Download 6th Grade Math Curriculum Map Created By Jason Hall Unit 1

6th Grade Math Curriculum Map
Created By Jason Hall
Unit 1: Whole Numbers Operations
Unit 2: Unit of Measurement
Unit 3: Geometric Figures
Unit 4: Plane Figures
Unit 5: Congruence and Motion Geometry
Unit 6: Perimeter
Unit 7: Area
Unit 8: Solid Figures
Unit 9: Volume
Unit 10: Number Theory
Unit 11: Decimals Operations
Unit 12: Add and Subtract Fractions
Unit 13: Multiplying and Divide Fractions and Mixed Numbers
Unit 14: Integers
Unit 15: Rational Numbers
Unit 16: Statistics, Probability, and Graphing
Unit 17: Expressions
Unit 18: Equations, Inequalities, and Variables
Unit 19: Patterns
Unit 20: Ratios and Proportions
Unit 21: Percent and Change
Created by Jason Hall for Owsley County School District
Page 1 of 30
1st Nine Weeks Grading Period
CCS
5.NBT.1
5.NBT.2
5.NBT.5
5.NF.5A
6.NS.2
Unit
1
Title
Whole Numbers Operations
(review)
6.RP.3d
2
Unit of Measurement
5.G.3
5.G.4
3
Geometric Figures
6.G.3
4
Plane Figures
5.G.3
5.G.4
5
Congruence and Motion
Geometry
Skill(s)
1. Whole Numbers and Place Value
2. Estimate with Whole Numbers
3. Add and Subtract Whole Numbers
4. Multiply and Divide Whole Numbers
5. Exponents
6. Order of Operations
7. Properties
8. Mental Math Strategies
1. Elapsed Time
2. Customary Measurements
3. Metric Measurements
4. Fahrenheit and Celsius
5. Appropriate Tools and Units
1. Points, Lines, and Planes
2. Angle Relationships
3. Congruent Line Segments and Angles
4. Classify Lines and Planes
5. Bisect Line Segments and Angles
1. Polygons
2. Triangles
3. Quadrilaterals
4. Draw Plane Figures
5. Circles
1. Similar and Congruent Figures
2. Transformations
3. Transformations on the Coordinate Plane
Duration
1-2 wks
1-2 wks
1 wk
2-3 wks
1 wk
Created by Jason Hall for Owsley County School District
Page 2 of 30
Review
6
Perimeter
6.G.1
7
Area
4. Symmetry
1. Find Perimeter
2. Perimeter Formulas
3. Estimate and Measure Perimeter
4. Circumference
5. Polygon Sides
6. Compare Perimeters
1. Estimate Area
2. Area of Squares, Rectangles, and Triangles
3. Area of Parallelograms and Trapezoids
4. Perimeter and Area
5. Area of Circles
1 wk
2-3 wks
2nd Nine Weeks Grading Period
6.G.4
8
Solid Figures
6.G.2
9
Volume
6.NS.4
10
Number Theory
6.NS.3
11
Decimals Operations
5.NF.1
5.NF.2
12
Add and Subtract Fractions
1. Types of Solid Figures
2. Views of Solid Figures
3. Nets of Solid Figures
1. Surface Area
2. Volume of Prisms
3. Volume of Cylinders
1. Divisibility
2. Prime and Composite Numbers
3. Prime Factorization
4. LCM and GCF
1. Decimals and Place Value
2. Estimate with Decimals
3. Add and Subtract Decimals
4. Multiply Decimals
5. Divide Decimals by Whole Numbers
1. Estimate Sums and Differences
2. Add and Subtract Fractions
1 wk
2 wks
1-2 wks
3-4 wks
2 wks
Created by Jason Hall for Owsley County School District
Page 3 of 30
3. Add and Subtract Mixed Numbers
4. Subtracting Equivalent Fractions
3rd Nine Weeks Grading Period
5.NF.4a
5.NF.5b
5.NF.6
6.NS.1
6.NS.5
13
6.NS.6a
6.NS.6b
6.NS.6c
6.NS.7a
6.NS.7b
6.NS.7c
6.NS.8
6.SP.1
6.SP.2
6.SP.3
6.SP.4
6.SP.5
6.EE.9
15
14
16
1. Estimate Products and Quotients
Multiplying and Divide
Fractions and Mixed Numbers 2. Multiply Fractions
3. Multiply Mixed Numbers
