Download Sixth Grade

VERTICAL ALIGNMENT
MATH: GRADE 6 – GRADE 8
6.1
6.1A
Sixth Grade
Number, operation, and quantitative
reasoning. The student represents
and uses rational numbers in a variety
of equivalent forms. The student is
expected to:
Compare and order non-negative
rational numbers.
7.1
7.1A
Including numbers represented as:
 Fractions
 Mixed numbers (with like and
unlike denominators)
 Decimals
6.1B
Generate equivalent forms of rational
numbers including whole numbers,
fractions, and decimals.
Seventh Grade
Number, operation, and quantitative
reasoning. The student represents
and uses numbers in a variety of
equivalent forms. The student is
expected to:
Compare and order integers and
positive rational numbers.
8.1
8.1A
Using multiple forms of positive
rational numbers, including numbers
represented as fractions, percents,
decimals, positive and negative
integers within a single problem.
7.1B
Including:
 Proper and improper fractions
 Multiple forms within the problem
Convert between fractions, decimals,
whole numbers, and percents mentally,
on paper, or with a calculator.
8.1B
Eighth Grade
Number, operation, and quantitative
reasoning. The student understands
that different forms of numbers are
appropriate for different situations.
The student is expected to:
Compare and order rational numbers in
various forms including integers,
percents, and positive and negative
fractions and decimals.
Using multiple forms of rational
numbers, including numbers
represented as fractions, percents,
decimals, positive and negative
integers within a single problem.
Select and use appropriate forms of
rational numbers to solve real-life
problems including those involving
proportional relationships.
Including mixed numbers
7.1C
Represent squares and square roots
using geometric models.
8.1C
Examples include:
Using multiple forms of fractions,
decimals, percents, positive and
negative integers within a single
problem.
Approximate (mentally and with
calculators) the value of irrational
numbers as they arise from problem
situations (such as Π, √2).
Including using geometric problems
using the square root of a number.
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6.1C
Use integers to represent real-life
situations.
8.1D
Including positive and negative
numbers.
6.1D
6.1E
6.1F
6.2
Express numbers in scientific notation,
including negative exponents, in
appropriate problem situations.
Including:
 Converting numbers back to
standard form
 Scientific notation using positive or
negative exponents
Write prime factorizations using
exponents.
Including using factor trees to find
prime factorizations to be written with
exponents.
Identify factors of a positive integer,
common factors, and the greatest
common factor of a set of positive
integers.
Include a set of at least 3 integers.
Identify multiples of a positive integer
and common multiples and the least
common multiple of a set of positive
integers.
Including:
 At least 3 integers in the set
 Correlation of the LCM to the LCD
Number, operation, and quantitative
reasoning. The student adds,
subtracts, multiplies, and divides to
solve problems and justify solutions.
The student is expected to:
7.2
Number, operation, and quantitative
reasoning. The student adds,
subtracts, multiplies, or divides to
solve problems and justify solutions.
The student is expected to:
8.2
Number, operation, and quantitative
reasoning. The student selects and
uses appropriate operations to solve
problems and justify solutions.
2
6.2A
Model addition and subtraction
situations involving fractions with
objects, pictures, words, and numbers.
7.2A
Including:
 Mixed numbers
 Like and unlike denominators
6.2B
Use addition and subtraction to solve
problems involving fractions and
decimals.
7.2B
Examples include:
 Problems with mixed numbers with
like and unlike denominators
 Simplifying answers (converting
improper fractions to whole or
mixed numbers in lowest terms)
 Decimal problems with answer
grids
Use multiplication and division of
whole numbers to solve problems
including situations involving
equivalent ratios and rates.
Examples include:
 Situations involving unit rate
 Fractions and decimals
 Problems involving ratios relating
numbers to the words associated
Including writing or selecting the
correct expression
Use addition, subtraction,
multiplication, and division to solve
problems involving fractions and
decimals.
Examples include:
Problems where your answer choices
are models
7.2C
6.2C
Represent multiplication and division
situations involving fractions and
decimals with models, including
concrete objects, pictures, words, and
numbers.
7.2D
Use models, such as concrete objects,
pictorial models, and number lines, to
add, subtract, multiply, and divide
integers and connect the actions to
algorithms.
Use division to find unit rates and
ratios in proportional relationships such
as speed, density, price, recipes, and
student-teacher ratio.
Including:

Fractions and decimals

Cross multiply and solve for x
8.2D
Use multiplication by a constant factor
(unit rate) to represent proportional
relationships.
Including:
 Using multiple forms of fractions,
decimals, percents, positive and
negative integers within a single
problem. (Example: 1 gallon = 4
quarts (g = 4q)).
