Standards Correlated to Exploring Math 8775 Level E
Texas Essential Knowledge and Skills (TEKS)
Grade 5
Mathematics
TEKS
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
TX.111.17. Mathematics, Grade 5.
(5.1)
Number, operation, and quantitative reasoning. The
student uses place value to represent whole numbers and
decimals. The student is expected to:
5.1 (A)
Use place value to read, write, compare, and order whole
numbers through the 999,999,999,999.
Correlated Lessons:
1.1 Place Value and Ordering Numbers Page 15
Objective 01: Read and order any whole number.
1.1 Place Value and Ordering Numbers Page 15
Objective 02: Order a set of whole numbers up to 10
digits.
1.4 Comparing and Rounding Whole Numbers Page 37
Objective 08: Compare and order numbers
1.4 Comparing and Rounding Whole Numbers Page 37
Objective 09: Write a large number in figures and words.
1.6 Rounding and Ordering Large Numbers Page 51
Objective 14: Order numbers to the millions place.
3.2 Multiplying by 10s, 100s, and 1,000s Page 21
Objective 75: Read large numbers
GRADE LEVEL
EXPECTATION
5.1 (B)
Use place value to read, write, compare, and order
decimals through the thousandths place.
Correlated Lessons:
4.6 Ordering Decimals Page 53 Objective 133: Identify
the largest and smallest decimals.
4.6 Ordering Decimals, 4.8 Working with Decimals Page
53, 69 Objective 132: Order a set of decimals.
4.8 Working with Decimals Page 69 Objective 138:
Know what each digit in a decimal represents.
4.8 Working with Decimals Page 69 Objective 139:
Identify a decimal that lies between two other decimals.
STUDENT
EXPECTATION
(5.2)
Number, operation, and quantitative reasoning. The
student uses fractions in problem-solving situations. The
student is expected to:
GRADE LEVEL
EXPECTATION
5.2 (B)
Generate a mixed number equivalent to a given improper
fraction or generate an improper fraction equivalent to a
given mixed number.
Correlated Lessons:
4.1 Mixed Numbers and Improper Fractions Page 15
Objective 120: Recognize the relationship between
improper fractions and mixed numbers.
4.1 Mixed Numbers and Improper Fractions Page 15
Objective 121: Convert between improper fractions and
mixed numbers.
GRADE LEVEL
EXPECTATION
5.2 (C)
Compare two fractional quantities in problem-solving
situations using a variety of methods, including common
denominators.
Correlated Lessons:
4.2 Ordering Fractions Page 21 Objective 123: Order a
set of fractions by finding a lowest common denominator
or an equivalent fraction.
4.4 Equivalent Fractions and Common Denominators
Page 37 Objective 128: Compare fractions by finding a
common denominator.
GRADE LEVEL
EXPECTATION
5.2 (D)
Use models to relate decimals to fractions that name
tenths, hundredths, and thousandths.
Correlated Lessons:
4.13 Fractions, Percents and Decimals Page 109
Objective 149: Make conversions among fractions,
decimals, and percents.
4.13 Fractions, Percents and Decimals, 4.14 Percent
Word Problems Page 109, 119 Objective 148: Recognize
the equivalence between fractions, percentages, and
decimals.
4.7 Converting Decimals into Fractions Page 61
Objective 135: Convert a fraction to a decimal.
4.7 Converting Decimals into Fractions Page 61
Objective 136: Convert a decimal to a fraction.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.3)
Number, operation, and quantitative reasoning. The
student adds, subtracts, multiplies, and divides to solve
meaningful problems. The student is expected to:
5.3 (A)
Use addition and subtraction to solve problems involving
whole numbers and decimals.
Correlated Lessons:
2.1 Written Methods for Addition Page 15 Objective 37:
Use written procedures for addition, including decimals.
2.1 Written Methods for Addition Page 15 Objective 38:
Evaluate written methods of addition.
2.1 Written Methods for Addition Page 15 Objective 39:
Refine written methods building on addition.
