Unit and Lesson Plan for Third Grade, Introduction to
Multiplication
Unit & Lesson plan developed by: Adelaida Kim, Cathy Davila,
Sarah Chang, Vivian Huang, Yvonne Kang
Title of the Unit:
Textbook: Houghton Mifflin Mathematics, 3rd Grade, Vol. 1,
Teacher Edition (published 2002)Brief description of the
UnitStudents will be introduced to multiplication using repetitive
addition and arrays. Using various methods of strategy, students
will learn how multiply with 2's, 5's and 10's.Goals of the Unit:
For students to make connections between repeated addition and
multiplication using equal groups. For students to model and use
multiplication to solve word problems in situations involving
arrays. For students to be familiar and use key math vocabulary to
communicate: product, factors, array, times, multiplication,
commutative property of multiplication For students to explain
their method of choice to solve the problem. For students to
understand the different methods learned for multiplication of
2,5,10.
Relationship of the Unit to the Standards:
[CCSS.MATH.CONTENT.2.NBT.A.2] Count within 1000; skip-count by
5s, 10s, and 100s. [CCSS.MATH.CONTENT.2.OA.C.3] Determine whether a
group of objects (up to 20) has an odd or even number of members,
e.g., by pairing objects or counting them by 2s; write an equation
to express an even number as a sum of two equal addends.
[CCSS.MATH.CONTENT.2.OA.C.4] Use addition to find the total number
of objects arranged in rectangular arrays with up to 5 rows and up
to 5 columns; write an equation to express the total as a sum of
equal addends.
This unit
[CCSS.MATH.CONTENT.3.OA.A.1] Interpret products of whole
numbers, e.g., interpret 5 7 as the total number of objects in 5
groups of 7 objects each. For example, describe a context in which
a total number of objects can be expressed as 5 7.
[CCSS.MATH.CONTENT.3.OA.A.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.
[CCSS.MATH.CONTENT.3.OA.B.5] Apply properties of operations as
strategies to multiply and divide. Examples: If 6 4 = 24 is known,
then 4 6 = 24 is also known. (Commutative property of
multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or
by 5 2 = 10, then 3 10 = 30. (Associative property of
multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8
7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive
property.) [CCSS.MATH.CONTENT.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 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.Background and Rationalea. Students will need to learn the
different methods of solving a multiplication problem, so they will
be prepared to learn to solve problems with bigger numbers.b.
Students will need to memorize the multiplication table later on,
but if they forget they can use what they will learn in this unit
to help them solve a problem. In a classroom I have done field
experience, a student was struggling to remember what 5x7 was but
the teacher reminded them the different methods they had learned to
solve multiplication problems.c. Students will build their
knowledge on multiplication by learning that multiplication is
similar to repeated addition and that multiplication is the basic
foundation of division. Students will see how and why 5x7 and 7x5
are different of question even though they have the same solution.
Consideration for Designing the Unit (Findings from your research)
Curriculum that our group used was a resource from a textbook in
the education book collection in the DePaul Lincoln Park library.
The section used in the book was a chapter on teaching introduction
to multiplication.
Article: Teaching for Mastery of Multiplication
Any memory of multiplication for us was memorization. But
according to the National Council of Teachers of Mathematics (NCTM)
memorization is not fluency. The book Principles and Standards for
School Mathematics states, Developing fluency requires a balance
and connection between conceptual understanding and computational
proficiency. Fluency in multiplication is defined as possessing a
deeper understanding and being able to apply what has been learned.
