This 6th grade "buffet-style" math course will benefit students in homeschool, public and private school settings when they partner with me, their math specialist, for learning, weekly support and success!

No prior knowledge is necessary for this course other than the completion of 6th grade math, or for those entering the 6th grade.  However, students needing remediation, on grade level practice, or above grade level challenge will also benefit from the material that is taught in this private class. "Sixth Grade Buffet-Style Math Concepts Review,"  will provide a menu of choices for the student. Students can pick and choose what they need help on based on diagnostics, if enrolled in prior multi-week classes, and/or by interest.  With my digital format, student work will be very individualized. PLEASE BEAR IN MIND, what you see listed below is curriculum for an entire year and CAN NOT be completed in 4 weeks, as this course is structured.  Therefore, the nature of this course is intended for the student to focus on specific areas of need with the teacher and NOT attempt to complete all that is listed in the entire 6th curriculum. This course can be taken mulitple times with each enrollment focusing on different concepts. Students make choices for each week based on what is offered in each segment. This class is offered for private tutoring only.

What Will Be Taught

Your Buffet choices are Skills from any of the Weeks Listed below and can be Determined by the Student, or suggested by the teacher if preferred (Week 5 is of particular importance for Pre-Algebra). "Learn All You Want!!"

Week 1

Understanding ratio concepts and use ratio reasoning to solve problems.

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
HOMEWORK:
Write a ratio: word problems (6-R.3)
Write a ratio (6-R.1)
Which model represents the ratio? (6-R.4)

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.
HOMEWORK:
Unit rates (6-R.9)

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
6.RP.3.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.
HOMEWORK:
Identify equivalent ratios (6-R.5)
Write an equivalent ratio (6-R.6)
Equivalent ratios: word problems (6-R.8)
Ratio tables (6-R.7)


Week 2    Ratios and Proportional Relationships continued.


6.RP.3.b Solve rate problems including those involving unit pricing and constant speed.
HOMEWORK:
Ratios and rates: word problems (6-R.15)
Unit prices (6-V.2)
Unit prices with fractions and decimals (6-V.3)

6.RP.3.c Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
HOMEWORK:
Convert and compare customary units (6-T.3)
Convert, compare, add, and subtract mixed customary units (6-T.4)
Customary unit conversions involving fractions and mixed numbers (6-T.6)
Convert and compare metric units (6-T.7)
Convert between customary and metric systems (6-T.8)
Multiply and divide mixed customary units (6-T.5)
Unit prices with customary unit conversions (6-V.4)

Week 3    The Number System, Part A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1 Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions.
HOMEWORK:
Reciprocals (6-L.2)
Divide fractions (6-L.5)
Divide fractions and mixed numbers (6-L.7)
Divide fractions by whole numbers in recipes (6-L.4)
Divide fractions and mixed numbers: word problems (6-L.8)
Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2 Fluently divide multi-digit numbers using an algorithm.
6.NS.2.a Convert a rational number to a decimal using long division.
HOMEWORK:
Convert fractions to decimals (6-I.9)

6.NS.2.b Know that the decimal form of a rational number terminates in 0s or eventually repeats.
Repeating decimals (6-F.9)
6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimals using an algorithm for each operation.
HOMEWORK:
Add and subtract decimal numbers (6-G.1)
Add and subtract decimals: word problems (6-G.2)
Maps with decimal distances (6-G.4)
Multiply decimals (6-H.2)
Divide decimals by whole numbers (6-H.4)
Divide decimals by whole numbers: word problems (6-H.5)
Multiply and divide decimals by powers of ten (6-H.6)
Division with decimal quotients (6-H.7)
Add, subtract, multiply, or divide two decimals (6-O.5)
Add, subtract, multiply, or divide two decimals: word problems (6-O.6)
KY.6.NS.4 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.


Week 4    The Number System, Part B
Apply and extend previous understanding of numbers to the system of rational numbers.

6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
HOMEWORK:
Understanding integers (6-M.1)

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes, using appropriate range and intervals, to represent points on the line and in the plane, that include negative numbers and coordinates.
6.NS.6.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize 0 is its own opposite and the opposite of a negative number is a positive, and the opposite of a negative number is a positive, such as –(–3) = 3.
HOMEWORK:
Absolute value (6-M.6)
Rational numbers: find the sign (6-P.11)

6.NS.6.b 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.
HOMEWORK:
Decimal number lines (6-F.8)
Integers on number lines (6-M.2)
Graph integers on horizontal and vertical number lines (6-M.3)
Rational numbers on number lines (6-P.1)
Objects on a coordinate plane (6-X.1)
Graph points on a coordinate plane (6-X.2)