4. Divide Fractions and Mixed Numbers
1. Understand Integers
Integers
2. Add Integers
3. Subtract Integers
4. Multiply Integers
5. Divide Integers
6. Operations with Integers
1. Rational Numbers
Rational Numbers
2. Compare and Order
3. Properties of Rational Numbers
4. Inequalities on a Number Line
5. Graph on a Coordinate Plane
Statistics, Probability, and
Graphing
1. Mean, Median, Mode and Range
2. Frequency Tables and Line Plots
3. Samples and Surveys
4. Make and Analyze Graphs
5. Stem-and-Leaf Plots and Histograms
6. Compare Graphs
7. Choose and Appropriate Graph
8. Box-and-Whisker Plots
9. Graph Functions
10. Graph Linear Equations
1-2 wks
2 wks
2 wks
4 wks
Created by Jason Hall for Owsley County School District
Page 4 of 30
11. Graph Relationships
12. Theoretical Probability
13. Experimental Probability
14. Make Predictions
15. Outcomes of Compound Events
16. Independent and Dependent Events
17. Permutations and Combinations
4th Nine Weeks Grading Period
6.EE.1
6.EE.2
6.EE.3
6.EE.4
17
Expressions
6.EE.5
6.EE.6
6.EE.7
6.EE.8
6.EE.9
18
Equations, Inequalities, and
Variables
5.OA.3
19
Patterns
6.RP.1
6.RP.2
6.RP.3a
6.RP.3b
20
Ratios and Proportions
1. Write Algebraic Expressions
2. Evaluate Algebraic Expressions
3. Words and Equations
4. Solve Addition Equations
5. Solve Subtraction Equations
6. Solve Multiplication and Division Equations
1. Understand Solving and Equation or Inequality
2. Use Substitution to Make an Equation True
3. Use Variables to Represent Numbers
4. Understand that a Variable can represent an
Unknown Number
5. Solve Word Problems with Equations
6. Inequalities
7. Dependent and Independent Variables
1. Patterns in Sequences
2. Number Patterns and Functions
3. Geometric Patterns
1. Ratios and Rates
2. Write and Solve Proportions
3. Distance, Rate, and Time
4. Ratios and Similar Figures
5. Scale Drawings
2-3 wks
2-3 wks
1 wk
2 wks
Created by Jason Hall for Owsley County School District
Page 5 of 30
6.RP.3c
21
Percent and Change
6. Proportional Reasoning
7. Golden Ratio
1. Percent
2. Percents, Decimals and Fractions
3. Percent of a Number
4. Discount and Sales Tax
5. Simple Interest
1-2 wks
Created by Jason Hall for Owsley County School District
Page 6 of 30
Unit 1: Whole Number Operations
Approximate Duration of Study: 1 - 2 weeks
CCS
Essential
Concept
Skills
Question
5.NBT.1
How do we compare
Place Value
 Relationship of digits in a multi-digit number
relationships between
The ones place is ten times as much as the place value to
place values?
the right.
5.NBT.2
How do I demonstrate Multiplying by Power of Ten
 Explain the patterns of zeros in whole numbers.
the patterns between
 Explain the patterns of the placement of decimal
numbers, quantities
points
and place value using
the power of ten?
5.NBT.5
How can we use the
Whole Number
 Solve two digit multiplication.
concept of
Multiplying
 Solve three digit multiplication.
multiplication to solve
problems?
5.NF.5a
How can we interpret
Comparing Sizes
 Evaluate the factors to estimate the product (size),
multiplication as
without multiplying
scaling (resizing)?
6.NS.2
What is the strategy to Divide multi-digit numbers
 Fluently divide multi-digit numbers using the
divide multi-digit
standard algorithm.
numbers?