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
with given numbers
Cross multiply and solve for x
Estimate and round to approximate
reasonable results and to solve
problems where exact answers are not
required.

6.2D
6.2E
Including:
 Working with problems that have
information expressed as ranges of
numbers in the problem itself or
ranges of numbers in its solution
 When rounding, use compatible
numbers (those numbers that are
easy to work with mentally; such
as, the numbers 240 and 60 are
compatible numbers for estimating
237 divided by 62
 In a series of numbers round to the
highest place of the smallest
number (not single digits)
 Rounding money to the nearest
cent
Use order of operations to simplify
whole number expressions (without
exponents) in problem solving
situations.
7.2E
Referring to the measurement side
of the TAKS chart
Simplify numerical expressions
involving order of operations and
exponents.
Including negative values
Including:
 Problems with both addition or
subtraction and multiplication or
division with and without
parentheses
 Simplifying order of operation
problems including the use of
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exponents
7.2F
Select and use appropriate operations
to solve problems and justify the
selections.
8.2A
Examples include:
 Problems with multiple operations
 Problems with answer grids
8.2B
7.2G
Determine the reasonableness of a
solution to a problem.
Including problems with the
appropriate range
8.2C
Select appropriate operations to solve
problems involving rational numbers
and justify the selections.
Including formulating equations with
appropriate order of operations.
(Addition, subtraction, multiplication,
division, square, and square root) with
positive and negative integers,
fractions, decimals, and percents.
Use appropriate operations to solve
problems involving rational numbers in
problem situations.
Including problems with multioperations (addition, subtraction,
multiplication, division, sqare, and
square root) and mixed forms of
rational numbers (positive and negative
integers, fractions, decimals, and
percents).
Evaluate a solution for reasonableness.
Including application problems for
money, measurement, and percent.
Examples include:
Reasonableness that can be determined
by estimating the solution and
determining how big or small the
answer should be. Then calculate your
answer. The estimate and your
calculation should be close to each
other.
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6.3
6.3A
Patterns, relationships, and algebraic
thinking. The student solves problems
involving direct proportional
relationships. The student is expected
to:
7.3
Patterns, relationships, and algebraic
thinking. The student solves problems
involving direct proportional
relationships. The student is expected
to:
Use ratios to describe proportional
situations.
8.3
8.3A
Including ratios that may or may not be
in lowest terms represented in a table,
equation, or verbal description.
6.3B
Represent ratios and percents with
concrete models, fractions, and
decimals.
7.3A
Estimate and find solutions to
application problems involving
percent.
8.3B
Estimating by rounding all the numbers
in a problem before doing any
calculations. Then perform the
operations with the rounded numbers.
Think about how rounding the
numbers, before calculating, causes
your estimate to be greater or less than
the answer.
Patterns, relationships, and algebraic
thinking. The student identifies
proportional or non-proportional
linear relationships in problem
situations and solves problems. The
student is expected to:
Compare and contrast proportional and
non-proportional linear relationships.
Including:
 Ratios that may not be in lowest
terms represented in a table, graph,
equation, verbal description and
geometric representations
 Setting up a proportion problem
from a verbal description
 Using data in a table
 Dilations (Enlargements and
reductions) or geometric figures
 Measurements using standard and
metric units
 Unit conversions
Estimate and find solutions to
application problems involving
percents and other proportional
relationships such as similarity and
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Including:
 Conversions of fractions, decimals,
and percents
 Reinforcing percent over 100
 Use of strategy “of” number goes
on bottom when finding percent of
a number
 Use of strategy “is” number goes
on top
Including:
 Percent increase
 Percent decrease
rates.
Including:
 Ratios that may not be in lowest
terms represented in a table, graph,
equation, verbal description and
geometric representations.
 Setting up a proportion problem
from a verbal description
 Using data in a table
 Dilations (Enlargements and
reductions) of geometric figures
 Measurements using standard and
metric units
 Unit conversions
IS = % (n)
OF
100
6.3C
Use ratios to make predictions in
proportional situations.
7.3B
Including:
 Setting up a proportion problem
from a verbal description
 Using data in a table
 Using conversions to express
compatible time, measurement, and
numbers
6.4
Patterns, relationships, and algebraic
thinking. The student uses letters as
variables in mathematical expressions
to describe how one quantity changes
when a related quantity changes. The
student is expected to:
7.4
Estimate and find solutions to
application problems involving
proportional relationships such as
similarity, scaling, unit costs, and
related measurement units.
