Voyages in Fourth Grade Math is aligned with the Common Core and focuses on Mathematical techniques and mechanics. There are 180 Lessons within this text. 715 pages. With it's thorough coverage of Fourth Grade Math concepts, this digital text engages student in learning and exploring such math concepts at place value, multiplication, division, factors, fractions, decimals, measurement and more! If you are exploring homeschool curriculum's, such as ABC Mouse, Ron Paul Homeschool, or Easy Peasy Homeschool, please review this Complete Curriculum first. Best Homeschool Curriculum and Cheap Homeschool Curriculum (Affordable)!

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2. Acknowledgments
Complete Curriculum’s K-12 curriculum has been team-developed by a consortium
of teachers, administrators, educational and subject matter specialists, graphic artists
and editors.
In a collaborative environment, each professional participant contributed to ensuring the quality,
integrity and effectiveness of each Compete Curriculum resource was commensurate with the
required educational benchmarks and contemporary standards Complete Curriculum had set
forth at the onset of this publishing program.
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sufficiency or otherwise the content of the web links listed herein.
Complete Curriculum recommends that instructors test web links prior to distributing the lesson.
If you see a broken link or changed link, please feel free to email omplete urriculuP at
contactus@completecurriculum.com.
v. 2v. 2
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21. Chart Your Path for Fourth Grade Math!
To the Student
Each daily Lesson begins with a question. This isn’t a trick question—you can’t study for
this question—but you do have to think about it before you answer. The more you think,
write or talk about your answer, the more relevant the material will become, the more
interested you will be in what you are about to learn, and the better you will be able to
understand and apply what you are about to learn.
3XEOLVKHG E
v. 2v. 2
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22. Fourth Grade Math Common Core Alignment Complete Curriculum Lesson
Operations and Algebraic Thinking
--Use the four operations with whole numbers to solve problems.
4.0A.1 Interpret a multiplication equation as a comparison, e.g.,
interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7
and 7 times as many as 5. Represent verbal statements of
multiplicative comparisons as multiplication equations.
28, 29, 30, 34
multiplicative comparisons as multiplication equations.
4.0A.2 Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and equations with
a symbol for the unknown number to represent the problem,
distinguishing multiplicative comparison from additive comparison.
32, 33, 34
4.0A.3 Solve multistep word problems posed with whole numbers
d h i h l b i th f ti
34, 37, 43, 45, 52
and having whole-number answers using the four operations,
including problems in which remainders must be interpreted.
Represent these problems using equations with a letter standing for
the unknown quantity. Assess the reasonableness of answers using
mental computation and estimation strategies including rounding and
explain why a rounded solution is appropriate.
--Gain familiarity with factors and multiples.Gain familiarity with factors and multiples.
4.0A.4 Find all factor pairs for a whole number in the range 1–100.
Recognize that a whole number is a multiple of each of its factors.
Determine whether a given whole number in the range 1–100 is a
multiple of a given one-digit number. Determine whether a given
whole number in the range 1–100 is prime or composite.
54, 56, 57, 58, 59, 60, 61, 62, 63
--Generate and analyze patterns.
4.0A.5 Generate a number or shape pattern that follows a given
rule. Identify apparent features of the pattern that were not explicit in
the rule itself. For example, given the rule “Add 3” and the starting
number 1, generate terms in the resulting sequence and observe that
the terms appear to alternate between odd and even numbers.
Explain informally why the numbers will continue to alternate in this
way.
54, 56, 69, 83, 168
Number and Operations in Base TenNumber and Operations in Base Ten
--Generalize place value understanding for multi-digit whole numbers.
4.NBT.1 Recognize that in a multi-digit whole number, a digit in
one place represents ten times what it represents in the place to its
right. For example, recognize that 700 ÷ 70 = 10 by applying
concepts of place value and division.