While learning and teaching multiplication can seem tedious
children need to learn and master multiplication or they will be at
a mathematical disadvantage that can hinder mathematical success in
the future. The teaching method that should be used is the
introduction to all of the multiplications teaching the easiest
ones first and moving to those that may be difficult. Once all the
multiplications have been covered teaching should consist of
multiplication applications and problem solving. The mastery of
multiplications will no longer come simply from memorization but
must establish a deeper connection. About the Unit and the
LessonThe unit plan we have constructed has been divided into 5
sections. Each section requires students to build upon skills and
concepts they have learned from the previous section. The first
section is composed of lesson 1. The students are introduced to the
concept of multiplication for the first time. We will be modeling
multiplication through repeated addition. Addition is a skill
students have previous learned and mastered. We will be showing
students how you can think about multiplication as repeated
addition. Students will learn about the symbol that represents
multiplication and how to write a multiplication sentence using the
symbol. In the second section, students will be learning about
arrays and multiplication. Students will learn how to formulate an
algorithm (multiplication sentence) from the given array. Students
will also learn about the Commutative Property of Multiplication.
Through various activities, students will see that the two factors
can be multiplied in any order and still come out with the same
product. The third section focuses on multiplying by 2. Now that
students have learned the basic foundational concepts of
multiplication, they are ready to learn how to multiply numbers. In
lesson 3 students will learn different ways to multiply when 2 is a
factor.The forth section focuses on multiplying with 5. Students
will learn different ways to multiply when 5 is a factor. The fifth
section focuses on multiplying by 10. Students will learn to find
the product, when one of the factors is a 5.
Flow of the UnitLesson NumberTitle and Learning Objectives# of
lesson periods
1 (Vivian)Modeling Multiplicationex. 2 + 2+ 2 +2 +2= 2 x 5
Understand that multiplication is similar to repeated
addition.Learn about the multiplication symbol and how to write a
multiplication sentence.
1 x 60 min.
2 (Sarah)Arrays and Multiplication
Solve word problem in situations involving arrays. Using arrays
to find solution to the multiplication problem.2 x 60 min.
3 (Adelaida)Multiply with Five
Using strategies previously learned and applying to
multiplication factor of 5.2 x 60 min.
4 (Cathy)Multiply with Two
Becoming familiar with the multiplication factor of 2 by using
different ways to multiply.
2 x 60 min.
5 (Yvonne)Multiply with Ten
Deepen understanding of strategies used and another way to
remember multiplication factor of 10.2 x 60 min.
Lesson 2: Vivian Pepperoni PizzasGoals of the Lesson:a.
[CCSS.MATH.CONTENT.3.OA.A.1] Interpret products of whole numbers,
e.g., interpret 5 7 as the total number of objects in 5 groups of 7
objects each. For example, describe a context in which a total
number of objects can be expressed as 5 7.b. For students to extend
their prior knowledge and understand multiplication as repeated
addition.c. For students to understand numerical representations in
a written algorithm expressed by verbal and visual form.
Flow of the lesson based on teaching through problem
solvingSteps, Learning ActivitiesTeachers Questions and Expected
Student ReactionsTeachers SupportPoints of Evaluation
1. Introduction Find the total number of eggs. Then write an
addition equation to express the total of eggs in the carton.
(2+2+2+2+2+2=12; 6+6=12) This serves as a quick review from what
students learned in second grade. CCSS.MATH.CONTENT.2.OA.C.4Use
addition to find the total number of object arranged in rectangular
arrays with up to 5 rows and up to 5 columns; write an equation to
express the total as a sum of equal addends.
2. Posing the Task
Ms. Huangs Uncle works at a pizzeria. He tells Ms. Huang that
every day for lunch, he makes four pizzas for his employee and each
pizza has exactly five pepperonis. However, he doesnt have enough
pepperonis to make pizzas for his employees for tomorrows lunch.
How many pepperonis does Ms. Huangs Uncle need total in order to
make lunch for his employees tomorrow? Show me a thumbs up if you
understand what to do. Are there any additional questions?Students
will display thumbs up if they understand their task, a thumb in
the middle if they have some questions, or thumbs down if they dont
understand the task at all.
3. Anticipated Student Responses
Students will use paper plates to represent pizzas and red
counters to represent pepperonis as math manipulatives.