2.10 Addition and Subtraction of Decimals Page 93
Objective 60: Add or subtract a pair of decimals, each
less than one with up to two decimal places.
2.10 Addition and Subtraction of Decimals Page 93
Objective 61: Explain in writing the process used in
mental addition and subtraction.
2.11 Addition and Subtraction Using Money Page 103
Objective 62: Add and subtract using various amounts of
money.
2.11 Addition and Subtraction Using Money Page 103
Objective 63: Use written methods of addition and
subtraction.
2.13 Reviewing Written Methods for Addition and
Subtraction Page 119 Objective 68: Add and subtract
whole numbers and decimals.
2.2 Written Methods for Subtraction Page 23 Objective
40: Subtract whole numbers and decimals using a variety
of methods.
2.2 Written Methods for Subtraction Page 23 Objective
41: Evaluate written methods of subtraction.
2.2 Written Methods for Subtraction Page 23 Objective
42: Refine written methods of building on subtraction.
2.3 Mental Strategies for Addition Page 29 Objective 43:
Use number facts and place value to understand and do
mental addition.
2.3 Mental Strategies for Addition Page 29 Objective 44:
Add four-digit multiples of 100.
2.3 Mental Strategies for Addition Page 29 Objective 45:
Count on to add decimals with units, tenths, and
hundredths to make the next higher whole number or
tenth.
2.4 Mental Strategies for Subtraction Page 37 Objective
46: Use a variety of mental strategies to calculate the
difference between two numbers.
2.5 Mental Strategies for Addition and Subtraction Page
47 Objective 48: Use a variety of strategies to add two
numbers mentally.
2.6 Subtraction Using Multiples of 100 Page 57 Objective
51: Subtract four-digit multiples of 100.
2.6 Subtraction Using Multiples of 100, 2.10 Addition
and Subtraction of Decimals Page 57, 93 Objective 50:
Use number facts and place value to understand and do
mental subtraction.
2.7 Addition and Subtraction as Inverse Operations Page
65 Objective 55: Use revisions of written methods of
addition and subtraction.
2.8 Adding Decimals Page 77 Objective 57: Add two or
more decimals up to four digits and up to two decimal
places.
2.8 Adding Decimals, 2.13 Reviewing Written Methods
for Addition and Subtraction Page 77, 119 Objective 56:
Develop and refine written methods for addition.
2.9 Subtracting Decimals Page 85 Objective 59: Subtract
decimals with up to four digits and up to two decimal
places.
2.9 Subtracting Decimals, 2.13 Reviewing Written
Methods for Addition and Subtraction Page 85, 119
Objective 58: Develop and refine written methods for
subtraction.
GRADE LEVEL
EXPECTATION
5.3 (B)
Use multiplication to solve problems involving whole
numbers (no more than three digits times two digits
without technology).
Correlated Lessons:
1.5 Number Operations using 10, 100, or 1,000 Page 43
Objective 12: Multiply a whole number by 10, 100, and
1,000.
3.1 Multiplication and Division Facts Page 15 Objective
70: Use knowledge of factors and closely related facts for
mental calculation.
3.1 Multiplication and Division Facts Page 15 Objective
71: Explain methods and reasoning about numbers orally
and in writing.
3.15 Review Written Methods of Multiplication Page 117
Objective 110: Understand the standard written mehtod
for long multiplication.
3.15 Review Written Methods of Multiplication Page 117
Objective 111: Use the standard written method for long
multiplication to solve problems.
3.6 Using a Grid and Partitioning Method in Simple
Problems Page 49 Objective 83: Develop written methods
for multiplying a three-digit number by a two-digit
number.
3.7 Using a Grid and Partitioning Method in Complex
Problems Page 55 Objective 84: Develop written methods
to find the product of two numbers.
GRADE LEVEL
EXPECTATION
5.3 (C)
Use division to solve problems involving whole numbers
(no more than two-digit divisors and three-digit dividends
without technology) , including interpreting the
remainder within a given context.
