/PublicPreviewBenchmark6333.aspx


























Unit 3 - Module 7

Applying Ratios and Rates and Conversion in Measurement




MAFS.K.12.MP.4.1:

Model with

mathematics.

MAFS.K.12.MP.7.1:

Look for and make

use of structure.

MAFS.6.RP.1.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities

compare additive and multiplicative relationships

represent mathematical and real-world problems involving ratios and rates using tables and graphs

solve problems with proportions

convert units within a measurement system

Measurement Conversion

Party Punch – Comparing Rates

Sara’s Hike

The Meaning of Pi


Omit Go Math- Lesson 7.4


Ratio Rate Proportion Scale Scale Drawing Units











Unit 3 - Module 8

Proportionality Ratios and Rates Percent




MAFS.K.12.MP.2.1:

Reason abstractly

and quantitatively.

MAFS.K.12.MP.4.1:

Model with

mathematics

MAFS.6.RP.1.3 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. MAFS.6.RP.1.3c 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.

represent percents with concrete models and fractions

generate equivalent forms of fractions, decimals, and percents using real-world problems

solve real-world problems involving percent

Associative and Commutative Expressions

Equal sides, Equivalent Expressions

Generating Equivalent Expressions

Go Math – Lessons 8.1, 8.2, 8.3


Percent Equivalent decimal Proportional reasoning













Unit 4 - Module 9

Equivalent Expressions: Numerical expression




MAFS.K.12.MP.2.1:

Reason abstractly and

quantitatively.


appropriately tools

strategically.

MAFS.6.EE.1.1: Write and evaluate numerical expressions involving whole-number exponents.

generate equivalent numerical expressions using exponents

generate equivalent numerical expressions using prime factorization

simplify numerical expressions using the order of operations

Cube House

Evaluating Exponents

Paul’s Pennies



Exponent Order of Operation Base Power









Unit 4 - Module 10

Equivalent Expression : Algebraic expression




MAFS.K.12.MP.2.1:

Reason abstractly

and quantitatively.

MAFS.6.EE.1.2a: Write expressions that record operations with numbers and with letters standing for numbers. MAFS.6.EE.1.2b: 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.

determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.

Parts of Expressions

Substitute Resolution

Writing Expressions

Go Math – (Lesson 10.1)

MAFS.6.EE.1.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

Equivalent Exponents

Equivalent Expressions

Identifying Equivalent Expressions

MAFS.6.EE.2.6 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.

Gavin’s Pocket

Writing Real-World Expressions

MAFS.6.EE.1.2c: 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).

evaluate algebraic expressions for the given value of a variable

Parts of Expressions

Substitute Resolution

Writing Expressions

Go Math – (Lesson 10.2)

MAFS.6.EE.1.3: Apply the properties of operations to generate equivalent expressions.

generate equivalent expressions using the properties of operations.

Associative and Commutative Expression

Equal Sides

Equivalent Expressions

Go Math- (Lesson 10.3)


Base Exponent Numerical expression Operations Order of operation Algebraic expression Coefficient

Constant Equivalent expressions Evaluating Simplify Like terms Term Variable



























Unit 5 – Module 11

Equations and Inequalities: Equations and Relationships




MAFS.K.12.MP.2.1:

Reason abstractly

and quantitatively.

MAFS.K.12.MP.4.1:

Model with

mathematics.

MAFS.K.12.MP.5.1:

Use appropriately tools

strategically.

MAFS.6.EE.2.5 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.

write one-variable, one-step equations to represent constraints or conditions within problems

write inequalities

Finding Solutions of Equations

Finding Solutions of Inequalities

Solutions of Equations

Solutions of Inequalities

Go Math – Lessons 11.1, 11.2, 11.3, 11.4

MAFS.6.EE.2.6 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.

model and solve one-variable, one-step equations that represent problems

Gavin’s Pocket

Writing Real-World Expressions

MAFS.6.EE.2.7 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 non-negative rational numbers.

write corresponding real-world problems given one-variable, one-step equations

Center Section

Equally Driven

Solar Solutions

University Parking

MAFS.6.EE.2.8 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.

understand the relationship and plot the relationship with more than one inequality (example 3 < x > -2)

solve two step equations and inequalities

Acres and Altitudes

Rational Number Lines

Roadway Inequalities

Transportation Number Lines


Algebraic expressions Solution Coeffient Inequalities Evaluating Like terms Equivalent expression

Term Properties of operation Variable




























Unit 5 - Module 12

Equation and Inequalities: Relationships in two variables




MAFS.K.12.MP.2.1:

Reason abstractly

and quantitatively.