2, 3, 5, 7, 13
4 NBT 2 Read and write multi-digit whole numbers using base-ten 1 4 5 6 8 9 10 11 12 134.NBT.2 Read and write multi-digit whole numbers using base-ten
numerals, number names, and expanded form. Compare two multi-
digit numbers based on meanings of the digits in each place, using ,
=, and symbols to record the results of comparisons.
1, 4, 5, 6, 8, 9 10, 11, 12, 13
4.NBT.3 Use place value understanding to round multi-digit whole
numbers to any place.
132,
--Use place value understanding and properties of operations to
perform multi-digit arithmetic.
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23. 4.NBT.4 Fluently add and subtract multi-digit whole numbers using
the standard algorithm.
14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27
4.NBT.5 Multiply a whole number of up to four digits by a one-digit
whole number, and multiply two two-digit numbers, using strategies
based on place value and the properties of operations. Illustrate and
explain the calculation by using equations, rectangular arrays, and/or
area models.
31, 34, 35, 36, 39, 40, 41, 42, 43, 44,
45, 46, 54, 55, 57, 58, 59
4 NBT 6 Fi d h l b ti t d i d ith t4.NBT.6 Find whole-number quotients and remainders with up to
four-digit dividends and one-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.
46, 49, 50-53, 55
Number and Operations—Fractions
--Extend understanding of fraction equivalence and ordering--Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n ×
a)/(n × b) by using visual fraction models, with attention to how the
number and size of the parts differ even though the two fractions
themselves are the same size. Use this principle to recognize and
generate equivalent fractions.
67, 71, 72, 83-85, 87, 88, 90, 91, 92,
93
4.NF.2 Compare two fractions with different numerators and
different denominators, e.g., by creating common denominators or
67, 71, 79, 80
different denominators, e.g., by creating common denominators or
numerators, or by comparing to a benchmark fraction such as 1/2.
Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with
symbols , =, or , and justify the conclusions, e.g., by using a visual
fraction model.
--Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.
4 NF 3 U d t d f ti /b ith 1 f f ti4.NF.3 Understand a fraction a/b with a 1 as a sum of fractions
1/b.
a. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
81, 82, 85, 88, 89, 93
b. Decompose a fraction into a sum of fractions with the same
denominator in more than one way, recording each decomposition by
an equation. Justify decompositions, e.g., by using a visual fraction
model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 +
81, 86
model. Examples: 3/8 1/8 1/8 1/8 ; 3/8 1/8 2/8 ; 2 1/8 1
1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by
replacing each mixed number with an equivalent fraction, and/or by
using properties of operations and the relationship between addition
and subtraction.
73, 75, 76, 79
d. Solve word problems involving addition and subtraction of fractions
referring to the same whole and having like denominators, e.g., by
using visual fraction models and equations to represent the problem
85, 93
using visual fraction models and equations to represent the problem.
4.NF.4 Apply and extend previous understandings of multiplication
to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a
visual fraction model to represent 5/4 as the product 5 × (1/4),
recording the conclusion by the equation 5/4 = 5 × (1/4).
*84
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24. b. Understand a multiple of a/b as a multiple of 1/b, and use this
understanding to multiply a fraction by a whole number. For example,
use a visual fraction model to express 3 × (2/5) as 6 × (1/5),
recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
84, 86
c. Solve word problems involving multiplication of a fraction by a
whole number, e.g., by using visual fraction models and equations to
represent the problem For example if each person at a party will eat
74, 84, 86
represent the problem. For example, if each person at a party will eat
3/8 of a pound of roast beef, and there will be 5 people at the party,
how many pounds of roast beef will be needed? Between what two
whole numbers does your answer lie?
--Understand decimal notation for fractions, and compare decimal
fractions.
4.NF.5 Express a fraction with denominator 10 as an equivalent *88, 94, 101, 105p q
fraction with denominator 100, and use this technique to add two
fractions with respective denominators 10 and 100.4 For example,
express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
, , ,
4.NF.6 Use decimal notation for fractions with denominators 10 or
100. For example, rewrite 0.62 as 62/100; describe a length as 0.62
meters; locate 0.62 on a number line diagram.
