Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Standards for Mathematical Practice
1
Make sense of problems and persevere in solving them.
Saxon Math Intermediate 5 Citations
This standard is covered throughout the program; the following are examples.
Instruction:
New Concept
Investigation(s)
Maintenance:
Problem Solving
2
Problem Solving Overview (pages 1–6),
Lessons 11, 16, 21, 35, 46, 60
1, 5
Lessons 17, 25, 28, 32, 33, 35, 39, 45,
46, 51, 53, 55, 57, 58, 60, 65, 74, 79,
83, 99, 100, 106, 109, 113
This standard is covered throughout the program; the following are examples.
Reason abstractly and quantitatively.
Instruction:
New Concept
1
Lessons 11, 14, 16, 21, 24, 72, 103,
114, 115
Investigation(s)
1, 4
Maintenance:
Problem Solving
Lessons 65, 90
Performance Task(s)
5
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
3
Descriptor
Construct viable arguments and critique the reasoning of others.
Saxon Math Intermediate 5 Citations
This standard is covered throughout the program; the following are examples.
Instruction:
New Concept
Lessons 24, 29, 36, 37, 42, 89
Investigation(s)
3 (see Investigate Further, page 191), 9
Maintenance:
Problem Solving
4
Lessons 7, 43, 51, 63, 66, 73, 74, 76,
83, 90, 100, 113
Written Practice
Lessons 22, 27, 34, 42, 43
Performance Task(s)
1, 5, 9
This standard is covered throughout the program; the following are examples.
Model with mathematics.
Instruction:
New Concept
Investigation(s)
Maintenance:
Problem Solving
2
Lessons 30, 35, 38, 39, 40, 41, 60, 64,
68, 84, 97, 107, 108
2, 3, 4, 5, 6, 7, 11
Lessons 40, 45, 49, 52, 55, 67, 91, 114,
115
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
5
6
Descriptor
Use appropriate tools strategically.
Saxon Math Intermediate 5 Citations
This standard is covered throughout the program; the following are examples.
Instruction:
New Concept
Lessons 27, 28, 43, 44, 55, 72, 98
Investigation(s)
3, 10
Maintenance:
Problem Solving
Lessons 65, 95, 104, 111
Written Practice
Lessons 27, 49
Calculator Activities
Lessons 11, 13, 22, 24, 49, 51, 72, 76,
81, 89, 96,
.
This standard is covered throughout the program; the following are examples.
Attend to precision.
Instruction:
New Concept
3
Lessons 27, 44, 47, 53, 56, 61, 65, 66,
73, 74, 77, 85, 88, 109, 110
Investigation(s)
5, 6, 7, 8
Maintenance:
Written Practice
Lessons 45, 46, 47
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
7
Descriptor
Look for and make use of structure.
Saxon Math Intermediate 5 Citations
This standard is covered throughout the program; the following are examples.
Instruction:
New Concept
8
Investigation(s)
4
Maintenance:
Problem Solving
Lessons
Written Practice
Lessons 24
This standard is covered throughout the program; the following are examples.
Look for and express regularity in repeated reasoning.
Instruction:
New Concept
Standard
Lessons 15, 22, 24, 26, 34, 48, 51, 54,
55, 56, 59, 75, 78, 86, 92, 94, 102, 106,
116, 117, 118, 119, 120
Descriptor
Lessons 13, 22, 25, 29, 35, 42, 59, 70,
71, 76, 79, 80, 81, 82, 90, 91, 95, 100,
101, 104, 111, 112, 113
Investigation(s)
2
Maintenance:
Written Practice
Lessons 43
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
Operations and Algebraic Thinking 5.OA
Write and interpret numerical expressions.
4
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
1
Use parentheses, brackets, or braces in numerical expressions, and evaluate
expressions with these symbols.