Correlated Lessons:
3.1 Multiplication and Division Facts Page 15 Objective
70: Use knowledge of factors and closely related facts for
mental calculation.
3.1 Multiplication and Division Facts Page 15 Objective
71: Explain methods and reasoning about numbers orally
and in writing.
3.10 Using Different Methods of Division Page 79
Objective 93: Use written methods to find the quotient of
two numbers.
3.12 Using Simple Division Page 95 Objective 100:
Write a quotient as a decimal when dividing by a whole
number.
3.12 Using Simple Division Page 95 Objective 99: Write
a quotient as a fraction when dividing by a whole
number.
3.13 More Division Problems with Remainders Page 103
Objective 102: Understand the concept of a remainder.
3.16 Review Written Methods of Division Page 125
Objective 113: Understand the standard written method
for long division.
3.16 Review Written Methods of Division Page 125
Objective 114: Use the standard written method for long
division to solve problems.
3.8 Using Written Methods of Division Page 61
Objective 87: Use written methods to divide a three-digit
number by a two-digit number.
3.8 Using Written Methods of Division Page 61
Objective 88: Write a remainder as a fraction.
3.9 Division Problems with Remainders Page 67
Objective 89: Use division strategies to establish answers.
3.9 Division Problems with Remainders Page 67
Objective 90: Find and express a quotient with a
remainder as a fraction.
3.9 Division Problems with Remainders Page 67
Objective 92: Express an answer as a fraction and as a
decimal.
STUDENT
EXPECTATION
(5.4)
Number, operation, and quantitative reasoning. The
student estimates to determine reasonable results. The
student is expected to use strategies, including rounding
and compatible numbers to estimate solutions to addition,
subtraction, multiplication, and division problems.
Correlated Lessons:
1.7 Rounding Large Numbers Page 59 Objective 17: Use
rounding to estimate the answers to calculations.
1.7 Rounding Large Numbers Page 59 Objective 18: Use
vocabulary for estimating and approximating.
1.8 Estimation and Rounding Page 69 Objective 19:
Make a sensible estimate of a range of objects.
1.8 Estimation and Rounding Page 69 Objective 20: Use
estimation to make an approximation of the answer.
3.7 Using a Grid and Partitioning Method in Complex
Problems Page 55 Objective 85: Use estimation before
working out an accurate answer.
3.9 Division Problems with Remainders Page 67
Objective 91: Round products and quotients to the nearest
whole number.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.5)
Patterns, relationships, and algebraic thinking. The
student makes generalizations based on observed patterns
and relationships. The student is expected to:
5.5 (A)
Describe the relationship between sets of data in graphic
organizers such as lists, tables, charts, and diagrams.
Correlated Lessons:
1.6 Rounding and Ordering Large Numbers Page 51
Objective 15: Interpret information in a table.
GRADE LEVEL
EXPECTATION
5.5 (B)
Identify prime and composite numbers using concrete
objects, pictorial models , and patterns in factor pairs.
Correlated Lessons:
1.10 Number Sense and Division Page 85 Objective 23:
Solve problems using factors and divisiblity.
1.9 Rules of Divisibility and Prime Numbers Page 79
Objective 22: Find prime numbers and prime factors.
STUDENT
EXPECTATION
(5.7)
Geometry and spatial reasoning. The student generates
geometric definitions using critical attributes. The student
is expected to identify essential attributes including
parallel, perpendicular, and congruent parts of two- and
three-dimensional geometric figures.
Correlated Lessons:
5.1 Properties of 3-Dimensional and 2-Dimensional
Shapes Page 15 Objective 153: Recognize features of two
dimensional and three dimensional shapes.
5.1 Properties of 3-Dimensional and 2-Dimensional
Shapes Page 15 Objective 155: Use correct vocabulary
when describing features of shapes.
5.1 Properties of 3-Dimensional and 2-Dimensional
Shapes Page 15 Objective 156: Describe characteristics
of two dimensional and three dimensional shapes.
