Transcript File

Unit 5 Lesson 1.1
Many Things Come in Groups
(No Notebook)
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
Objectives:
1. I can understand multiplication as combining equal groups.
2. 2. I can write and solve multiplication problems in context.
Essential Question:
When doing addition, why might it be helpful to notice when things come in equal groups?
Teacher Input:
1. Start a class list of things that come in groups on separate sheets of chart paper for each number from 2 to 12. Record student ideas for
each group.
2. Using items on the class list, pose two questions that can be solved using multiplication (e.g. How many ears total do three people have?)
3. Have students pick items on the list and work together as a class to come up with two multiplication questions.
4. Record the questions. Have students work in pairs to solve the questions.
Independent:
1. Have the students work in pairs to brainstorm for new items to add to the class list. (Over the next few days, challenge them to find an item
to add to each group from 2 to 12.)
2. Questions to ask while they work:
What are the most common numbers that things are grouped in?
Which numbers were hard to find?
Why do you think some numbers occur more often than others?
3. Have students complete Unit 5 page 1 of the student book.
Closing:
Facilitate a discussion about the problems on page 1 and have the students explain how they solved them.
Homework:
Unit 5 page 2 (students record items that come in groups and indicate how many are in a group)
Many Things Come in Groups
Objectives: I will understand multiplication as
combining equal groups.
I will write and solve multiplication problems in
context.
EQ: Why might it be helpful to notice when things
come in equal groups?
Name Things That Come In Groups!

We are going to name a few things that
we notice come in groups. We’ll jot these
down on chart paper so that we can add
more to our list throughout the week.

Can you name things that come in 2s, 3s,
4s, 5s, 6s, 7s, 8s, 9s, 10s, 11s, or 12s?
Multiplication Questions

Looking at the list, I can ask you
multiplication questions!
Example: Here are ears. Each head comes
with 2 ears. How many ears are there
on/in 7 heads?
Can you answer the problem?
How Did You Solve the
Problem?
Explain how you solved the problem:
Some of you used repeated addition.
Let’s think back to the problem. We
made note that there are 2 ears on each
head. We wanted to know how many
ears there would be on 7 heads.
 That means we need to add 2 ears 7
times: 2 + 2 + 2 + 2 + 2 + 2 + 2 =

Multiplication Questions

Now I am going to ask you questions
using items on our list. Here is a
template (that looks a lot like a sticky
starter) that I can use to create
multiplication problems.
Here are (items). Each (group of items)
comes with (# of items in a group). How
many (items) are there on/in (# of
groups)?
Class Multiplication Questions

Your turn. Let’s come up with two hard
questions that we can write on the board
using items on our list.
Question1:

Question 2:

Flash quiz! You and the person next to you
Move this for the flash quiz challenge
have 30 seconds
to solve both questions.