R1: 5+5+5+5=20R2: Students counting each pepperoniR3:
4+4+4+4+1+1+1+1=20R4: 4*5=20
Follow Up Question What is another way Ms. Huangs Uncle can use
the same number of pepperonis but with a different number of
pizzas? Write an addition algorithm and multiplication algorithm
for each visual you draw
R1: 20 pizza 1 pepperoni on
each1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=2020x1=20 R2: 10 pizza
2 pepperoni on each (2+2)+(2+2)+(2+2)+(2+2)+(2+2)=20 10x2=20
R3: 2 pizza 10 pepperoni on each (10)+(10)=20 2x10=20
Students will have various ways of responding. As the teacher, I
will take note of all the different responses and use it in the
class discussion. For students who have incorrect solutions, I will
ask them to explain how they got their answer and explain what
their algorithm represents. If students finish early, I will
instruct them to develop a different algorithm different from the
first algorithm they came up with. The teacher will select students
who finished early to go to the board and display the various
methods used. The purpose of this lesson is for students to see and
understand how multiplication is just repeated addition.
4. Comparing and Discussing After the selected students have
displayed their method and math work on the board, the teacher will
select other students to explain what their classmates did and what
their algorithm represented in the image. Despite the order of
algorithms presented on the board, the student solutions will be
displayed in the order shown above in Anticipated Student Response.
Then as a class we will observe and analyze the picture.- There are
4 pizza- Each one has 5 pepperonis- 5+5+5+5=20 pepperonisHow many
groups of pepperonis are there?- 4 groupsHow many pepperonis are in
each pizza?- 5 pepperonisAnother way we can write the total of
pepperonis is using multiplication.- # of groups x # in each group-
4 x 5=20- There are 4 groups of 5 pepperonis
If we had four pizzas with 4 pepperonis on each AND four pizzas
with 1 pepperoni on each, what will the math equation look
like?
R1: 4+4+4+4+1+1+1+1=20
What do you notice about the math equation?
R: There are a lot of 4s and 1s.
Very good observation. What would you suggest we should do to
make the equation look simpler?
R: Group them together!
What do we group together?
R: The number of 4s and the number of 1s
How many groups of each number do we have? Imagine each digit is
a pizza group and each number is how many pepperonis are in each
group.
R: There are 4 pizza groups and 4 pepperonis on each one. So 4
groups of 4. There are 4 pizza groups and 1 pepperoni on each
one.
What will our multiplication equation look like?
R: 4x4 and 4x1
What do we do with these equations now?
R: Add them together! (4x4)+(4x1)= 16+4=20 Ideas to focus on
during the discussion are the various algorithms the students use
to represent the image. Then students will be shown despite the
various methods of solution, the methods will result in the same
answer by simplifying the equation. This will also display a method
to check their work.The teacher will use student verbal
understanding of how the numbers in the algorithm represents
aspects of the image will indicate the students are benefiting from
the discussion as well as the questions they ask
5. Summing up Today, we learned how to find the total number of
objects using multiplication. We know the total can be found using
the number of groups multiplied by the number in each group.
Evaluationa) Did students understand how to write an algorithm
to represent the images represented?b) Did students understand what
the numbers and operation symbols represent in the algorithm?c) Was
there enough time for students to investigate the problem and
develop a solution?d) How many students were able to understand the
problem and methods of solutions they used?e) How comfortable were
students using numbers and operation symbols to represent their
understanding?
Lesson 2: Sarah An example of lesson plan format for teaching
through problem solving (TTP)Goals of the Lesson: a)
[CCSS.MATH.CONTENT.3.OA.A.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.b) For students to model and use multiplication to solve
word problems in situations involving arrays. c) For students to
know and understand the Commutative Property of Multiplication.d)
For students to appreciate the usefulness of multiplication and its
efficiency.