Instruction:
New Concept
Maintenance:
Power Up
2
Write simple expressions that record calculations with numbers, and interpret
numerical expressions without evaluating them. For example, express the
calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3
x (18932 + 921) is three times as large as 18932 + 921, without having to
calculate the indicated sum or product.
Analyze patterns and relationships.
3
Generate two numerical patterns using two given rules. Identify apparent
relationships between corresponding terms. Form ordered pairs consisting of
corresponding terms from the two patterns, and graph the ordered pairs on a
coordinate plane. For example, given the rule “Add 3” and the starting number
0, and given the rule “Add 6” and the starting number 0, generate terms in the
resulting sequences, and observe that the terms in one sequence are twice the
corresponding terms in the other sequence. Explain informally why this is so.
Number and Operations in Base Ten 5.NBT
Understand the place value system.
5
Lessons 24, 48, 51, 52, 78
Lessons 82, 83, 84, 85, 86, 87, 88, 89,
90
Written Practice
Lessons 24, 25, 27, 28, 29, 31, 33, 35,
37, 38, 40, 41, 42, 44, 47, 48, 49, 50,
51, 52, 53, 55, 57, 62, 63, 65, 66, 67,
68, 69, 70, 71, 72, 77, 79, 81, 85, 86,
90, 91, 93, 94, 95, 96, 97, 99, 102, 103,
104, 108, 109, 112, 113, 114, 119
Learning Stations
Lessons 24, 48
Instruction:
New Concept
Lessons 13, 24, 49, 51
Maintenance:
Written Practice
Lessons 13, 14, 15, 16, 17, 18, 24, 25,
51, 52, 53, 54, 56, 59
Instruction:
Investigation(s)
4, 6, 8
Maintenance:
Written Practice
Lessons 45, 47, 48, 49, 56, 76
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
1
Recognize that in a multi-digit number, a digit in one place represents 10 times
as much as it represents in the place to its right and 1/10 of what it represents
in the place to its left.
Instruction:
New Concept
Maintenance:
Written Practice
2
3
3a
Explain patterns in the number of zeros of the product when multiplying a
number by powers of 10, and explain patterns in the placement of the decimal
point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10.
Read, write, and compare decimals to thousandths.
Read and write decimals to thousandths using base-ten numerals, number
names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x
(1/10) + 9 x (1/100) + 2 x (1/1000).
Lessons 3, 7, 8, 24, 29, 52, 56, 66, 69,
80
Learning Stations
Lessons 3, 52, 64
Instruction:
New Concept
Lessons 29, 64, 68, 78, 111, 118
Maintenance:
Written Practice
Lessons 30, 34, 35, 46, 64, 78, 79, 80,
111, 112, 113, 114, 115, 116, 117, 118,
119, 120
Learning Stations
Lessons 29, 64, 111
N/A
Instruction:
New Concept
Lessons 64, 67, 68, 106
Maintenance:
Written Practice
Learning Stations
6
Lessons 3, 7, 52, 64, 106
Lessons 64, 68, 74, 81, 82, 85, 102,
105, 109, 110, 111, 112
Lesson 68
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
3b
Compare two decimals to thousandths based on meanings of the digits in each
place, using >, =, and < symbols to record the results of comparisons.
Instruction:
New Concept
Maintenance:
Written Practice
4
Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5
Fluently multiply multi-digit whole numbers using the standard algorithm.
7
Lessons 69, 70, 71, 106
Lessons 70, 71, 73, 74, 75, 76, 77, 79,
83, 102, 117
Learning Stations
Lessons 69, 106
Instruction:
New Concept
Lessons 62, 64, 104, 106
Maintenance:
Power Up
Lesson 105
Written Practice
Lessons 104, 105, 106, 107, 110
Instruction:
New Concept
Lessons 17, 29, 51, 55, 56
Maintenance:
Power Up
Lessons 23, 25, 26, 27, 28, 45, 68, 118
Written Practice
Lessons 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 29, 30, 31, 32, 33, 37, 40,
45, 46, 47, 48, 49, 51, 56, 57, 58, 59,
65, 70, 71, 74, 75, 79, 86, 91, 103, 116,
Learning Stations
Lessons 29, 51, 55, 56
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
6
Find whole-number quotients of whole numbers with up to four-digit dividends
and two-digit divisors, using strategies based on place value, the properties of
operations, and/or the relationship between multiplication and division.