Independent
1.
Find a partner. Using a note card or
sticky note, I want you and your partner
to brainstorm for new items to add to
the class list. (5-10 minutes)
2.
Complete Unit 5 page 1 of the
investigations student book.
Unit 5 Lesson 1.2
How Many in Several Groups
CCSS: 3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.73.OA.8, 3.OA.9
SFO:
1. I can understand multiplication as combining groups
2. I can identify the number of groups, the number in each group, and the product in a multiplication situation.
3. I can understand the relationship among skip counting, repeated addition, and multiplication.
Teacher Input:
·
Introduce math lesson using the Power Point.
·
Pass out notes to each child for them to glue in their interactive notebooks.
·
Begin the lesson by assigning each student a number to work with (Ex. You could use numbers 1-12 and go higher for those students who need some enrichment)
·
Students will choose an item from the lists you brainstormed yesterday of things that come in that number. For example if a student had the number 2 they might draw mittens, eyes,
shoes, or twins.
·
Tell students to draw several of those items
·
Students will then need to write three sentences that tell how many groups, how many in each group, and how many in all. For example a student who got the number 4 might draw 4
stars and write here are 4 stars (number of groups) as their first sentence, each star has 5 points for their second sentence (number in each group), and there are 20 points in all (product).
·
Have students make at least 3 pictures of groups with each picture showing a different number of groups. Students should be filling in the blanks in their notes.
Here are ___________.
Each _____ has ______.
There are _____ in all.
·
Once students are finished ask a couple students to share their strategies for finding the product in their multiplication situations. Most students will probably have used skip counting,
repeated addition, or a combination of the two. Make sure to share both strategies with the class.
·
Introduce the multiplication notation:
(ie. 4 x 5 = 20). Using the example:
Here are 4 stars
Each star has 5 points
There are 20 points in all
Explain to students that you could represent that using an addition equation such as 5+5+5+5=20 or a multiplication equation such as 4x5=20. Explain that they mean the same thing. It is
important for students to recognize and use standard notation for multiplication both vertically and horizontally. The way you would teach students to read the multiplication notation is (4x5)
4 groups of 5. Tell students that it is important that they represent their pictures with multiplication equations.
Independent Practice on left of notebook:·
-Students will create a 4 tab foldable
-On the outside of each tab the students will draw a picture of several groups of an item.
-On the inside left students will write 3 sentences about the three pieces of mathematical information in their picture.
-On the inside right they will write the multiplication and addition equations that represent their picture.
Closing: Have several students share an example from their foldable.
Assessment: Left side of interactive notebook
Homework: Teacher Created Worksheet
Unit 5
Lesson 1.2 How Many in
Several Groups?
Objectives:
I can understand that multiplication is combining
groups.
I can identify the number of groups, the number
in each group, and the product in a multiplication
situation.
Pictures of Things that Come in Groups
Here are _______ stars.
Each star has _______ points.
There are _____ points in all.
Pictures of Things that Come in Groups
• Here are 5 stars.
• Each star has 5 points.
• There are 25 points in all.
What would my addition equation be?
5 + 5 + 5 + 5 + 5 = 25
What would my multiplication equation be?
5 x 5 = 25
This is called the product. A product is the answer to
a multiplication equation. What is the answer to an
addition problem?
Do You See a Relationship
Between Addition and
Multiplication?
• 5 + 5 + 5 + 5 + 5 = 25
• 5 x 5 = 25
Explain!
Another Example
Here are _______ wagons.
Each wagon has _______
wheels.
There are _____ wheels
in all.
Multiplication Equation:
_______________________
You’re Turn…
• Each student will be assigned a number to work with
• Choose an item from the list of things that come in
that number that we created yesterday as a class
and draw several of that item (you decide how many).
• Write three sentences about that item that tell how
many groups, how many in each group, and how many
in all. See below on how to complete in your notes.
Draw items
here!
Let’s Share…
Questions to Discuss w/ a Partner
•
•
•
•
•
•
What number did you have?
What items did you choose?
What were your 3 sentences?
What strategy did you use?
What was the multiplication equation?
What was the addition equation?
Word Problem Practice
• There are 5 people sitting at my table.
Each person has 5 fingers on each hand.
How many fingers are there altogether?
1.3 Solving Multiplication Problems
CCSS: 3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.73.OA.8, 3.OA.9
SFO:
1. I can use and understand multiplication notation
2. I can write and solve multiplication problems in context.
Teacher Input:
·
Introduce the math lesson using the Power Point.
·
Pass out notes to each child for them to glue in their interactive notebook.
·
Introduce the activity “Counting Around the Class.” You will use this throughout the unit.
·
You will count by some number and each person will take a turn. For example you might count by 2’s, 3’s, 5’s. Before beginning, ask students to try and figure out what number the last
person will say. Share student predictions after they have thought about it for a minute. Record student predictions on the board. Choose a couple of close predictions and ask those students to
explain their thinking.
·
Pause in the middle of the activity several times by saying, “Stop! How many people have counted so far?”
·
Extend that activity by asking the following questions:
1. If we continued counting around the class again, starting with the next number, what would the ending number be?
2. Let’s look at the predictions you made. Which predictions were possible? Which ones were not possible?
·
Review yesterday’s lesson by having students solve these problems with a partner:
1.
In this picture there are 4 flowers. Each flower has 5 petals. How many petals are there?
2.
In this picture there are 3 girls. Each girl has 8 braids. How many braids are there?
·
Review with students that in yesterday’s lesson we talked about the three pieces of mathematical information in a multiplication equations. Ask students what information was given to
them just now and what was missing. Students should realized that in both problems the number of groups and the number in each group were given, but the product was missing. Review with
students that the number of items in a multiplication situation or the total number is the product.
·
As a class complete the first picture problem. Make sure to share strategies used and write the multiplication equation.
·
Have students work with a partner to solve the picture problems on their notes. Go over these together as a class to check their answers.
Independent Practice on Left Side of Notebook:
Students will create 2 of their own word problems. They will then exchange notebooks with a partner and their partner will solve. The person that created the problems must check their
partners work and correct any mistakes with them.
Closing: Have a few students share the word problems they created and have their partner share what strategy they used to solve it.
Assessment: Left side of interactive notebook
Unit 5 Lesson
1.3 Solving Multiplication
Problems
Objectives:
-I can write and solve multiplication
problems in context.
-I can use and understand multiplication
notation.
Activity:
Counting Around the Class
The class should stand in a circle. I will begin by
giving one student a number to begin counting by.
The person next to that student will continue
counting by that number and so on. This will
continue until I say stop. When I say stop, you must
predict what the last person in the class will say
without finishing counting. Hint: You have to
remember how many students we have in our class!
Let’s begin with counting by 2’s. Be prepared to
share your predictions and your strategy.
Vocabulary
• Product – answer to a multiplication problem
• Example: 4 x 4 = 16
• Factors – numbers that are multiplied
together
• Example: 4 x 4 = 16
What am I Missing?
Directions: Determine if I am missing a factor or
product then complete table on notes and solve.
1. There are 4 flowers. Each flowers has 5
petals. How many petals are there?
2. Jack drew some triangles. Each triangle has 3
sides. There are 30 sides in all. How many
triangles did Jack draw?
4 flowers
5 petals
3 sides
______ petals in all
4 x 5 = ______
______ sides in all
3 x _____ = 30
Use these problems to complete your chart. Some are
missing factors and some are missing the product.