94, 95, 96, 97, 100, 101, 105
4 NF 7 Compare two decimals to hundredths by reasoning about *98 99 101 102 103 104 1054.NF.7 Compare two decimals to hundredths by reasoning about
their size. Recognize that comparisons are valid only when the two
decimals refer to the same whole. Record the results of comparisons
with the symbols , =, or , and justify the conclusions, e.g., by using
the number line or another visual model.
*98, 99, 101, 102, 103, 104, 105
model and symbol not yet included
Measurement and Data
--Solve problems involving measurement and conversion ofSolve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one
system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.
Within a single system of measurement, express measurements in a
larger unit in terms of a smaller unit. Record measurement
equivalents in a two-column table. For example, know that 1 ft is 12
times as long as 1 in. Express the length of a 4 ft snake as 48 in.
G t i t bl f f t d i h li ti th b
133-135, 141
Generate a conversion table for feet and inches listing the number
pairs (1, 12), (2, 24), (3, 36), ...
4.MD.2 Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects, and
money, including problems involving simple fractions or decimals,
and problems that require expressing measurements given in a
larger unit in terms of a smaller unit.
32, 33, 97, 141
4.MD.3 Apply the area and perimeter formulas for rectangles in 136, 142, 143, 1454.MD.3 Apply the area and perimeter formulas for rectangles in
real world and mathematical problems. For example, find the width of
a rectangular room given the area of the flooring and the length, by
viewing the area formula as a multiplication equation with an
unknown factor.
136, 142, 143, 145
--Represent and interpret data.
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25. 4.MD.4 Make a line plot to display a data set of measurements in
fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition
and subtraction of fractions by using information presented in line
plots. For example, from a line plot find and interpret the difference in
length between the longest and shortest specimens in an insect
collection.
*85
--Geometric measurement: understand concepts of angle and
measure anglesmeasure angles.
4.MD.5 Recognize angles as geometric shapes that are formed
wherever two rays share a common endpoint, and understand
concepts of angle measurement:
a. An angle is measured with reference to a circle with its center at
the common endpoint of the rays, by considering the fraction of the
circular arc between the points where the two rays intersect the
circle. An angle that turns through 1/360 of a circle is called a “one-
*156, 157, 165
g g
degree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an
angle measure of n degrees
*156, 157, 165
4.MD.6 Measure angles in whole-number degrees using a
protractor. Sketch angles of specified measure.
*156, 157, 165
--Geometric measurement: understand concepts of angle and
measure anglesmeasure angles.
4.MD.7 Recognize angle measure as additive. When an angle is
decomposed into non-overlapping parts, the angle measure of the
whole is the sum of the angle measures of the parts. Solve addition
and subtraction problems to find unknown angles on a diagram in
real world and mathematical problems, e.g., by using an equation
with a symbol for the unknown angle measure.
*156, 157, 165
Geometryy
--Draw and identify lines and angles, and classify shapes by
properties of their lines and angles.
4.G.1 Draw points, lines, line segments, rays, angles (right, acute,
obtuse), and perpendicular and parallel lines. Identify these in two-
dimensional figures.
151-153, 157, 158, 164, 165
4.G.2 Classify two-dimensional figures based on the presence or
absence of parallel or perpendicular lines, or the presence or
b f l f ifi d i R i i ht t i l
154, 155, 159
absence of angles of a specified size. Recognize right triangles as a
category, and identify right triangles. (Two dimensional shapes
should include special triangles, e.g., equilateral, isosceles, scalene,
and special quadrilaterals, e.g., rhombus, square, rectangle,
parallelogram, trapezoid.)
4.G.3 Recognize a line of symmetry for a two-dimensional figure
as a line across the figure such that the figure can be folded along
the line into matching parts. Identify line-symmetric figures and draw
166, 169-172
the line into matching parts. Identify line symmetric figures and draw
lines of symmetry.
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