Hueneme Elementary School District
Staff Development Day #3
March 10, 2014
CCSS Mathematic Unit of Study
Grade 3
Introductions
Year at a Glance…..
• Unit 1 :
Number Sense
• Unit 4:
Geometry: Shapes, Area,
and Perimeter
• Unit 2:
Patterns in Multiplication
and Division
• Unit 5:
Fractions
• Unit 3:
Relationships Between
Multiplication and Division
• Unit 6:
Measurement and Data
Grade 3: Math Unit of Study #3
Title:
Relationships between Multiplication
and Division
Length:
@ 30 days
Key Points
*Explore the relationships between
multiplication and division.
*Explore Fact Families and develop
a knowledge of the Basic Facts
(from 1 – 10)
*Apply properties of operations as
strategies to multiply and divide.
(Commutative, Associative, and
Distributive property.)
*Know that any division problem
can be solved using multiplication
facts.
*Solve real-world problems
Essential Standards
Guaranteed:
Taught and Assessed (Re-taught if necessary)
• 3.OA.1. Interpret products of whole numbers; 5 X 7 is 5 groups of 7 objects.
• 3.OA.2. Interpret whole-number quotients of whole numbers; 56/8 is 56 objects
partitioned equally into 8 shares.
• 3.OA.3. Use multiplication and division within 100 to solve word problems use
drawings, equations, and symbols for the unknown number.
• 3.OA.4. Determine the unknown whole number in a multiplication or division equation; 8
X ? = 48,
5 = 􀃍 / 3, 6 X 6 = ?.
• 3.OA.5. Apply properties of operations as strategies to multiply and divide.
Commutative, Associative, and Distributive property.
• 3.OA.6. Understand division as an unknown-factor problem.
• 3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship
between multiplication and division.
By the end of Grade 3, know from memory all products of two one-digit numbers.
Supporting Standards
(Taught in conjunction with the Essential Standards)
 3.OA.8. Solve two-step word problems, using equations with a letter standing for the unknown
quantity. Assess the reasonableness of answers using rounding, mental computation and
estimation strategies .
 3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table),
and explain them using properties of operations.
 3.MD.1. Tell and write time to the nearest minute and measure time intervals in minutes.
 3.MD.2. Measure and estimate liquid volumes and masses of objects using standard units of
grams (g), kilograms (kg), and liters (l).
 3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several
categories.
 3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and
fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in
appropriate units—whole numbers, halves, or quarters.
Enduring Understandings and Essential Questions
Enduring Understandings
Essential Questions
A statement about the concept behind the
content that we want students to transfer to
different learning experiences and subject
areas.
Questions based on the Enduring Understanding
that teachers can use during instruction and
assessment.
Basic facts and algorithms for operations
with rational numbers use notions of
equivalence to transform calculations into
simpler ones.
The same number sentence (e.g. 12-4 = 8)
can be associated with different concrete or
real-world situations, AND different number
sentences can be associated with the same
concrete or real-world situation.
* How are multiplication and division related?
* What patterns of multiplication can we discover
by studying a times table chart?
* What strategies are there to help learn and
memorize multiplication facts?
* What strategies can help you solve real world
multiplication and division problems?
* How can you use multiplication facts to solve
unknown factor problems?
Academic Vocabulary
(Explicitly taught throughout the course of the unit)
Tier 2
multiply
divide
interpret
equal
calculate
record
explain
predict
estimate
solve
reason
Tier 3
whole number
product
quotient
divisor
dividend
factor
commutative property
associative property
distributive property
array
number model
Chapter 1 of 3
Days: @ 10
(Chapter = series of lessons/tasks)
MULTIPLICATION
Focus Standards
3.OA.1. Interpret products of whole numbers,
e.g., interpret 5 X 7 as the total number of
objects in 5 groups of 7 objects each.
3.OA.3. Use multiplication and division within
100 to solve word problems in situations
involving equal groups, arrays, and
measurement quantities, e.g., by using
drawings and equations with a symbol for the
unknown number to represent the problem
3.OA.5. Apply properties of operations as
strategies to multiply and divide.
(Commutative, associative, & distributive
properties.)