Illustrate and explain the calculation by using equations, rectangular arrays,
and/or area models.
Instruction:
New Concept
Maintenance:
Written Practice
Learning Stations
7
Add, subtract, multiply, and divide decimals to hundredths, using concrete
models or drawings and strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Instruction:
New Concept
Maintenance:
Written Practice
Learning Stations
Number and Operations—Fractions 5.NF
Use equivalent fractions as a strategy to add and subtract fractions.
1
Add and subtract fractions with unlike denominators (including mixed
numbers) by replacing given fractions with equivalent fractions in such a way
as to produce an equivalent sum or difference of fractions with like
denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general,
a/b + c/d = (ad + bc)/bd.)
8
Lessons 54, 92
Lessons 54, 55, 57, 58, 59, 60, 61, 62,
63, 64, 65, 66, 67, 68, 69, 70, 72, 75,
79, 81, 82, 84, 86, 87, 89, 91, 94, 96,
98, 99 101, 103, 114, 116, 119, 120
Lessons 54, 92
Lessons 13, 17, 26, 29, 51, 54, 56, 73,
99, 102, 109, 110, 111, 117, 118, 119
Lessons 73, 75, 78, 80, 85, 99, 100,
101, 102, 103, 105, 106, 107, 108, 109,
110, 111, 112, 113, 114, 115, 116, 117,
118, 119, 120
Lessons 99, 102, 109, 110, 111, 117,
118, 119
Instruction:
New Concept
Lesson 116
Maintenance:
Written Practice
Lessons 116, 117, 118, 119, 120
Learning Stations
Lesson 116
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
2
Solve word problems involving addition and subtraction of fractions referring
to the same whole, including cases of unlike denominators, e.g., by using
visual fraction models or equations to represent the problem. Use benchmark
fractions and number sense of fractions to estimate mentally and assess the
reasonableness of answers. For example, recognize an incorrect result 2/5 +
1/2 = 3/7, by observing that 3/7 < 1/2.
Instruction:
New Concept
Maintenance:
Written Practice
Learning Stations
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷
Instruction:
New Concept
b). Solve word problems involving division of whole numbers leading to
answers in the form of fractions or mixed numbers, e.g., by using visual
fraction models or equations to represent the problem. For example, interpret
Maintenance:
Written Practice
3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3,
and that when 3 wholes are shared equally among 4 people each person has a
share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by
Learning Stations
weight, how many pounds of rice should each person get? Between what two
whole numbers does your answer lie?
4
4a
Apply and extend previous understandings of multiplication to multiply a
fraction or whole number by a fraction.
Interpret the product (a/b) x q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a x q ÷ b. For example,
use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context
for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x
(c/d) = ac/bd.)
Lessons 26, 28, 31, 32, 66, 67, 72, 86,
87, 94, 99, 101, 107, 110, 112, 113,
114, 116, 118
Lessons 41, 59, 60, 63, 75, 91
Lessons 40, 43, 58
Lessons 41, 42, 44, 46, 47, 49, 53, 57,
58, 59, 61, 62, 66, 67, 68
Lessons 40, 43
N/A
Instruction:
New Concept
Maintenance:
Written Practice
Learning Stations
9
Lessons 23, 41, 43, 59, 60, 63, 75, 91,
39, 116
Lessons 46, 76, 86
Lessons 48, 49, 50, 53, 54, 55, 56, 57,
58, 65, 76, 88, 89, 96, 104, 111, 115,
117, 118
Lesson 76
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
4b
5
5a
5b
6
Find the area of a rectangle with fractional side lengths by tiling it with unit
squares of the appropriate unit fraction side lengths, and show that the area is
the same as would be found by multiplying the side lengths. Multiply
fractional side lengths to find areas of rectangles, and represent fraction
products as rectangular areas.
