TEKS Reasoning Mind Curriculum Alignment for 5th Grade
Source: The provisions of this §111.17 adopted to be effective September 1, 1998, 22 TexReg 7623; amended to be effective August 1,
2006, 30 TexReg 7471.
Introduction
In this day and age of accountability, teachers and administrators need reassurance that the curriculum they are using meets state and
district standards. Though this document can be used to help teachers plan their Reasoning Mind (RM) curriculum, its main purpose
is to provide certainty that RM’s curriculum is aligned.
Note: Objectives 14 through 16 of the Texas Essential Knowledge and Skills deals with “underlying processes
and mathematical tools.” These skills are not addressed in isolation, but are incorporated throughout the entire
Reasoning Mind curriculum.
TEKS
Explanation
Objective
5.1
5.1A
5.1B
5.2
5.2A
RM Objective
TAKS Objective 1: Number, operation, and quantitative reasoning
Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and
decimals.
Use place value to read, write, compare, and order whole
 Whole Numbers and the Decimal System
numbers through 999,999,999,999
 Comparing Whole Numbers
 Convenient Addition (Expanded Form; Adding by
Place)
Use place value to read, write, compare, and order
 Decimals Basics. Percent
decimals through the thousandths place
 Comparing Decimals
Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations.
Generate a fraction equivalent to a given fraction such as
 Mini-Lesson: Fractions
1/2 and 3/6 or 4/12 and 1/3
 Fraction Basics
 Fractions, Division, and Ratios
 Comparing Fractions in Simple Cases
1
5.2B
5.2C
5.2D
5.3
5.3A
Generate a mixed number equivalent to a given improper
fraction or generate an improper fraction equivalent to a
given mixed number



Fractions, Division, and Ratios
Mixed Numbers
Add and Subtract Mixed Numbers with Like
Denominators
Compare two fractional quantities in problem-solving
 Mini-Lesson: Fractions
situations using a variety of methods, including common
 Fraction Basics
denominators
 Fractions, Division, and Ratios
 Comparing Fractions with Like Denominators
 Comparing Fractions in Simple Cases
Use models to relate decimals to fractions that name
 Mini-Lesson: Decimals
tenths, hundredths, and thousandths
 Fraction Basics
 Decimals Basics. Percent
Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve
meaningful problems.
Use addition and subtraction to solve problems involving
 SOC: Addition and Subtraction within 20
whole numbers and decimals
 Mini-Lesson: Decimals
 Operation of Addition
 Convenient Addition
 Column Addition
 Definition of Subtraction; Subtrahend, Minuend
 Subtraction Basics
 Properties of Subtraction
 Column Subtraction
 Numerical Expressions; Parentheses
 Solving Problems Using Numerical Expressions
 Algebraic Expressions
 Equalities and Equations
 Order of Operations
 Order of All Operations
2
5.3B
Use multiplication to solve problems involving whole
numbers (no more than 3 digits times 2 digits without
technology)


























Distributive Property
Ways to Simplify Calculations
Solving Problems Using Algebraic Expressions
Adding Decimals
Subtracting Decimals
SOC: Multiplication Table
SOC: Multiplying a 2-Digit Number by a 1-Digit
Number
Operation of Multiplication
Properties of Multiplication
Multiplying by Powers of 10 and Round Numbers
Column Multiplication by a One-Digit Number
Column Multiplication by a Two-Digit Number
Powers of Numbers
Order of Operations
Solving Equations with Multiplication and Division
Order of All Operations
Distributive Property
Ways to Simplify Calculations
Solving Problems Using Algebraic Expressions
Formulas Basics
Distance, Speed, Time
Price, Amount, Cost
Area of a Geometric Shape
Unit Conversion
Volume of a Geometric Solid
GCFs and LCMs
3
5.3C
5.3D
5.3E
5.4
5.5
Use division to solve problems involving whole numbers
(no more than 2-digit divisors and 3-digit dividends
without technology), including interpreting the remainder
within a given context
