• Alan sees 5 wagons. Each wagon has 4 wheels. How
many wheels does Alan see?
• Jack bought 5 cartons of eggs. Each carton has 12 eggs.
How many eggs does Jack have?
• Sally had $4 in one dollar bills. She exchanged it for
quarters to go to the car wash. There are 4 quarter in a
dollar. How many quarters does Sally have?
• Sarah drew some octagons. Each octagon has 8 sides.
There are 40 sides in all. How many octagons did Sarah
draw?
Word Problem
Directions: For each problem show your work, the
multiplication equation, and write the related addition
equation.
There are 6 flowers. Each flower has 5 petals. How many petals
are there in all?
How could I solve this problem using addition? Write one
Statement explaining how they are related and also write the
addition equation.
Independent Practice – Left Side
Create a 3-tab foldable: Outside tab is the boxes.
Tab 1) Jimmy bought packs of soda for his party.
Each pack had 6 sodas. He came to the party
with 42 sodas. How many packs did he buy?
Tab 2) Ken bought 13 boxes of pizza for his
naughty class of third graders. There were
273 slices for the students. How many slices
were each pizza cut into?
Tab 3) Create your own.
Skip Unit 5 Lesson 1.4 Mini Assessment (Will do a quiz next week) & Unit 5 Lesson 2.1 Highlighting Multiples on 100 Charts
CCSS: 3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.73.OA.8, 3.OA.9
SFO:
1. I can find the multiples of the numbers 2, 5, and 10 by skip counting.
Teacher Input:
·
As a class highlight the numbers we say when we skip count by 2’s. Explain that all of these numbers are multiples of two’s.
·
Ask students to point out any patterns that they see among the multiples of two’s. Students should notice that they are all even numbers.
·
Next have students complete the skip counting circles on the bottom of the 100 chart so that they can make the connection between skip
counting and multiplication.
·
Optional: Have students make towers of 5 and 10 blocks to help them when counting by 5’s and 10’s.
·
Have students highlight multiples of 10 on a separate hundreds chart.
·
Ask students if they notice any patterns of the multiples of 10.
·
Continue completing the third hundreds chart by highlighting multiples of 5.
·
Ask students if they notice any patterns of the multiples of 5.
·
Ask students to identify any relationships they see among the multiples of 5 and 10.
Independent Practice Left Side of Interactive Notebook:
·
Have students write two riddles each for a multiple of 2, 5, and 10. They can either create a 6 tab foldable or just write the riddles directly
into their notebook. For example they might say…
“I am a multiple of 10. I started counting at 30 and I counted by 10’s 3 times. If you say the number 70 you went too far.” Have students write
down the answers to their riddles.
Closing: Have students share one of their riddles with other students and have them answer each other’s riddles. Report out 1 or 2 to the class.
Assessment:
Left side of interactive notebook
Homework:
Teacher Created Worksheet
Unit 5
Lesson 2.1
Objectives:
-I can find the multiples of the numbers 2, 5,
and 10 by skip counting.
-I can find identify patterns of multiples of
numbers.
• Counting around the class by 10’s.
• Students will stand in a circle. One
student will begin counting by 10’s.
When the teacher says stop, students
will predict what the last person will
say. We will do this also with 5’s.
What is a multiple?
• The multiple of a number is the product of
the number and any other whole number
• The multiples sheets you will be your notes
for the day. You will keep them in your math
folder until you complete the multiples of 212, then we will compile into a book (unless
your teacher wants to do this differently)
Use a red colored pencil
to circle multiples of 2.
Multiples of 2
Multiples of 2
Using the same sheet, draw an
X on multiples of 4 with a blue
colored pencil.
Multiples of 4
Multiples of 4
Use a red colored pencil
to circle multiples of 5.
Multiples of 5
Multiples of 5
Using the same sheet, draw an
X on multiples of 10 with a blue
colored pencil.
Multiples of 10
Multiples of 10
Independent Multiples Game
• Have students make groups of 3 or 4.
• Give each group a hundred chart, 3 dice, and tokens of some sort.
• Students will take turns rolling the dice, and manipulating the
numbers (by adding, subtracting or multiplying) to come up with a
multiple of 10. They will place a token on that multiple, write the
equation they used, and score a point. That multiple is taken and
nobody can use that multiple again.
• If a student is unable to create a multiple, they lose their turn.
• Once the board is completely filled, the student with the most
points wins.
• When the game is over, play again finding different multiples (2, 4,
or 5)
Unit 5 Lesson 2.2 More Multiples
(3, 6, 9)
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-I can find the multiples of 3, 6, and 9 by skip counting
-I can describe and compare characteristics of the multiples of a number
Teacher Input:
-10 Minute Math: Play the counting around the class game by 10’s, Begin counting by 10’s and have students try to guess what the last person
will say without actually counting.
-Have students look back at their hundreds charts that were created last class and ask students to identify patterns that they see in 5 & 10 and 2
and 4.
-Highlight multiples of 3 and 6 on their hundreds chart.
-Ask the students to identify patterns that they see.
-Next highlight multiples of 9 on their hundreds chart.
-Play the multiples game from last lesson by now writing the numbers 2, 4, 5, 10, 3, 6, and 9 on index cards.
Assessment:
Students can either write multiples riddles for multiples of 3, 6, and 9 or you can have students write the next 5 multiples beyond what is on
their hundreds chart for 3, 6, and 9 on an index card as an exit ticket.
Homework: Teacher-generated sheet
Unit 2 Lesson 2.2
Multiples of 3, 6, & 9
Objectives:
I can find the multiples of 3, 6, and 9 by skip counting
I can describe and compare characteristics of multiples
of a number
• Counting around the room by 3’s. Students
will get into a circle. One student will begin
counting by 3’s. When I say stop students will
predict what number the last student in the
circle will say. Be prepared to share strategies.
Patterns
• Look back at your multiples of 2 & 4 and 5 &
10. What patterns do you see? First, discuss
with a partner and be ready to share with the
class.
Multiples of 3
Multiples of 3
Multiples of 6
Multiples of 6
Multiples of 9
Multiples of 9
Independent Multiples Game
• Have students make groups of 3 or 4.
• Give each group a hundred chart, 3 dice, and tokens of some sort. They will record
their equations on the left-side.
• Students will take turns rolling the dice, and manipulating the numbers (by adding,
subtracting or multiplying) to come up with a multiple of 9. They will place a token
on that multiple, write the equation they used, and score a point. That multiple is
taken and nobody can use that multiple again.
• If a student is unable to create a multiple, they lose their turn.
• Once the board is completely filled, the student with the most points wins.
• When the game is over, play again finding different multiples (3 or 6)
Unit 5 Lesson 2.3 Solving Related Story Problems & Multiples of 7, 8
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-I can use known multiplication combinations to determine the product of more difficult combinations
-I can write and solve multiplication problems in context.
Teacher Input:
-10 Minute Math: Play the counting around the class game by 3’s, Begin counting by 3’s and have students try to guess what the last person will
say without actually counting.
-Identify multiples of 7 and 8 as a class on students’ hundreds charts.
-Display the following problems on the board.
1. Mrs. Johnson’s class counted around the class by 3’s. What number did the fourth person say?
2. Later, the class counted by 6’s. What number did the fourth person say?
-Have students work with a partner to solve these problems. Discuss what is the same about these problems and what is different.
-Display one more example on the board. Students work with a partner to solve this time, when Mrs. JOhnson’s class counted by 3’s, she
stopped at the fifth person. What number did the fifth person say? What if they counted by 6’s?
-Have students complete pages 14-16 in their student activity books.
Assessment: Student activity booklet pages
Homework:Teacher generated worksheet
Unit 5
Lesson 2.3
Story Problems
Objectives:
-I can use known multiplication combinations to solve
more difficult ones.
-I can identify multiples of 7, 8, 11, and 12.
Multiples of 7
Multiples of 7
Multiples of 8
Multiples of 8
Multiples of 11
Multiples of 11
Multiples of 12
Multiples of 12
Solve and Write an Equation
• Mrs. Johnson’s class counted around
the class by 3’s. What number did
the fourth person say?
Solve and Write an Equation
• Later, the class counted by 6’s. What
number did the fourth person say?
Solve and Write an Equation
• Mrs. Johnson’s class counted around