3.OA.7. Fluently multiply and divide within
100, by the end of Grade 3, know from memory
all products of two one-digit numbers
Enduring Understandings
*Multiplication can be demonstrated through a
rectangular array
*Multiplication is repeated addition and follows
a pattern
Essential Questions
*
* What patterns of multiplication can we
discover by studying a times table chart?
* What strategies are there to help learn
and memorize multiplication facts?
Learning Objectives
*Interpret and describe a given
multiplication problem as the total number
of objects in a group by the number of
groups. (OA.1)
*Apply commutative property of operations
as a strategy to multiply. (OA.5)
*Use multiplication to solve real world
situations using equal groups, arrays, and
measurement quantities. (OA.3)
Suggested Resources for Chapter 1
MULTIPLICATION
Everyday Mathematics
Online Lessons
* EDM Skills Links (BlueBook) pages 29, 38, 39, *http://www.apples4theteacher.com/math/multiplica
41, 42, 48, 53, 58, 60, 68, 75, 80, 91, 94, 101
tion/kids-books/
* EDM Lessons: 4.1, 4.2, 4.5, 4.6, 4.7, 7.1, 7.2, 7.3,
7.5, 7.6, 7.8, 9.2, 9.3, 9.4, 9.5, 9.9, 9.11, 9.12
*http://www.apples4theteacher.com/math/multiplica
* EDM Games and Projects: Baseball
tion/flashcards/
Multiplication, Multiplication Bingo, Top-It:
*
Multiplication, Beat the Computer: Multiplication Videos/Interactives/Games
*School House Rock - Multiplication
Math Routines
* http://nlvm.usu.edu/en/nav/vlibrary.html
* Multiplication Timed Tests (ex: Rocket Math)
* I have, Who has?
* EDM math message and slate routines
*Quiz- Quiz- Trade
*http://m.youtube.com/watch?v=xrFEJa2R24s
(multiply by 9, cowboy song)
Literature (Fiction/Informational Text)
* Bats on Parade by Appely (arrays, multiplication) *
Other - iPad Apps
* Artic Fives Arrive by Pinczes (skip counting)
Math Bingo, Mathboard, Bubbles +x
* How Many Ants? by Brimner (skip counting)
*https://itunes.apple.com/us/app/math-bingo-for* The Multiplying Menace: The Revenge of
kids/id507126705?mt=8
Rumpelstiltskin by Calvert (multiplication
adventure)
*https://itunes.apple.com/us/app/mathboardaddition/id381884632?mt=8
*https://itunes.apple.com/us/app/additionHomework
multiplication-number/id467091416?mt=8
*Daily Practice of basic facts
Chapter 2 of 3 Days: @10
(Chapter = series of lessons/tasks)
DIVISION
Focus Standards
3.OA.2. Interpret whole-number quotients
of whole numbers
3.OA.5. Apply properties of operations as
strategies to multiply and divide
3.OA.6. Understand division as an
unknown-factor problem.
Enduring Understandings
*Division is the inverse of multiplication
*Division is solving an un-known factor
*Basic facts and algorithms for operations
with rational numbers use notions of
equivalence to transform calculations into
simpler ones.
Essential Questions
• How are multiplication and division related?
• How can you use multiplication facts to solve unknown
factor problems?
• How do the properties help us solve multiplication and
division problems?
• How can you use your knowledge of multiplication and
division to solve an unknown factor?
• How can you apply knowledge of division to real life
situations?
• How can you determine what information is essential to
solving the problem?
Learning Objectives
• Interpret whole-number quotients with no remainders.
(3.OA.2)
• Apply properties of operations as strategies to multiply
and divide. (Commutative, Associative, and Distributive
property.)(3.OA.5)
• Understand division as an unknown-factor problem.
(3.OA.6)
• Use division within 100 to solve word problems in
situations involving equal groups, arrays, and
measurement quantities. (3.OA.3)
Suggested Resources for Chapter 2
DIVISION
Everyday Mathematics
* EDM Skills Links (BlueBook) pages 39, 53,
58, 68, 73, 91, 101.