5.10 Identifying Shapes by Plotting Points on a Grid Page
75 Objective 179: Use the properties of quadrilaterals to
answer specific questions.
5.2 Sorting Shapes Using a Venn Diagram Page 23
Objective 159: Use statements to define shapes.
5.3 Circles Page 31 Objective 160: Know the vocabulary
relating to circles.
5.4 Making a Cube Page 37 Objective 162: Describe
solids in terms of vertices, edges, and faces.
5.5 Types of Triangles Page 43 Objective 164: Identify
and name triangles.
5.5 Types of Triangles Page 43 Objective 165: Know the
definitions of different triangles, e.g. equilateral,
isosceles, and scalene, and identify their attributes.
5.5 Types of Triangles Page 43 Objective 166: Measure
length to identify different triangles.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.8)
Geometry and spatial reasoning. The student models
transformations. The student is expected to:
5.8 (A)
Sketch the results of translations, rotations, and
reflections on a Quadrant I coordinate grid.
Correlated Lessons:
5.17 Rotation Page 125 Objective 207: Use coordinates in
all four quadrants.
5.9 Reflective Symmetry on a Grid Page 69 Objective
177: Reflect shapes on the x- and y-axes, including two
reflections.
GRADE LEVEL
EXPECTATION
5.8 (B)
Identify the transformation that generates one figure from
the other when given two congruent figures on a
Quadrant I coordinate grid.
Correlated Lessons:
5.17 Rotation Page 125 Objective 205: Identify a
rotation.
STUDENT
EXPECTATION
(5.9)
Geometry and spatial reasoning. The student recognizes
the connection between ordered pairs of numbers and
locations of points on a plane. The student is expected to
locate and name points on a coordinate grid using ordered
pairs of whole numbers.
Correlated Lessons:
5.6 Parts of a Coordinate System Page 49 Objective 167:
Recognize position and direction and use coordinates.
5.6 Parts of a Coordinate System, 5.9 Reflective
Symmetry on a Grid Page 49 Objective 169: Plot
coordinates on a pair of axes.
5.7 Plotting Coordinates on a Grid Page 55 Objective
170: Plot points in all four quadrants.
5.7 Plotting Coordinates on a Grid Page 55 Objective
171: Read coordinates in all four quadrants.
5.7 Plotting Coordinates on a Grid Page 55 Objective
172: Complete a shape by plotting the missing point.
5.9 Reflective Symmetry on a Grid Page 69 Objective
176: Plot coordinates on a pair of axes.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.10)
Measurement. The student applies measurement concepts
involving length (including perimeter), area,
capacity/volume, and weight/mass to solve problems. The
student is expected to:
5.10 (A)
Perform simple conversions within the same
measurement system (SI (metric) or customary).
Correlated Lessons:
6.2 Estimating, Measuring, and Recording Lengths Page
21 Objective 212: Convert customary units of
measurement.
6.2 Estimating, Measuring, and Recording Lengths Page
21 Objective 213: Convert metric units of measurement.
6.3 Measuring Weight Using Metric and U.S. Customary
Scales Page 27 Objective 216: Convert small units to
larger units and vise versa.
6.4 Using Scales for Measurement Page 35 Objective
219: Use metric and customary conversions.
6.5 Measuring Capacity, 6.6 Length, Weight, and
Capacity Page 41, 47 Objective 221: Use conversions for
metric and customary units.
GRADE LEVEL
EXPECTATION
5.10 (B)
Connect models for perimeter, area, and volume with
their respective formulas.
Correlated Lessons:
6.10 Calculating Volumes Page 77 Objective 230: Know
and use formulas for finding the volume of cubes,
rectangular prisms, and cylinders.
6.10 Calculating Volumes Page 77 Objective 231: Use
correct units when calculating volume.
6.10 Calculating Volumes Page 77 Objective 232: Apply
knowledge of volume to real-life situations.