Including:
 Setting up a proportion problem
from word problems
 Using data in a table
 Measurements using standard and
metric units
 Unit conversions
Patterns, relationships, and algebraic
thinking. The student represents a
relationship in numerical, geometric,
verbal, and symbolic form. The
student is expected to:
8.4
Patterns, relationships, and algebraic
thinking. The student makes
connections among various
representations of a numerical
relationship. The student is expected
to:
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6.4A
Use tables and symbols to represent
and describe proportional and other
relationships such as those involving
conversions, arithmetic sequences
(with a constant rate of change),
perimeter, and area.
8.4A
Generate a different representation of
data given another representation of
data (such as a table, graph, equation,
or verbal description).
Including:
 Multiple representations of a table,
graph, equation, sequence, or
verbal description within a single
context of a problem
 Present and future incremental
predictions
 Vocabulary: (i.e. Interval, scale, nth
term, coordinate plane, position,
sequence, trend, correlation,
relationships, variables, positive,
and negative)
Including
 Metric conversions for length
 Standard conversion for length
 Equations using variables (define)
Graphs to include:
 Line Graph
 Bar Graph
 Multiple Bar Graph
 Pictograph
 Circle Graphs
 Line Plots
 Stem & Leaf
8.5
Graphs to include:
 Line Graph
 Bar Graph
 Multiple Bar Graph
 Histogram
 Scatter plot
 Pictograph
 Circle Graph
 Line Plots
 Stem and Leaf
 Venn Diagram
Patterns, relationships, and algebraic
thinking. The student uses graphs,
tables, and algebraic representations
to make predictions and solve
problems. The student is expected to:
8
6.4B
Use tables of data to generate formulas
representing relationships involving
perimeter, area, volume of a
rectangular prism, etc.
Including:
 Perimeter of regular polygons
 Circumference of a circle
 Vocabulary: (i.e. diameter, radius,
Π (3.14 and 22/7)
 Area of squares, rectangles, circles,
and triangles
 Vocabulary: (i.e. height and base of
triangle
 Volume of cubes, rectangular
prisms and cylinders
 Find the nth term in a sequence
 Given area, find length or width
7.4A
Generate formulas involving unit
conversions, perimeter, area,
circumference, volume, and scaling.
Including:
 Perimeter of regular polygons
 Circumference
 Area of squares, rectangles,
triangles, circles, trapezoids
 Volume of rectangular prism,
cylinders, cubes
 Conversion from one standard unit
to another as listed on the formula
chart
 Conversion from one metric unit to
another as listed on the formula
chart
8.5A
Predict, find, and justify solutions to
application problems using appropriate
tables, graphs, and algebraic equations.
Including:
 Multiple representations of a table,
graph, equation, sequence or verbal
description within a single context
of a problem
 Present and future incremental
predictions
 Vocabulary: (i.e. Interval, scale, nth
term, coordinate plane, position,
sequence, trend, correlation,
relationships, variables, positive,
negative, algebraic equations,
evaluate, rule prediction, between,
pattern, exceed, arithmetic
sequence, term)
 Positive, negative, and no
correlation or trend.
 Answer choices in the form of an
inclusive/exclusive relationship
(Example: Between 5 and 12) (>,
<, ≥, ≤)
Graphs to include:
 Line Graph
 Bar Graph
 Multiple Bar Graph
 Histogram
 Scatter Plot
 Pictographs
 Circle Graph
 Line Plots
9

7.4B
7.4C
Stem and Leaf
Graph data to demonstrate
relationships in familiar concepts such
as conversions, perimeter, area,
circumference, volume, and scaling.
Including:
 Vocabulary (i.e. independent and
dependent variable)
 Data that models a linear
relationship. Example: Perimeter
and conversions
 Data that models a quadratic
(second degree) relationship.
Example: Area
 Data that models a third degree
relationship. Example: Volume
Use words and symbols to describe the
relationship between the terms in an
arithmetic sequence (with a constant
rate of change) and their positions in
the sequence.
Including:
 The nth term table
 Finding the nth term
 Using nth term to find a specific
term
8.5B
Find and evaluate an algebraic
expression to determine any term in an
arithmetic sequence (with a constant
rate of change).
Including:
 Expressions in which the constant
rate of change is expressed as a
fraction or a decimal
 Nth term table
 Finding the nth term
 Using the nth term to find a
specific term
 Number’s position in a sequence
 The formula for the arithmetic
sequence (answers should be in
distributive format) [The first term
+ common difference (n – 1) ]
10

6.5
Patterns, relationships, and algebraic
thinking. The student uses letters to
represent an unknown in and
equation. The student is expected to:
7.5
7.5A
6.5A
Formulate equations from problem
situations described by linear
relationships.