6.NS.6.c Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize the similarity between whole numbers, their negative opposites and their positions on a number line, ordered pairs differ only by signs and their locations on one or both axes.
HOMEWORK:
Quadrants (6-X.3)

6.NS.7 Understand ordering and absolute value of rational numbers.
6.NS.7.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
HOMEWORK:
Compare integers (6-M.7)

6.NS.7.b Write, interpret and explain statements of order for rational numbers in real-world contexts.
HOMEWORK:
Compare rational numbers (6-P.4)
Put rational numbers in order (6-P.5)
Compare temperatures above and below zero (6-T.9)

6.NS.7.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.
HOMEWORK:
Absolute value (6-M.6)
Absolute value of rational numbers (6-P.8)
Understanding absolute value (6-M.5)
Absolute value and integers: word problems (6-M.10)

6.NS.7.d Distinguish comparisons of absolute value from statements about order.
HOMEWORK:
Put rational numbers in order (6-P.5)
Absolute value of rational numbers (6-P.8)
Integer inequalities with absolute values (6-M.9)

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.
HOMEWORK:
Coordinate planes as maps (6-X.4)
Distance between two points (6-X.5)
Follow directions on a coordinate plane (6-X.6)


Week 5     Expressions and Equations, Part A
Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
HOMEWORK:
Write multiplication expressions using exponents (6-D.1)
Write powers of ten with exponents (6-D.3)
Evaluate exponents (6-D.2)
Find the missing exponent or base (6-D.4)
Exponents with decimal bases (6-D.5)
Exponents with fractional bases (6-D.6)

6.EE.2 Write, read and evaluate expressions in which letters stand for numbers.
6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers. For example,
HOMEWORK:
Write variable expressions: one operation (6-Y.1)
Write variable expressions: two operations (6-Y.2)

6.EE.2.b Identify parts of an expression using mathematical terms (sums, term, product, factor, quotient, coefficient); view one or more parts of an expression in a single entity. For example,
HOMEWORK:
Sort factors of numerical expressions (6-E.13)
Identify terms and coefficients (6-Y.8)
Sort factors of variable expressions (6-Y.9)

6.EE.2.c Evaluate expressions for specific values of their variables, including values that are non-negative rational numbers. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example,
HOMEWORK:
Evaluate numerical expressions involving whole numbers (6-O.3)
Evaluate numerical expressions involving decimals (6-O.7)
Evaluate numerical expressions involving fractions (6-O.10)
Evaluate variable expressions with whole numbers (6-Y.4)
Evaluate multi-variable expressions (6-Y.5)
Evaluate variable expressions with decimals, fractions, and mixed numbers (6-Y.6)
Convert between Celsius and Fahrenheit (6-T.10)

6.EE.3 Apply the properties of operations to generate equivalent expressions.
HOMEWORK:
Write equivalent expressions using properties (6-Y.16)
Multiply using the distributive property (6-Y.13)
Factor using the distributive property (6-Y.14)

Week 6     Expressions and Equations, Part B
6.EE.4 Identify when two expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them.
HOMEWORK:
Identify equivalent expressions I (6-Y.18)
Identify equivalent expressions II (6-Y.19)
Reason about and solve one-variable equation and inequalities.

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.
HOMEWORK:
Solutions to inequalities (6-AA.1)
Does x satisfy an equation? (6-Z.1)
Which x satisfies an equation? (6-Z.2)

K6.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.
HOMEWORK:
Write variable expressions: word problems (6-Y.3)

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.
HOMEWORK:
Model and solve equations using algebra tiles (6-Z.5)
Write and solve equations that represent diagrams (6-Z.6)
Solve one-step addition and subtraction equations with whole numbers (6-Z.7)
Solve one-step multiplication and division equations with whole numbers (6-Z.8)
Solve one-step equations with whole numbers (6-Z.9)
Solve one-step multiplication and division equations with decimals, fractions, and whole numbers (6-Z.11)
Solve one-step equations: word problems (6-Z.15)

6.EE.8 Write an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on vertical and horizontal number lines.
HOMEWORK:
Graph inequalities on number lines (6-AA.2)
Write inequalities from number lines (6-AA.3)

Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9 Use variables to represent two quantities in a real-world problem that changes in relationship to one another;
6.EE.9.a Appropriately recognize one quantity as the dependent variable and the other as the independent variable.
HOMEWORK:
Identify independent and dependent variables: word problems (6-BB.4)

6.EE.9.b 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.
HOMEWORK:
Solve word problems by finding two-variable equations (6-BB.7)
Write a two-variable equation (6-BB.10)
Write an equation from a graph using a table (6-BB.3)