MAFS.K.12.MP.4.1:

Model with

mathematics.

MAFS.6.NS.3.6b: 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.

Identify and graph in all four quadrants




Locating Quadrants

Point Locations

What is the Opposite?

Go Math – (Lessons 12.1)

MAFS.6.NS.3.6c: Find and position integers and other

rational numbers on ... number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

MAFS.6.NS.3.8: 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.

Describe the location of points. For example five units right and two units up. (also use north, south , east, west)

Bike Lot Coordinates

Garden Area

Garden Coordinates

MAFS.6.EE.3.9: 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.

Analyzing the Relationship

Bicycling Equations

Grinding Equations

Table to Equation


Axis Coordinate plane Dependent variables Independent variables Ordered Pair Coordinate Origin

Quadrant x-axis y-axis y-coordinate x-coordinate

























Unit 6 - Module 13

Geometry : Area and Polygons




MAFS.K.12.MP.1.1: Make

sense of problems and

persevere in solving them

MAFS.K.12.MP.2.1: Reason

abstractly and

quantitatively.

MAFS.K.12.MP.3.1:

Construct viable arguments

and critique the

reasonableness of others.

MAFS.K.12.MP.4.1: Model

with mathematics.

MAFS.6.G.1.1: Find the area of triangles, special quadrilaterals, and polygons.

model area formulas for parallelograms, trapezoids, and rhombuses by decomposing and rearranging parts of these shapes

model area formulas for triangles by decomposing and rearranging parts of shapes

write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles where dimensions are positive rational numbers

write equations that represent problems related to the volume of right rectangular prisms where dimensions are positive rational numbers

Area of Kite

Area of Quadrilateral

Area of Triangle

Lost Key

Swimming Pool Walkway

Go Math – Lesson 13.1, 13.2, 13.3, 13.4

MAFS.6.EE.2.7: 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 non-negative rational numbers.

Center Section

Equally Driven

Solar Solutions

University Parking


Parallelogram Rhombus Trapezoid Triangle Polygon Quadrilateral Rectangular prism


















Unit 6 - Module 14

Geometry: Distance and Area in Coordinate Plane




MAFS.K.12.MP.2.1:


quantitatively.

MAFS.K.12.MP.3.1:

Construct viable

arguments and critique

the reasonableness of

others.

MAFS.6.NS.3.6b: Understand signs of numbers in ordered 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.

use absolute value to find distances between points in the coordinate plane

solve problems that involve drawing polygons in the coordinate plane and finding the length of a side




Locating Quadrants

Point Locations

What is the Opposite?

Go Math -Lessons 14.1, 14.2

MAFS.6.NS.3.8: 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.

Bike Lot Coordinates

Garden Area

Garden Coordinates

MAFS.6.G.1.3: 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 same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

solve problems that involve drawing polygons in the coordinate plane and finding the length of a side

Fence Length

Patio Area

Polygon Coordinates

Polygon Grid


Area Axis Perimeter Polygon Reflection Vertex Vertices





















Unit 6 - Module 15

Geometry: Surface Area and Volume




MAFS.K.12.MP.4.1:

Model with mathematics

MAFS.K.12.MP.6.1:

Attend to precision

MAFS.6.G.1.2: 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.

Find volume using the volume formula.

Use nets to find surface area

Bricks

Clay Blocks

Moving Truck

Prism Packing

Go Math – Lesson 15.1, 15.2, 15.3

MAFS.6.G.1.4: 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.

Pyramid Project Rust Protection Skateboard Ramp

Windy Pyramid

MAFS.6.EE.2.7: 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 non-negative rational numbers.

Solve equations of the form x + p = q and px = q

Center Section

Equally Driven

Solar Solutions

University Parking


Net Base Height Rectangular prism Volume Pyramid Surface area


http://www.floridastandards.org/Standards/PublicPreviewBenchmark6333.aspx


























Unit 7- Module 16

Measurement and Data: Summarizing Data


Highlighted Math Practice Florida Math Standard Students should be able to: MFAS Tasks Suggested Instructional Resources


abstractly and quantitatively.