6.7 Calculating Perimeter and Area Page 59 Objective
225: Use formulas for perimeter and area of rectangles.
GRADE LEVEL
EXPECTATION
5.10 (C)
Select and use appropriate units and formulas to measure
length, perimeter, area, and volume.
Correlated Lessons:
6.1 Metric and Customary Units of Measurement Page 15
Objective 209: Know and use standard metric units for
length.
6.1 Metric and Customary Units of Measurement Page 15
Objective 210: Know and use customary units for length.
6.10 Calculating Volumes Page 77 Objective 230: Know
and use formulas for finding the volume of cubes,
rectangular prisms, and cylinders.
6.10 Calculating Volumes Page 77 Objective 231: Use
correct units when calculating volume.
6.10 Calculating Volumes Page 77 Objective 232: Apply
knowledge of volume to real-life situations.
6.11 Real-Life Problems Involving Measurement Page 85
Objective 233: Identify appropriate units of measurement
and equipment for measuring.
6.2 Estimating, Measuring, and Recording Lengths Page
21 Objective 211: Estimate, measure, and record lengths.
6.7 Calculating Perimeter and Area Page 59 Objective
225: Use formulas for perimeter and area of rectangles.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.12)
Probability and statistics. The student describes and
predicts the results of a probability experiment. The
student is expected to:
5.12 (C)
List all possible outcomes of a probability experiment
such as tossing a coin.
Correlated Lessons:
7.11 Using Probability Diagrams Page 91 Objective 263:
Know that probability folllows a particular set of
outcomes.
7.9 Probability Page 77 Objective 257: Know that events
have an outcome.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.13)
Probability and statistics. The student solves problems by
collecting, organizing, displaying, and interpreting sets of
data. The student is expected to:
5.13 (A)
Use tables of related number pairs to make line graphs.
Correlated Lessons:
7.6 Line Graphs Page 55 Objective 252: Collect and
organize data on a line graph.
GRADE LEVEL
EXPECTATION
5.13 (B)
Describe characteristics of data presented in tables and
graphs including median, mode, and range.
Correlated Lessons:
7.1 Mode, Range, and Median Page 15 Objective 241:
Find the mode, range and median of a set of data.
7.2 Mode, Range, Median, and Mean Page 23 Objective
242: Find the mode, range, median, and mean of a set of
data.
GRADE LEVEL
EXPECTATION
5.13 (C)
Graph a given set of data using an appropriate graphical
representation such as a picture or line graph.
Correlated Lessons:
7.6 Line Graphs Page 55 Objective 252: Collect and
organize data on a line graph.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.14)
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. The student is expected to:
5.14 (B)
Solve problems that incorporate understanding the
problem, making a plan, carrying out the plan, and
evaluating the solution for reasonableness.
Correlated Lessons:
1.10 Number Sense and Division Page 85 Objective 27:
Use inverse operations to calculate and check answers.
1.14 Reasoning About Numbers Page 115 Objective 34:
Make decisions about how to approach mathematical
problems.
2.12 Magic Squares, 3.6 Using a Grid and Partitioning
Method in Simple Problems Page 111, 49 Objective 66:
Choose the most appropriate method to solve problems.
2.6 Subtraction Using Multiples of 100 Page 57 Objective
52: Apply mental strategies in problem solving situations.
2.6 Subtraction Using Multiples of 100 Page 57 Objective
53: Explain the problem solving process used to solve
problems.
2.7 Addition and Subtraction as Inverse Operations Page
65 Objective 54: Use addition and subtraction as inverse
operations to check the accuracy of an answer.
2.7 Addition and Subtraction as Inverse Operations Page
65 Objective 55: Use revisions of written methods of
addition and subtraction.
3.11 Multiplication, Addition, and Division Page 85
Objective 97: Choose the appropriate strategy to solve
problems.
3.11 Multiplication, Addition, and Division Page 85
Objective 98: Check calculations using equivalent or
inverse operations.