Vocabulary: addend, sum, subtrahend, minuend, difference, factor, product, divisor, dividend, quotient, estimation, operations,
ordering, place value
Created by Jason Hall for Owsley County School District
Page 7 of 30
Unit 2: Unit of Measure
Approximate Duration of Study: 1 - 2 weeks
CCS
Essential
Concept
Skills
Question
6.RP.3d
How can we use ratio Measurement units
 Use ratio reasoning to convert measurement units
and rate reasoning to
 Manipulate and transform units appropriately
solve real world and
when multiplying or dividing quantities
mathematical
problems?
Vocabulary: capacity, Celsius, Fahrenheit, metric, customary, elapsed time, ante meridiem, post meridiem, unit rate
Created by Jason Hall for Owsley County School District
Page 8 of 30
Unit 3: Geometric Figures
Approximate Duration of Study: 1 week
CCS
5.G.3
Essential
Question
How can the
characteristics of
shapes helps us
categorize multiple
figures?
Concept
Categorize
5.G.4
Skills
 Understand that a two-dimensional shape can be
classified using different categorization (side
lengths, degrees of angles, number of sides)
e.g. All rectangles have right angles, a square is
rectangle, so all squares have right angles.
 Organize two-dimensional shapes as being
classified as more than one figure in order from
simplest to most complex.
How can we
Classify
sequentially order
shapes according the
properties from
simplest to most
e.g. shape, quadrilateral, parallelogram, rhombus, square
complex?
Vocabulary: Two- Dimensional Shapes, Lengths, Degrees, Angles, Sides, Quadrilateral, Square, Parallelogram, Rhombus, Trapezoid,
Rectangle, Angles, Degrees, Classify, Simple, and Complex.
Created by Jason Hall for Owsley County School District
Page 9 of 30
Unit 4: Congruence and Motion Geometry
Approximate Duration of Study: 1 week
CCS
5.G.3
Essential
Question
How do we classify
angles?
How do we measure
using a protractor?
How do you classify a
polygon?
Concept
Angles
Skills
 Name an angle (right, acute, or obtuse)
 Draw an angle (right, acute, or obtuse)
 Measure an angle (right, acute, or obtuse)
 Use the properties of lines, points, and angles to
classify polygons.
 Name a polygon based on the polygons properties.
 Identify the total number of diagonals within a
polygon.
 Evaluate a polygon to determine lines of
symmetry.
Vocabulary: similar figures, corresponding angles, corresponding sides, exterior, interior, right, acute, obtuse, adjacent, ray, line,
segment, straight, supplementary, complementary, parallel, perpendicular, bisect, midpoint, compass, protractor
5.G.4
Polygons
Created by Jason Hall for Owsley County School District
Page 10 of 30
Unit 5: Plane Figures
Approximate Duration of Study: 2 - 3 weeks
CCS
6.G.3
Essential
Question
How can I draw
polygons in the
coordinate plane?
Concept
Draw polygons
Skills
 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 to solving real-world and
mathematical problems
How can I find the
dimensions of a given
polygon on the
coordinate plane using
the coordinates?
Vocabulary: acute triangle, equilateral triangle, isosceles triangle, obtuse, right, scalene, diagonal, polygon, heptagon, decagon,
vertex, nonagon, regular polygon
Created by Jason Hall for Owsley County School District
Page 11 of 30
Unit 6: Perimeter
Approximate Duration of Study: 1 week
CCS
Review
Essential
Question
How do you solve for
the perimeter?
Concept
Perimeter of polygons
5.NF.4b
5.NF.5a
5.NF.6
Skills
 Understand the concept of the perimeter of
polygons
 Use addition to solve for the perimeter
 Use the formulas: (l + l + w + w) or (2 x l) + (2 x
w)
How does the
perimeter relate to
architecture?
5.G.3
How do you solve for Circumference of Circles
 Understand the concept of the perimeter of circles
5.G.4
the circumference?
 Use formulas: (π • d) or (2πr)
Vocabulary: Perimeter, Circumference, Diameter, Radius, Length, Width, and Sum.