the class by 4’s. They stopped at the
fifth person. What number did the
fifth person say?
Solve and Write an Equation
• Later, they counted by 8’s. What
number did the fifth person say now?
Independent Practice – Left Side
• Complete student activity workbook
pages 14-16, OR word problems print
out.
• If you finish play multiples game.
Unit 5 Lesson 2.4 - Patterns and Relationships
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
- I can describe and compare characteristics of the multiples of a number.
- I can use known multiplication combinations to figure out the project of more difficult combinations.
- I can understand that doubling one factor in a multiplication expression doubles the product.
EQ: Why is it important to notice patterns between the multiples of different numbers?
Teacher Input: (Follow the ppt through the lesson)
1. Display activator problem on the board using ppt.
2. Have students look at the related problem sets they worked on the day before and have them explain how they solved the problems. Guided
questions to use: How did you figure out each answer? Explain what you did, including any tools you used. Think about ways that you could have
used the answer to the first problem to help you figure out the answer to the second problem.
3. Bring out the point that5x6 is 30, and in order to figure out problem 2, you can just add 3 more groups of 6 to get 8 groups.
4. Have students bring out their multiples of 3 and 6 charts. Remind them of the idea of double when counting by 3s and 6s.
5. Have the students count by 6s up to 60 and record the sequence of the first ten multiples of 6 on the board. (6, 12, 18 etc.)
6. Have the students count by 3s and record the first ten multiples of 3 under the multiples of 6 on the board. (3, 6, 9 etc.)
7. Have the students explain what they notice about the two lists of multiples. Bring out the point that the 6s sequence is double the 3s
sequence.
8. Using the ppt, display the story problem that demonstrates the doubling concept.
9. Discuss student solutions to the problem.
Independent:
Using the ppt, display the problem found in the student book in Unit 5 pg. 19. Have the students use a number line, a 100 chart, or a picture to
determine whether the statement is true.
Homework:
Teacher-generated sheet
Unit 5 Lesson 2.4
Patterns and Relationships
Objectives:
I can describe and compare characteristics of the multiples of a
number.
I can use known multiplication combinations to determine the
product of more difficult combinations.
I can understand that doubling (or halving) one factor in a
multiplication expression doubles (or halves) the product.
1. Oscar bought juice boxes that come in packages
of 6. He bought 5 packs. How many juice boxes
did he buy?
2. Jean bought 8 packs of juice boxes. How many
juice boxes did she buy?
-
How did you figure out each answer?
-
How can you use the answer to the first problem
to help you figure out the answer to the second
problem?
1. Oscar bought juice boxes that come in packages
of 6. He bought 5 packs. How many juice boxes
did he buy? 5 x 6 = 30
2. Jean bought 8 packs of juice boxes. How many
juice boxes did she buy?
So for #1, we figured out that 5x 6 = 30… But did
you notice that we already solved part of the
answer to eight groups of juice boxes?
Since 5 x 6 = Can
30 you
and
3 x Make
6 = sure
18,towe
can just add 30 +
explain?
take notes…
18 to figure out 8 x 6. 8 x 6 = 48.
More Patterns
• Take out your multiples of 3 and 6 chart.
• Let’s count by 6s while I write the multiples on
the board… then we’ll count by 3s and do the
same.
6, __, __, __, __, __, __, __, __, __
3, __, __, __, __, __, __, __, __, __
What do you notice about the two lists of
multiples?
More Patterns Continued
6, 12, 18, 24, 30, 36, 42, 48, 54, 60
3, 6,9, 12, 15, 18, 21, 24, 27, 30
Nice. You noticed the pattern of doubling. Using that pattern, quickly
work in pairs and solve this problem…
1.
Ms. Ross owns an apple orchard. She was making bags to sell
with three apples in each bag. If she made ten bags of apples,
how many apples did she use?
2.
On another day, she decided to put six apples in each bag. If she
made ten bags of apples, how many apples did she use this time?
Time is up! Explain your thinking!
Independent (Left Side)
One day Ms. Johnson’s class counted around the
room by 6s. The 30th person said 180.
The next day they counted around by 3s. Some
students in the class said they knew that this
time the 30th person would say 90.
Use a number line, a 100 chart, or a picture to
show if that is true. (I will show you an
example on the board)
Unit 5 Lesson 2.6 - Common Core Insert.
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
- I can understand the relationship between addition and multiplication properties.
EQ: Why it is important to know multiplication properties?
Teacher Input:
1. Review the addition properties.
2. Using the ppt, go over the multiplication properties one by one while the students fill in the guided notes.
3. After each property, have the students quickly solve a multiplication problem that demonstrate that property.
Independent:
1. Have students create a 3-column table (left side). For the first column, the students will name one property. For the second column, they will
draw a picture that helps them to remember the property. For the third column, the students will write the mathematical expression that
demonstrates the property.
Homework:
None over weekend.
Multiplication
Properties
Objectives:
I can identify multiplication properties when given an
equation.
I can solve unknown equations using the properties of
multiplication.
Multiplication Properties
Commutative Property
Associative Property
Identity Property
Zero Property
Distributive Property
Why Should you Learn about the
Properties of Multiplication?
It helps you solve problems without
working them out.
It helps with mental math.
It makes understanding math easier.
Commutative Property
Video
The order of the numbers doesn’t
change the result (answer to the
problem)
pXq=qXp
Example: 2 x 3 = 3 x 2
Commutative Property
9X3=3Xw
56 X p = 11 X 56
qX8=8X4
5X9=rX5
The answers are on the next slide.
Commutative Property
9X3=3X9
56 X 11 = 11 X 56
4X8=8X4
5X9=9X5
Associative Property
Video
The grouping of the factors doesn’t
change the answer.
(p X q) X r = p X (q X r)
Example: (3 x 4) x 5 = 3 x (4 x 5)
Associative Property
3 X (4 X 2) = (n X 4) X 2
4 X (p X 7) = (4 X 1) X 7
5 X (7 X 2) = (5 X 7) X n
(2 X z) X 5 = 2 X (8 X 5)
Associative Property
3 X (4 X 2) = (3 X 4) X 2
4 X (1 X 7) = (4 X 1) X 7
5 X (7 X 2) = (5 X 7) X 2
(2 X 8) X 5 = 2 X (8 X 5)
Identity Property
Any number multiplied by 1 will give
you the original number.
23,487 X 1 = 23,487
Identity Property
234 X 1 = z
q X 2,567 = 2,567
98,765 X d = 98,765
Answers are on the next slide.
Identity Property
234 X 1 = 234
1 X 2,567 = 2,567
98,765 X 1 = 98,765
Zero Property
When any number is multiplied with
zero, the answer is zero.
98,756,432 X 0 = 0
Zero Property
7,547,598,375 X c = 0
758,375,937 X 0 = b
z X 75,879,705 = 0
Distributive Property
Video
The distributive property lets you
multiply a sum or difference by
multiplying each addend separately
and then add the products.
23 X 4 = (20 X 4) + (3 X 4)
9 X (20 - 3) = (9 X 20) – (9 X 3)
8 X (40 + 5) = (8 X 40) + (8 X 5)
8 X 45 = (8 X 40) + (8 X 5)
Distributive Property
4 X 509 = (4 X 500) + (4 X m)
6 X 310 = (6 X n) + (6 X 10)
s X 205 = (5 X 200) + (5 X 5)
195 X 5 = (200 X 5) – (5 X t)
The answers are on the next slide.
Distributive Property
4 X 509 = (4 X 500) + (4 X 9)
6 X 310 = (6 X 300) + (6 X 10)
5 X 205 = (5 X 200) + (5 X 5)
195 X 5 = (200 X 5) – (5 X 5)
Test Yourself
Create a 6 tab brochure. On the cover write My
Multiplication Properties. Label each page of the brochure
with the properties. Read the problems below and write
then under what property they are an example of. Solve
the equation for the letter.
10. (2 X z) X 5 = 2 X (8 X 5)
1. 9 X 3 = 3 X w
11. q X 2,567 = 2,567
2. 3 X (4 X 2 ) = (n X 4) X 2
12. 12. 195 X 5 = (200 X 5) – (5 X t)
3. 234 X 1 = z
13. z X 75,879,705 = 0
4. 56 X p = 11 X 56
14. 98,765 X d = 98,765
5. 7,547,598,375 X c = 0
15. 5 X 9 = r X 5
6. q X 8 = 8 X 4
16. s X 205 = (5 X 200) + (5 X 5)
7. 5 X (7 X 2) = (5 X 7) X n
8. 4 X 509 = (4 X 500) + (4 X m) 17. 4 X (p X 7) = (4 X 1) X 7
9. 6 X 310 = (6 X n) + (6 X 10) 18. 758,375,937 X 0 = b
Test Yourself Answers
1. 9 X 3 = 3 X 9 Commutative
2. 3 X (4 X 2) = (3 X 4) X 2
3.
4.
5.
6.
7.
8.
9.
10. (2 X 8) X 5 = 2 X (8 X 5)
Associative
Associative
11. 1 X 2,567 = 2,567 Identity
234 X 1 = 234 Identity
12. 195 X 5 = (200 X 5) – (5 X 5)
Distributive
56 X 11 = 11 X 56 Commutative
13. 0 X 75,879,705 = 0 Zero
7,547,598,375 X 0 = 0 Zero
14. 98,765 X 1 = 98,765 Identity
4 X 8 = 8 X 4 Commutative
15. 5 X 9 = 9 X 5 Commutative
5 X (7 X 2) = (5 X 7) X 2
Associative
16. 5 X 205 = (5 X 200) + (5 X 5)
Distributive
4 X 509 = (4 X 500) + (4 X 9)
Distributive
17. 4 X (1 X 7) = (4 X 1) X 7
Associative
6 X 310 = (6 X 300) + (6 X 10)
Distributive
18. 758,375,937 X 0 = 0 Zero
How did you do?
18
17
