Math 1 advanced: 6th grade                  This course has been changed. The old advanced course is now called honors.                             

In Volusia county we structure courses by Common Core State Standards (CCSS.) We used to use the Florida's Next Generation Sunshine State Standards (NGSSS) and associated benchmarks. YOU WILL BE TESTED THIS YEAR ACCORDING TO NGSSS.

We divide the courses by Essential Questions. The Essential Questions are then divided by Measurement Topics which are then outlined with learning targets.

Unit 1: The Number System
Essential Question(s): How does my knowledge about multiplication and division facts help me to solve problems?

MACC.6.NS.2.2 Fluently divide multi-digit numbers using the standard algorithm

 divide positive integers.  use the standard algorithm to fluently divide multi-digit numbers.

MACC.6.NS.2.4 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.

 determine all factors of any given number, less than or equal to 100.  determine the greatest common factor of any two numbers, less than or equal to 100.  create a list of multiples for any number less than or equal to 12.  determine the least common multiple of any two numbers, less than or equal to 12.  apply the distributive property to rewrite a simple additional problem when the addends have a common factor.

 

Unit 2: Ratios and Proportional Relationships
Essential Question(s): How can ratios and proportional relationships be used to determine unknown quantities? How are ratios and proportional relationships used to express how quantities are related and how quantities change in relation to each other?

MACC.6.RP.1.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.	 define the term ratio and demonstrate my understanding by giving various examples.  write a ratio that describes a relationship between two quantities  explain the relationship that a ratio represents.
MACC.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.	 define the term “unit rate” and demonstrate my understanding by giving various examples.  recognize a ratio written as a unit rate, explain a unit rate, and give an example of a unit rate.  convert a given ratio to a unit rate.  describe the ratio relationship represented by a unit rate.
MACC.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. a. 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. b. Solve unit rate problems including those involving unit pricing and constant speed. c. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.	 solve real-world problems involving proportional reasoning by using various diagrams.  create a table of equivalent ratios.  Use the proportional relationship to find missing values in a table of equivalent ratios.  compare ratios presented in various tables.  plot corresponding values from an equivalent ratio table on a coordinate plane.  apply proportional reasoning to solve unit rate problems.  use visual representations (e.g., strip diagrams, percent bars, one-hundred grids) to model percents.  write a percent as a rate per one-hundred.  apply proportional reasoning to find the percent of a given numbers.  apply proportional reasoning to find the whole when given both the part and the percent.  use a ratio as a conversion factor when working with measurements of different units.

Unit 3: Concepts of Rational Numbers
Essential Question(s): How can rational numbers be represented in multiple ways? How are rational numbers useful when examining situations involving numbers that are not whole?

MACC.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.	 describe and give examples of how positive or negative numbers are used to describe quantities having opposite directions or opposite values.  recognize that positive and negative signs represent opposite values and/or directions.  explain that the number zero is the point at which direction or value will change.  use positive and negative numbers along with zero to represent real world situations.
MACC.6.NS.3.6 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. a. 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. b. 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 sign, the locations of the points are related by reflections across one or both axes. c. 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.	 show and explain why every rational number can be represented by a point on a number line.  plot a point on a number line or coordinate plane.  read a point from a number line or a coordinate plane.
MACC.6.NS.3.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. c. 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. d. Distinguish comparisons of absolute value from statements about order.	 describe the relative position of two numbers on a number line when given an inequality.  interpret a given inequality in terms of a real world situation.  define absolute value as it applies to a number line.  describe absolute value as the magnitude of the number in a real world situation.  compare between using a signed number and using the absolute value of a signed number when referring to real world situations.
MACC.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.	 graph points in any quadrant of the coordinate plane to solve real-world and mathematical problems.  use absolute values to find the distance between two points with the same x-coordinates or the same y-coordinates.

Unit 4: Applications of Rational Numbers
Essential Question(s): In what ways can rational numbers be useful?