Created by Jason Hall for Owsley County School District
Page 12 of 30
Unit 7: Area
Approximate Duration of Study: 2-3 weeks
CCS
6.G.1
Essential
Question
How can I find the
area of polygons by
composing or
decomposing them
into other shapes?
Concept
Area
Skills
 Find the area of right triangles, or 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
Vocabulary: area, length, width, base, height, decompose, composing
Created by Jason Hall for Owsley County School District
Page 13 of 30
Unit 8: Solid Figures
Approximate Duration of Study: 1 - 2 weeks
CCS
6.G.4
Essential
Question
How can I use a net to
represent a threedimensional figure?
Concept
Three-dimensional figures
How can I use a net to
find the surface area of
a three-dimensional
figure?
Vocabulary: net, base, lateral face, polyhedron, surface area
Skills
 Represent three-dimensional figures using nets
made up of rectangles and triangles
 Use the nets to find the surface area of these
figures
 Apply these techniques to solving real-world and
mathematical problems
Created by Jason Hall for Owsley County School District
Page 14 of 30
Unit 9: Volume
Approximate Duration of Study: 2 weeks
CCS
6.G.2
Essential
Question
How can I find the
volume of a right
rectangular prism
using unit cubes?
Concept
Volume
How can I find the
volume of a right
rectangular prism
using the formulas for
volume?
Vocabulary: volume, cylinder, prism
Skills
 Find the volume of a right rectangular prism with
fractional edge lengths by packing it with unit
cubes
 Show that the volume is the same as would be
found by multiplying the edge lengths of the prism
 Apply the formulas V = lwh and V = bh to find
volumes of right rectangular prisms with fractional
edge lengths
Created by Jason Hall for Owsley County School District
Page 15 of 30
Unit 10: Number Theory
Approximate Duration of Study: 1-2 weeks
CCS
6.NS.4
Essential
Question
How do you find the
greatest common
factor of two whole
numbers less than
100?
Concept
Greatest common factor and
least common multiple
Skills
 Find greatest common factor of two whole
numbers less than or equal to 100.
 Find least common multiple of two whole numbers
less than or equal to 12.
 Use distributive property to express an equation as
a multiple of a sum of two whole numbers with no
common factor.
How do you find the
least common multiple
of two whole numbers
less than or equal to
12?
Vocabulary: greatest common factor, least common multiple, composite, common multiple, factor, prime number, opposites,
standard form, divisibility, expression
Created by Jason Hall for Owsley County School District
Page 16 of 30
Unit 11: Decimals Operations
Approximate Duration of Study: 3-4 weeks
CCS
Essential
Concept
Question
6.NS.3
What is the strategy to Add, subtract, multiply and
add, subtract,
divide multi-digit decimals
multiply, and divide
multi-digit decimals?
Vocabulary: comparing, equivalent, algorithm
Skills
 Fluently add, subtract, multiply and divide multidigit decimals using the standard algorithm for
each operation.
Created by Jason Hall for Owsley County School District
Page 17 of 30
Unit 12: Add and Subtract Fractions and Mixed Numbers
Approximate Duration of Study: 2 weeks
CCS
5.NF.1
Essential
Question
How do we convert
fractions to common
denominators?
Concept
Skills
Unlike Denominators
(changing to common
denominators)
 Add Fractions
 Subtract Fractions
How do we use
fraction conversions in
our daily life (cooking,
slices, etc.)?
How can we
demonstrate fractions
through story
problems?
Unlike Denominators
With Mixed Numbers
 Add Mixed Numbers
 Subtract Mixed Numbers
 Use fraction models to represent the problem.
 Use equations to represent the problem.
 Estimate mentally using benchmark fractions and
number sense to assess the reasonableness of an
answer.
Story Problems
 Use fraction models to represent the problem.
(Addition/Subtraction Unlike
 Use equations to represent the problem.
Denominators)
 Estimate mentally using benchmark fractions and
number sense to assess the reasonableness of an
answer.
Vocabulary: Sum, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, and Factors.
