Helping Children
Learn in the Primary and
Elementary Years
MATH
Kindergarten to Grade 5
A G U I D E T O T H E M AT H C O M M O N C O R E S TAT E S TA N D A R D S
F O R PA R E N T S A N D S T U D E N T S
This brochure is a product of the Tennessee State Personnel Development Grant,
and was researched and compiled by Dr. Reggie Curran through a partnership between
TN SPDG and UT/Knoxville/CLEE.
LO
TH
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RE
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O F I N N O VA
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Veronica McDonald, Grant Director
Tennessee Department of Education, Division of Special Populations
710 James Robertson Parkway
Nashville, TN 37243
615-532-8228
[email protected]
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Equity
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School and
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INITIATIVE
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RTI Literacy
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For more information about the Common Core State Standards and Child Development,
check out these websites:
Tennessee Common Core at
www.TNCORE.org
Read Tennessee website at
www.Readtennessee.org
This project is supported by the U.S. Department of Education, Office of Special Education
Programs (OSEP). Opinions expressed herein are those of the authors and do not necessarily
represent the position of the U.S. Department of Education.
UT PUBLICATION NO.: R01-1704-113-002-13
Purpose of This Booklet
This booklet has two goals:
■ to help parents understand more about what their children are learning in school, and
■ to help students know if they have mastered the skills their teachers expect them to
know in each grade
This booklet will explain what the Common Core
State Standards are, and about the skills on which
Tennessee teachers will focus math instruction
while transitioning to the Common Core State
Standards. You will find general information that
will give you an overview of what the standards
are and why states are using them.
At the end of each grade’s lists of standards and
explanations, you will find a box with an “I can
do it!” checklist. These are short statements about
the skills your children will be expected to have
mastered by the end of the year. Ask your children
to look at them to see if they feel they have
mastered those skills, or if they need some extra
help in specific areas.
T
eachers work from a set of standards
that tell them what to teach. Each state
has created its own standards, and those
standards have not been the same across our
country. However, most states have recently agreed
to use the same set of standards — the Common
Core State Standards. More information is
included about the Common Core State Standards
in the following pages.
We hope you will find this booklet helpful in your
effort to be a partner in your child’s education and
development.
If you come across a math term and
don’t remember what is or what it means,
check out the Math is Fun dictionary at
www.mathisfun.com/definitions
2
What are the Common Core State Standards?
A
will balance procedural skills with
understanding by finding find ways
to engage students in good practices
that will help them understand the
math content as they grow in math
maturity and expertise throughout the elementary,
middle, and high school years.
cademic standards are
statements that describe
the goals of schooling
— what children should know
or be able to do at the end of the
school year. For example, the second grade math
standards state that by the end of the school year,
a second grader should be able to count to 120
and understand what each digit in a three-digit
number represents.
The Common Core State Standards will provide
students, teachers, and parents with a shared
understanding of what students are learning.
With students, parents, and teachers all on the
same page and working together for shared goals,
we can increase the likelihood that students will
make progress each year and will graduate from
school prepared to succeed and to build a strong
future for themselves and the country.
However, standards have not been the same
across the United States. In the past, states have
had their own sets of standards. This means that
children in one state may be learning different
things at different times (and in different years)
than children in another state. Many states have
recently agreed to use a common set of standards
for learning that takes place in their classrooms;
these are the Common Core State Standards
(CCSS).
Parents: In this booklet, you will find an overview
of the standards for each grade, showing you what
your children should be able to do by the end of
the school year. At the end of the section, you will
find a box with this “I can do it!” symbol. Discuss
these items with your child to see if he/she is able
to complete these tasks.
One major benefit of having common standards
across states is that children are being required
to learn the same information in the same years
in each of those states, so that a child moving
from one state to another will not be behind
the children in the new location. A common
set of standards ensures that all students, no
matter where they live, are focused on graduating
from high school prepared for postsecondary
education and careers.
Students: Find the “I can
do it!” box at the end of each
section and check yourself
to see if you can do all those
things.