Instruction:
New Concept
Lessons 76
Maintenance:
Written Practice
Lessons 77, 115
Learning Stations
Lesson 76
Interpret multiplication as scaling (resizing), by:
Comparing the size of a product to the size of one factor on the basis of the
size of the other factor, without performing the indicated multiplication.
N/A
Instruction:
New Concept
Lesson 86
Explaining why multiplying a given number by a fraction greater than 1 results
in a product greater than the given number (recognizing multiplication by
whole numbers greater than 1 as a familiar case); explaining why multiplying a
given number by a fraction less than 1 results in a product smaller than the
given number; and relating the principle of fraction equivalence a/b =
(nxa)/(nxb) to the effect of multiplying a/b by 1.
Instruction:
New Concept
Lessons 86, 120
Maintenance:
Learning Stations
Lesson 86
Solve real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent the
problem.
Instruction:
New Concept
Lessons 76, 86, 120
Maintenance:
Written Practice
Lessons 78, 96, 111, 115, 117
Learning Stations
Lesson 120
Performance Task(s)
4
10
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
7
Apply and extend previous understandings of division to divide unit
fractions by whole numbers and whole numbers by unit fractions. 1
N/A
[1 Students able to multiply fractions in general can develop strategies to divide
fractions in general, by reasoning about the relationship between multiplication
and division. But division of a fraction by a fraction is not a requirement at this
grade.]
7a
7b
7c
Interpret division of a unit fraction by a non-zero whole number, and compute
such quotients. For example, create a story context for (1/3) ÷ 4, and use a
visual fraction model to show the quotient. Use the relationship between
multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4
= 1/3.
Instruction:
New Concept
Lessons 87, 95
Maintenance:
Written Practice
Lessons 87, 92, 93, 95, 96, 97
Learning Stations
Lessons 87, 95
Interpret division of a whole number by a unit fraction, and compute such
quotients. For example, create a story context for 4 ÷ (1/5), and use a visual
fraction model to show the quotient. Use the relationship between
multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) =
4
Instruction:
New Concept
Lessons 87, , 96
Maintenance:
Written Practice
Lessons 90, 93, 96
Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using
visual fraction models and equations to represent the problem. For example,
how much chocolate will each person get if 3 people share 1/2 lb of chocolate
equally? How many 1/3-cup servings are in 2 cups of raisins?
Instruction:
New Concept
Lesson 87
Maintenance:
Written Practice
Lessons 92, 93, 94, 95
Measurement and Data 5.MD
Convert like measurement units within a given measurement system.
11
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
1
Convert among different-sized standard measurement units within a given
measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions
in solving multi-step, real world problems.
Instruction:
New Concept
Lessons 44, 46, 47, 65, 66, 74, 77, 85
Maintenance:
Represent and interpret data.
2
Make a line plot to display a data set of measurements in fractions of a unit
(1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems
involving information presented in line plots. For example, given different
measurements of liquid in identical beakers, find the amount of liquid each
beaker would contain if the total amount in all the beakers were redistributed
equally.
Power Up
Lessons 76, 78, 91, , 99, 100, 106, 107,
110, 111, 112, 114, 117, 118
Written Practice
Lessons 44, 45, 46, 47, 50, 65, 67, 74,
75, 77, 85, 86, 89, 90, 97
Learning Stations
Lessons 47, 65, 66, 74, 77, 85
Instruction:
New Concept
Lesson 74
Investigation
5
Maintenance:
Written Practice Lessons 52
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
3
Recognize volume as an attribute of solid figures and understand concepts N/A
of volume measurement.
3a
A cube with side length 1 unit, called a “unit cube, ” is said to have “one cubic Instruction:
New Concept
unit” of volume, and can be used to measure volume.