16
14
12
correct
correct
- 15 correct
- 13 correct
– 0 correct
Excellent
Very Good
Good
Passing
You need more practice.
Doubling and Halving Lesson
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
- I can use my knowledge of doubling and halving factors to solve multiplication problems that go beyond 2-12’s facts.
EQ: How might doubling or halving help you solve multiplication problems?
Teacher Input:
Follow PPT
Independent:
See Independent work in PPT.
Homework:
Teacher-created worksheet.
Doubling/Halving
Objectives:
I can understand the relationship among skip counting, counting repeated addition, and
multiplication.
I can understand that doubling (or halving) one factor in a multiplication expression doubles (or
halves) the product.
S
Review
S Do not forget to do the spiral review!
The following equations demonstrate which properties?
23 x 8 = (20 x 8) + (3 x 8)
921 x p = 921
(3 x 4) x 5 = p x (4 x 5)
Note Taking
S We are going to use a thinking map to take notes. Set up
your right side like this:
Doubling
Tripling
Halving
Beyond
Problem 1
Ms. Watson owns a peanut shop. She was making bags that
each held 4 peanuts. In order to fill up 30 bags, she used
120 peanuts.
That next day she was filling bags that held 8 peanuts. How
many peanuts did she use to fill up 30 bags?
Write out the equation for each paragraph:
What do you notice?
Doubling
We talked about this concept briefly, but we can extend beyond
doubling, so pay attention…
The two statements are represented with the following
equations:
30 x 4 = 120
30 x 8 = ___
Notice that only one of the factors doubled from 4 to 8. Any
time you notice that just one factor is doubled, we
automatically know that the product is also doubled.
To understand why this works, let’s look at how it would be
solved with repeated addition…
Doubling
30 x 4 can be solved using repeated addition: (technically I
should use 30 groups of 4… 4 + 4 + 4… blah blah, but
remember, commutative property lets me move the factors
around!)
So here it is…
30 + 30 + 30 + 30 = 120
That’s simple right? Well, let’s compare 30 x 4 to 30 x 8
30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 = 240
120
+
120
= 240
Guided Practice Part 1
With that in mind, let’s solve this next problem:
Kimmy Jimmel had 12 packs of pencils. Each pack came with
7 pencils. How many pencils did Kimmy Jimmel have?
Lavid Detterman had 24 packs of pencils. Each pack came
with 7 pencils. How many pencils did Lavid Detterman
have?
Halving and Guided Practice
Part 2
The doubling concept works backwards too! Using the equations
from the last problem, notice what happens to the product when
only one factor is halved.
24 x 7 = 168
12 x 7 = 84
When only one factor is halved, the product is halved too!
So with that in mind, let’s solve this problem together:
Hana had 10 pony tails. Each pony tail had 56 bows. How many
bows does Hana have?
Mr. Hiroshige had 5 pony tails. Each pony tail had 56 bows. How
many bows does Mr. Hiroshige have?
*Going Beyond (Tripling)
Since we are masters at doubling and halving, it is worth noting that
tripling, quadrupling, and beyond works as well. It makes sense
when we look at how these problems are solved with repeated
addition:
Again…
30 + 30 + 30 + 30 = 120
That’s simple right? Well, let’s compare 30 x 4 to 30 x 12
30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 = 360
120
+
120
+
120
= 360
Independent (skip to the next
one if you want a tripling
problem as well)
Mr. Hiroshige’s class was counting by 11s. The 20th person said 220
(11 x 20 = 220). Mr. Hiroshige laughed at the simplicity of
counting by 11s. He snickered and thought, “Well, if these
students can count by 11s, and they know doubling well, I am
going give them a super hard challenge.”
Then, Mr. Hiroshige asked a question that seemed to stop time and
tear the fabric of space:
If we counted by 22s, what would the 20th person say? (22 x 20 = ?)
What about 44s?
Independent Challenge Problem
Mr. Hiroshige’s class was counting by 11s. The 20th person said 220
(11 x 20 = 220). Mr. Hiroshige laughed at the simplicity of
counting by 11s. He snickered and thought, “Well, if these
students can count by 11s, and they know doubling well, I am
going give them a super hard challenge.”
Then, Mr. Hiroshige asked a question that seemed to stop time and
tear the fabric of space:
If we counted by 22s, what would the 20th person say? (22 x 20 = ?)
If we counted by 33s, what would the 20th person say? (33 x 20 = ?)
Multiplication Combinations (Applying the Distributive Property) Lesson
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
- I can utilize the distributive property to solve multiplication problems that go beyond 2-12’s facts.
EQ: How might the distributive property help you solve difficult multiplication problems?
Teacher Input:
Follow PPT
Independent:
See Independent work in PPT.
Homework:
Teacher-created worksheet.
Combinations
(Distributive Property)
Objectives:
I can use the distributive property to solve multiplication problems that go beyond
the 2-12’s facts.
S
Review
S Do not forget to do the spiral review!
Quickly Solve:
1.
7 x 8 = _____
2.
7 x 16 = _____
3.
14 x 8 = _____
4.
7 x 4 = _____
Note Taking
S We are going to use a circle map to take notes. Set up your
right side like this:
Problem 1
Mr. Wackyshige owns a pet store. He had large cages that held
19 kittens. 7 of these cages were filled. How many kittens
does he have?
What equation can we use?
Would you believe me if I said you could solve this problem in
your head in less than 3 seconds? Here is how…
Combinations
We talked about the distributive property. This property is incredibly useful in
solving difficult multiplication problems because it allows us to break down
one factor into more manageable (smaller) pieces. Side note, it is possible to
break down both factors… but it’s not as easy as you might think… so don’t
do that until you are taught how, or you’ll get a lot of problems wrong on
tests!
The previous word problem could be solved using 7 x 19. Since we are not
familiar with the 19’s multiplication facts, we can use the distributive property
to break down 19 into smaller, recognizable parts.
Let’s break 19 down into a 10 and 9.
Solve: So now we can multiply… 7 x 10 = _____ and 7 x 9 = _____
Now that we have those products, we need to put them back together by adding:
Understanding Why it Works
Let’s take a look at why we can break a factor apart. Remember, multiplication
is the same as repeated addition…
Let’s write out 19 x 7 using repeated addition: (Side note, you may have noticed
that I flipped the factors… what property let me do that!?)
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 133
10 x 7
9x7
(10 x 7) + (9 x 7) =
70 + 63 = 133
Guided Practice
With that in mind, let’s solve these problems:
1.
17 x 6 =
2.
Garret had 15 jars of coins. Each jar held 8 dollars. How
many dollars did Garret have?
Independent Challenge Problem
You can create a foldable, or just use the left side. Solve the
following problems using the distributive property. You
MUST write out the equation correctly:
1.
13 x 9
2.
6 x 15
3.
4 x 18
4.
Peypey had 17 dolls. Each doll had 5 freckles. How many
freckles did the dolls have altogether?
Multiplication Quiz
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
Math: 5: 3.1 Arranging Chairs
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-I can use arrays to model multiplication situations
-I can use arrays to find factors of 2-digit numbers up to 50.
EQ: How can I use arrays to find factors?
-What are arrays?
-What do arrays represent?
Teacher Input:
1. Hand out 12 cubes to each student. Explain that the cubes represent chairs, and that they need to arrange the chairs so that there are the
same number of chairs in every row with none left over. Guided Questions: How many different ways could you do this? How many chairs
would be in each row? How many rows would there be?
2. Hand out 12 cubes and allow the students time to come up with as many different arrangements as possible. (Guided Questions: How many
different ways could you do this? How many chairs would be in each row? How many rows would there be?)
3. Discuss two possible arrangements with the class. Model using the words dimension and by.
4. Using chart paper, show all of the possible arrangements. Label them and include the equations.
Independent:
-Have the students use cubes to find all the possible arrays for the number x (determined by individual students’ ability).
-Have the students draw the arrays using Grid Paper, cut the arrays out, and glue them on colored paper. Have them title the paper “Ways to
Arrange x Chairs,” label the dimensions of each array, and list the dimensions at the bottom of the paper (See Unit 5 Investigations book, pg. 84
for an example.)
-While they work, make the connection between pairs of dimensions and factors.
Homework:
Teacher-generated
Objectives:
I can use arrays to model multiplication.
I can use arrays to find factors of 2-digit numbers up to 50.
EQ: What do arrays represent?
How can I use arrays to find factors?