MAFS.K.12.MP.3.1: Construct

viable arguments and critique the

reasonableness of others.

MAFS.K.12.MP.4.1: Model with

mathematics.


appropriately tools strategically.

MAFS.6.SP.1.1: Recognize a statistical question as

one that anticipates variability in the data related to

the question and accounts for it in the answers.

represent numeric data graphically, including dot plots, histograms, and box plots

use graphical representations of numeric data to describe the center, spread, and shape of a data distribution

summarize numeric data with numerical summaries, including the mean and median and the range and interquartile range (IQR)

interpret numeric data summarized in dot plots, histograms, and box plots

summarize categorical data with numerical and graphical summaries, including mode and relative frequency tables

Questions About a Class

TV Statistics

Go Math – Lesson 16.1, 16.2, 16.3, 16.4, 16.5

MAFS.6.SP.1.3: 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.

Compare Measures of Center and Variability

Explain Measures of Center

Explain Measures of Variability

MAFS.6.SP.2.4: Display numerical data in plots on

a number line, including dot plots, histograms, and box plots.

Basketball Histogram

Chores Data

Shark Attack Data

MAFS.6.SP.2.5: Summarize numerical data sets in

relation to their context, such as by: MAFS.6.SP.2.5c: 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. MAFS.6.SP.2.5d: 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.

Analyzing Physical Activity

Florida Lakes

Quiz Mean and Deviation

Select the Better Measure


Upper quartile Data Survey Box plot Histogram Interquartile range Lower quartile

Mean absolute deviation Median Mode Measure of center Measure of spread Range Statistical questions


































Unit 8 - Module 17

Number System – Integers Addition and Subtraction




appropriately tools strategically. Click

here for video examples from Inside

Mathematics


abstractly and quantitatively. Click


Mathematics

MAFS.K.12.MP.1.1: Make sense of

problems and persevere in solving

them. Click here for video examples

from Inside Mathematics

MAFS.7.NS.1.1: Apply and extend

previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MAFS.7.NS.1.1.c: Understand subtraction

of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. MAFS.7.NS.1.1.d: Apply properties of

operations as strategies to add and subtract rational numbers.

Students represent integer operations with concrete models and connect the actions with the models to standardized algorithms:

add integers fluently

subtract integers fluently

solve multi-step problems involving addition and subtraction of integers

Adding Integers

Exploring Additive Inverse

Finding the Difference

Rational Addition and Subtraction

Rational Water Management

Go Math – Lesson 17.1, 17.2, 17.3, 17.4

MAFS.7.NS.1.3: Solve real-world and

mathematical problems involving the four operations with rational numbers.

Positive and Negative Fractions

A Rational Number Expression

Complex Fractions

Monitoring Water Temperatures

Trail Mix Munchies


Difference Integers Negative numbers Opposites Positive number Sum Whole number

Absolute value Additive inverse Expressions Model








http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-1-make-sense-of-problems-persevere-in-solving-them

























Unit 8 - Module 18

Number Systems: Multiply and Dividing Integers




abstractly and quantitatively. Click


Mathematics

MAFS.K.12.MP.4.1: Model with mathematics. Click here for video examples from

Inside Mathematics

MAFS.K.12.MP.7.1: Look for and

make use of structure. Click here for

video examples from Inside

Mathematics

MAFS.7.NS.1.2: Apply and extend previous

understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Students represent integer operations with concrete models and connect the actions with the models to standardized algorithms.

Applying Rational Number Properties

Find Decimal Using Long Division

Integer Division

Negative Times

Negative Explained

Quotients of Integers

Understanding Products

Go Math – Lessons 18.1, 18.2, 18.3

MAFS.7.NS.1.1.b: Understand that

integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -( p _ q) = ___ (-p) q = ___p (-q) . Interpret quotients of rational numbers by describing real-world contexts. MAFS.7.NS.1.1.c: Apply properties of

operations as strategies to multiply and divide rational numbers.

multiply integers fluently

divide integers fluently

Adding Integers





MAFS.7.NS.1.3: Solve real-world and

mathematical problems involving the four operations with rational numbers.

use the order of operations to solve multistep problems involving integers



Complex Fractions


Trail Mix Munchies


Divide Dividend Divisor Integers Multiply Negative number Operation

Opposites Positive number Product quotient







http://www.insidemathematics.org/index.php/standard-7






































Unit 8 - Module 19

Number System : Rational Numbers




MAFS.K.12.MP.2.1:

Reason abstractly

and quantitatively.