The Common Core State Standards for Math
have two components: Standards for Mathematical
Practice and Standards for Mathematical Content.
The Practice Standards describe the kind of
math teaching and learning that will produce
the most successful learning and that will help
students dig deeper and better understand math.
The Content Standards outline the concepts
and skills to be learned in each grade; teachers
3
I can
do it!
Overview of Goals for Standards for Mathematical Practice
The Standards for Mathematical
Practice describe skills and
behaviors that all students should
be developing in their particular
grades. These practices include
important processes (ways of
doing things) and proficiencies
(how well we do things), including
problem solving, reasoning
and proof, communication,
representation, and making
connections. These practices
will allow students to understand
and use math with confidence.
Following is what children will
be working to be able to do with
increasing ease:
Construct arguments and
evaluate the reasoning of
others
UÊ1˜`iÀÃÌ>˜`Ê>˜`ÊÕÃiʈ˜vœÀ“>̈œ˜Ê
to build arguments
UÊ>ŽiÊ>˜`ÊiÝ«œÀiÊ̅iÊÌÀÕ̅ʜvÊ
estimates and guesses
UÊÕÃ̈vÞÊVœ˜VÕȜ˜ÃÊ>˜`ÊÀi뜘`Ê
to arguments of others
Model with mathematics
UÊ««Þʓ>̅Ê̜ʫÀœLi“Ãʈ˜Ê
everyday life
UÊ`i˜ÌˆvÞʵÕ>˜ÌˆÌˆiÃÊ­>“œÕ˜ÌÃ]Ê
numbers) in a practical situation
UÊ*ÀiÃi˜Ì]ÊŜÜ]ʜÀÊiÝ«>ˆ˜Ê̅iÊ
problem and solution in an
understandable way
Make sense of problems and
persevere in solving them
Uʈ˜`Ê̅iʓi>˜ˆ˜}ʈ˜Ê«ÀœLi“Ã
Uʘ>Þâi]Ê«Ài`ˆVÌ]Ê>˜`Ê«>˜Ê̅iÊ
path to solve a problem
UÊ6iÀˆvÞÊ>˜ÃÜiÀÃ
UÊÎÊ̅i“ÃiÛiÃÊ̅iʵÕiÃ̈œ˜\Ê
“Does this make sense?”
Use appropriate tools
strategically
UÊ
œ˜Ãˆ`iÀÊ̅iÊ>Û>ˆ>LiÊ̜œÃÊ
when solving problems, and
know which tool is most
appropriate in the situation
UÊiÊv>“ˆˆ>ÀÊ܈̅Ê̜œÃÊ
appropriate for their grade
level or course (pencil and
Reason abstractly and
paper, concrete models,
quantitatively
ruler, protractor, calculator,
UÊiÊ>LiÊ̜ÊÌÀ>˜Ã>ÌiÊ̅iʓi>˜ˆ˜}Ê
spreadsheet, computer
of each math term in any
programs, digital content on a
iµÕ>̈œ˜
website, and other technological
UʘÌiÀ«ÀiÌÊÀiÃՏÌÃʈ˜Ê̅iÊVœ˜ÌiÝÌÊ
tools)
(setting) of the situation
Be precise
UÊiÊ>LiÊ̜ÊVœ““Õ˜ˆV>ÌiÊ
accurately with others
UÊ1ÃiÊVi>ÀÊ`iw˜ˆÌˆœ˜Ã]ÊÃÌ>ÌiÊ̅iÊ
meaning of symbols, and be
careful when specifying units of
measure and labeling axes (the
“x” and “y” lines that cross at
right angles to make a graph) in
math figures
UÊ
>VՏ>ÌiÊ>VVÕÀ>ÌiÞÊ>˜`Ê
efficiently
Look for and make use of
structure
UÊ,iVœ}˜ˆâiÊ«>ÌÌiÀ˜ÃÊ>˜`Ê
structures
UÊ-Ìi«ÊL>VŽÊ̜Êw˜`Ê̅iÊLˆ}Ê«ˆVÌÕÀiÊ
and be able to shift perspective
UÊ-iiÊVœ“«ˆV>Ìi`Ê̅ˆ˜}ÃÊ>ÃÊ
single objects, or as being made
up of several objects
Look for and identify ways to
create shortcuts when doing
problems
UÊ7…i˜ÊV>VՏ>̈œ˜ÃÊ>ÀiÊÀi«i>Ìi`]Ê
look for general methods,
patterns, and shortcuts
UÊiÊ>LiÊ̜ÊiÛ>Õ>ÌiÊ܅i̅iÀÊ>˜Ê
answer makes sense
The major domains included in the math standards for Grades K-5 are listed below. In each grade, students
build on what they learned previously to form a progression of increasing knowledge, skill, or sophistication.