7.5B
Including:
 Equations in the form of ab=c
where a and c are numbers in the
problem
 Using variables to represent an
unknown in an equation
 Using more than one variable in an
equation
 Using multiplication in various
forms (parentheses, 3n, and •)
6.6
Examples include:
 C = 5 (h + 25)
 X = 3n
 X = 30 • 8
 Matching an equation with a real
life situation
Geometry and spatial reasoning. The
Vocabulary: (i.e. substitute,
algebraic expression, expression,
rule, nth term, prediction, pattern,
correlation, term, sequence)
Patterns, relationships, and algebraic
thinking. The student uses equations
to solve problems. The student is
expected to:
Use concrete and pictorial models to
solve equations and use symbols to
record the actions.
Including equations with two variables
Formulate problem situations when
given a simple equation and formulate
an equation when given a problem
situation.
Including prerequisites of:
 Translating word phrases to
algebraic expressions
 Translating word phrases to
algebraic equations.
Including focusing on operational
vocabulary (Examples: difference,
total, product, and quotient)
7.6
Geometry and spatial reasoning. The
8.6
Geometry and spatial reasoning. The
11
student uses geometric vocabulary to
describe angles, polygons, and circles.
The student is expected to:
6.6A
6.6B
Use angle measurements to classify
angles as acute, obtuse, or right.
Including:
 A variety of objects with acute,
obtuse, or right angles
 Reviewing geometric vocabulary
including:
o Triangle vocabulary (i.e.
acute, obtuse, right
(define legs and
hypotenuse),
equiangular, isosceles,
equilateral, and scalene
o Quadrilateral terms: (i.e.
parallelogram,
rectangle, square,
trapezoid, and rhombus)
Identify relationships involving angles
in triangles and quadrilaterals.
7.6A
student compares and classifies twoand three-dimensional figures using
geometric vocabulary and properties.
The student is expected to:
Use angle measurements to classify
pairs of angles as complementary or
supplementary
student uses transformational
geometry to develop spatial sense.
The student is expected to:
Including:
 Diagrams with multiple angles
 Prerequisite: name angles with
three points
7.6B
Including:
 Understand sum of degrees in a
triangle and a quadrilateral
 Understand use of ‘hash marks’ to
describe congruent sides
 Define isosceles, scalene, and
equilateral triangles.
7.6C
Use properties to classify triangles and
quadrilaterals
Including:
 Triangle vocabulary: (i.e. acute,
obtuse, right (define legs and
hypotenuse), equiangular,
isosceles, equilateral, and scalene)
 Quadrilateral terms: (i.e.
parallelogram, rectangle, square,
trapezoid, and rhombus)
Use properties to classify threedimensional figures, including
12
pyramids, cones, prisms, and cylinders.
7.6D
Including vocabulary (i.e. faces, edges,
vertices, bases, and lateral face)
Use critical attributes to define
similarity.
8.6A
Include:
 All polygons
 Corresponding sides are
proportional
 Corresponding angles are
congruent
 Using proportions to find missing
sides
 Identifying pictorially similar
figures
 Students needing to identify
corresponding angles and sides by
a similarity statement. Example:
∆ABC similar ~ ∆DEF
6.6C
6.7
Generate similar figures using dilations
including enlargements and reductions.
Including:
 Figures graphed on a coordinate
grid
 Figures with dimensions labeled in
the diagram
 Vocabulary: (i.e. similar, dilation,
enlargement, reduction, coordinate,
plane, vertex, dimension,
proportional, corresponding side,
scale factor)
 Multiply to solve for dilations by
using the scale factor
 Enlargements – scale factor greater
than 1
 Reductions – scale factor less than
1
Describe the relationship between
radius, diameter, and circumference of
a circle.
Including:
 Identifying a method for finding
the radius, diameter, or
circumference of a circle. d= C/Π
 Vocabulary (i.e. chord and
segment)
 Using C = Πd & 2Πr
Geometry and spatial reasoning. The
7.7
Geometry and spatial reasoning. The
8.7
Geometry and spatial reasoning. The
13
6.7A
student uses coordinate geometry to
identify location in two dimensions.
The student is expected to:
Locate and name points on a
coordinate plane using ordered pairs of
non-negative rational numbers.
7.7A
Include:
 Only quadrant one
 Using a variety of grids (using
different incremental units)
 Locating points using fraction and
decimal coordinates
 (x,y) Use strategy “you have to
crawl on the x before you can stand
up and walk on the y” or “you
have to go over to the elevator
before you can go up or down”
when plotting points.
 Vocabulary: x-axis, x-coordinate,
y-coordinate, quadrants, y-axis,
origin)
student uses coordinate geometry to
describe location on a plane. The
student is expected to:
Locate and name points on a
coordinate plane using ordered pairs of
integers.
