Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Lesson Plan: Working Toward Fluency When Multiplying by 2 (This lesson should be adapted, including instructional time, to meet the
needs of your students.)
Background Information
Content/Grade Level
Unit/Cluster:
Essential Questions/Enduring
Understandings Addressed in
the Lesson
Mathematics Grade 3
Domain: 3.OA Operations and Algebraic Thinking
Cluster: 3.OA.C Multiply and Divide within 100
Multiply and Divide within 100
Essential Questions:
 Why do I need mathematical operations?
 How do mathematical operations relate to each other?
 What do I know from the information shared in the problem? What do I need to find?
 How do I know which computational method (mental math, estimation, paper and pencil, and
calculator) to use?
 How do you solve problems using multiplication or division in real world situations?
 How can you decide that your calculation is reasonable?
 How do you begin to solve a problem when the product or quotient is unknown?
 How can one fact help you solve another?
 What do you know about addition and subtraction that can help you with multiplication and
division?
Enduring Understanding:
 Operations create relationships among numbers.
 Addition, subtraction, multiplication, and division operate under the same properties in algebra as
they do in arithmetic.
 The relationships among the operations and their properties promote computational fluency.
 Mathematical reasoning and number models can be used to manipulate practical applications and
to solve problems.
 Through the properties of numbers we understand the relationships of various mathematical
functions.
 Knowing the reasonableness of an answer comes from using good number sense and
estimation strategies.

July 10, 2013
Page 1 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Standards Addressed in This
Lesson
3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of
operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
NOTE: Finding single-digit products and related quotients is a required fluency for grade 3. Reaching
fluency will take much of the year for many students. These skills and the understandings that support
them are crucial; students will rely on them for years to come as they learn to multiply and divide with
multi-digit numbers and to add, subtract, multiply, and divide with fractions. After multiplication and
division situations have been established, reasoning about patterns in products (e.g., products involving
factors of 5 and 9) can help students remember particular products and quotients. Practice – and if
necessary, extra support – should continue all year for those who need it to attain fluency.
It is critical that the Standards for Mathematical Practice are incorporated in ALL lesson activities
throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be
evident in every lesson. The Standards for Mathematical Practice make an excellent framework on which
to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.
Lesson Topic
Use and apply strategies and properties to fluently multiply and divide within 100.
Relevance/Connections
This work begins in Grade 2 when students use rectangular arrays and addition to build the foundation for
this learning. Making connections to that study will help students use what they know to inform their
learning in this unit.
Student Outcomes
The student will:
 Know from memory all products of two one-digit numbers (2s).
 Use various strategies to determine products involving the factor 2.
 Relate repeated addition to multiplication.
 Use skip counting to develop an understanding of multiplication.
Prior Knowledge Needed to
Support This Learning
Students must have:
 An understanding of equal groups
 An understanding repeated addition and subtraction
 An understanding of skip counting patterns
 Constructed knowledge and made meaning of multiplication and division and are ready to apply
July 10, 2013
Page 2 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.



Method for determining student
readiness for the lesson

them to strategies.
Knowledge of rectangular arrays.
Previous exposure to the properties of multiplication
Students have shown an understanding of at least one strategy they can use to solve
multiplication and division problems within 100.
Refer to clarification section of this unit for other ways to determine whether or not students are
ready for fluency.
Learning Experience
Component
Warm Up
Details
Materials Needed:
 Resource Sheet 1: One-Minute Facts Assessment
(one copy per student)


Motivation
Distribute Resource Sheet 1: One Minute Facts
Assessment to each student.
Give them 1 minute to complete the fact test.
Counting Around the Classroom:




Have all students stand up behind their desks.
Explain that they will be counting by 2s until all
students have counted.
Have students predict what the final number will be
and record two or three predictions on the board.
Begin on one side of the room and have students
count by 2s all the way around while you record the
multiplication facts on the board.
July 10, 2013
Which Standards for Mathematical
Practice(s) does this address? How is the
Practice used to help students develop
proficiency?
SMP 6: Attend to Precision
 Students must accurately answer each
problem while moving quickly.
SMP 7: Look for and make use of structure
 Students should recognize the pattern of
skip counting by 2s.
SMP 2: Reason abstractly and quantitatively
 Students must be able to keep track and
follow the pattern and say their answer
appropriately.
SMP 3: Construct Viable Arguments and critique
the reasoning of others
 Teacher should encourage discourse
among students if disagreements occur
while counting.
Page 3 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Learning Experience