Hand out 12 cubes to each student.
The cubes represent chairs. You will need to
arrange the chairs so that there are the same
number of chairs in every row with none left
over.
How many chairs are in each row?
How many rows are there?
How many different ways could you do this?

Let’s take a look at two different
arrangements (In math we call these
arrangements arrays!). They are drawn as a
rectangle. The dimensions of this rectangle
are 2 by 6 since there are 2 rows with 6
chairs in each row.
6
2

Here is an array of 3 rows with 4 chairs in
each row. What are the dimensions of this
rectangle?
4
3

How is this related to multiplication?

Let’s draw all the different possible arrangements on chart
paper!

These arrangements will represent the different ways to
make 12:
12 = 1 x 12
12 = 12 x 1
12 = 2 x 6
12 = 6 x 2
12 = 3 x 4
12 = 4 x 3
You might notice that the different dimensions of the
arrangements correspond to the different factors that
make 12!

Use cubes to find all the possible arrays for one of these
numbers: 18, 24, 32

For each arrangement you find, neatly draw and color the
array on blank paper.

When you finish drawing and coloring all possible arrays,
grab a colored paper and title it, “Ways to Arrange (#)
Chairs.”

Cut out the arrays and glue them on the colored paper. Be
sure to label the dimensions of each array.

List all of the dimensions at the bottom of the paper (e.g.
12 = 1 x 12, 12 = 12 x 1)
Math: 5: 3.2 Investigating Arrays
Materials:
-Notes
-Power Point
-Array Cards (You will need to make these unless you already have them pre-made in your math kit)
-Optional - Materials to play prime, composite, and square enrichment game
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-I can use arrays to identify characteristics of numbers, including prime and square numbers.
-I can use arrays to find factors of 2 digit numbers up to 50
EQ:
What is an array?
What are prime and square numbers?
How do I use arrays to find factors?
Optional: What are composite numbers?
Teacher Input:
-Introduce this lesson using the Power Point. Make sure to pass out student notes that will go along with the power point.
-Remind students that items grouped in equal rows to form rectangles are called arrays.
-Ask students what they noticed as they looked at the arrays that people made during the Arranging Chairs lesson for their numbers?
-As students share their observations, introduce the concept of square numbers by asking the following questions:
1. What numbers made up square arrays?
2. What else did you notice about these numbers?
3. What other numbers do you think would make square arrays?
-Now introduce prime numbers by asking some of the following questions:
1. What kind of arrays does the number 17 make? (1 by 17 and 17 by 1)
2. What are the factors of 19? What types of arrays can you make from 19?
3. What other numbers make only 2 arrays?
Let students know that numbers with only 2 factors, the number itself and one are called prime numbers.
-Now ask students about numbers with many arrays. Optional: You can introduce these numbers as composite numbers. You may ask some of the following questions:
*Did the largest numbers have the most arrays?
*What if we look at 24 and 25, which one has more arrays?
*What do you think would happen if we tried some larger numbers such as 56, 99, or 100? Do you think there are large numbers that are prime numbers? Which ones?
Independent Practice:
-Students will make and label their own array cards (Pg. M17-M24) if you don’t have the ones in your math kit.
-See directions on pg. M25. Students will label the dimensions on the front and write the answer on the back.
Enrichment/Left Side:
If your array cards are already labeled you can play the prime, square, and composite game. Students will roll 2 dice to create a 2 digit number. They will then use graph paper to try and list all the factors of that
numbers. They will determine if that number is prime, composite, or square. They will create a 3 tab foldable and on the outside write prime, composite, and square. When they solve it they will write it under that
column on the left side of their interactive notebook. Make sure to tell students that they must show their work on the graph paper. If you don’t want to introduce composite to your students just have them write
numbers with many factors.
Assessment:
Left side of interactive notebook
Homework:Teacher created
3.2 Investigating
Arrays
Objectives:
-I can use arrays to identify characteristics of
numbers, including prime and square numbers.
-I can use arrays to find factors of 2 digit
numbers up to 50
What is an array?
Discovery Education Array Video
Arrays
• Are an arrangement of items or objects in
rows and columns.
• Examples:
• Can you think of more?
Draw as many arrays as you can for each of the following.
What do you notice about the shapes?
Which are similar and which are different?
16
12
11
25
You should have noticed…
• Some numbers made square arrays and
others did not.
Brainstorm with a partner…
• What numbers make square arrays?
• What else did you notice about these
numbers?
• What other numbers do you think would
make square arrays?
There are called Square
Numbers
• Square numbers are numbers that have
square arrays or numbers that you can
multiply two of the same factors.
• Example: 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16,
5 x 5 = 25
You should have noticed…
• Some numbers only have 2 arrays that
you can draw. For example for 11 you
can only draw a 1 by 11 array and an 11
by 1 array.
• What other numbers make only 2
arrays?
These are called Prime Numbers
• Prime numbers are numbers that have
only 2 arrays or 2 factors, which are 1
and itself.
• Examples: 7 (1x7), 5 (1x5), 13 (1x13)
You should have noticed…
• Do the largest numbers have the most
arrays? For example take a look at 91
and 16.
• Are there large prime numbers?
----------------------------------------------• Some numbers have many arrays that do
not have square arrays.
These are called composite
numbers
• Composite numbers are numbers that
have more than 2 arrays and no square
arrays.
• Examples:
12 (1x12, 3x4, 2x6)
18 (1x18, 2x9, 3x6)
Game Time:
Prime, Composite, or Square Dice Roll
• Directions: Students will work with a partner. They will
roll 2 die to create a 2 digit number. They can choose the
lower or higher number that the die make. They will then
determine if that number is prime, composite, or square.
To prove they are correct, they will use graph paper to
draw all of the arrays possible for the number. Students
should also create a 3 tab foldable and label prime,
composite, and square on the front. They will list each
number they roll inside the correct tab. Tell students to
be sure to write all factors next to that number in their
foldable. They do not have to draw the arrays again in
their foldable only on the graph paper. Once time is up
have students add all of the numbers together in their
foldable. The student with the highest total number will
win!
Math 5: 3.3 - Finding the number of squares in an array
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.MD.7.a, 3.MD.7.b
SFO:
- I can use arrays to find a product by skip counting.
- I can break an array into parts to find the product represented by the array.
-I can identify and learn multiplication combinations.
EQ: How can arrays help me with multiplication?
Teacher Input:
1. Display a 4 x 6 array (ppt).
2. Have students demonstrate their strategies in finding the number of squares in the array.
3. Log students’ strategies on chart paper and keep it posted to reference.
4. Explain that finding the total number of squares is an array is the same as finding the product.
5. Display a 6 x 13 array.
6. Ask students to demonstrate how they could use doubles or combination strategies to determine the number of squares in the array.
7. If needed, demonstrate how to use doubles (3 x 13 + 3 x 13) or a combination (10 x 6 + 3 x 6) to find the product of the 6 x 13 array.
Independent:
1. Display 3 arrays.
2. Have students make a 3-tab foldable (left side).
3. On the first tab, have them draw each array.
4. On the inside left, have them write the name of the strategy they will use to find the product (skip counting, doubles, combinations).
5. On the inside right, have them represent their strategy with an equation and solve.
Homework:
Teacher-generated
Objectives:
I can use arrays to find a product by skip counting.
I can break an array into parts to find the product represented by the
array.
I can identify and learn multiplication combinations.
EQ: How can arrays help me with multiplication?


How many squares are there in this array?
Let’s write down the strategies you used on
chart paper. (Counting by 1s, skip counting
by a dimension)


When you find the total number of squares in
an array, you are finding the product.
Who has a different way of finding the
product of an array that does not involve
counting the squares by ones or skip
counting?
6
4

Let’s see if we can use our knowledge of doubles
and combinations to determine the number of
squares in this array.
13
6

How many squares are there? How did you figure
it out?
Some of you knew that 3 x 13 = 39. With
that knowledge, you figured out:
6 x 13 = (3 x 13) + (3 x 13) = 39 + 39 =

13
3
3
Some of you figured out that it was easier to
break 13 into smaller parts to multiply:
6 x 13 = (6 x 10) + (6 x 3) = 60 + 18 =

10
3
6
Bonus Question: What property did we use to
simplify the multiplication problem?