MAJOR DOMAINS FOR
MATH STANDARDS
Counting and Cardinality
Operations and Algebraic Thinking
Numbers and Operations – Base Ten
GRADE
KINDERGARTEN
1
2
3
4
5
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Numbers and Operations – Fractions
Measurement and Data
Geometry
4
Fourth Grade Math
Focus Clusters for Fourth Grade – in fourth grade, teachers will focus
instruction on these areas:
UÊÝÌi˜`Ê՘`iÀÃÌ>˜`ˆ˜}ʜvÊvÀ>V̈œ˜ÊiµÕˆÛ>i˜ViÊ>˜`ʜÀ`iÀˆ˜}°
UÊՈ`ÊvÀ>V̈œ˜ÃÊvÀœ“Ê՘ˆÌÊvÀ>V̈œ˜ÃÊLÞÊ>««Þˆ˜}Ê>˜`ÊiÝ«>˜`ˆ˜}Ê«ÀiۈœÕÃÊ
understanding of operations of whole numbers.
UÊ1ÃiÊ̅iÊvœÕÀʜ«iÀ>̈œ˜ÃÊ܈̅Ê܅œiʘՓLiÀÃÊ̜Ê܏ÛiÊ«ÀœLi“ðÊ
UÊi˜iÀ>ˆâiÊ«>ViÊÛ>ÕiÊ՘`iÀÃÌ>˜`ˆ˜}ÊvœÀʓՏ̈‡`ˆ}ˆÌÊ܅œiʘՓLiÀðÊ
Skills that focus on these areas appear in the shaded box below. While
these skills are priority areas, students will be learning all of the skills listed
in the following sections.
For fourth graders, the math standards
expect the following skills to be developing,
so that a student can say, “I can … (insert
math goal),” for example, I can explain why
one fraction is equal to another.” Help your
child develop skills in these areas:
Numbers and Operations – Fractions
■Ê Ý«>ˆ˜Ê܅ÞÊ>ÊvÀ>V̈œ˜Ê>ÉLʈÃÊiµÕˆÛ>i˜ÌÊ̜Ê>ÊvÀ>V̈œ˜Ê
3____
x 6 18
6
= __ = _
(n x a)/(n x b) (n being any number) by using visual fraction models.
3 x 8 24
8
Multiplying by the same number in the numerator (top or first number)
and denominator (bottom or second number) gives the same fraction. For example, (3
x a) / (3 x b) or (12 x a) / (12 x b) gives the same fraction as a/b.
■ Compare two fractions with different numerators and different denominators by
3
_
VÀi>̈˜}ÊVœ““œ˜Ê`i˜œ“ˆ˜>̜ÀÃʜÀʘՓiÀ>̜ÀðʜÀÊiÝ>“«i]Ê̜ÊÃiiʈvÊÊÊÊÊʈÃÊrÊ­iµÕ>Ê
8
6
to), < (less than), or > (more than) __ , change the denominators of each fraction to
12
9
the same number (in this case, 24). The new fractions would become __ (8 into 24 =
24
12
__
3, multiply the numerator (3) by 3) and 24 (12 into 24 = 2, multiply numerator (6) by 2).