Activity 1
UDL Components
 Multiple Means of
Representation
 Multiple Means for
Action and
Expression
 Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
Students will use this list to self-check their
assessments.
Representation: Teacher may provide appropriate
manipulatives to students if necessary. Highlighting the
patterns of 2s and using visual cues. Using prior knowledge
of addition doubles.
Expression: Teacher is breaking the long-term goal of
fluency within 100 into reachable short-term objectives by
focusing on only 2s.
Engagement: Students are self-regulating by checking their
own understanding of the multiples of 2s.
SMP 6: Attend to Precision
 Students must accurately answer their
problem.
SMP 7: Look for and make use of structure
 Students should recognize the pattern of
skip counting by 2s.
SMP 2: Reason abstractly and quantitatively
 Students will notice which facts they
know and which ones they don’t know.
SMP 6: Attend to Precision
 Students are sorting facts based on the
accuracy of their fact test.
SMP 7: Look for and make use of structure
 Students should recognize the pattern of
skip counting by 2s.
Materials Needed:
 Resource Sheet 2: Facts Cards for Two (one set per
student)
I Know or I Don’t Know:
 Distribute a copy of Resource Sheet 2: Facts Cards
to each student.
 Have them cut out all cards and sort them into two
different piles, “Do know” or “Don’t Know” based on
their responses from the fact assessment.
 Please refer students to fact list on board for correct
answers.
July 10, 2013
Page 4 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Learning Experience
Activity 2
UDL Components
 Multiple Means of
Representation
 Multiple Means for
Action and
Expression
 Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
Representation: Students are highlighting patterns of 2s on
the 100s. Students are also using an organizer, 100s chart,
or prior knowledge of skip counting.
Expression: Teacher is breaking the long-term goal of
fluency within 100 into reachable short-term objectives by
focusing on only 2s. Teacher could use various materials for
students to work with (highlighters, pencil/pen, computer,
overlays).
Engagement: Students are self-regulating by checking their
own understanding of the multiples of 2s. Teacher could
have grouping structures set up to support all learners.
Materials Needed:
 Resource Sheet 3: Hundred Chart
 Highlighters, pencils, or crayons
SMP 2: Reason abstractly and quantitatively
 Students must be able to keep track and
follow the pattern and say their answer
appropriately.
SMP 5: Use tools strategically and appropriately
 Students will use a 100s chart to show
skip-counting pattern of 2.
SMP 6: Attend to Precision
 Students must accurately color the skip
counting patterns.
SMP 7: Look for and make use of structure
 Students will recognize the pattern made
when skip counting by 2.
Pattern on 100s chart:
 Distribute Resource Sheet 3: Hundred Chart to each
student.
 Have students highlight or color multiples of 2 by
starting at 2 and skip counting forward until they
reach 100.
 Discuss what patterns students see on their charts.
Activity 3
UDL Components
 Multiple Means of
Representation
 Multiple Means for
Action and
Representation: Teacher can supply a variety of dominoes
to help students notice the dot patterns. Color paper and
physical dominoes are two options. Students are drawing
and writing numeric expressions for the numbers of dots.
SMP 2: Reason abstractly and quantitatively
 Students must be able to keep track and
follow the pattern and say their answer
appropriately.
Expression: Students can use a variety of dominoes and
recording methods. Activity can be composed in multiple
media sources including text, drawing, and interactive
SMP 3: Construct Viable Arguments and critique
the reasoning of others
 Students work together to help and
July 10, 2013
Page 5 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Learning Experience
Expression
 Multiple Means for
Engagement
Key Questions
Formative Assessment
Summary
whiteboard lessons.