Benchmark Fraction: Benchmark fractions are common fractions that you can judge other numbers against. Normally, 1/4, 1/2, 3/4,
and often 1/10 (because of its relationship with decimals) are referred to as benchmark fractions.
5.NF.2
Story Problems
(Addition/Subtraction Common
Denominators)
Created by Jason Hall for Owsley County School District
Page 18 of 30
Unit 13: Multiplying and Dividing Fractions and Mixed Numbers
Approximate Duration of Study: 1-2 weeks
CCS
5.NF.4a
Essential
Question
How do we multiply
fractions?
What are rules to
multiplying fractions?
Concept
Skills
Multiplying Fractions/
Fractions
 Multiply fractions with fractions e.g. (a/b x c/d
=ac/bd)
Multiplying Whole Numbers to
Fractions
 Multiply fractions with whole numbers e.g. (a/b x
q = aq/b)
 Explain why multiplying a fraction greater than
one by a given number will result in a larger
product
 Explain why multiplying a fraction less than one
by a given number will result in a smaller product
 Solve real world problems using fractions and
mixed numbers
 Use fraction models and equations to represent the
problem
 Compute quotient of fractions
 Solve word problems involving division of
fractions by fractions
5.NF.5b
How do we anticipate
the product of
fractions?
Multiplying Fractions
5.NF.6
How does
multiplication relate to
real world scenarios?
Real World Problems of
Multiplication
6.NS.1
What is the strategy to
compute quotients of
fractions?
Dividing fractions by fractions
Vocabulary: Product, Difference, Equivalent, Compare, Numerator, Denominator, Common Denominator, Mixed Number, and
Factors, Reciprocal
Created by Jason Hall for Owsley County School District
Page 19 of 30
Unit 14: Integers
Approximate Duration of Study: 2 weeks
CCS
Essential
Concept
Skills
Question
6.NS.5
How can we
Positive and negative numbers
 Understand that positive and negative numbers are
understand that
used to describe quantities having opposite
positive and negative
directions.
numbers are used to
 Be able to explain meaning of zero in relation to +
describe quantities
and – numbers.
having opposite
directions?
Vocabulary: absolute value, integer, positive number, negative number, additive inverse, ordering, patterns, opposites
Created by Jason Hall for Owsley County School District
Page 20 of 30
Unit 15: Rational Numbers
Approximate Duration of Study: 2 weeks
CCS
6.NS.6a
6.NS.6b
6.NS.6c
6.NS.7a
6.NS.7b
Essential
Question
How can we recognize
opposite signs of
numbers on a number
line?
Concept
How can we
understand signs of
numbers in ordered
pairs as locations on a
coordinate plane?
How can we find and
position integers and
other rational numbers
on a horizontal and
vertical number line?
Rational numbers and the
number line
How can we interpret
statements of
inequality as
statements about the
relative position of
two numbers on a
number line?
How can we write,
interpret, and explain
order for rational
Ordering and absolute value of
rational numbers
Rational numbers and the
number line
Rational numbers and the
coordinate plane
Rational numbers and the
number line
Skills
 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 itself.
 Understand signs of numbers in ordered pairs as
locations in quadrants of the coordinate plane;
 Recognize that when two ordered pairs differ only
by signs, the locations will be reflections across
one or both axes.
 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.
 Interpret statements of inequality as statements
about the relative position of two numbers on a
number line diagram.
 Write, interpret, and explain statements of order
for rational numbers in real-world contexts.
Created by Jason Hall for Owsley County School District
Page 21 of 30
numbers in real-world
contexts?
6.NS.7c
How can we
 Understand the absolute value of a rational number
understand the
as its distance from zero on the number line;
absolute value of a
 Interpret absolute value as magnitude for a positive
rational number as its
or negative quantity in a real-world situation.
distance from zero on
a number line?
6.NS.7d
How can we
 Distinguish comparisons of absolute value from
distinguish
statements about order.
comparisons of
absolute value from
statements about
order?