9
12
3
6
Since 12 is more than 9, __ is less than (<) __ , so _ < __ .
24
24
8 12
25
1
1
■ Compare two fractions to a benchmark fraction, like _ or _ . Be able to use a visual
2
3
fraction model. Understand addition and subtraction of fractions
as joining and separating parts referring to the same whole.
Benchmark fractions are common fractions that you can judge
1 __
3
1
__
other numbers against. Often, __
, 12 , __
, and often 10
4
4
(because of its relationship with decimals) are referred to as
benchmark fractions.
3
_
5
>
1
_
3
■ Decompose a fraction into a sum of fractions with the same denominator, and be able
̜ʍÕÃ̈vÞÊ̅i“Ê܈̅ÊiµÕ>̈œ˜Ã°Ê
_ = 8
_ + 8
_ + 1
_ .
_ , and 1 + 1 + 1
_ =1
_ + 1
_ + 1
For example, 3
8
8 8 8
8 8
8 8
■ Add and subtract mixed numbers (a whole number and a fraction combined into one
“mixed” number) with like denominators by replacing each mixed number with an
iµÕˆÛ>i˜ÌÊvÀ>V̈œ˜°ÊÊ
_+21
_ = x; 2 1
_=7
_ or 14
__ and 2 1
_ =5
_ or 15
__,
For example, to solve 2 1
3
2
3 3
6
2 2
6
14
15
29
5
__
__
__
_
so
+
= , or 4
6 6
6
6
■ Solve word problems involving addition and subtraction of fractions referring to the
same whole number and having like denominators by using visual fraction models and
iµÕ>̈œ˜ÃÊ̜ÊÀi«ÀiÃi˜ÌÊ̅iÊ«ÀœLi“°ÊœÀÊiÝ>“«i]ʈvÊ̅iÀiÊ>ÀiÊnÊ«ˆiViÃʜvÊ«ˆââ>]Ê>˜`Ê
ˆÊ>ÌiÊÎÊ>˜`Ê-ÕiÊ>ÌiÊÓ]ʅœÜʓ>˜ÞÊ«ˆiViÃÊ>ÀiʏivÌÊ>˜`Ê܅>ÌÊvÀ>V̈œ˜ÊœvÊ̅iÊ«ˆââ>ÊÜ>ÃÊ
eaten?
3
2
__
1 - ( __ +
)
8
8
2
8
8 5
3
3
__
- ( __ + __ ) = __ - __ = __
8
8
8 8
8
8
a
1
■ Understand a fraction _ as a multiple of _ and use this understanding to multiply a
b
b
2
_
1
fraction by a whole number. For example, 3 x 5 could be shown as 6 x _ , with the
5
n x a , with n being any number.
_ = _____
_; n x a
product being 6
b
b
5
26
■ Solve word problems involving multiplication of a fraction by a whole number by using
vÀ>V̈œ˜Ê“œ`iÃÊ>˜`ÊiµÕ>̈œ˜Ã°ÊœÀÊiÝ>“«i]ʈvÊi>V…Ê«iÀܘÊ>ÌÊ>Ê«>ÀÌÞÊ܈Êi>ÌÊÎÉnÊ
pounds 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?
7
1__
8
3 = 15
7
__ = 1__
5 x __
8
8
8
-5
-4
-3
-2
-1
0
1
2
3
4
5
More Numbers and Operations – Fractions
■ Ý«ÀiÃÃÊ>ÊvÀ>V̈œ˜Ê܈̅Ê`i˜œ“ˆ˜>̜ÀÊ£äÊ>ÃÊ>˜ÊiµÕˆÛ>i˜ÌÊvÀ>V̈œ˜Ê܈̅Ê`i˜œ“ˆ˜>̜ÀÊ£ää]Ê
>˜`ÊÕÃiÊ̅ˆÃÊÌiV…˜ˆµÕiÊ̜Ê>``ÊÌܜÊvÀ>V̈œ˜ÃÊ܈̅ÊÀiëiV̈ÛiÊ`i˜œ“ˆ˜>̜ÀÃÊ£äÊ>˜`Ê£ää°Ê
3
30
3
4
3
30
4
34
For example, express __ as ___ , and add __ + ___ ( __ = ___ ) + ___ = ___
10
100
10 100 10 100
100 100
■ Use decimal notation for fractions with denominators 10 or 100. For example,
52
rewrite __ as .52, and show .52 on the number line.