SOC: The Basic Concept of Division
SOC: Division within the Multiplication Table
Operation of Division
All Properties of Division
Division with a Remainder
Long Division
Order of Operations
Solving Equations with Multiplication and Division
Order of All Operations
Distance, Speed, Time
GCFs and LCMs
Unit Conversion
Fractions, Division, and Ratios
Identify common factors of a set of whole numbers
GCFs and LCMs
Model situations using addition and/or subtraction
Add and Subtract Fractions with Like Denominators
involving fractions with like denominators using concrete
Add and Subtract Mixed Numbers with Like
objects, pictures, words, and numbers
Denominators
Number, operation, and quantitative reasoning. The
 Mini-Lesson: Decimals
student estimates to determine reasonable results.
 Rounding Natural Numbers
 Convenient Addition
The student is expected to use strategies, including
 Ways to Simplify Calculations
rounding and compatible numbers, to estimate solutions to
 Rounding Decimals
addition, subtraction, multiplication, and division
 Estimating Sums and Differences
problems.
 Overestimates and Underestimates
 Estimating Products and Quotients
TAKS Objective 2: Patterns, relationships, and algebraic thinking
Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns and
relationships.
4
5.5A
Describe the relationship between sets of data in graphic
organizers such as lists, tables, charts, and diagrams
5.5B
Identify prime and composite numbers using concrete
objects, pictorial models, and patterns in factor pairs
Patterns, relationships, and algebraic thinking. The
student describes relationships mathematically.
5.6
The student is expected to select from and use diagrams
and equations such as y = 5 + 3 to represent meaningful
problem situations.
5.7
5.8
5.8A












Mini-Lesson: Patterns and Sequence
GCFs and LCMs
Working with Tables, Graphs, and Charts
Mini-Lesson: Primes
GCFs and LCMs
Algebraic Expressions
Equalities and Equations
Solving Equations with Multiplication and Division
Solving Problems Using Algebraic Expressions
Formulas Basics
Distance, Speed, Time
Price, Amount, Cost
Related Objectives:
 Numerical Expressions; Parentheses
 Solving Problems Using Numerical Expressions
TAKS Objective 3: Geometry and spatial reasoning
Geometry and spatial reasoning. The student generates
 Mini-Lesson: Geometry
geometric definitions using critical attributes.
 Lines, Segments, Rays
 Polygons Basics
The student is expected to identify essential attributes
 Angles
including parallel, perpendicular, and congruent parts of 2 Types of Triangles and Quadrilaterals
and 3-dimensional geometric figures.
 The Circle and the Disk
 Simple Transformations; Congruence and Symmetry
 Polyhedrons
Geometry and spatial reasoning. The student models transformations.
Sketch the results of translations, rotations, and reflections
 Mini-Lesson: Geometry
on a Quadrant I coordinate grid
 Simple Transformations; Congruence and Symmetry
5
5.8B
5.9
5.10
5.10A
5.10B
5.10C
Identify the transformation that generates one figure from
the other when given 2 congruent figures on a Quadrant I
coordinate grid
Geometry and spatial reasoning. The student recognizes
the connection between ordered pairs of numbers and
locations of points on a plane.