8.7D
Include:
 All four quadrants
 Vocabulary: (i.e. x-axis, xcoordinate, y-coordinate,
quadrants, origin)
7.7B
Graph reflections across the horizontal
or vertical axis and graph translations
on a coordinate plane.
Include all four quadrants
 Reflection across x-axis (x,y) →
(x,-y)
 Reflection across y-axis (x,y) →
(-x,y)
student uses geometry to model and
describe the physical world. The
student is expected to:
Locate and name points on a
coordinate plane using ordered pairs of
rational numbers
Including:
 Using all four quadrants
 Vocabulary (i.e. x-axis, y-axis, xcoordinate, y-coordinate,
quadrants, origin)
8.6B
Graph dilations, reflections, and
translations on a coordinate plane.
Including:
 All four quadrants
 Reflections across the x or y axes
 Dilations include enlargements or
reductions
 Vocabulary: (i.e. similar, dilation,
enlargement, reduction, coordinate,
plane, vertex, dimension,
proportional, corresponding side,
scale factor, translation, and
14
7.8
7.8A
Geometry and spatial reasoning. The
student uses geometry to model and
describe the physical world. The
student is expected to:
Sketch three-dimensional figures when
given the top, side, and front views
8.7
8.7A
reflection)
Geometry and spatial reasoning. The
student uses geometry to model and
describe the physical world. The
student is expected to:
Draw three-dimensional figures from
different perspectives.
Include:
 Drawing three dimensional figures
when given a specified view
 Drawing two dimensional views
when a three dimensional figure is
given
7.8B
7.8C
Make a net (two-dimensional model)
of the surface area of a threedimensional figure.
Include figures such as:
 Cylinders
 Cones
 Prisms
 Pyramids
 Cube
Use geometric concepts and properties
to solve problems in fields such as art
and architecture.
8.7B
Include all two- and three-dimensional
figures listed on the formula chart and
combinations of figures such as a half
circle and rectangle pieced together.
8.7C
Use geometric concepts and properties
to solve problems in fields such as art
and architecture.
Include:
 Using the given data to solve for
perimeter, circumference, area,
volume, or dimension
 Various representations of limits of
measures
Use pictures or models to demonstrate
15
the Pythagorean Theorem.
6.8
6.8A
Measurement. The student solves
application problems involving
estimation and measurement of
length, area, time, temperature,
volume, weight, and angles. The
student is expected to:
Estimate measurements (including
circumference) and evaluate
reasonableness of results.
Including:
 Length, perimeter, and
circumference in metric and
standard units
 Area in metric and standard units
 Understanding and utilizing the
conversions and formulas on the
mathematics chart to solve
problems
 Recognizing abbreviations of
measurement units
 Recognizing symbol (≈) means
approximately equal to
 Recalling rounding fractions and
decimals when estimating to
nearest 0, ½ , or 1.
 Understanding elapsed time
7.9
7.9A
Measurement. The student solves
application problems involving
estimation and measurement. The
student is expected to:
Estimate measurements and solve
application problems involving length
(including perimeter and
circumference) and area of polygons
and other shapes.
8.8
8.8A
Including:
 When inscribed in a circle or
polygon and/or real life pictorial
examples
 Vocabulary: (i.e. hypotenuse, leg,
radius, diameter)
Measurement. The student uses
procedures to determine measures of
three-dimensional figures. The
student is expected to:
Find lateral and total surface area of
prisms, pyramids, and cylinders using
concrete models and nets (twodimensional models).
No spheres, no cones
Include:
 All polygons on the formula chart
 Using rulers on formula chart
 Problems with answer grids
Including:
Unit conversions in two and three
dimensions
Using formula chart rulers and
formulas
Various representations of limits of
measures of edges
Vocabulary (i.e. surface area, prism,
rectangular prism, triangular prism,
cylinder, pyramid, lateral surface
area, edge, face, vertex, height,
base, total surface area, net)
 Recognizing symbol (≈) means
approximately equal to
16
7.9B
Connect models for volume of prisms
(triangular and rectangular) and
cylinders to formulas of prisms
(triangular and rectangular) and
cylinders.
8.8B
Including matching nets and models to
appropriate formulas to problem solve.
6.8B
Select and use appropriate units, tools,
or formulas to measure and to solve
problems involving length (including
perimeter), area, time, temperature,
volume, and weight.
