MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Unit Description
Big Idea(s)
What enduring
understandings are
essential for application
to new situations within or
beyond this content?
Essential Question(s)
What questions will
provoke and sustain
student engagement
while focusing learning?
Standards
Curriculum and Instruction
Unit 2
Foundations of Multiplication and Division
Suggested Length: 3 weeks
Enduring Understanding
Develop an Understanding And Fluency in Multiplication and Division
Enduring Skills Rubric measures competency of the following skills:
 Consistently demonstrates understanding of multiplicative comparison.
 Consistently identifies factors and multiples of a given whole number 1-100.
 Consistently identifies a whole number 1-100 as prime or composite.
 Consistently solves multi-step word problems that include unknowns.
 How is addition related to multiplication?
 How is subtraction related to division?
 What is the difference between a product and a quotient?
 How do we know if a number is prime or composite?
 What patterns do I notice when I am multiplying whole numbers that can
help me multiply more effectively?
 What is the meaning of a remainder in a division problem?
 How can we use clues and reasoning to find an unknown number?
 How can we organize our work when solving a multistep word problem?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students make
sense of problems involving multiplication and division.
2. Reason abstractly and quantitatively. Students demonstrate abstract
reasoning about numbers, identifying which are prime and composite and
explaining their identification.
3. Construct viable arguments and critique the reasoning of others. Students
construct and critique arguments regarding number strategies including
multiplication and division strategies.
4. Model with mathematics. Students use area models and rectangular arrays
to model understanding of multiplication and division concepts.
5. Use appropriate tools strategically. Students select and use tools such as
multiplication charts, rectangular arrays, using materials and area models
to identify types of numbers, factors and multiples and solve multiplication
and division problems.
6. Attend to precision. Students attend to the language of real-world
situations to determine if multiplication and division answers are
reasonable.
7. Look for and make use of structure. Students relate the structure of an area
model or rectangular array to determine the answers to multiplication and
division problems.
8. Look for and express regularity in repeated reasoning. Students relate the
structure of a multiplication chart to identify prime and composite
numbers, as well as, factors and multiples of numbers.
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Supporting
Standard(s)
Which related standards
will be incorporated to
support and enhance
the enduring standards?
Curriculum and Instruction
Standards for Mathematical Content
 4.OA.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.
 4.OA.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.
 4.OA.3 Solve multistep word problems posed with whole numbers 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.
 4.OA.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.
 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. 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. Represent measurement quantities using diagrams such as
number line diagrams that feature a measurement scale.
 4.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.
 4.OA.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 unknown factor.
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Instructional
Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
I am learning to….
4.OA.1
1. interpret a multiplication equation as a comparison
(e.g. 18=3 times as many as 6)
2. represent verbal statements of multiplicative comparisons as
multiplication equations
4.OA.2
1. explain the relationship between multiplication and repeated
addition
2. solve multiplication and division word problems using visual models
3. apply the use of a variable within a multiplication word problem
4. explain the relationship between division and repeated subtraction
5. apply the use of a variable within a division word problem
4.OA.3
1. identify multistep word problems
2. determine the appropriate operation(s) to solve multistep word
problems
3. solve division story problems that include remainders
4. determine how a remainder affects the answer to a word problem
5. assess the reasonableness of an answer in solving a multistep word
problem using mental math and estimation strategies (including
rounding)
4.OA.4
1. identify the multiples of a whole number
2. identify factors in a multiplication sentence
3. identify all factor pairs for a given whole number within the range
of 1-100
4. analyze the factor pairs of a given whole number to determine if
the number is prime or composite
Essential Vocabulary
factor pairs
relationship
additive comparison
model
remainder
area model
multiple
repeated addition
array
multiplicative comparison repeated subtraction
columns
multi-step
rounding
composite
prime
rows
divisibility
product
strategy
equation
reasonableness
“times as much”
estimation
variable
factor
Supporting Vocabulary
area
cm (centimeter)
conversion
Curriculum and Instruction
km (kilometer)
l (liter)
lb (pound)
m (meter)
2015-2016
ml (milliliter)
number line diagram
oz (ounce)
pattern
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Resources/Activities
What resources could we
use to best teach this
unit?