***This lesson is anticipated to take about 2-3 days to
complete. Flow of the lesson based on teaching through problem
solvingSteps, Learning ActivitiesTeachers Questions and Expected
Student ReactionsTeachers SupportPoints of Evaluation
1. IntroductionIn the previous lesson, students learned about
how multiplication is similar to repeated addition. Instead of
adding all the numbers up, students can use multiplication to
efficiently solve for the solution. They also learned about the
multiplication symbol and how to properly write a multiplication
sentence.
For part two of the introduction, I will present the students
with a story problem. Problem: Jenny collects flags from different
states. She has her flags hung up on a wall in her room. How many
flags are on her wall?
If you look at the flags on Jennys wall they are arranged in an
array. Can anyone take an educated guess on what an array might be?
An array is a number of objects arranged into rows and columns. How
many rows are there? 4Can someone tell me something you notice
about each row? Each row in the array has an equal number of flags.
How many flags are in each row? 5How many flags are there
altogether? 20
I will ask students to write a multiplication sentence that
correlates with the picture. They will be given no more than 2
minutes to complete this.
Once they have written their math sentence, the students and I
will go over it as a class. 4 x 5= 20 4 represents the number of
rows 5 represents the number of flags in each row 20 represents the
total number of flags
Part 2: After we go over part 2, I will present the students
with another question in regards to the same problem. Jenny wants
to change the layout of the flags, so she turns it around. Does the
total number of flags change? Why or why not? Write a math sentence
that represents the new design to support your answer.
We will be going over the answer as a class. I will have
students share their answers and explanations.
Afterwards we will talk about both multiplication sentences and
how the total does not change. This will set me up into introducing
the students to a new vocabulary word: Commutative Property of
Multiplication. Students will already know about the Commutative
Property of Addition and I will explain how it is very similar.
Commutative Property of Multiplication: When multiplying
factors, the order in which you multiply the factors does not
change the product. If I change the order of the factors it does
not change the product. Example: 4 x 5 = 20 and 5 x 4 = 20
**Mention how if I use 4 x 5 = 20 it means that I have four rows
with 5 flags in each row. If I use 5 x 4 = 20 it means I have 5
rows with 4 flags in each row.
Give students example: Will 3 x 5 give me the same product as 5
x 3? Will 6 x 7 give me the same product as 7 x 6? Will 5 x 3 give
me the same product as 5 x 4? Why? I will be looking for students
to say because they do not have the same factors. In order for the
commutative property of multiplication
If students are struggling to answer this question, I will ask
them what they notice about the picture and how they are arranged.
I will point to the picture and show the students how all of Jennys
flags are arranged in rows and columns.
Might need to go over how the first number in the multiplication
sentence represents the number of groups and the second number
represent the number of items in a group.
Part 2: If the students are having a difficult time writing the
number sentence then I will ask them a couple of questions to get
them thinking. How many rows do you see? How many flags are in each
row? How many flags are there altogether?
See if students are able to write a math sentence based off the
array they see
If students are able to explain their math sentence and what
each factor represents
Part 2: Write a multiplication sentence that correlates with the
array
Able to identify the number of rows and the number of flags in
each row
Understand the commutative property of multiplication.
2. Posing the TaskStudents will be given a total of 24 m&ms.
They will be asked to come up with as many arrays and write a
multiplication sentence for each array. They must use all 24
m&ms. I will give them a worksheet to draw and write each array
and multiplication sentence they come up with.
Remind students that each row must have the same (equal) amount
of m&m (Cannot have 6 in one row, 10 in another, and 8 in
another). Because we know the total number of m&ms what should
the product of all our math sentences be?
Based of the arrays and multiplication sentences they created
and whether or not the two correlate, I will know whether or not
students understand arrays and multiplication.
If the array and multiplication sentence do not match, I will
know that the students have not mastered this skill yet and
something we need to work on more.