Including:
 Measure with the ruler on the
mathematics chart
 Utilize the conversions and
formulas on the mathematics chart
to solve problems
 Recognize abbreviations of
measurement units
 Use of answer grid
 Recall degree scale of a
thermometer
 Use the given dimensions of a
figure to solve problems
 Find perimeter of regular and
irregular polygons
 Find area of the following
geometric shapes: squares,
parallelograms, rectangles,
triangles, trapezoids, and circles
7.9C
Estimate measurements and solve
application problems involving volume
of prisms (rectangular and triangular)
and cylinders.
8.8C
Connect models of prisms, cylinders,
pyramids, spheres, and cones to
formulas for volume of these objects.
Including:
 Matching nets and models to
appropriate formulas to problem
solve
 Real-life models (i.e. spherebasketball)
Estimate measurements and use
formulas to solve application problems
involving lateral and total surface area
and volume.
Including:
 Measurements in metric and
standard units for cubes, cylinders,
cone, spheres, and prisms
 Rounding all dimensions to whole
numbers
 Using “3” for (pi symbol)
 The capital B on the formula chart
is the area of the base
 Vocabulary: (i.e. surface area,
prism, rectangular prism, triangular
prism, cylinder, pyramid, lateral
surface area, edge, face, vertex,
height, base, total surface area, net,
volume)
 Real-life models (i.e. rectangular
prism = a present or a shoe box)
17
6.8C
6.8D
Measure Angles
Including:
 Use a pictorial representation of a
protractor and use an actual
protractor to measure and construct
angles
 Measure angles in a given
geometric figure
 Understand angle symbols
 Using the actual protractor to
measure angles to the nearest
degree
 Measure angles where the rays do
not lie on zero degree
 Recall geometry vocabulary
 Find measure of adjacent angles
Convert measures within the same
measurement system (customary and
metric) based on relationships between
units.
Include:
 All measures on the formula chart
 Utilizing the King Henry acronym
for converting metrics
 Using the given dimensions of a
figure to solve problems
 Recognizing abbreviations of
measurement units
8.9
8.9A
Measurement. The student uses
indirect measurement to solve
problems. The student is expected to:
Use the Pythagorean Theorem to solve
real-life problems.
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8.9B
8.10
8.10A
Including:
 When inscribed in a circle or
polygon and/or real life pictorial
examples
 Vocabulary: (i.e. hypotenuse, leg,
radius, diameter)
Use proportional relationships in
similar two-dimensional figures or
similar three-dimensional figures to
find missing measurements.
Including:
 Setting up proportions or using a
scale factor
 Identifying the corresponding sides
of similar figures when the figure is
rotated and/or not rotated
 Vocabulary: (i.e. similar,
corresponding, scale factor,
dimensions, rotation, proportional
and two- and three-dimensional
figures)
Measurement. The student describes
how changes in dimensions affect
linear, area, and volume
measurements. The student is
expected to:
Describe the resulting effects on
perimeter and area when dimensions of
a shape are changed proportionally.
Including:
 Using a scale factor and/or
dilations with whole numbers or
19
fractions
Finding missing dimensions or area
or perimeter
 Using the same scale factor
proportionately in a figure the
effects
 Vocabulary: (i.e. perimeter, area,
scale factors, dilation/dilated,
enlargement, reduction, similar,
dimension, proportional)
 Generalizing the effects on
perimeter, area and volume if the
length, width, and height are
changed by the same scale factor
Describe the resulting effect on volume
when dimensions of a solid are
changed proportionally.
Probability and statistics. The student
applies concepts of theoretical and
experimental probability to make
predictions. The student is expected
to:

8.10B
6.9
Probability and statistics. The student
uses experimental and theoretical
probability to make predictions. The
student is expected to:
7.10
6.9A
Construct sample spaces using lists and
tree diagrams.
7.10A
6.9B
Including:
 Vocabulary: (i.e. sample space, tree
diagram)
 Matching a situation with a
situation with sample space that
lists all possible combinations or
select the missing portion of a
given sample space
Find the probabilities of a simple event
Probability and statistics. The student
recognizes that a physical or
mathematical model can be used to
describe the experimental and
theoretical probability of real-life
events. The student is expected to:
Construct sample spaces for simple or
composite experiments.
8.11
Including with and without
replacement.

Construct tree diagrams
7.10B
Find the probability of independent
8.11A
Find the probabilities of dependent and
20
and its complement and describe the
relationship between the two.
Including:

Vocabulary: (i.e. theoretical
probability, experimental
probability, complement, simple
event, outcome, likely, and
random)

Flipping a coin

Drawing an object from a box
without looking
events.
independent events.
Including:
 Flipping a coin
 Drawing an object from a box
without looking
 Compound events: Drawing an
object from a box without looking,
replacing the object, and drawing
another object (and/or situations)
Including:
 Displaying the results as a fraction
or a decimal or percent
 Working the problem from a verbal
description
 Analyzing data from a table or
graph
 Using experimental results and
comparing those results with the
theoretical results.