Create a 3-tab foldable.
On the outside of each tab, draw each of the arrays using the
dimensions below. On the inside left, write the name of the strategy
you are using to find the # of squares in the array (doubles, triples,
combination). On the inside right, represent the strategy with an
equation and solve.
Array #1: 7 x 13
Array #2: 4 x 17
Array #3: 8 x 15
Math 5: 3.4 - Array Games Part 1 & Mini-Assessment
Materials:
-1 copy of Factor Pairs directions pg. M26 per teacher
-Each student will need to rip out pg. 31 from Unit 5 from their student activity books
-Set of array cards (already cut and labeled from previous lessons)
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.MD.7.a, 3.MD.7.b
SFO:
-I can use arrays to find a product by skip counting by one of its dimensions
-I can identify and learn multiplication combinations not yet known
EQ:
-What are some strategies I can use to solve multiplication combinations that are unknown?
Teacher Input:
-The array game Factor Pairs is designed to help students learn their multiplication combinations with products up to 50. Introduce the game to the class.
-Students will need to rip out pg. Unit 5 pg.31 from their math workbooks called Combinations ‘I Know and Combinations I am Working On. Students will work by themselves
or with a partner. You will find the directions to this game also on pg. M26.
They will also need a set of array cards
Game Directions:
1. Spread out all of the Array Cards in front of you with the dimensions side up
2. Choose an array card and put your finger on it. Say the number of squares in the array if you know it. Do not pick up the card until you say the answer. If you do not know
it, use a strategy to figure it out. Find a way to figure out how many squares there are without counting every single one.
3. Turn the card over and check your answer. If your answer is correct, keep the card.
4. If you are playing with a partner, take turns choosing cards and finding the number of squares in each array. Play until you have picked up all the cards.
5. While you are playing make a list for yourself of combinations that I know or knew right away and combinations I didn’t know or had to take a minute or few seconds to
figure it out.
Enrichment:
Once students play the game one time. Challenge them to try putting 2 array cards together to figure out the total number of squares. They could even put 3 cards together
if they complete putting 2 together.
Allow 15 minutes for students to take the array mini-assessment at the end of math class
Homework: Teacher Created
3.4
Array Games
Part 1
Objectives:
1. Using arrays to find a product by skip counting
by one of its dimensions
2. Identifying and learning multiplication
combinations not yet known
3. Using known multiplication combination to
determine the product of more difficult
combinations
You will want
to tear this
page out of
your student
activity book!
3.5 A Using what you know SKIP According to CMS Math Wiki
3.5B Learning Multiplication Combinations from Common Core Book
Materials:
-Power Point
-Multiplication Cards
-Optional Dice and loose leaf paper for enrichment game
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.MD.7.a, 3.MD.7.b
SFO:
-I can identify and learn multiplication combinations not yet known
-I can use known multiplication combinations to determine more difficult ones
-I can use arrays and rectangles made from square tiles to illustrate the distributive property.
EQ:
-How do I use simple combinations to solve more difficult combinations?
Teacher Input:
-Explain to students that they can solve more difficult combinations by solving simpler combinations.
-Begin this lesson by looking closely at one or two of the harder combinations that your students seem to find difficult (ie. 12 x 8, 9 x 7)
-Begin by solving the problem 8 x 9/9 x 8. Remind students that this is the commutative property and we will get the same answer. Show the students that you could break
apart the 8 into two groups of 4 and instead of doing 8 x 9 do 4 x 9 and 4 x 9. Show this visually to the students and explain to them that these smaller combinations
combined will equal the larger combinations so they must add them together. Make the connection to students of when we broke down numbers to add and subtract.
-Show students that you could also instead of multiplying 9 x 8 you could break down the 9 into three groups of 3 and do 3x8, 3x8, and 3x8. These smaller combinations equal
the larger combinations so I would have to add the products together. Finally, show students that you could also do 8x8 and 1x8 to equal 9x8.
-Pass out math multiplication cards to students. Have them work in groups of 2 or 3 students. Have students write the answers on the back and also write clues on the front
of other combinations (easier ones) that they could use to solve the problem. Have students do this for all the multiplication cards and then take turns quizzing each other to
gain fluency with their math facts.
Enrichment:
-Once students show fluency with their math facts 1-12 give them 2 dice. Have them roll the dice 2 times to get a 2 digit number and once to get a 1 digit number. They will
try multiplying a 1 digit by a 2 digit and using smaller combinations that they know to solve the multiplication problems. For example if they are solving 45 x 3 they might do
45x1 and 45x2 and then add them together or they might do 25x3 and 20x3. Both of these will give students the same answer. Give students graph paper and loose leaf lined
paper to show their work.
Assessment: Exit Ticket using Socrative
Homework: None over the weekend!
3.5B Learning Multiplication
Combinations
Objectives
• I can identify and learn multiplication
combinations not yet known
• I can use known multiplication
combinations to determine more
difficult ones
• I can use arrays and rectangles made
from square tiles to illustrate the
distributive property.
What multiplication combinations are
most difficult for you to solve?
THINK: Is there a way I can solve more
difficult combinations by using other
combinations with the same factors?
Example: 12 x 9
What other combinations with 12 or
9 as a factor could I use to help me
figure out the product of 12 x 9?
Let’s Brainstorm and list ideas…
12 x 9 =
12 x 9
• I could do 12 x 10 = 120 and subtract 12
• I could do 12 x 5 = 60 and 12 x 4 = 48 then
add 60 plus 48
• I could do 10 x 9 = 90 and 2 x 9 = 18 then
add 90 plus 18
• I could do 11 x 9 = 99 and 1 x 9 = 9 then
add 99 plus 9
Try to solve another combination that is
difficult for you by using more simple
combinations. Choose a combination, work
with a partner and solve.
Be ready to share!!!
Enrichment
• Materials: 2 dice, lined paper, pencil
• If you finish your multiplication flash cards, have
practiced, and you feel like you have mastered all of them
fluently have your teacher check them and you could be
ready for an enrichment game.
Directions:
• Roll the dice 2 times to get a 2 digit number and one time
to get a 1 digit number. You will multiply a 1 digit by a 2
digit number using smaller combinations that you know to
solve the multiplication problems. For example if you are
solving 42 x 4 you might do 41 x 2 and 42 x 2 and then
add them together. If this is too difficult for you then
multiply the dice to make two 1 digit numbers. Show your
work on the game recording sheet.
Math: 5: 3.6 Array Games Part 2
CCSS:
.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.MD.7.a, 3.MD.7.b
SFO:
- I will break an array into parts to find the product represented by the array.
- I will identify and learn multiplication combinations not yet known.
- I will use known multiplication combinations to determine the product of more difficult combinations.
EQ: How can you determine which of two arrays has more squares?
Teacher Input:
1. Display a 6x6 and 5x7 array.
2. Have the students determine which is bigger and explain their strategy.
3. Optional: Display a 6x13 and 7x11 array.
4. Have the students determine which is bigger and explain their strategy.
5. Explain the rules to the Count and Compare game (in ppt).
Independent:
1. Have students play the Count and Compare game.
2. While students are playing the game, rotate around the room and observe: With which multiplication combinations are students developing fluency? What strategies are
students using to determine the bigger array when two arrays appear close in size? Are students recognizing that arrays that have different shapes can have the same
product?
Homework:
Dreambox
Optional: Teacher-generated comparing arrays sheet.
3.6
Array Games
Part 2
Objectives:
1. I will break an array into parts to find the
product represented by the array.
2. I will identify and learn multiplication
combinations not yet known.
3. I will use known multiplication combinations to
determine the product of more difficult
combinations.
Which array has more squares?
6
6
7
5
Explain your thinking!
Super Challenge (can skip) Which array has more squares?
13
11
6
7
Explain your thinking!
Count and Compare Game (The
War card game)
1.
Deal the Array Cards so that all players have the same number of cards. Set
aside any cards that are left over.
2.
Players place their cards in a stack in front of them with the dimensions side
up.
3.
Each player places the top card from his or her stack, dimension side up, in
the middle of the table.
4.
Players decide whose card has the largest array by skip counting, using a
known multiplication combination, or some other strategy.
5.
The player with the largest array takes all the cards from the round and places
them on the bottom of his or her stack. If all arrays in the round have the
same product, players will place a second card on top of the first card in the
middle of the table. The players with the largest array of all the second cards
takes all the cards in the middle.
When one player runs out of cards, the players with the most cards wins.
6.
Unit 5 Lesson 4.1 Solving division problems
Materials:
-Power Point
-Pg. 39-40 from student activity book
-Things that come in groups posters from multiplication lessons
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-I can understand division as the splitting of a quantity into equal groups
-I can use the inverse relationship between multiplication and division to solve problems
Teacher Input:
-Tell students that you are going to choose something from your list of things that come in groups to make a problem for them to solve. Tell them it is going to be different
than the problems they have been solving.
-Read the following problem aloud: Frogs usually have 4 legs. In a pond, there are 16 legs altogether. How many frogs are there in the pond?
-Tell students to work with a partner to solve the problem. Have them think about what is the same and what is different between this one and the ones they’ve been
writing.
-Give them 2-4 minutes and then share strategies aloud.
-Have students solve the 4 division problems from pg. 39 & 40 of the student activity book. They may work with a partner. Encourage them to share ideas and strategies as
they work.
-After giving the students some time to work come back together as a class and go over as a class. After going over the first problem make sure to tell the class that they are
solving division problems. Also, be sure to share different strategies on how they solved their division problems.
Assessment: Give students a division problem to complete and have them answer on an index card or post it note and hand in.
Homework: Teacher Created
4.1
Solving Division Problems
Objectives:
•Understanding division as the splitting of a quantity into equal groups
•Using the inverse relationship between multiplication and division to solve problems
Read the problem below.
Remember the lists of things that come in groups we created. I have chosen an item from our list to create a
word problem. What is different about this word problem and the ones we have been creating?
Frogs usually have four legs. In a pond, there are 16
legs altogether. How many frogs are in the pond?
"Let's break it down and give each member of our
group the same amount of blocks. But how many
should we give them?"
"Wow, our tower has 25 total blocks in it!"
"Well we have 5 members in our group..."