10
-5
-4
-3
-2
-1
0
1
2
3
4
5
■Ê œ“«>ÀiÊÌܜÊ`iVˆ“>ÃÊ̜ʅ՘`Ài`̅ÃÊLÞÊÀi>ܘˆ˜}Ê>LœÕÌÊ̅iˆÀÊÈâi°Ê,iVœ}˜ˆâiÊ̅>ÌÊ
comparisons are valid only when two decimals refer to the same whole. Record the
results of comparisons with pictures or with the symbols >, =, or <.
.5 > .25 .1 < .25
0.5
0.25
0.1
27
Operations and Algebraic Thinking
■ Use the four operations (+, -, ×, ÷) with whole numbers to solve problems.
UÊ ˜ÌiÀ«ÀiÌÊ>ʓՏ̈«ˆV>̈œ˜ÊiµÕ>̈œ˜Ê>ÃÊ>ÊVœ“«>ÀˆÃœ˜ÆÊvœÀÊiÝ>“«i]ʈ˜ÌiÀ«ÀiÌÊ35 = 5 x 7
as a statement that 35 is 5 times as many as 7 or 7 times as many as 5.
UÊ ÕÌˆ«ÞʜÀÊ`ˆÛˆ`iÊ̜Ê܏ÛiÊܜÀ`Ê«ÀœLi“Ãʈ˜ÛœÛˆ˜}ʓՏ̈«ˆV>̈œ˜ÊVœ“«>ÀˆÃœ˜ÃÊLÞÊÕȘ}Ê
`À>܈˜}ÃÊ>˜`ÊiµÕ>̈œ˜ÃÊ܈̅Ê>ÊÃޓLœÊvœÀÊ̅iÊ՘Ž˜œÜ˜Ê˜Õ“LiÀÊ̜ÊÀi«ÀiÃi˜ÌÊ
the problem.
★★ ★★★
★★
★★★ ★★
★★
★★ ★★★ ★★★
★★
★★
★★★ ★★
★
★
★ ★
35
÷
÷
★★
★★
★★★
7
= x
=
5
UÊ -œÛiʓՏ̈‡ÃÌi«ÊܜÀ`Ê«ÀœLi“ÃÊ«œÃi`Ê܈̅Ê܅œiʘՓLiÀÃÊ>˜`ʅ>ۈ˜}Ê܅œiʘՓLiÀÊ
answers using the four operations (+, -, x, ÷) including problems in which remainders
must be interpreted. (37 ÷ 4 = 9 with a remainder of 1) Use a letter to stand for the
՘Ž˜œÜ˜ÊµÕ>˜ÌˆÌÞ°Ê(37 ÷ 4 = a).
■ Gain familiarity with factors and multiples.
UÊ ˆ˜`Ê>Êv>V̜ÀÊ«>ˆÀÃÊvœÀÊ>Ê܅œiʘՓLiÀʈ˜Ê̅iÊÀ>˜}iʜvÊ£ÊqÊ£ää°Ê
Example: 3 and 4 are factors of 12, because 3 x 4 =12. Also, 2 x 6 = 12 so 2 and
6 are also factors of 12, and 1 x 12 = 12 so 1 and 12 are factors of 12 as well.
So ALL the factors of 12 are 1, 2, 3, 4, 6 and 12, as well as -1, -2, -3, -4, -6
and -12.