3. Anticipated Student ResponsesR1: 1 x 24 = 24 R2: 2 x 12 =
24R3: 3 x 8 = 24R4: 4 x 6 = 24R5: 6 x 4 = 24R6: 8 x 3 = 24R7: 12 x
2 = 24R8: 24 x 1 = 24
I will encourage students to work together and share their
solutions with one another. If there are students who are stuck, I
will have them ask a peer first and if they are unable to find the
answer, then I will step in and help them.
I will also tell students to come up with as many arrays as
possible.
If I see an a multiplication sentence that does not correlate
with the array they have, I will ask them various questions so that
they notice this mistake as well. The goal of this task is not to
have students come up with all the arrays. Instead the goal of this
lesson is to see whether or not the array students have drawn
matches the multiplication sentence they have written. Are students
able to write a multiplication sentence based on the array they
see?
4. Comparing and DiscussingI will give students 3-5 minutes to
come up to the board and draw their array and math sentence (can
only come up once).Then as a class, we will go over each array and
whether or not the math sentence that is under it is correct.
After we go over each array, we will group the
arrays/multiplication sentences based on similar factors. 1 x 24 =
24, 24 x 1 = 24 2 x 12 = 24, 12 x 2 = 24 3 x 8 = 24, 8 x 3 = 24 4 x
6 = 24, 6 x 4 = 24
I will ask the students if they notice anything about the pairs.
I will use this opportunity to go over commutative property of
multiplication again.
Writing a multiplication sentence Drawing an array using the
given number of objects Writing a multiplication sentence that
correlates with the array Notice factors Commutative Property of
Multiplication When students are able to challenge one anothers
solutions/explanations.
Students use vocabulary terms: product, factors, array,
multiplication, commutative property of multiplication
5. Summing upToday we learned about how to use multiplication to
solve for the total number of objects in an array. We know how to
formulate a multiplication sentence using the information we found
from looking at the array. We learned about the Commutative
Property of Multiplication and how the order in which you multiply
the factors does not matter because you get the same answer.
Evaluationa) Do students know and understand what an array is?b)
Are students able to see the relationship between the array and
multiplication sentence? c) Were students able to write an
algorithm that correctly represents the array?d) Were students
given enough time to explore the problem and come up with multiple
solutions?e) Are the students comfortable with writing a
multiplication sentence for each array? How comfortable?
Lesson 3: Adelaida Goals of the Lesson:a.
[CCSS.MATH.CONTENT.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 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.b. For students
to extend their prior knowledge and understand multiplication as
repeated addition.c. For students to understand numerical
representations in a written algorithm expressed by verbal and
visual form. Flow of the lesson based on teaching through problem
solving
Steps, Learning ActivitiesTeachers Questions and Expected
Student ReactionsTeachers SupportPoints of Evaluation
1. Introduction a. Show students a sequence of multiplication of
5. Ask students if they see any patterns.
b. Show students a hundreds chart with some of multiplication of
5 highlighted. Ask students what other numbers would be
highlighted.
c. Ask students if 4,560 and 85,675 can also be highlighted. d.
Pass out a sheet that has a blank circle and tell students to make
a clock. Tell them to write the numbers 12 and 6 in the outlier of
the middle in the clock first and go on from there. If students
have hard time remembering the hour hand, tell them they can also
write down 3 and 9 first to give them a better image of the clock.
e. Once students are done writing down the numbers on their clock,
pass out the chart that has numbers written down along with empty
minute box. Students are to write the minutes according the number
that the minute hand is pointing to.
Students should be familiar with looking at the time. The
activity is to give students confidence that the multiplication of
5 is something they already know even without trying to memorize
the numbers.Do you see any pattern in this number sequence? Can you
tell me the pattern you see? In this hundreds chart, we see that
numbers on the washing line are highlighted yellow. What other
numbers would be also highlighted? If the this box were to continue
for a long time and numbers 4,560 or 85,675 appearedcan these
numbers still be highlighted? Now, were going to change our gear
just a little bit and make a clock. Dont look at any clocks in the
room and try to make your own clock with the sheet of paper I just
passed out.Students see the 5 and 0 pattern from the sequence. They
should also realize that the numbers are increasing by. Students
say any numbers with 0 or 5 tenths or any numbers that are vertical
from the highlighted box could be highlighted.Students can explain
that any numbers if 0 or 5 at the end could be highlighted.