3.12 Using Simple Division Page 95 Objective 101: Use
the inverse operations to check results.
GRADE LEVEL
EXPECTATION
5.14 (C)
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.
Correlated Lessons:
1.14 Reasoning About Numbers Page 115 Objective 34:
Make decisions about how to approach mathematical
problems.
2.12 Magic Squares, 3.6 Using a Grid and Partitioning
Method in Simple Problems Page 111, 49 Objective 66:
Choose the most appropriate method to solve problems.
2.6 Subtraction Using Multiples of 100 Page 57 Objective
52: Apply mental strategies in problem solving situations.
2.6 Subtraction Using Multiples of 100 Page 57 Objective
53: Explain the problem solving process used to solve
problems.
3.11 Multiplication, Addition, and Division Page 85
Objective 97: Choose the appropriate strategy to solve
problems.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.15)
Underlying processes and mathematical tools. The
student communicates about Grade 5 mathematics using
informal language. The student is expected to:
5.15 (A)
Explain and record observations using objects, words,
pictures, numbers, and technology.
Correlated Lessons:
1.12 Number Patterns, 3.18 Solving Money Word
Problems Page 99, 139 Objective 31: Explain and record
how a problem was solved.
2.1 Written Methods for Addition Page 15 Objective 37:
Use written procedures for addition, including decimals.
2.10 Addition and Subtraction of Decimals Page 93
Objective 61: Explain in writing the process used in
mental addition and subtraction.
2.11 Addition and Subtraction Using Money Page 103
Objective 63: Use written methods of addition and
subtraction.
2.12 Magic Squares Page 111 Objective 67: Explain
reasoning when making a choice.
2.2 Written Methods for Subtraction Page 23 Objective
40: Subtract whole numbers and decimals using a variety
of methods.
2.8 Adding Decimals, 2.13 Reviewing Written Methods
for Addition and Subtraction Page 77, 119 Objective 56:
Develop and refine written methods for addition.
2.9 Subtracting Decimals, 2.13 Reviewing Written
Methods for Addition and Subtraction Page 85, 119
Objective 58: Develop and refine written methods for
subtraction.
GRADE LEVEL
EXPECTATION
5.15 (B)
Relate informal language to mathematical language and
symbols.
Correlated Lessons:
1.12 Number Patterns, 3.18 Solving Money Word
Problems Page 99, 139 Objective 31: Explain and record
how a problem was solved.
2.10 Addition and Subtraction of Decimals Page 93
Objective 61: Explain in writing the process used in
mental addition and subtraction.
2.12 Magic Squares Page 111 Objective 67: Explain
reasoning when making a choice.
STUDENT
EXPECTATION
GRADE LEVEL
EXPECTATION
(5.16)
Underlying processes and mathematical tools. The
student uses logical reasoning. The student is expected to:
5.16 (A)
Make generalizations from patterns or sets of examples
and non-examples.
Correlated Lessons:
1.10 Number Sense and Division Page 85 Objective 24:
Make predictions and find patterns.
GRADE LEVEL
EXPECTATION
5.16 (B)
Justify why an answer is reasonable and explain the
solution process.
Correlated Lessons:
1.10 Number Sense and Division Page 85 Objective 27:
Use inverse operations to calculate and check answers.
2.1 Written Methods for Addition Page 15 Objective 38:
Evaluate written methods of addition.
2.2 Written Methods for Subtraction Page 23 Objective
41: Evaluate written methods of subtraction.
2.7 Addition and Subtraction as Inverse Operations Page
65 Objective 54: Use addition and subtraction as inverse
operations to check the accuracy of an answer.
2.7 Addition and Subtraction as Inverse Operations Page
65 Objective 55: Use revisions of written methods of
addition and subtraction.
3.11 Multiplication, Addition, and Division Page 85
Objective 98: Check calculations using equivalent or
inverse operations.
3.12 Using Simple Division Page 95 Objective 101: Use
the inverse operations to check results.