Mini-Lesson: Geometry
Simple Transformations; Congruence and Symmetry


Mini-Lesson: Graphs
The Plane and the Coordinate Grid
Related Objective:
The student is expected to locate and name points on a
 Lines, Rays, Segments (Number Ray)
coordinate grid using ordered pairs of whole numbers.
TAKS Objective 4: Measurement
Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume,
and weight/mass to solve problems.
Perform simple conversions within the same measurement
 Unit Conversion
system (SI (metric) or customary)
Connect models for perimeter, area, and volume with their
 Mini-Lesson: Volume Rectangular Prism
respective formulas
 Polygons Basics (The Perimeter of a Polygon)
 Area of a Geometric Shape
 Volume of a Geometric Solid
Select and use appropriate units and formulas to measure
 SOC: Measuring Length Basics
length, perimeter, area, and volume
 SOC: Measuring Capacity Basics
 Mini-Lesson: Volume Rectangular Prism
 Lines, Segments, Rays
 Polygons Basics (The Perimeter of a Polygon)
 Formulas Basics
 Area of a Geometric Shape
 Volume of a Geometric Solid
Related Objective:
 Angles (Measuring Angles)
6
5.11A
Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees
Fahrenheit and Celsius).
Solve problems involving changes in temperature
 SOC: Measuring Temperature Basics
5.11B
Solve problems involving elapsed time
5.12
TAKS Objective 5: Probability and Statistics
Probability and statistics. The student describes and predicts the results of a probability experiment.
5.12A
Use fractions to describe the results of an experiment
5.12B
Use experimental results to make predictions
5.12C
List all possible outcomes of a probability experiment such
as tossing a coin
5.11
5.13
5.13A
5.13B
5.13C







SOC: Measuring Time basics
Mini-Lesson: Fractions
Mini-Lesson: Probability and Statistics
Experiments and Random Events
Equally Likely Simple Events; Probability
Mini-Lesson: Probability and Statistics
Equally Likely Simple Events; Probability
 Mini-Lesson: Probability and Statistics
 Tree Diagrams; Combinations
 Experiments and Random Events
 Equally Likely Simple Events; Probability
Probability and statistics. The student solves problems by collection, organizing, displaying, and interpreting sets of
data.
Use tables of related number pairs to make line graphs
 Working with Tables, Graphs, and Charts
Describe characteristics of data presented in tables and
 Mini-Lesson: Graphs
graphs including median, mode, and range
 Mini-Lesson: Median, Mode, Range
 Working with Tables, Graphs, and Charts
 Statistical Data: Range, Median, and Mode
Graph a given set of data using an appropriate graphical
 Mini-Lesson: Graphs
representation such as a picture or line graph.
 Working with Tables, Graphs, and Charts
7
5.14
5.14A
5.14B
5.14C
5.14D
5.15
5.15A
TAKS Objective 6: Underlying processes and mathematical tools
Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected
to everyday experiences and activities in and outside of school.
Identify the mathematics in everyday situations
 Included in all objectives
Solve problems that incorporate understanding the
problem, making a plan, carrying out the plan, and
evaluating the solution for reasonableness
Select or develop an appropriate problem-solving plan or
strategy, 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
Use tools such as real objects, manipulatives, and
technology to solve problems
Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal
language.
Explain and record observations using objects, words,
 Included in all objectives
pictures, numbers, and technology
5.15B
Relate informal language to mathematical language and
symbols
5.16
5.16A
Underlying processes and mathematical tools. The student uses logical reasoning.
Make generalizations from patterns or sets of examples
 Included in all objectives
and non-examples
5.16B
Justify why an answer is reasonable and explain the
solution process.
8
TEKS Reasoning Mind Curriculum Alignment for 6th Grade (ordered by TEKS objective)
Source: The provisions of this §111.22 adopted to be effective September 1, 1998, 22 TexReg 7623; amended to be effective August 1,
2006, 30 TexReg 1930.
Introduction
In this day and age of accountability, teachers and administrators need reassurance that the curriculum they are using meets state and
district standards. Though this document can be used to help teachers plan their Reasoning Mind (RM) curriculum, its main purpose
is to provide certainty that RM’s curriculum is aligned.
Note: Objectives 11 through 13 of the Texas Essential Knowledge and Skills deals with “underlying processes
and mathematical tools.” These skills are not addressed in isolation, but are incorporated throughout the entire
Reasoning Mind curriculum.
TEKS
Explanation
Objective
6.1
6.1A
RM Objective
TAKS Objective 1: Number, operation, and quantitative reasoning
Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of
equivalent forms.
Compare and order non-negative rational numbers
 SOC: Comparing Fractions with Like Denominators
 SOC: Comparing Fractions in Simple Cases
 SOC: Comparing Decimals
 Mini-Lesson: Decimals
 Review: Comparing Decimals
 Review: Compare, Add, Subtract Fractions with Like
Denom’s
 Comparing Fractions with Different Denominators
 Positive and Negative Integers
 Number Line
 Comparing Integers; Inequalities
9
6.1B
Generate equivalent forms of rational numbers including
whole numbers, fractions, and decimals
















