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CCSS Numbers and Operations in
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Base 10 (NBT)
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Unpacking the Standards
Grade 4
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Standard: 4.NBT.1
Math Practices: MP2, MP6, MP7
Cluster (m/s/a)
Related CA Standard
NEW
Recognize that 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.
Essential Skills/Concepts
Read and write numbers up to 1,000,000
based on the meanings of the digits in
each place both in real-life situations
and abstractly
Understand that each place is 10 times
the value of the place to the immediate
right
Understand that by multiplying by 10,
each unit in a place becomes one unit in
the next left place
Understand the role of commas in large
numbers
Be able to read each sequence of three
digits made by commas as hundreds,
tens, and ones followed by the name of
the unit (e.g., thousand, million)
Academic Vocabulary:
Place value
standard form
Digit
word form
Unit
expanded form
Period
Value
Teaching Notes/Strategies
Build larger numbers by using graph paper with very small squares or
dot array paper and labeling examples in each place with digits and
words (e.g. ten thousand and 10,000) to mimic Base 10 blocks
Use Base 10 blocks, dot array paper, or have students make drawings
of numbers (mimicking base 10 blocks) to increase understanding of
x 10
Use 0-9 digit cards in a place- value pocket chart to read numbers and
solve problems.
Use clearboards with place value charts inserted and have students
write numbers and read them.
Play “What’s My Number?” riddles by giving clues about each digit in a
number such as:


The digit in the thousands place is 10 times the digit in the ones place
The digit in the hundred thousands place is 200 times the number in
the tens place.
Etc.
Play “I Have… Who Has...?” card game to practice reading large
numbers properly.
Ask “If” types of questions about numbers (i.e., “If this digit were to
move to the thousands place, it would have a value of__.” OR “If I
wanted to move this digit to the ten thousands place, I would need to
multiply by ___.”
Use cards that show the values of numbers (i.e., 7,000; 800; 90; 6 and
have students create numbers by overlapping them—this would be the
number 7,896)
Resources
Manipulatives:
Base 10 blocks
Graph paper
with very small
squares or dot
array paper
Place value
charts/mats
Clearboards
with place value
charts to write
on
Math Journal
with place value
chart
Anchor chart of
place value
chart showing
x10 for each
place value to
the left.
Value Number
cards
Standard: 4.NBT.2 Cluster (m/s/a)
Math Practices: MP2, MP4, MP6, MP7
Related CA Standard
4.NS.1.1, 4.NS.1.2
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.
Essential Skills/Concepts
Teaching Notes/Strategies
Read and write numbers up to 1,000,000
based on the meanings of the digits in
each place both in real-life situations
and abstractly
Play “I Have… Who Has...?” card game to practice
reading and writing large numbers properly.
Manipulatives:
Base 10 blocks
Use cards that show the values of numbers (i.e.,
7,000; 800; 90; 6 and have students create
numbers by overlapping them—this would be the
number 7,896)
Place value charts/mats
Use clearboards with place value charts inserted
and have students write numbers, read them, and
compare them.
Math Journal with place value
chart
Create numbers using drawings or base 10 blocks
to compare them.
Numeral, Word and Expanded
Understand the role of commas in large
numbers
Be able to read each sequence of three
digits made by commas as hundreds,
tens, and ones followed by the name of
the unit (e.g., thousand, million)
Be able to compare large numbers by
using the <, =, or > signs.
Academic Vocabulary:
Place value
standard form
Digit
word form
Unit
expanded form
Period
Value
Less than and < sign
Greater than and > sign
Equal and = sign
Align numbers in a place value chart to compare
them.
Resources
Clearboards with place value
charts to write on
Form
Place Value Triangle
Both available at
http://www.k5mathteachingresources.com
Math Practices: MP2, MP6
Standard: 4.NBT.3 Cluster (m/s/a)
Related CA Standard
4.NS.1.3
Use place value understanding to round multi-digit whole numbers to any place.
Essential Skills/Concepts
Know and understand the names
of the place values up to the
millions place
Know and understand the values
of each digit in a number up to
the millions place in real-life
situations and abstractly
Build on the skill of rounding
from previous grades to round
to the nearest 10s , 100s,
1,000s, 10,000s, 100,000s,
and/or 1,000,000s place of a
multi-digit number
Make reasonable estimates of
numerical values using the skill
of rounding.
Academic Vocabulary:
Rounding
Estimate
Place value
Digit
Teaching Notes/Strategies
Sample problem:
The population of Midtown, USA, was last recorded to be
76,398. The city council wants to round the population to the
nearest thousand for a business brochure. What number should
they round the population to?
Stack numbers vertically to see the relationships between
the rounded number before/after the number to be
rounded:
Resources
Manipulatives:
Base 10 blocks
Dot arrays
Number line counting by 10s
Number line counting by 100s
Number line counting by 1000s,
Etc.
77,000
76,398
76,000
Use a number line counting by 10s, 100s, 1,000s, etc. to
help determine which number is closest to the number
being rounded.
Use dot arrays to represent numbers and the “10” or
“100” before/after to determine the closest number.
Use a rounding “algorithm” or song (Example: put a box
around the place to round to, circle the numbers after it
to become zeros, draw an arrow to the number to the
right of the box—4 or less stays the same, 5 or more add
one more.)