Use theoretical probabilities and
experimental results to make
predictions and decisions.
8.11B
8.11C
Including:
 Displaying the results as a fraction
or a decimal or percent
 Working the problem from a verbal
description
 Analyzing data from a table or
graph
 Using experimental results and
comparing those results with the
theoretical results.
Select and use different models to
simulate an event.
Including:
 Displaying the results as a fraction
or a decimal or percent
 Using experimental results from
independent and dependent events
and comparing those results with
21
6.10
6.10A
Probability and statistics. The student
uses statistical representations to
analyze data. The student is expected
to:
Select and use an appropriate
representation for presenting and
displaying different graphical
representations of the same data
including line plot, line graph, bar
graph, and stem and leaf plot.
7.11
7.11A
Including:
Vocabulary: (i.e. scale and interval)
Probability and statistics. The student
understands that the way a set of data
is displayed influences its
interpretation. The student is
expected to:
Select and use an appropriate
representation for presenting and
displaying relationships among
collected data, including line plot, line
graph, bar graph, stem and leaf plot,
circle graph, and Venn diagrams, and
justify the selection.
8.12
8.12C
Including:
 Frequency tables
 Vocabulary (i.e. intervals, scale)
7.11B
Make inferences and convincing
arguments based on an analysis of
given or collected data.
8.12B
Including using the data to make
predictions.
7.12
6.10B
Identify mean (using concrete objects
7.12A
Probability and statistics. The student
uses measures of central tendency and
range to describe a set of data. The
student is expected to:
Describe a set of data using mean,
8.12
the theoretical results (such as
using spinners, dice, and/or marbles
in a sack in a probability event)
Probability and statistics. The student
uses statistical procedures to describe
data. The student is expected to:
Select and use an appropriate
representation for presenting and
displaying relationships among
collected data, including line plots, line
graphs, stem and leaf plots, circle
graphs, bar graphs, box and whisker
plots, histograms, and Venn diagrams,
with and without the use of technology.
Including:

Frequencly tables

Vocabulary (i.e. intervals, scale)
Draw conclusions and make
predictions by analyzing trends in
scatter plots.
Including:
 Scatter plots that show no real trend
 Positive, negative, and no
correlations or trends
 Describe the scatter plot in words
(increasing and decreasing)
Probability and statistics. The student
uses statistical procedures to describe
data. The student is expected to:
22
and pictorial models), median, mode,
and range of a set of data.
median, mode, and range.
Including: matching the mean, median,
mode, and/or range with a given set of
data which may be listed in the text of
the item or presented in a graphical
representation.
Introduce: Identifying the missing
piece of data that will produce a target
mean, mode, median, and/or range for
a data set.
7.12B
Choose among mean, median, mode, or
range to describe a set of data and
justify the choice for a particular
situation.
8.12A
Including problems such as:
 Given a set of data the student
selects the “best” measure of
central tendency to describe that
data
6.10C
Sketch circle graphs to display data.
6.10D
Including knowledge of relationship
between percent and fractions.
Solve problems by collecting,
organizing, displaying, and interpreting
data.
Select the appropriate measure of
central tendency or range to describe a
set of data and justify the choice for a
particular situation.
Including:
 Finding mean, median, mode and
range to justify an answer
 The effects of changing data on
mean, median, mode, and range
8.13
8.13A
Probability and statistics. The student
evaluates predictions and conclusions
based on statistical data. The student
is expected to:
Evaluate methods of sampling to
23
determine validity of an inference
made from a set of data.
8.13B
6.11
6.11A
6.11B
Underlying processes and
mathematical tools. The student
applies Grade 6 mathematics to solve
problems connected to everyday
experiences, investigations in other
disciplines, and activities in and
outside of school. The student is
expected to:
Identify and apply mathematics to
everyday experiences, to activities in
and outside of school, with other
disciplines, and with other
mathematical topics.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Use a problem-solving model that
incorporates understanding the
problem, making a plan, carrying out
the plan, and evaluating the solution
7.13
7.13A
7.13B
Underlying processes and
mathematical tools. The student
applies Grade 7 mathematics to solve
problems connected to everyday
experiences, investigations in other
disciplines, and activities in and
outside of school. The student is
expected to:
Identify and apply mathematics to
everyday experiences, to activities in
and outside of school, with other
disciplines, and with other
mathematical topics.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Use a problem-solving model that
incorporates understanding the
problem, making a plan, carrying out
the plan, and evaluating the solution
8.14
8.14A
8.14B
Including biased sampling due to
methods of collecting the data.