UÊ ,iVœ}˜ˆâiÊ̅>ÌÊ>Ê܅œiʘՓLiÀʈÃÊ>ʓՏ̈«iʜvʈÌÃÊv>V̜ÀÃÊ(for example, the factors
of 12 are 1 x 12, 2 x 6, 3 x 4).
UÊ iÌiÀ“ˆ˜iÊ܅i̅iÀÊ>Ê}ˆÛi˜Ê܅œiʘՓLiÀʈ˜Ê̅iÊÀ>˜}iÊ£ÊqÊ£ääʈÃÊ>ʓՏ̈«iʜvÊ>Ê}ˆÛi˜Ê
one-digit number. Example: Is 25 a multiple of 5? Yes! Is it a multiple of 3? No!
UÊ iÌiÀ“ˆ˜iÊ܅i̅iÀÊ>Ê}ˆÛi˜Ê܅œiʘՓLiÀʈ˜Ê̅iÊÀ>˜}iÊ£ÊqÊ£ääʈÃÊ«Àˆ“iʜÀÊVœ“«œÃˆÌi°
A prime number can be divided evenly (without having a remainder) only by 1, or itself.
A prime number’s only positive factors are 1 and itself.
Example: 5 can only be divided evenly by 1 or 5, so it is a prime number.
But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is
a composite number).
28
■Ê i˜iÀ>ˆâiÊ>˜`Ê>˜>ÞâiÊ«>ÌÌiÀ˜Ã°
UÊ i˜iÀ>ÌiÊÃiÛiÀ>Ê˜Õ“LiÀÊ«>ÌÌiÀ˜ÃÊ̅>ÌÊvœœÜÊ>Ê}ˆÛi˜ÊÀՏi°Ê`i˜ÌˆvÞÊ>««>Ài˜ÌÊvi>ÌÕÀiÃÊ
of the pattern that were not explicit in the rule itself. For example, given the rule
“add 3” and the starting number 1 (1, 4, 7, 10, 13, 16…) see that the resulting
sequence appears to alternate between odd and even numbers. Can students
tell why the numbers will continue to alternate in this way?
Numbers and Operations in Base Ten
■Ê i˜iÀ>ˆâiÊ«>ViÊÛ>ÕiÊ՘`iÀÃÌ>˜`ˆ˜}ÊvœÀʓՏ̈‡`ˆ}ˆÌÊ܅œiʘՓLiÀð
UÊ ,iVœ}˜ˆâiÊ̅>Ìʈ˜Ê>ʓՏ̈‡`ˆ}ˆÌÊ܅œiʘՓLiÀ]Ê>Ê`ˆ}ˆÌʈ˜Êœ˜iÊ«>ViÊÀi«ÀiÃi˜ÌÃÊÌi˜Ê̈“iÃÊ
what it represents in the place to its right. 700 = 70 x 10
UÊ ,i>`Ê>˜`ÊÜÀˆÌiʓՏ̈‡`ˆ}ˆÌʘՓLiÀÃÊÕȘ}ÊL>Ãi‡Ìi˜Ê˜Õ“iÀ>ÃÊ(73), number names,
(seventy-three) and expanded form (7 tens and 3 ones), and compare two multidigit numbers using >, <, and = (23 > 19).
UÊÊ 1ÃiÊ«>ViÊÛ>ÕiÊ՘`iÀÃÌ>˜`ˆ˜}Ê̜ÊÀœÕ˜`Ê܅œiʘՓLiÀÃÊ̜Ê>˜ÞÊ«>Vi°
100 Rounding Chart
0
10
20
30
40
50
60
70
80
90
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9 10
19 20
29 30
39 40
49 50
59 60
69 70
79 80
89 90
99 100
■ Use place value understanding and properties of operations to perform multi-digit
arithmetic.
UÊ Õi˜ÌÞÊ>``Ê>˜`ÊÃÕLÌÀ>VÌʓՏ̈‡`ˆ}ˆÌÊ܅œiʘՓLiÀðÊ(23 + 32 = 55; 55 – 23 = 32)
UÊ ÕÌˆ«ÞÊ>Ê܅œiʘՓLiÀʜvÊÕ«Ê̜ÊvœÕÀÊ`ˆ}ˆÌÃÊLÞÊ>ʜ˜i‡`ˆ}ˆÌÊ܅œiʘՓLiÀ]Ê>˜`ʓՏ̈«ÞÊ
two two-digit numbers.