g (gram)
min (minute)
hr (hour)
kg (kilogram)
Stepping Stones (www.origoeducation.com)
4.OA.1
o Module 6: Lessons 1-6
4.OA.2
o Module 6: Lessons 2-6
4.OA.3 (also support standard in Units 1, 5, 6, 7, 8)
o Module 2: Lesson 9
o Module 3: Lesson 8
o Module 4: Lessons 7,8
o Module 7: Lesson 8
o Module 8: Lesson 12
o Module 9: Lesson 11
o Module 10: Lesson 8
o Module 11: Lesson 9,12
o Module 12: Lesson 11,12
o Module 8: Lesson 6
4.OA.4
o Module 3: Lessons 1-5
o Module 5: Lessons 4,5
perimeter
sec (second)
*4.OA.5 – supporting standard --- also a support for Units 3 &4
o Module 1, Lessons 10-12
*4.MD.1– supporting standard --- also a support for Units 3 &4
o Module 2, Lessons 11, 12
o Module 8, Lessons 7-12
o Module 9, Lessons 10-12
o Module 11, Lessons 8-12
o Module 12, Lessons 8-12
Origo Fundamentals Online Interactive Activities
www.origoeducation.com Log in to SLATE, then choose “channels” on the
left side of dashboard. Choose “Fundamentals” then search titles for the
following activities:
o “Multiplication Mania”
o “Perfect Pairs”
o “Factor Find”
o “Nice and Easy”
o “Nice and Easy Too”
o “Friendly Factors”
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Engage NY (https://www.engageny.org/resource/grade-4-mathematics)
o Module 3: Topics A, D, E, F
o Supporting 4.MD.1 standard:
o Module 2: Topic A
o Module 7: Topics A, B, C
o Module 6: Topics A, B, C, D
Howard County website
o https://grade4commoncoremath.wikispaces.hcpss.org/4.OA.1
o https://grade4commoncoremath.wikispaces.hcpss.org/4.OA.2
o https://grade4commoncoremath.wikispaces.hcpss.org/4.OA.3
o https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.OA
.4
K-5 Math Teaching Resources
4.OA.1
o http://www.k-5mathteachingresources.com/supportfiles/multiplication-equations-and-comparison-statements.pdf
4.OA.2
o http://www.k-5mathteachingresources.com/supportfiles/comparison-problems.pdf
4.OA.3
o http://www.k-5mathteachingresources.com/support-files/interpretthe-remainder.pdf
o http://www.k-5mathteachingresources.com/supportfiles/4oa3multistepwordproblems.pdf
o http://www.k-5mathteachingresources.com/support-files/aremainder-of-one.pdf
4.OA.4
o http://www.k-5mathteachingresources.com/support-files/findingmultiples.pdf
o http://www.k-5mathteachingresources.com/support-files/prime-orcomposite.pdf
o http://www.k-5mathteachingresources.com/support-files/primenumber-hunt.pdf
o http://www.k-5mathteachingresources.com/support-files/commonmultiples.pdf
o http://www.k-5mathteachingresources.com/support-files/leastcommon-multiple.pdf
o http://www.k-5mathteachingresources.com/support-files/find-thefactor.pdf
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Illustrative Mathematics
4.OA.1
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/tasks/356
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/tasks/357
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/1/tasks/1809
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/1/tasks/1808
4.OA.2
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/2/tasks/263
4.OA.3
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/3/tasks/1289
o https://www.illustrativemathematics.org/contentstandards/4/OA/A/3/tasks/876
4.OA.4
o https://www.illustrativemathematics.org/contentstandards/4/OA/B/tasks/959
o https://www.illustrativemathematics.org/contentstandards/4/OA/B/tasks/1484
o https://www.illustrativemathematics.org/contentstandards/4/OA/B/tasks/1493
o https://www.illustrativemathematics.org/contentstandards/4/OA/B/4/tasks/938
Illuminations
o http://illuminations.nctm.org/Search.aspx?view=search&cc=1973_1983
Remember there are other sources in your school that may not be listed on
this common resources list due to variation in each individual school.
Examples of other great resources your school may have access to
include: Everyday Math Games, Investigations, Everyday Partner Games,
AVMR file folders, Ongoing Assessment Project, etc. The Kentucky
Numeracy Project is also a great resource that can be searched by AVMR
strand, CCSS, and grade level. Find this resource at
http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky teachers
can use it for free. Just put in your school email address and the username
“bluegrass”, and password is “math”.
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Curriculum and Instruction
2015-2016
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Curriculum and Instruction
2015-2016
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