Students can draw the hour hand of the clock accurately.
Students can write down correct minutes according to each number
in the box.
2. Posing the TaskMs. Kim decides to give her teacher friends
some chocolates. In order to find out how many chocolates she could
give to each teacher, Ms. Kim must find out how many chocolate she
has in total. There are 4 groups of 5 chocolates inside the box.
How many chocolates does Ms Kim have in total?
Once you are done with the problem, solve 9x6 using your prior
knowledge on multiplication of 5.Students will have different
strategies to solve the problem. The teacher should consider all
the anticipated student responses and use some of them in the class
discussion.
3. Anticipated Student Responses R1: 5 10 15 20R2: 5+5+5+5R3:
5x4R4: 4 8 12 16 20R5: 4+4+4+4+4R6: 4x5 The teacher will pick three
anticipated responses that all have different strategies. The
purpose of discussion is too see that all different methods will
have the only one solution.Were students able to understand that
even if they grouped the circle differently (horizontally or
vertically), they would still get the same answer?
4. Comparing and DiscussingSelect three students to come to the
board that had different strategy to solve to the problem. R1:
R4:
R5: 4x5=20
5. Summing upToday, we learned that there is a sequence in the
multiplication of 5. To find the solution, we need to add 5
continuously. We also know that any number that ends with 0 or 5
can be dividend by 5.
Evaluationa. Did students understand that multiplication is a
sequence of numbers?b. Did students understand that that clock is a
representation of multiplication of 5?c. Did students understand
any number that ends with 0 or 5 could be dividend by 5?d. How many
students were able to understand the problem and methods of
solutions they used?e. How comfortable were students using numbers
and operation symbols to represent their understanding ?Lesson 4:
Cathy
Goals of the Lesson:a) [CCSS.MATH.CONTENT.3.OA.A.1]Interpret
products of whole numbers, e.g., interpret 5 7 as the total number
of objects in 5 groups of 7 objects each. For example, describe a
context in which a total number of objects can be expressed as 5
7.b) For students to model and use multiplication to solve word
problems. c) For students to associate addition to multiplication.
d) For students to understand there are multiple strategies when
multiplying (repeated addition, array, picture, break-apart).
Steps, Learning ActivitiesTeachers Questions and Expected
Student ReactionsTeachers SupportPoints of Evaluation
1. Introduction
In previous lessons students have learned: multiplication is
repeated addition, the Commutative Property of Multiplication, and
how to using arrays to solve word problems.
Part One:
In the beginning of the introduction, we will have a brief
review of what the students learned in the previous lesson. Next,
students will have the following worksheet:
1. 2+2+2= 2 x 3 2. 2+2+2+2+2= 2 x 53. 2+2= 2 x 2 4.
2+2+2+2+2+2+2+2+2+2+2+2= 2 x 12 5. 2+2+2+2+2+2= 2 x 66.
2+2+2+2+2+2+2+2+2= 2 x 9 7. 2+2+2+2= 2 x 4 8. 2 = 2 x 1 9.
2+2+2+2+2+2+2= 2 x 7 10. 2+2+2+2+2+2+2+2+2+2= 2 x 1011.
2+2+2+2+2+2+2+2= 2 x 8 12. 2+2+2+2+2+2+2+2+2+2=2= 2 x 11
The multiplications on the right side will NOT be present.
I will then ask students to raise there hands to share ideas of
how we can solve these 12 problems faster and in an easier
manner.
At the end of the lesson we will review this worksheet
again.