6.NS.8
How can we solve
Coordinate Plane
 Solve real-world and mathematical problems by
real-world and math
graphing points in all four quadrants of the
problems by graphing
coordinate plane;
points on a coordinate
 Include use of coordinates and absolute value to
and use coordinates to
find distances between points with the same first
find distances between
coordinate or the same second coordinate.
points on a coordinate
plane?
Vocabulary: comparing, rational numbers, irrational numbers, coordinates, ordered pairs, coordinate plane, quadrant, absolute value,
inequality
Created by Jason Hall for Owsley County School District
Page 22 of 30
Unit 16: Statistics, Probability, and Graphing
Approximate Duration of Study: 4 weeks
CCS
6.SP.1
6.SP.2
6.SP.3
6.SP.4
6.SP.5
Essential
Question
What is the process of
taking a survey and
displaying the results?
How do mean, median
and mode describe a
set of data?
What method would
you use to describe a
given set of data using
mean, median, mode
and range?
What questions should
you ask to determine
which numerical set of
data would be the
most appropriate to
use for the data given?
How can you show the
distribution of data
using a box-andwhisker plot?
Concept
Statistical questions
Set of data
Measure of data
Displaying numerical data
Summarize numerical data sets
Skills
 Recognize a statistical question as one that
anticipates variability in the data related to the
question and accounts for it in the answers
 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
 Recognize that a measure of center for a numerical
data set summarizes all of its values with a single
number
 Recognize that a measure of variation describes
how its values vary with a single number
 Display numerical data in plots on a number line,
including dot plots, histograms, and box plots
 Report the number of observations
 Describe the nature of the attribute under
investigation including how it was measured and
its units of measurement
 Give quantitative measures of median and/or mean
and interquartile range and/or mean, as well as
describing any overall pattern and deviations with
reference to the context in which the data was
gathered
Created by Jason Hall for Owsley County School District
Page 23 of 30
6.EE.9
How do we use
variables to represent
two quantities?
Dependent and independent
variables
How do we write an
equation to express the
dependent variable to
the independent
variable?
 Relate the choice of measures of center and
variability to the shape of the data distribution and
the context in which the data was gathered
 Use variables to represent two quantities in a realworld problem that change in relationship to one
another
 Write an equation to express the dependent
variable in terms of the independent variable
 Analyze the relationship between the dependent
variable and the independent variable using graphs
and tables, and relate these to the equation
How do we analyze
the relationship
between the dependent
and independent
variable using graphs
and tables?
Vocabulary: Probability, chance, ratio, mean, median, mode, range, frequency, survey, variables, histogram, stem-and-leaf plot, boxand-whisker plot, data, circle graph, line graph, bar graph, pictograph, frequency table, cumulative frequency, variables, comparing,
census, averages, outlier, interquartile, predictions, random, events, dependent, independent, permutation, outcomes, estimation,
scatter plots
Created by Jason Hall for Owsley County School District
Page 24 of 30
Unit 17: Expressions
Approximate Duration of Study: 2-3 weeks
CCS
6.EE.1
6.EE.2
Essential
Question
How do we solve a
numerical expression
using exponents?
How do we solve the
value of an unknown?
Concept
Skills
Numerical expressions
 Write and evaluate numerical expressions
involving whole-number exponents
Letters in expressions
 Write expressions that record operations with
numbers in which letters stand for numbers
 Identify parts of an expression using mathematical
terms
 View one or more parts of an expression as a
single entity
 Evaluate expressions at specific values of their
variables
 Include expressions that arise from formulas used
in real-world problems
 Perform arithmetic operations in the conventional
order when there are no parenthesis
 Apply the properties of operations to generate
equivalent expressions
How do we solve an
expression using the
order of operations?
6.EE.3
How do we apply the
Properties of operations
properties of
operations to generate
equivalent
expressions?
6.EE.4
How do we identify
Equivalent expressions
 Identify when two expressions are equivalent
when two expressions
are equivalent?