Engagement: Students will be working with partners which
will allow for peer support and tutoring. Working with a
partner will emphasize effort and improvement.
Materials Needed:
 Resource Sheets 4A-E: Dominoes (one set cut and
bagged for each pair of students)
 Resource Sheet 5: Domino Recording Sheet
Seeing Doubles:
 Distribute a set of Domino Cards to pairs of students.
 Have students pull all of the doubles out and flip them
upside down.
 One student at a time will flip over 1 card and say the
product. The other student will check the card to
make sure response is correct.
 Both students will record a picture of the domino, an
addition equation, and a multiplication equation on
Resource Sheet 4: Domino Recording Sheet.
 Repeat until all cards have been chosen.
Closure
Have pairs of students quiz each other on their “Don’t Know”
stacks and or all of their cards, for fluency.
support each other.
Student pairs will have discussions about
the facts during this activity.
SMP 5: Use tools strategically and appropriately
 Students will use the dominoes to help
build understanding of 2s facts.
SMP 6: Attend to Precision
 Students must accurately answer and
record their problems.
SMP 7: Look for and make use of structure
 Students will recognize the patterns of
repeated addition or skip counting 2s.
SMP 3: Construct Viable Arguments and critique
the reasoning of others
 Students work together to help and
support each other.
 Student pairs will have discussions about
the facts during this activity.
SMP 6: Attend to Precision
 Students must accurately answer their
July 10, 2013
Page 6 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Learning Experience
fact cards.
Supporting Information
Interventions/Enrichments
 Special
Education/Struggling
Learners
 ELL
 Gifted and Talented
Interventions:
 Revisit and Reteach Standards 3.OA.A.1 & 3.OA.A.3 & 3.OA.B.5 to provide more time to
develop multiplication/division strategies.
 Teacher can pull those students to work with individually or in small pairs who need more
guidance during activities.
Enrichment:
 Move to the Lesson Seeds to provide fluency work with the multiples of 3-9.
Materials









Resource Sheet 1: One Minute Facts Assessment
Resource Sheet 2: Facts Cards for Two
Resource Sheet 3: Hundred Chart
Resource Sheets 4A-E: Dominoes
Dominoes (optional and in place of Resource Sheet 4)
Resource Sheet 5: Domino Recording Sheet
Chart Paper
Highlighters, markers, pencils, or crayons
Baggies
Technology







http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html
http://mathcats.com/microworlds/multiplyit.html
http://investigations.terc.edu/library/components/qa-1ed/array_card.cfm
http://superteachersworksheets.com/multiplication.html
http://investigations.terc.edu/library/components/qa-1ed/array_card.cfm
http://investigations.terc.edu/library/components/Array_Card.pdf
http://investigations.terc.edu/library/curric-gl/sample_g4_u1_sab21-22.pdf
July 10, 2013
Page 7 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply and divide within 100.
Resources
(must be available to all
stakeholders)
See Unit Plan for complete resource list.
July 10, 2013
Page 8 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 1
One Minute Facts Assessment
Name:________________________________
Score: ( _____/ 20)
Time: 1 minute
2x1=
4x2=
2x0=
9x2=
7x2=
3x2=
2x7=
2x4=
2x8=
2x5=
1x2=
6x2=
2x2=
8x2=
5x2=
2x9=
0x2=
2x3=
2x6=
2x2=
July 10, 2013
Page 9 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Facts Cards for Two
Resource Sheet 2
2x0
0x2
2x5
5x2
2x1
1x2
2x6
6x2
2x2
2x7
7x2
2x3
3x2
2x8
8x2
2x4
4x2
2x9
9x2
July 10, 2013
Page 10 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Hundred Chart
Resource Sheet 3
1
2
3
4
5
Name _____________________________
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53
54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
July 10, 2013
Page 11 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 4A
Dominoes
July 10, 2013
Page 12 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 4B
Dominoes
July 10, 2013
Page 13 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 4C
Dominoes
July 10, 2013
Page 14 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 4D
Dominoes
July 10, 2013
Page 15 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 4E
Dominoes
July 10, 2013
Page 16 of 17
Grade 3: Unit 3.OA.C.7, Operations and Algebraic Thinking--Multiply
and divide within 100.
Resource Sheet 5
Domino Recording Sheet
Name:___________________________________
Directions: Record the double addition fact and the multiplication fact for each domino.
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ x _____ = _____
_____ x _____ = _____
_____ x _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ x _____ = _____
_____ x _____ = _____
_____ x _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
_____ x _____ = _____
_____ x _____ = _____
_____ x _____ = _____
July 10, 2013
Page 17 of 17