345 x 6 = (6 x 5 = 30) + (6 x 40 = 240) + (6 x 300 = 1800) = 2070
29
UÊ ˆ˜`Ê܅œiʘՓLiÀʵ՜̈i˜ÌÃÊ>˜`ÊÀi“>ˆ˜`iÀÃÊ܈̅ÊÕ«Ê̜ÊvœÕÀ‡`ˆ}ˆÌÊ`ˆÛˆ`i˜`ÃÊ>˜`Ê
one-digit divisors using strategies based on place value, properties of operations,
and the relationship between multiplication and division.
Quotient = the answer after you divide one number by another
dividend ÷ divisor = quotient or 375 ÷ 25 = 15
Remainder = the amount left over after division.
4
19 ÷ 5 = 3 R 4 = 3 __
5
Example: 19 cannot be divided evenly by 5. The
closest you can get without going over is 3 x 5 = 15,
which is 4 less than 19. So the answer of 19 ÷ 5 is 3
with a remainder of 4.
remainder
Measurement and Data
■ Solve problems involving measurement and conversion of measurements from a larger
unit to a smaller unit.
UÊ ˜œÜÊÀi>̈ÛiÊÈâiÃʜvÊ՘ˆÌÃÊ܈̅ˆ˜Êœ˜iÊÃÞÃÌi“ÊœvÊ՘ˆÌÃ]ʈ˜VÕ`ˆ˜}ʎˆœ“iÌiÀÃ]ʓiÌiÀÃ]Ê
kilograms, grams, pounds, ounces, liters, minutes, hours, and seconds. Be able to
express a large unit in terms of a smaller unit.
A 2 ft snake is 24 in, a 3 ft snake is 36 in, and a 4 ft snake is 48 in.
An hour has 60 seconds, and a day has 24 hours.
UÊ 1ÃiÊ̅iÊvœÕÀʜ«iÀ>̈œ˜ÃÊ­+, -, x, ÷) to solve word problems involving distances, intervals
œvÊ̈“i]ʏˆµÕˆ`ÊۜÕ“iÃ]ʓ>ÃÃiÃʜvʜLiVÌÃ]Ê>˜`ʓœ˜iÞ]ʈ˜VÕ`ˆ˜}Ê«ÀœLi“Ãʈ˜ÛœÛˆ˜}Ê
simple fractions or decimals.
UÊ ««ÞÊ̅iÊ>Ài>Ê>˜`Ê«iÀˆ“iÌiÀÊvœÀ“Տ>ÃÊvœÀÊÀiVÌ>˜}iÃʈ˜ÊÀi>ÊܜÀ`Ê>˜`ʓ>̅i“>̈V>Ê
«ÀœLi“ðʜÀÊiÝ>“«i]Êw˜`Ê̅iÊ܈`̅ʜvÊ>ÊÀiVÌ>˜}Տ>ÀÊÀœœ“Ê}ˆÛi˜Ê̅iÊ>Ài>Ê­£ÓäÊõÊvÌ®ÊÊ
>˜`ʏi˜}̅ʭ£ÓÊv̮ʜvÊ̅iÊyœœÀˆ˜}]ÊLÞÊۈi܈˜}Ê̅iÊ>Ài>ÊvœÀ“Տ>Ê>ÃÊ>ʓՏ̈«ˆV>̈œ˜ÊiµÕ>̈œ˜Ê
with an unknown factor. (Area = l x w; area ÷ l = w, so 120 ÷ 12 = 10)
■ Represent and interpret data.
Line Plot
UÊ >ŽiÊ>ʏˆ˜iÊ«œÌÊ̜Ê`ˆÃ«>ÞÊ>Ê`>Ì>ÊÃiÌÊ
of measurements in fractions of a unit
1 , __
1 , __
1 ).