6.1C
Use integers to represent real-life situations








SOC: Fractions Basics (Some Special Fractions;
Percent)
SOC: Fractions, Division, and Ratios
SOC: Mixed Numbers
SOC: Comparing Fractions in Simple Cases
(Equivalent Fractions)
SOC: Decimals Basics. Percent
SOC: Comparing Decimals (Equivalent Decimals)
Mini-Lesson: Decimals
Mini-Lesson: Fractions
Mini-Lesson: Percentage
Review: Decimals Basics
Review: Fraction Basics
Review: Mixed Numbers
Equivalent Fractions; Reducing Fractions
Bringing Fractions to a Common Denominator
Add and Subtract Fractions with Unlike Denom’s
Add and Subtract Mixed Numbers with Unlike
Denom’s
Fractions and Mixed Numbers Multiplication
Finding Fraction of a Number
Dividing Fractions and Mixed Numbers
Finding the Number Given a Fraction of it
Fractional Expressions Basics
Ratios Basics
Positive and Negative Integers
Increase and Decrease of a Value
10
6.1D
6.1E
6.1F
6.2
6.2A
Write prime factorizations using exponents

Mini-Lesson: Primes
Related Objectives (prime factorization without exponents):
 Review: Factors, Prime and Composite Numbers,
GCFs
 Finding GCF and LCM by Prime Factorization
Identify factors of a positive integer, common factors,
 Review: Factors, Prime and Composite Numbers,
and the greatest common factor of a set of positive
GCFs
integers
 Divisibility by 2, 5, and 10
 Divisibility by 3 and 9
 Divisibility by 4 and 25
 Finding GCF and LCM by Prime Factorization
Identify multiples of a positive integer and common
 Review: Multiples and LCMs
multiples and the LCM of a set of positive integers
 Finding GCF and LCM by Prime Factorization
Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems
and justify solutions.
Model addition and subtraction situations involving
 SOC: Add and Subtract Fractions with Like
fractions with objects, pictures, words, and numbers
Denominators
 SOC: Add and Subtract Mixed Numbers with Like
Denominators
 Mini-Lesson: Fractions
 Review: Fraction Basics
 Review: Mixed Numbers
 Review: Compare, Add, Subtract Fractions with Like
Denom’s
 Review: Add and Subtract Mixed Numbers with Like
Denom’s
11
6.2B
Use addition and subtraction to solve problems involving
fractions and decimals










6.2C
Use multiplication and division of whole numbers to
solve problems including situations involving equivalent
ratios and rates














SOC: Add and Subtract Fractions with Like
Denominators
SOC: Add and Subtract Mixed Numbers with Like
Denominators
SOC: Adding Decimals
SOC: Subtracting Decimals
Mini-Lesson: Fractions
Review: Adding and Subtracting Decimals
Review: Compare, Add, Subtract Fractions with Like
Denom’s
Add and Subtract Fractions with Unlike Denom’s
Review: Add and Subtract Mixed Numbers with Like
Denom’s
Add and Subtract Mixed Numbers with Unlike
Denom’s
SOC: Unit Conversion
Mini-Lesson: Ratios
Ratios Basics
Ratios of Amounts which have Different Units
Rates
Rates of Speed; Movement Formulas
Proportions Basics
The Main Property of Proportions
Solving Proportions
Direct Proportionality
Proportional Division of a Quantity
Solving Percent Problems Using Proportions
Conversion of Metric Units Using Proportions
Conversion of Customary Units Using Proportions
12
6.2D
Estimate and round to approximate reasonable results
and to solve problems where exact answers are not
required
6.2E
Use order of operations to simplify whole number
expressions (without exponents) in problem solving
situations
6.3
6.3A
6.3B
6.3C