Vocabulary: algebraic, evaluating, numerical, order of operations, equivalent, variables
Created by Jason Hall for Owsley County School District
Page 25 of 30
Unit 18: Equations, Inequalities, and Variables
Approximate Duration of Study: 2-3 weeks
CCS
6.EE.5
6.EE.6
6.EE.7
6.EE.8
Essential
Question
How do we solve an
equation and/or
inequality?
How do we use
substitution to
determine whether a
given number in a set
makes an equation?
How do we use
variables to represent
numbers?
How do we write
expressions when
solving real word
problems?
How do we solve real
world problems by
writing equations?
How do we write an
inequality?
Concept
Skills
Solving an equation or inequality
 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
Variables
 Use variables to represent numbers and write
expressions when solving real-world or
mathematical problems
 Understand that a variable can represent an
unknown number or any number in a specified set
Equations
 Solve real-world and mathematical problems by
writing and solving equations in the form of x + p
= q and px = q for cases in which p, q and x are all
nonnegative rational numbers
 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 infinite solutions
Inequalities
How do we recognize
that inequalities have
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 Represent solutions of such inequalities on number
line diagrams
infinite solutions?
6.EE.9
How do we represent
solutions of
inequalities on a
number line?
How do we use
variables to represent
two quantities?
Dependent and independent
variables
How do we write an
equation to express the
dependent variable to
the independent
variable?
 Use variables to represent two quantities in a realworld problem that change in relationship to one
another
 Write an equation to express the dependent
variable in terms of the independent variable
 Analyze the relationship between the dependent
variable and the independent variable using graphs
and tables, and relate these to the equation
How do we analyze
the relationship
between the dependent
and independent
variable using graphs
and tables?
Vocabulary: equations, inequalities, variables, analyze, substitution
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Unit 19: Patterns
Approximate Duration of Study: 1 week
CCS
5.OA.3
Essential
Question
What are the
relationships between
corresponding terms?
Concept
Ordered Pairs
Why are the
relationships relevant?
How can we use
ordered pair to
develop relationships
in numbers?
Skills
 Generate two number patterns using a given rule:
X-value add 3, Y-value add 6.
 Find ordered pair relationships (rule)
 Compare two sequences of numbers to develop
pattern.
Add 3, starting at 0 and Add 6 starting at 0, then identify
that the sequence is twice the corresponding term.
Vocabulary: Ordered Pairs, Relevancy, Corresponding Terms, Term, Patterns, X-Value, Y-Value, Sequence, and Rule
Created by Jason Hall for Owsley County School District
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Unit 20: Ratios and Proportions
Approximate Duration of Study: 2 weeks
CCS
6.RP.1
6.RP.2
6.RP.3a
6.RP.3b
Essential
Question
What is a ratio?
What is ratio language
to describe a ratio
relationship?
What is unit rate
associated with a
ratio?
How do you use rate
language in the
context of a ratio
relationship?
How can we use ratio
and rate reasoning to
solve real world and
mathematical
problems?
How can we use ratio
and rate reasoning to
solve real world and
mathematical
problems?
Concept
Skills
Ratios
Ratio language
 Use ratio language to describe relationship
between two quantities
Unit rate
Ratio relationships
 Understand the concept of unit rate a/b associated
with a ratio a:b with b ≠ 0
 Use rate language in the context of a ratio
relationship
Make and use tables of
equivalent ratios
 Make tables of equivalent ratios relating quantities
with whole number measurements
 Find missing values within the tables
 Plot the pairs of values on the coordinate plane
 Use tables to compare ratios
 Solve unit rate problems including those involving
unit pricing and constant speed
Unit rate problems
Vocabulary: ratio, proportion, equivalent ratios, rate, unit rate, scale, scale drawing, odds
Created by Jason Hall for Owsley County School District
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Unit 21: Percent and Change
Approximate Duration of Study: 1-2 weeks
CCS
6.RP.3c
Essential
Question
How can we use ratio
and rate reasoning to
solve real world and
mathematical
problems?
Concept
Percents
Skills
 Find a percent of a quantity as a rate per 100
 Solve problems finding the whole, given a part and
a percent
Vocabulary: sales tax, discount, percent
Created by Jason Hall for Owsley County School District
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