( __
2 4 8
30
4
x
x
3
x
x
x
2
x
x
x
x
1
x
x
x
x
1
__
4 inch
1
__
2 inch
3
__
4 inch
1 inch
■ Geometric Measurement
Ê ,iVœ}˜ˆâiÊ>˜}iÃÊ>ÃÊ}iœ“iÌÀˆVÊÅ>«iÃÊ̅>ÌÊ>ÀiÊ
formed whenever two rays share a common
endpoint, and understand concepts of
angle measurement. Be able to use a
protractor to measure angles.
Geometry and Spatial Sense
■ Draw and identify lines and angles, and classify shapes by properties of their lines and
angles.
UÊ À>ÜÊ«œˆ˜ÌÃ]ʏˆ˜iÃ]ʏˆ˜iÊÃi}“i˜ÌÃ]ÊÀ>ÞÃ]Ê>˜}iÃÊ­Àˆ}…ÌÊ>˜}iʈÃÊ>Ê™ä ¨ÊÊ>˜}i]Ê>VÕÌiÊ>˜}iÊ
ˆÃʏiÃÃÊ̅>˜Ê™ä¨Ê]Ê>˜`Ê>˜ÊœLÌÕÃiÊ>˜}iʈÃʜ˜iÊ̅>ÌʈÃʓœÀiÊ̅>˜Ê™ä¨Ê®Ê>˜`Ê«iÀ«i˜`ˆVՏ>ÀÊ
and parallel lines.
O
X
Y
parallel lines
perpendicular
C
F
obtuse angle
right angle
acute angle
E
D
A
B
Angle measurement is 90º.
31
Fourth Grade Student Self-Check List
I can
do it!
Students: You have been working on learning these skills this
year. The green shaded boxes are the areas teachers gave extra
focus to this year. Are you able to do these things? Check the
box next to the skill if you can do it.
Use addition, subtraction, multiplication, and division with whole numbers
to solve word problems.
Learn about factors and multiples, i.e.,
UÊ*œÃˆÌˆÛiÊv>V̜ÀÃʜvÊÓ{Ê>Ài\Ê£]ÊÓ]ÊÎ]Ê{]ÊÈ]Ên]Ê£Ó
UÊ-œ“iʓՏ̈«iÃʜvÊ{Ê>Ài\Ê{]Ên]Ê£Ó]Ê£È]ÊÓäo
Make and describe patterns with objects and numbers.
1˜`iÀÃÌ>˜`Ê>˜`ÊÕÃiÊ«>ViÊÛ>ÕiÊ̜Ê}i˜iÀ>ˆâiÊ̜ʣ]äää]äää°Ê
UÊÝ«>˜`i`ÊvœÀ“\ÊÈÇnÎÊrÊÈäääʳÊÇääʳÊnäʳÊÎ
Compute with multi-digit numbers.
Solve problems involving using multiplication of multi-digit by two-digit numbers.
Divide multi-digit numbers by one-digit divisor.
Round multi-digit numbers to any place.
Ո`Ê՘`iÀÃÌ>˜`ˆ˜}ʜvÊiµÕˆÛ>i˜ÌÊvÀ>V̈œ˜ÃÊ>˜`ʜÀ`iÀˆ˜}ÊvÀ>V̈œ˜Ã°Ê
Compare two fractions with different numerators and different denominators by
making common denominators.
Add and subtract fractions and mixed numbers with like denominators.
Understand the decimal notation for fractions.
Compare decimals.
Solve problems using measurement conversions.
Apply area and perimeter formulas for rectangles.
"À}>˜ˆâiÊ>˜`ÊiÝ«>ˆ˜Ê`>Ì>ÊÕȘ}Ê>ʏˆ˜iÊ«œÌ°Ê
Understand and measure angles.
Draw and identify lines and angles.
Describe and sort shapes by their lines and angles.
32