Scale
The Mean
SOC: Rounding Natural Numbers
SOC: Estimating Sums and Differences
SOC: Overestimates and Underestimates
SOC: Estimating Products and Quotients
Review: Rounding Decimals
SOC: Order of Operations
SOC: Order of All Operations
Related objective:
 Offline lesson 1: Distributive Property to Simplify
Calculations
 Offline lesson 2: Distributive Property to Simplify
Expressions
 Offline lesson 3: Distributive Property to Simplify
Equations
TAKS Objective 2: Patterns, relationships, and algebraic thinking
Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional
relationships.
Use ratios to describe proportional situations
 SOC: Fractions Basics (Some Special Fractions;
Percent)
Represent ratios and percents with concrete models,
 SOC: Decimals Basics. Percent
fractions, and decimals
Use ratios to make predictions in proportional situations
 Mini-Lesson: Ratios
 Mini-Lesson: Percentage
 Ratios Basics
 Proportions Basics
 The Main Property of Proportions
 Solving Proportions
13
6.4
6.4A
6.4B
6.5
 Direct Proportionality
 Proportional Division of a Quantity
 Solving Percent Problems Using Proportions
 Conversion of Metric Units Using Proportions
 Conversion of Customary Units Using Proportions
 Scale
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.
Use tables and symbols to represent and describe
 Direct Proportionality
proportional and other relationships such as those
 Solving Percent Problems using Proportions
involving conversions, arithmetic sequences (with a
 Conversion of Metric Units using Proportions
constant rate of change), perimeter and area
 Conversion of Customary Units using Proportions
 Mini-Lesson: Patterns and Sequence
Use tables of data to generate formulas representing
 We will provide supplemental materials
relationships involving perimeter, area, volume of a
rectangular prism, etc.
Patterns, relationships, and algebraic thinking. The
 SOC: Algebraic Expressions
student uses letters to represent an unknown in an
 SOC: Equalities and Equations
equation.
 SOC: Formulas Basics
 SOC: Distance, Speed, Time
The student is expected to formulate equations from
 SOC: Price, Amount, Cost
problem situations described by linear relationships.
 Finding the Number Given a Fraction of it
 Direct Proportionality
 Proportional Division of a Quantity
 Solving Percent Problems Using Proportions
 Conversion of Metric Units Using Proportions
 Conversion of Customary Units Using Proportions
 Scale
14
6.6
6.6A
6.6B
6.6C
6.7
6.8
TAKS Objective 3: Geometry and spatial reasoning
Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles.
Use angle measurements to classify angles as acute,
 SOC: Angles
obtuse, or right
 SOC: Types of Triangles and Quadrilaterals
 Mini-Lesson: Geometry
 Review: Angles
 Types of Triangles
Identify relationships involving angles in triangles and
 SOC: Polygons Basics
quadrilaterals
 SOC: Types of Triangles and Quadrilaterals
 Mini-Lesson: Geometry
 Review: Polygons Basics
 Regular Polygons
 Sum of the Angles of a Triangle and Quadrilateral
 Types of Triangles
 Trapezoids and Parallelograms
Describe the relationship between radius, diameter, and
 SOC: The Circle and the Disk
circumference of a circle
 Mini-Lesson: Geometry
 Review: Circle and Disk
 Circumference of a Circle; Area of a Disk
Geometry and spatial reasoning. The student uses
 SOC: The Plane and the Coordinate Grid
coordinate geometry to identify location in two
 Coordinate Plane
dimensions.
The student is expected to locate and name points on a
coordinate plane using ordered pairs of non-negative
rational numbers.
TAKS Objective 4: Measurement
Measurement. The student solves application problems involving estimation and measurement of length, area, time,
temperature, volume, weight, and angles.
15
6.8A
6.8B
6.8C
6.8D
6.9
6.9A