Click here for video

examples from Inside

Mathematics

MAFS.K.12.MP.3.1:

Construct viable

arguments and

critique the

reasonableness of

others. Click here for

video examples from

Inside Mathematics

MAFS.K.12.MP.4.1:

Model with

mathematics. Click

here for video

examples from Inside

Mathematics

MAFS.7.NS.1.1.c: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Students represent and use rational numbers in a variety of forms:

write rational numbers as decimals

add, subtract, multiply, and divide rational numbers fluently

Adding Integers





Go Math –Lessons 19.1 to 19.7

MAFS.7.NS.1.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAFS.7.NS.1.2.d: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Applying Rational Number Properties

Find Decimal Using Long Division

Integer Division

Negative Times

Negative Explained

Quotients of Integers

Understanding Products

MAFS.7.NS.1.3: Solve real-world and mathematical problems involving the four operations with rational numbers.



Complex Fractions


Trail Mix Munchies

MAFS.7.EE.1.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Equivalent Perimeters

Equivalent Rational Expressions

Factored Forms

Identify Equivalent Multistep Expressions

MAFS.7.EE.2.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Alexa’s Account

Discount and Tax

Gas Station Equations

Reeling in Expressions

Using Estimation




http://www.insidemathematics.org/common-core-resources/mathematical-practice-standards/standard-3-construct-viable-arguments-critique-the-reasoning-of-others






















































http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/60895http:/www.cpalms.org/Public/PreviewResourceAssessment/Preview/60895




Rational number Repeating decimal Terminating decimal Integer Negative number Pattern Positive number

Whole numbers Additive inverse Opposite Rational number

Unit 9 - Module 20

Rates and Proportionality

(Approximately 7days )



MAFS.K.12.MP.2.1:


quantitatively. Click here


Inside Mathematics

MAFS.K.12.MP.4.1:

Model with



Inside Mathematics

MAFS.7.RP.1.1: Compute unit rates associated with ratios

of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Students represent and solve proportional relationships:

calculate unit rates from rates

represent constant rates of change given a table, verbal description, equation, or graph

determine constant of proportionality in real-world situations

Comparing Unit Rates

Computing unit Rates

Unit Rate Area

Unit Rate Length

Go Math – Lessons 20.1, 20.2, 20.3















MAFS.7.RP.1.2a: Decide whether two quantities are in a

proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. MAFS.7.RP.1.2b: Identify the constant of proportionality

(unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. MAFS.7.RP.1.2c: Represent proportional relationships by equations. MAFS.7.RP.1.2d: Explain what a point (x, y) on the graph

of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Babysitting Graph

Constant of Proportionality Trip

Deciding If Proportional

Finding Constant of Proportionality

Graphs of Proportional Relationships

Identifying Constant of Proportionality in Equations

Serving Size

Teacher to Student Ratios

Writing An Equation

MAFS.7.RP.1.3: Use proportional relationships to solve

multistep ratio and percent problems. Finding Fees

Gasoline Prices

Making Cookies

Tiffany‘s Tax


Constant Conversion factor Equivalent ratio Percent Rate Ratio Complex fraction

Constant of proportionality

Proportion Proportional relationship Rate of change Unit rate



























Unit 9 - Module 21

Proportions and Percent




MAFS.K.12.MP.2.1:


quantitatively. Click here


Inside Mathematics

MAFS.K.12.MP.4.1:

Model with



Inside Mathematics


appropriately tools

strategically. Click here


Inside Mathematics

MAFS.7.RP.1.3: Recognize and represent proportional relationships between quantities.

Students represent and solve problems involving proportional relationships:

solve problems involving percent increase, percent decrease, and percent of change

solve markup and markdown problems

use percents to find sales tax, tips, total cost, simple interest

Finding Fees Gasoline Prices

Making Cookies

Tiffany‘s Tax


MAFS.7.EE.1.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Explain Equivalent Expressions

Rectangle Expressions

MAFS.7.EE.2.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Alexa’s Account Discount and Tax Gas Station Equations Reeling in Expressions

Using Estimation


Proportion Percent Rate Ratio Unit rate Percent of decrease Percent of increase

Principal Simple interest






















Grade Six Advanced Mathematics Curriculum...

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