Present “real-life” situations to give context to rounding
and have students practice giving reasonable estimates.
Have partner discussions/journal writes about why
estimates are reasonable or not.
Place value chart to stack
numbers vertically
Round to the nearest ten
Round to the nearest hundred
Both available at
http://www.k5mathteachingresources.com
Standard: 4.NBT.4 Cluster (m/s/a)
Math Practices: MP2, MP5, MP7, MP8
Related CA Standard
4.NS.3.1
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Essential Skills/Concepts
Fluency in basic addition/subtraction
facts (not essential, but desired)
Know the steps of the standard
algorithm to add and subtract multidigit numbers to 1,000,000
Teaching Notes/Strategies
Use Base 10 blocks to demonstrate one-forten trades between adjacent places in a
number they are adding or subtracting
Direct Instruction on the steps of the
algorithm.
Resources
Manipulatives:
Base 10 blocks
Graph paper
Board math
Understand and can explain or
demonstrate what the steps of the
standard algorithm mean mathematically
Have students explain to a partner or write in
a journal the steps of the algorithm and what
they mean mathematically
Touchmath
Use one-for-ten trades between
adjacent places in a number they are
adding or subtracting
Use different colors during the steps of the
algorithm for emphasis on each step
White boards or clearboards
Academic Vocabulary:
Trades, regrouping, or exchanging
Use graph paper to keep numbers aligned as
students rewrite problems from a book. This
can reduce errors and emphasize place value.
Use Touchmath counting and worksheets for
students who are having difficulty
remembering/understanding the steps or
make frequent errors (ask Kirsten Werk for
these resources).
White board or clearboard practice
Small group instruction/practice
Error analysis of problems
Colored pencils/pens
Place value charts to align
numbers
Adding and Subtracting Multi-Digit
Numbers
Addition and Subtraction Number
Stories
Both available at http://www.k5mathteachingresources.com
Standard 4.NBT.5 Cluster (m/s/a)
Math Practices: MP2, MP3, MP4, MP5, MP7
Related CA Standard
4.NS.3.2, 4.NS.3.3
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.
Essential Skills/Concepts
Extend learning from previous grades to
multiplying and dividing with numbers
greater than 100 using methods the
student understands and can explain.
Use visual representations such as area
and array models to draw and connect to
equations to support reasoning and
explanation of methods.
After extensive work and mastery of
understanding with the above, students
can come to learn the standard
algorithms as abbreviations or
summaries of their previous reasonings.
Academic Vocabulary:
Area
Array
Factoring
Teaching Notes/Strategies
Use various methods to teach multiplying with
numbers greater than 100. Some of these may
include:
 Area models with and without base 10
blocks
 Rectangular array models
 Use of base 10 blocks
 Use factoring
 Use repeated addition
 Use expanded notation
Use real-life scenarios to give meaning to
multiplication/division.
Estimate for reasonableness.
Have students write their explanations in a math
journal or chat with a partner to discuss their
method.
Resources
Manipulatives:
Base 10 blocks
Graph paper
Clearboards
Math journals
Multiplication Strategy: Doubling
and Halving
Multiplication Strategy: Partial
Products (1)
Multiplication Strategy: Partial
Products (2)
Multiplication Race (1 x 3 digit)
Multiplication Race (2 x 2 digit)
Multiplication Number Story
Breaking Apart a Factor
Multiplication Bump (x100)
Make the Largest Product
Make the Smallest Product
Expanded notation
All available at http://www.k-
Reasonable
5mathteachingresources.com
Estimate
Standard: 4.NBT.6 Cluster (m/s/a
Math Practices: MP2, MP3, MP4, MP5, MP7
Related CA Standard
4.NS.3.2, 4.NS.3.4
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.
Essential Skills/Concepts
Relate area models used to teach
multiplication to teach the related
division problem.
Begin teaching standard division
algorithm, but it will continue in 5th
grade and mastery by 6th grade.
Find whole number quotients with
remainders and know the appropriate
way to write the result (ex: 195÷9 = 21
with 6 leftover can be written as 195 =
21(9) + 6. Equations should be given
context for understanding and can be
related to 195÷9 = 21 6/9 which
students will write in later grades. Avoid
195÷9 = 21 R 6.
Teaching Notes/Strategies
Resources
Use various methods to teach dividing with
numbers greater than 100. Some of these may
include:
 Using properties of operations
 Using the relationship between
multiplication and division
 Using equations
 Using rectangular array models
 Using area models
 Use factoring
 Use repeated subtraction
 Use expanded notation
 “Divvy Out”
 Stacking Method for division
Manipulatives:
Base 10 blocks
Use real-life scenarios to give meaning to
division.
Division Strategy: Partition the
Estimate for reasonableness.
Estimate the Quotient
Have students write their explanations in a
math journal or chat with a partner to discuss
their method.
Ver.1
Graph paper
Clearboards
Math journals
At http://www.k5mathteachingresources.com
Division Strategy: Partial Quotients
(1)
Division Strategy: Partial Quotients
(2)
Dividend
Remainders
Who Has the Largest Quotient?
Who Has the Largest Quotient? Ver.
2
Academic Vocabulary:
Area
estimate
Various Math symbols for division
array
remainders
, /, ¼, ÷
expanded notation
reasonable
divisor
quotient