6.9B
 SOC: Measuring Time Basics
 SOC: Measuring Temperature Basics
 SOC: Measuring Length Basics
 SOC: Measuring Mass and Weight Basics
 SOC: Measuring Capacity Basics
 SOC: Area of a Geometric Shape
 Review: Area
 Area of Triangle and Trapezoid
 Circumference of a Circle; Area of a Disk
Select and use appropriate units, tools, or formulas to
All of the above, and also the following:
measure and to solve problems involving length
 SOC: Polygons Basics (The Perimeter of a Polygon)
(including perimeter), area, time, temperature, volume,
 SOC: Formulas Basics
and weight
 SOC: Volume of a Geometric Solid
Measure angles
 Review: Angles
Convert measures within the same measurement system
 SOC: Unit Conversion
(customary and metric) based on relationships between
 Conversion of Metric Units Using Proportions
units
 Conversion of Customary Units Using Proportions
TAKS Objective 5: Probability and Statistics
Probability and Statistics. The student uses experimental and theoretical probability to make predictions.
Construct sample spaces using lists and tree diagrams
 SOC: Tree Diagrams; Combinations
 SOC: Experiments and Random Events
 SOC: Equally Likely Simple Events; Probability
 Review: Tree Diagrams; Combinations
 Review: Experiments and Random Events
 Review: Equally Likely Outcomes, Probability
 Sample Spaces and Complement Events
Find the probabilities of a simple event and its
 Review: Equally Likely Outcomes, Probability
complement and describe the relationship between the
 Sample Spaces and Complement Events
two
Estimate measurements (including circumference) and
evaluate reasonableness of results
16
6.10
6.10A
6.10B
6.10C
6.10D
6.11
6.11A
6.11B
Probability and statistics. The student uses statistical representations to analyze data.
Select and use an appropriate representation for
 SOC: Working with Tables, Graphs, and Charts
presenting and displaying different graphical
 Mini-Lesson: Graphs
representations of the same data including line plot, line
 Graphs on Coordinate Plane
graph, bar graph, and stem and leaf plot
 Line Plots; Stem and Leaf Plots
Identify mean (using concrete objects and pictorial
 SOC: Statistical Data: Range, Median, and Mode
models), median, mode, and range of a set of data
 Review: Range, Median, and Mode
 The Mean
Sketch circle graphs to display data
 Mini-Lesson: Graphs
Solve problems by collecting, organizing, displaying,
 SOC: Experiments and Random Events
and interpreting data
 SOC: Equally Likely Simple Events; Probability
 SOC: Statistical Data: Range, Median, and Mode
 Graphs on Coordinate Plane
 Review: Range, Median, and Mode
 The Mean
 Line Plots; Stem and Leaf Plots
 Review: Tree Diagrams; Combinations
 Review: Experiments and Random Events
 Sample Spaces and Complement Events
TAKS Objective 6: Underlying processes and mathematical tools
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.
Identify and apply mathematics to everyday experiences,
 Included in all objectives.
to activities in and outside of school, with other
disciplines, and with other mathematical topics
Use a problem-solving model that incorporates
understanding the problem, making a plan, carrying out
the plan, and evaluating the solution for reasonableness
17
6.11C
6.11D
6.12
6.12A
6.12B
6.13
6.13A
6.13B
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
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.
Communicate mathematical ideas using language,
 Included in all objectives.
efficient tools, appropriate units, and graphical,
numerical, physical, or algebraic mathematical models
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.
Make conjectures from patterns or sets of examples and
 Included in all objectives.
non-examples
Validate his/her conclusions using mathematical
properties and relationships
18