Maintenance:
Written Practice
Learning Stations
12
Lesson 103
Lessons 103, 104, 105, 106, 107, 108,
109, 113, 117, 119, 120
Lesson 103
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
3b
A solid figure which can be packed without gaps or overlaps using n unit cubes
is said to have a volume of n cubic units.
Instruction:
New Concept
Maintenance:
Written Practice
4
5
5a
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft,
and improvised units.
Relate volume to the operations of multiplication and addition and solve
real world and mathematical problems involving volume.
Find the volume of a right rectangular prism with whole-number side lengths
by packing it with unit cubes, and show that the volume is the same as would
be found by multiplying the edge lengths, equivalently by multiplying the
height by the area of the base. Represent threefold whole-number products as
volumes, e.g., to represent the associative property of multiplication.
13
Lesson 103
Lessons 103, 104, 105, 106, 107, 108,
109, 113, 117, 119, 120
Learning Stations
Lesson 103
Instruction:
New Concept
Lesson 103
Maintenance:
Problem Solving
Lessons 77, 87, 98, 103, 108, 118
Written Practice
Lessons 103, 104, 105, 106, 107, 108,
109, 113, 117, 119, 120
Performance Task(s)
11
N/A
Instruction:
New Concept
Lessons 103, 104
Maintenance:
Problem Solving
Lessons 77, 87, 98, 103, 108, 118
Learning Stations
Lesson 103
Performance Task(s)
11
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
5b
5c
Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find
volumes of right rectangular prisms with whole-number edge lengths in the
context of solving real world and mathematical problems.
Recognize volume as additive. Find volumes of solid figures composed of two
non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.
Geometry 5.G
Graph points on the coordinate plane to solve real-world and mathematical problems.
1
Use a pair of perpendicular number lines, called axes, to define a coordinate
system, with the intersection of the lines (the origin) arranged to coincide with
the 0 on each line and a given point in the plane located by using an ordered
pair of numbers, called its coordinates. Understand that the first number
indicates how far to travel from the origin in the direction of one axis, and the
second number indicates how far to travel in the direction of the second axis,
with the convention that the names of the two axes and the coordinates
correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
14
Instruction:
New Concept
Lessons 103, 104, 114
Maintenance:
Problem Solving
Lessons 105, 108
Written Practice
Lessons 103, 104, 105, 106, 107, 108,
109, 113, 117, 119, 120
Learning Stations
Lesson 104
Instruction:
New Concept
Lessons 103, 104, 114
Maintenance:
Problem Solving
Lesson 118
Instruction:
Investigation
8
Maintenance:
Written Practice
Lessons 101, 103, 104, 105, 107, 112
Saxon Math Intermediate 5 ©2008
correlated to the
Common Core States Standards for Mathematics (June 2010)
Grade 5
Standard
Descriptor
Saxon Math Intermediate 5 Citations
Italic references indicate foundational.
2
Represent real world and mathematical problems by graphing points in the first
quadrant of the coordinate plane, and interpret coordinate values of points in
the context of the situation.
Instruction:
Investigation
Maintenance:
Written Practice
Classify two-dimensional figures into categories based on their properties.
3
Understand that attributes belonging to a category of two-dimensional figures
also belong to all subcategories of that category. For example, all rectangles
have four right angles and squares are rectangles, so all squares have four
right angles.
4
Classify two-dimensional figures in a hierarchy based on properties.
15
8
Lessons 84, 101, 103, 104, 105, 107,
112
Instruction:
New Concept
Lessons 32, 36, 45
Maintenance:
Written Practice
Lessons 44, 45, 46
Learning Stations
Lesson 32
Instruction:
New Concept
Lessons 32, 36, 45
Maintenance:
Power Up
Lessons 47, 57, 67
Written Practice
Lessons 32, 36, 37, 38, 41, 42, 54
Learning Stations
Lessons 32, 36, 45