Part Two:
Before moving forward we will complete one row of the
Multiplication Strategy Review Sheet
https://www.pinterest.com/pin/514958538615572642/
Part Three:
Students will watch the following video:
https://www.youtube.com/watch?v=PE_oUqJ41oI
Part One:
When students have completed worksheet we will have a brief
discussion. We just completed this work. Can someone tell me what
we have been learning in previous lessons and how this connect to
what we did just a few seconds ago. At this time, talk in your
table about ways we can show this in a faster and easier way. After
write your ideas in your math journal.
Thumbs up if you are done and a thumbs down if you need more
time to write your ideas down.
At this time you may put this sheet away. We will be looking at
it once again towards the end of class.
Remember we are going to be using the 2s multiplication
Part Three:
Part One:
Students should recognize that it is repeated addition. They
should be able to identify that this is the 2s multiplication.
Students should be brainstorming ideas: array, repeated
addition, drawings.
Students should mention the following: repeated addition array
drawing (possibly)
The array, drawing, repeated addition is not new to students and
should know how to complete the chart. If there is a disconnection
in any section I will be able to see which students need additional
help in a certain area.
Part Three:
Classroom will all be singing.
2. Posing the Task
Students will use the concept of repeated addition to solve the
following problem.
Problem: Ms. Davila wants to know how many computers there are
at Blank Elementary. There are 12 classrooms at Blank Elementary
and each classroom has two computers. Help Ms. Davila figure out
how many computers there are.
I will remind students that they can use their Multiplication
Strategy Review Sheet or the following chart will also be
available.
Students should write the problem in math journal.
As students solve problem they should show all their work and
label each part of their work as well.
Students should be able to solve problem using any of the four
strategies shown in the Multiplication Strategy Review Sheet.
3. Anticipated Student Responses
R1: 2+2+2+2+2+2+2+2+2+2+2+2 = 24 [correct]
R2: 2 x 12 = 24 [correct]
R3: 12 x 12 = 24 [ incorrect number sentence; correct
product]
R4: 12 + 2 = 14 [incorrect]
I would review with the whole class the following:
# of groups x # in each group = product.
Students who finished early could review their 2s flashcards for
additional review.
4. Comparing and Discussing
I would have a student with the correct answer and a student
with the incorrect answer come to the board and have them walk the
class through. I would stop and facilitate in area that need to
more attention.As a class we will review both problems and learn
together.
I will ask for the students to point to the # of groups and # in
each group.
Students will be learning from their peers.
Students will be able to question and comment the work their
peers show.
5. Summing up
Students will take out the worksheet completed Part One of the
Introduction. Next to the repeated addition they will write the 2s
multiplication. 1. 2+2+2= 2 x 3 2. 2+2+2+2+2= 2 x 53. 2+2= 2 x 2 4.
2+2+2+2+2+2+2+2+2+2+2+2= 2 x 12 5. 2+2+2+2+2+2= 2 x 66.
2+2+2+2+2+2+2+2+2= 2 x 9 7. 2+2+2+2= 2 x 4 8. 2 = 2 x 1 9.
2+2+2+2+2+2+2= 2 x 7 10. 2+2+2+2+2+2+2+2+2+2= 2 x 1011.
2+2+2+2+2+2+2+2= 2 x 8 12. 2+2+2+2+2+2+2+2+2+2=2= 2 x 11
Then, as a table students will discuss and brainstorm a
summary.
Students will write their tables brainstormed summary and then a
classroom/teacher summary.
Student Summary:
Class Summary: Today as a class we reviewed arrays, repeated
addition,and the Commutative Property of Multiplication. We also
practiced our 2s multiplication understanding that they are
doubles.
Students will share out brainstormed summary.
Evaluation
1. Did students understand that the 2s multiplication table is
doubles?2. Do students understand # of groups x # in each group =
product? 3. Were students able to create a correlation between
2+2+2+2= and 2 x 4 and the concept of repeated addition? 4. What
are other ways the 2s can be taught?5. What can I do different next
time?