Recognize misuses of graphical or
numerical information and evaluate
predictions and conclusions based on
data analysis.
Including analyzing all parts of a bar
graph (title, vertical and horizontal
scale) and table of values for possible
misleading information.
Underlying processes and
mathematical tools. The student
applies Grade 8 mathematics to solve
problems connected to everyday
experiences, investigations in other
disciplines, and activities in and
outside of school. The student is
expected to:
Identify and apply mathematics to
everyday experiences, to activities in
and outside of school, with other
disciplines, and with other
mathematical topics.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Use a problem-solving model that
incorporates understanding the
problem, making a plan, carrying out
the plan, and evaluating the solution
24
6.11C
6.11D
6.12
6.12A
for reasonableness.
for reasonableness.
for reasonableness.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Select or develop an appropriate
problem-solving strategy from a
variety of different types, including
drawing a picture, looking for a
pattern, systematic guessing and
checking, acting it out, making a table,
working a simpler problem, or working
backwards to solve a problem.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Select or develop an appropriate
problem-solving strategy from a
variety of different types, including
drawing a picture, looking for a
pattern, systematic guessing and
checking, acting it out, making a table,
working a simpler problem, or working
backwards to solve a problem.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Select or develop an appropriate
problem-solving strategy from a
variety of different types, including
drawing a picture, looking for a
pattern, systematic guessing and
checking, acting it out, making a table,
working a simpler problem, or working
backwards to solve a problem.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Select tools such as real objects,
manipulatives, paper/pencil, and
technology or techniques such as
mental math, estimation, and number
sense to solve problems.
Underlying processes and
mathematical tools. The student
communicates about Grade 6
mathematics through informal and
mathematical language,
representations, and models. The
student is expected to:
Communicate mathematical ideas
using language, efficient tools,
appropriate units, and graphical,
numerical, physical, or algebraic
mathematical models.
7.13C
7.13D
7.14
7.14A
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Select tools such as real objects,
manipulatives, paper/pencil, and
technology or techniques such as
mental math, estimation, and number
sense to solve problems.
Underlying processes and
mathematical tools. The student
communicates about Grade 7
mathematics through informal and
mathematical language,
representations, and models. The
student is expected to:
Communicate mathematical ideas
using language, efficient tools,
appropriate units, and graphical,
numerical, physical, or algebraic
mathematical models.
8.14C
8.14D
8.15
8.15A
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Select tools such as real objects,
manipulatives, paper/pencil, and
technology or techniques such as
mental math, estimation, and number
sense to solve problems.
Underlying processes and
mathematical tools. The student
communicates about Grade 8
mathematics through informal and
mathematical language,
representations, and models. The
student is expected to:
Communicate mathematical ideas
using language, efficient tools,
appropriate units, and graphical,
numerical, physical, or algebraic
mathematical models.
25
6.12B
6.13
6.13A
6.13B
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Evaluate the effectiveness of different
representations to communicate ideas.
Underlying processes and
mathematical tools. The student uses
logical reasoning to make conjectures
and verify conclusions. The student is
expected to:
Make conjectures from patterns or sets
of examples and non-examples.
Including:
 Defining a concept introduced at a
higher grade
 Showing a pattern, examples,
and/or non-examples
 Expecting students to choose a
correct response by analyzing the
pattern, examples, or non-examples
Validate his/her conclusions using
mathematical properties and
relationships.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
7.14B
7.15
7.15A
7.15B
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Evaluate the effectiveness of different
representations to communicate ideas.
Underlying processes and
mathematical tools. The student uses
logical reasoning to make conjectures
and verify conclusions. The student is
expected to:
Make conjectures from patterns or sets
of examples and non-examples.
Including:
 Defining a concept introduced at a
higher grade
 Showing a pattern, examples,
and/or non-examples
 Expecting students to choose a
correct response by analyzing the
pattern, examples, or non-examples
Validate his/her conclusions using
mathematical properties and
relationships.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
8.15B
8.16
8.16A
8.16B
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
Evaluate the effectiveness of different
representations to communicate ideas.
Underlying processes and
mathematical tools. The student uses
logical reasoning to make conjectures
and verify conclusions. The student is
expected to:
Make conjectures from patterns or sets
of examples and non-examples.
Including:
 Defining a concept introduced at a
higher grade
 Showing a pattern, examples,
and/or non-examples
Expecting students to choose a correct
response by analyzing the pattern,
examples, or non-examples
Validate his/her conclusions using
mathematical properties and
relationships.
This student expectation can be tested
in every strand including one or more
than one TEKS at a time.
26