MACC.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. a. Describe situations in which opposite quantities combine to make 0. b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 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. d. Apply properties of operations as strategies to add and subtract rational numbers.	 describe real-world situations where opposite quantities have a sum of zero.  use a number line or positive/negative chips to show than an integer and its opposite will always have a sum of zero.  use a number line to show addition as a specific distance from a particular number in one direction or the other, depending on the sign of the value being added.  interpret the addition of integers by relating the values to real-world situations.  rewrite a subtraction problem as an addition problem by using the additive inverse.  show that the distance between two integers on a number line is the absolute value of their difference.  describe real-world situations represented by the subtraction of integers.  apply the properties of operations to add and subtract rational numbers.
MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems.	 convert decimals to fractions, fractions to decimals.  apply equivalent forms of fractions, decimals, and percents to solve real-world problems.  convert between fractions, decimals and percents to solve real-world problems.
MA.6.A.5.2 Compare and order fractions, decimals, and percents, including finding their approximate location on a number line.	 identify and/or plot approximate locations of fractions, decimals or percents on a number line.
MA.6.A.5.3 Estimate the results of computations with fractions, decimals, and percents, and judge the reasonableness of the results.	 develop reasonableness to estimate multiplication computation and division computations with fractions, decimals, and percents.
MA.6.A.1.3 Solve real-world problems involving multiplication and division of fractions and decimals.	 solve real world problems involving the division of fractions and interpret the quotient in the context of the problem.
MACC.7.NS.1.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 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. c. Apply properties of operations as strategies to multiply and divide rational numbers. 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.	 use patterns and properties to explore the multiplication of integers.  use patterns and properties to develop procedures for multiplying integers.  use the relationship between multiplication and division to develop procedures for dividing integers.  explain why the property of closure exists for the division of rational numbers, but not for whole numbers.  describe real-world situations represented by the division of integers.  interpret the quotient in relation to the original problem.  generalize the procedures for multiplying and dividing integers to all rational numbers.  use long division to convert a rational number to a decimal.  verify that a number is rational based on its decimal equivalent.
MACC.7.NS.1.3 Solve real-world and mathematical problems involving the four operations with rational numbers.	 solve real-world problems that involve addition, subtraction, multiplication, and/or division of rational numbers.
MACC.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.	 compute a unit rate by iterating (repeating) or partitioning give rate.  compute a unit rate by multiplying or dividing both quantities by the same factor.  explain the relationship between using composed units and a multiplicative comparison to express a unit rate.
MACC.7.RP.1.2 Recognize and represent proportional relationships between quantities. a. 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. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. 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.	 determine whether two quantities are proportional by examining the relationship given in a table, graph, equation, diagram, or as a verbal description.  identify the constant of proportionality when presented with a proportional relationship in the form of a table, graph, equation, diagram, or verbal description.  write an equation that represents a proportional relationship.  use words to explain the relevance of a specific point on the graph of a proportional relationship.
MACC.7.RP.1.3: Use proportional relationships to solve multistep ratio and percent problems.	 use proportional reasoning to solve real-world problems, including those with multiple steps.  use proportional reasoning to solve real-world percent problems, including those with multiple steps.

 

Here are the old Essential Questions for the math 1 adv course: (scroll down to see measurement topics and learning targets)

• Using rational numbers, can the student apply all mathematical operations and understand their context?
• Can the student use order of operations and properties to simplify mathematical expressions?
• Can the student solve real world problems with fractions and decimals and convert back and forth between them?
• Can the student use linear equations to solve real world problems? Can students solve and graph linear equations?
• Can the student use inequalities to solve real world problems? Can students solve and graph inequalities?
• Can the student distinguish between direct and inverse variation? Can the student use proportions to solve real-world problems?
• Can the students apply geometric formulas to solve real life situations involving 2 and 3 dimensional figures?
• Can the student use given data, graph and analyze appropriately?

During the first grading we period we will include: 

• Measurement Topic	Learning Target	NGSSS
  Integers	compare and order integers.	MA.7.A.3.1
  	compute integers using mathematical operation of addition.	MA.7.A.3.1 MA.7.A.3.2
  	compute integers using mathematical operation of subtraction.	MA.7.A.3.1 MA.7.A.3.2
  	compute integers using mathematical operations of multiplication and division.	MA.7.A.3.1 MA.7.A.3.2
  	identify and plot points in a coordinate plane.	MA.7.G.4.3
  Numbers & Expressions	evaluate and write variable expressions.	MA.6.A.3.1
  	apply powers to describe repeated multiplication.	MA.7.A.3.2
  	apply the order of operations to evaluate expressions.	MA.7.A.3.2
  	apply properties of addition and multiplication to simplify or evaluate expressions.	MA.6.A.3.5
  	apply the distributive property to expressions.	MA.6.A.3.5 MA.7.A.3.4
  	simplify variable expressions.	MA.6.A.3.1 MA.7.A.3.4
  Rational Numbers	write fractions as decimals. write decimals as fractions.	MA.6.A.5.1 MA.6.A.5.2 MA.6.A.5.3 MA.7.A.5.1
  	compute fractions using mathematical operation of addition and/or subtraction. (like and unlike)	MA.7.A.3.2
  	compute fractions and mixed numbers usig mathematical operation of multiplication.	MA.6.A.1.1 MA.6.A.1.2 MA.6.A.5.3 MA.7.A.3.2
  	compute fractions and mixed numbers using mathematical operation of division.	MA.6.A.1.1 MA.6.A.1.2 MA.6.A.5.3 MA.7.A.3.2
  	compute decimals using mathematical operation of division multiplication and division.	MA.6.A.1.1 MA.6.A.1.2 MA.6.A.5.3 MA.7.A.3.2 MA.7.A.5.1
  	solve real-world problems involving multiplication and/or division of fractions and decimals	MA.6.A.1.3

   

links on this site

Exponential notation           Percent            converting fractions and decimals        6th grade FCAT sample test (2.0)

pre algebra sample questions        rates and proportions

greatest common factor        least common multiple        prime factorization

 Introduction to rules for using exponents

 

links off site

brightstorm.com

khanacademy.org

webmath.com        aaamath.com         www.mathway.com/            math.com/students/homeworkhelp.html

algebrahelp.com            algebra.com