Lesson 5- YvonneGoals of the Lesson:a)
[CCSS.MATH.CONTENT.3.OA.A.1] Interpret products of whole numbers,
e.g., interpret 5 7 as the total number of objects in 5 groups of 7
objects each. For example, describe a context in which a total
number of objects can be expressed as 5 7.b) For students to
explain their method of choice to solve the problem.c) For students
to understand the different methods learned for multiplication of
10.
Steps, Learning ActivitiesTeachers Questions and Expected
Student ReactionsTeachers SupportPoints of Evaluation
1. IntroductionStudents will review the different ways to solve
a one-digit multiplication problem using addition, arrays and the
different methods for multiples of five and two.Students will also
go over the multiple of 1, as it will lead them into the main
lesson of multiple of 10. Two methods of x10.For example, for 10 x
5.1) I will show the students that they can solve it by simply
taking the number that is not 10 and then adding a 0 to the end.
This examples answer would look like this: 10 x 5= 50Explanation: I
used the rule of putting one zero on the end of the number 52)
students can use the first method they learned in the beginning of
the unit by adding. Students will always use the number 10 and then
add the amount of number that 10 is multiplying by. For example,10
x5= 10+10+10+10+10=50I will help them review by asking what those
different methods are of solving a one-digit multiplication
problem. I may need to give couple problems that relate to what
they have learned already.
I will determine to see if the students are understanding the
methods but having the students do another practice problem
themselves by themselves in the next step of this lesson.
2. Posing the Task-Students will use what they have learned
throughout this whole unit to solve a multiplication story problem
with the multiple of 10.-The multiplication story problem I will
give the students is The monkeys had 7 trees. There were 10 bananas
in each tree. How many bananas are there together? -Students will
use the number given in the information and multiply those two
numbers. Students will be asked to show their work and also explain
in one sentence how they have solved this problem as we did in the
beginning of the lesson.If students need additional help and dont
know where to start, I will have them fill the boxes with the two
numbers they will use to solve this problem.
I will see if the students understand by looking at the one
sentence explanation. Students will be expected to explain how they
got their answer.
3. Anticipated Student ResponsesIf students are not familiar
with multiplying, they might add the numbers straight down from the
problem. -R1: 10 x 7= 7+7+7+7+7+7+7+7+7+7 [correct]I added the
number 7 ten times. - R2: 10 x 7= 170 (incorrect)I put a zero after
putting the other numbers. I can help students to fix their answer
by questioning them what they did to solve the problem. Their
reasoning should be one of the methods the students have learned
earlier in the lesson.--The method student one used had the right
answer and explanation, but there is also another way to solve that
problem. Students can add 10 seven times.R1:
10+10+10+10+10+10+10=70--The method the second student used were
correct, but the number they used was incorrect. Students fixed
responses should look like this:R2: 10x7=70Explanation: I added a 0
at the end of the number I am multiplying the 10 with.I will know
if the students understand the task if they get the right answer
and also have a good explanation.
4. Comparing and DiscussingI will have the students share their
method depending on how they have solved the problem. I will have
one student from each method taught to share their solution
methods.I will also share one problem that is incorrect so that the
students can discuss why the solution is incorrect.Students should
discuss the method that is used in the incorrect problem I have
shared. The discussion should include students explaining why the
method works or doesnt. I will be able to see if the students are
benefiting from the discussion if students are participating and
discussing the incorrect problem.
5. Summing upI will summarize the main idea of the lesson by
discussing the different methods once again to solve the
multiplication of 10s. Students should know how to explain how they
have solved a multiplication of 10 problems.I will look to see if I
can proceed by giving them additional problems that relate to the
ones we have learned today.
Evaluation1. Do students understand the different methods of
solving a multiplication of 10s problem?2. Do students understand
the information given in the world problem?3. Are students using a
method learned for the multiplication of 10?4. Were students giving
an accurate explanation of their solution?5. Do students have the
right answer?
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