* EDM Lessons: 4.3, 4.4, 4.6, 7.6, 9.7, 9.8
* EDM Games and Projects: Baseball
Multiplication, Multiplication Bingo, Top-It:
Multiplication, Beat the Computer:
Multiplication
Math Routines
* Multiplication Timed Tests (ex: Rocket
Math)
* EDM math message and slate routines
Literature (Fiction/Informational Text)
*The Doorbell Rang by Hutchins (dividing)
*Divide and Ride by Murphy (dividing)
*One Hundred Angry Ants by Pinczes
(dividing, arrays)
Homework
*Daily Practice of basic facts
Online Lessons
*http://www.apples4theteacher.com/math/div
ision/. (Printable Flash Cards, Vocabulary,
Word Search, Worksheets, Book Review)
Videos/Interactives/Games
*School House Rock - Multiplication
* http://nlvm.usu.edu/en/nav/vlibrary.html
* I have, Who has?
*Quiz- Quiz- Trade
Other - iPad Apps:
Math Bingo, Mathboard, Bubbles +x
*https://itunes.apple.com/us/app/math-bingofor-kids/id507126705?mt=8
*https://itunes.apple.com/us/app/mathboardaddition/id381884632?mt=8
*https://itunes.apple.com/us/app/additionmultiplication-number/id467091416?mt=8
Chapter 3 of 3 Days: @ 10
(Chapter = series of lessons/tasks)
REAL-WORLD PROBLEMS (multi. & division)
Focus Standards
Essential Questions
3.OA.4. Determine the unknown whole
number in a multiplication or division
equation relating three whole numbers
.
3.OA.5. Apply properties of operations
as strategies to multiply and divide.
•
•
•
How can you use estimation to adjust your
answer for better accuracy and precision?
How can you use patterning, skip counting,
basic facts, missing factors, decomposing and
square numbers to understand multiplication
and division?
What strategies can help you solve real world
multiplication and division problems?
3.OA.7. Fluently multiply and divide
within 100, using strategies such as the
relationship between multiplication and Learning Objectives
division
• Students will fluently and accurately
Enduring Understandings
•
*Multiplication and division are inverses
of each other and can be used to solve
real world problems
* Patterns, skip counting, basic facts,
•
and other methods can be used to
solve multiplication and division
problems
multiply and divide from 1 to 100.
(3.OA.7)
Solve two-step word problems using
variables and assess the reasonableness
using estimation, rounding, and mental
computation. (3.OA.8)
Students will apply concepts of
multiplication and division in real life
applications.
Suggested Resources for Chapter 3
REAL-WORLD PROBLEMS
(multi. & division)
Everyday Mathematics
*EDM Skills Links (BlueBook) pages 32, 33, 75, 80,
95, 99, 100.
*EDM Lessons: 4.5, 4.8, 4.9, 7.3, 7.7, 7.9, 9.1, 9.7,
9.8, 9.9, 9.10
*EDM Games and Projects: Baseball Multiplication,
Multiplication Bingo, Top-It: Multiplication, Beat the
Computer: Multiplication, CA Project 8
Math Routines
* Multiplication Timed Tests (ex: Rocket Math)
* EDM math message and slate routines
Literature (Fiction/Informational Text)
* The Great Divide by Dodds (division)
* The Multiply Menace Divides by Calvert (division)
* A Remainder of One by Pinczes (division with
remainders)
Homework
*Daily Practice of basic facts
Online Lessons
*http://www.apples4theteacher.com/math
/division/
*(Printable Flash Cards, Worksheets, Book
Review)
Videos/Interactives/Games
*School House Rock - Multiplication
*http://nlvm.usu.edu/en/nav/vlibrary.html
* I have, Who has?
* Quiz- Quiz- Trade
Other - iPad Apps:
Math Bingo, Mathboard, Bubbles +x
*https://itunes.apple.com/us/app/math-bingofor-kids/id507126705?mt=8
*https://itunes.apple.com/us/app/mathboardaddition/id381884632?mt=8
*https://itunes.apple.com/us/app/addition
-multiplication-number/id467091416?mt=8
Assessment
Formative
Summative
• Teacher created/selected
• Teacher created/selected
• Measured Progress:
Testlets
• Measured Progress:
Benchmarks
• Smarter Balanced
Assessment (3-8)