6.EE.9.c Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the question.
HOMEWORK:
Find a value using two-variable equations (6-BB.5)
Find a value using two-variable equations: word problems (6-BB.6)
Complete a table for a two-variable relationship (6-BB.8)
Identify the graph of an equation (6-BB.11)
Graph a two-variable equation (6-BB.13)
Interpret a graph: word problems (6-BB.14)


Week 7   GEOMETRY

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

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and quadrilaterals; apply these techniques in the context of solving real-world and mathematical problems.
HOMEWORK:
Area of triangles (6-FF.6)
Area of trapezoids (6-FF.8)
Area of quadrilaterals (6-FF.10)
Area of compound figures (6-FF.11)
Area of compound figures with triangles (6-FF.12)

6.G.2 Find the volume of a right rectangular prism with rational number edge lengths. Apply the formulas V =lwh and V = bh to find volumes of right rectangular prisms with rational number edge lengths in the context of solving real-world and mathematical problems.
HOMEWORK:
Volume of cubes and rectangular prisms (6-FF.18)
Volume of cubes and rectangular prisms: word problems (6-FF.20)

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.
HOMEWORK:
Area and perimeter of squares and rectangles on the coordinate plane (6-X.7)
Graph triangles and quadrilaterals (6-CC.8)
KY.6.G.4 Classify three-dimensional figures including cubes, prisms, pyramids, cones and spheres.



Week 8   STATISTICS AND PROBABLITY

Develop understanding of the process of statistical reasoning.

6.SP.0 Apply the four-step investigative process for statistical reasoning.
6.SP.0.a Formulate Questions: Formulate a statistical question as one that anticipates variability and can be answered with data.
HOMEWORK:
Identify statistical questions (6-HH.1)

6.SP.0.b Collect Data: Design and use a plan to collect appropriate data to answer a statistical question.
.6.SP.0.c Analyze Data: Select appropriate graphical methods and numerical measures to analyze data by displaying variability within a group, comparing individual to individual and comparing individual to group.
HOMEWORK:
Choose the best type of graph (6)

6.SP.0.d Interpret Results: Draw logical conclusions and make generalizations from the data based on the original question.
Develop understanding of statistical variability.
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.
HOMEWORK:
Identify statistical questions (6-HH.1)
6.SP.2 Understand that a set of numerical data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape.
HOMEWORK:
Create line plots (6-GG.4)
Interpret stem-and-leaf plots (6-GG.21)
Create stem-and-leaf plots (6-GG.22)
Box plots (6-GG.23)

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number to describe a typical value, while a measure of variation describes how the values in the distribution vary.
HOMEWORK:
Calculate mean, median, mode, and range (6-HH.2)
Mean, median, mode, and range: find the missing number (6-HH.4)
Changes in mean, median, mode, and range (6-HH.5)

Summarize and describe distributions.
6.SP.4 Display the distribution of numerical data in plots on a number line, including dot plots, histograms and box plots.
HOMEWORK:
Create line plots (6-GG.4)
Create and interpret line plots with fractions (6-GG.5)
Create histograms (6-GG.15)
Box plots (6-GG.23)

6.SP.5 Summarize numerical data sets in relation to their context, such as by:
6.SP.5.a Reporting the number of observations.
HOMEWORK:
Interpret line plots (6-GG.3)
Interpret histograms (6-GG.14)
KY.6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Identify representative, random, and biased samples (6-HH.11)
6.SP.5.c Determining quantitative measures of center (median and/or mean) to describe distribution of numerical data.
HOMEWORK:
Calculate mean, median, mode, and range (6-HH.2)
Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)
Mean, median, mode, and range: find the missing number (6-HH.4)

6.SP.5.d Describing distributions of numerical data qualitatively relating to shape (using terms such as cluster, mode(s), gap, symmetric, uniform, skewed-left, skewed-right and the presence of outliers) and quantitatively relating to spread/variability (using terms such as range and interquartile range).
HOMEWORK:
Calculate mean absolute deviation (6-HH.6)
Calculate quartiles and interquartile range (6-HH.7)
Identify an outlier (6-HH.8)
Identify an outlier and describe the effect of removing it (6-HH.9)
KY.6.SP.5.e Relating the choice of measures of center and variability to the shape of the data distribution.



Class Structure

PRIVATE and highly individualized.

Teaching Style

Teacher discussion with lots of guided practice, which could include games, manipulative, video clips and an abundance of interaction and practice on my interactive math website will be utilized. Instruction will be nurturing and supportive.  My teaching style is guided by this motto: "Learning takes place over Time. It's all about the Effort!" We will learn to say this together at the beginning and ending of each class.  Remember, parents, productive struggle is an important part of learning.  It's ok when students do. It's a valuable part of the learning process.

Conclusion:
5.  Assignments will be given for the upcoming week, which MUST BE completed by the next scheduled class. Class will dismiss after clarification of any points that may be needed.