"So, each member gets 5 blocks...
because 25 blocks divided by 5
people equals 5 blocks!"
We just did division! What is
division??
To divide means to separate into
equal groups.
25 blocks divided by 5 people equals 5 blocks for
each person.
BrainPOP Division Video
25
5
5
Divide 9 balloons among 3 children.
drag the balloons.
Click and
Each child has 3 balloons. So 9 balloons divided by 3
children equals 3 balloons each. This is DIVISION!
9
3
3
Let's practice some more division...
Divide these ants into 3 equal groups. Click and drag the ants into
the circles below.
Now write a number sentence that represents the ants in
the circles.
divided by
equals
12 ants divided by 3 groups equals 4 ants in
each group.
12
3
4
*Move the green rectangle to check your number sentence.
Easy steps for division...
1. Figure out how many in all.
2. Figure out how many equal groups you need.
3. Divide the total number by how many equal
groups you need.
12 ants in all
3 equal groups
12
3
4
Write a number sentence below to go with the
picture.
___ ÷ 4 = ___
*Move the green rectangle to check your answer.
16 ÷ 4 = 4
True or False:
When given 2 numbers and asked to divide one
of the numbers into the other, it doesn't matter
which number goes first.
*Move red square to reveal answer.
FALSE! The bigger number always needs to go first so
that the smaller number can be divided into it.
Work with a partner to solve!
Be prepared to share strategies you used!
There are 24 chairs in the classroom. The teacher puts them in groups
of 6. How many groups of desks are there altogether?
Work with a partner to solve!
Be prepared to share strategies you used!
Ms. Smith brought in 32 toy robots to school. She wants to divide
them equally among her 16 students. How many would each
student receive?
Interactive Notebook Left Side: Solve the following problem and illustrate by drawing pictures in
your notebook. Write the division equation when you're finished!
Mrs. Shirley and her family were going on a trip to Washington DC. There were a total of 28 people in
her family. They were taking 7 cars and wanted the same number of people in each car. How many
people would have to ride in each car?
Complete Unit 5 pg. 39-40 out of your student activity book with a partner when you finish!
Math: 5: 4.2 – Multiply or Divide
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
- I will use the relationship between multiplication and division to solve problems.
- I will use multiplication combinations to solve division problems.
- I will use and understand division notation.
EQ: How is multiplication and division related?
Teacher Input:
1. Display word problem #1 from the student book on page 42 (4 x 6, ppt)
2. Have students describe the problem and explain what they are trying to find out.
3. Explain that the problem identifies the number of groups and number of items in each group.
4. Give the students 5-10 minutes to complete all of the problems on page 42 and 43 of the student book: Remind them to read carefully to determine if they need to figure
out the # of group, the # of items in each group, or the total # of items in all groups.
5. Once the students complete pages 42 and 43, display problems 2 and 3 on the board.
6. Have the students determine the similarities and differences between problems 2 and 3. Have them state the known information in both problems.
7. Have students identify that problem 2 is a division problem because we were told the total number, but needed to find the # of groups. Problem 3 is a multiplication
problem because we were told the # of groups and the # of items in each group, but needed to find the total.
8. Display and explain the division notation for problem 2, and facilitate a discussion on how students solved it.
9. Display the multiplication and division chart (you may want to do this on chart paper and display it in your classroom), and have the students help you fill in the known
information for problem 2. Then fill in the unknown information.
10. Do the same with the information from problem 3.
Independent:
Have students complete page 44 of the student book while filling out the multiplication and division chart (left side).
Homework:
Teacher generated.
Objective:
I will use the relationship between multiplication and division
to solve problems.
I will use multiplication combinations to solve division
problems.
I will use and understand division notation.
EQ: How is multiplication and division related?
Problem 1
1. A robot has 4 hands. Each hand has 6 fingers. How many fingers does
the robot have altogether?
Describe this problem. What do you know and what are you trying to find
out?
Well, the problem identifies the number of groups and the number
of items in each group. So all we need to figure out is how many
What I noticed…
there are altogether. THIS IS A MULTIPLICATION PROBLEM!
Work in Pairs
 Find a partner and complete pages 42 and 43 in the student
book.
 Be sure to pay close attention to the information that is
given and what you need to find out!
 You have 5-10 minutes!
Problems 2 and 3
2. We made 20 muffins for the bake sale. We put the muffins in bags to sell. We
put 4 muffins in each bag. How many bags of muffins did we have to sell?
3. We bought 5 packs of yogurt cups. Each pack had 4 yogurt cups. How many
yogurt cups did we buy?
What is the known information for each of these problems? What
do we need to find for each problem?
Number 3 is a multiplication problem. Multiplication problems tell
you the number of groups and the number of items in each
group, but do not tell you the total number of items in all
groups.
Number 2 is a division problem. Division problems tell you the total
number of items in all groups, but leave out the number of
groups OR the number of items in each group.
Division Notation
2. We made 20 muffins for the bake sale. We put the muffins in bags to
sell. We put 4 muffins in each bag. How many bags of muffins did we
have to sell?
Here are two common ways you may see division written out:
Here are some ways to solve the problem…
How did you solve this problem?
Count by 4 until you reach 20, Start with 20 and keep making groups
of 4 until you run out of muffins, Already know that 5 x 4 = 20.
Multiplication and Division
Chart
2. We made 20 muffins for the bake sale. We put the muffins in bags to sell.
We put 4 muffins in each bag. How many bags of muffins did we have to sell?
3. We bought 5 packs of yogurt cups. Each pack had 4 yogurt cups. How many
yogurt cups did we buy?
Looking at these problems, let’s fill out this chart with the known information so
that we can easily see which problem is multiplication and division:
# of Groups
# in each Group
Product
Equation
Guided Practice
Fill out the Multiplication and Division chart for the following problems.
1. Gael bought 54 pieces of chicken altogether. There were 6 pieces of chicken
in each bag that he bought. How many bags of chicken did Gael buy?
2. April has 12 boxes of candy. Each box has 7 pieces of candy. How many pieces
of candy does April have altogether?
# of Groups
# in each Group
Product
Equation
Independent Work
• Complete page 44 in the student book.
• As you read each problem, fill out the information in
the multiplication and division chart (left side).
Make sure your equation reflects whether the
problem is a multiplication or division problem!
Unit 5 Lesson 4.3 Writing Story Problems
Materials:
-Power Point
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-I can understand division as the splitting of a quantity into equal groups
-I can write and solve multiplication problems in context
-I can write and solve division problems in context
-I can understand multiplication and division notation
Teacher Input:
-Explain that over the next few days each student will write two related story problems. One will be about division and one will be about multiplication. All of the problems
will be put together into a classroom Multiplication/Division Book.
-Display the following problems on board:
6x3 and
18 divided by 3
-Have students create story problems for both of these with a partner. After a few minutes call the class back together. Share 2 story problems for each example. Check
students’ understanding by making sure the division problems begin with the quantity 18 and the multiplication combine 3 groups of 6.
-For the rest of the math time students will write and solve problems for the class book. Tell students to write a story and draw a picture for it on the front of their paper. Tell
students to solve the problem and write the answer on the back of their paper.
-Students may use any numbers they would like. Students that have mastered their 1-12 facts may choose to do more challenging problems by doing 1 digit by 2 digits.
-When students finish have them switch their problems with a partner and try to solve each others.
-You could put all students together in a book or hang in your room or the hallway.
Assessment: Student story problems
Homework: Have students create 2 multiplication and 2 division problems and then solve them. Use lined paper.
4.3 Writing Story Problems
Objective(s):
-I can understand division as the splitting of a
quantity into equal groups.
-I can write and solve multiplication and division
problems in context.
--I can understand multiplication and division notation.
Class Multiplication/Division Book
Over the next few days each student will
write two related story problems. One
that is about a division situation and one
that is about a multiplication situation. All
of the problems will be put together into
a class book.
Work with a partner to come up with a
story problem for each equation.
6x3
18 ÷ 3
Problems for the Class Book
• Write a multiplication story and draw a picture for it on the
front of your paper (MUST BE NEAT AND COLORFUL).
• Solve the problem and write the answer ON THE BACK.
• On a new sheet of paper, write the related division story and
draw a picture for it on the front of your paper.
• Solve the problem and write the answer ON THE BACK.
• These problems must be related. E.g. The multiplication word
problem word problem may be 4 x 3. The division problem must
be either 12 divided by 3 or 12 divided by 4.
• Once you complete the 2 problems, you can move on to
dreambox. If the work is not thoughtfully completed, you will
have to do it over again.
Math: 5: 4.4 – Missing Factors
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9
SFO:
-- I will use the relationship between multiplication and division to solve problems.
- I will use multiplication combinations to solve division problems.
- I will use and understand division notation.
EQ: How are arrays related to division?
Teacher Input:
1. Display an array card with the dimension 4 and product 24.
2. Explain to the students that they will play a new array game called missing factors.
3. Have the students explain what information is provided on the array card, and solve for the missing dimension.
4. Explain that the missing dimension is also called the missing factor.
5. Go over strategies to finding the missing factor: building the array, skip counting, and using known multiplication combinations.
6. Display the game rules and demonstrate how to play
Independent:
-Have the students play the Missing Factors game.
Objective:
I will use the relationship between multiplication and division
to solve problems.
I will use multiplication combinations to solve division
problems.
I will use and understand division notation.
EQ: How are arrays related to division?
Missing Factors
• Today we will play a new array game. In this game, you place your Array
Cards in front of you with the product side facing up.
•What is the information that you know about this array?
4
24
•What is the missing dimension of this array?
•We call this missing dimension the missing factor.
Strategies
• In order to figure out the missing dimension, we can use a few strategies.
• Building the array: Since we know there are 4 rows, we can draw those in and then
draw in columns until we reach 24.
•Skip counting: We could just skip count by 4 up to 24 so see how many 4s are in 24.
•Use known combinations: We know that 4 x 3 = 12, so we can build on that knowledge to
figure out the missing factor.
4
• What equation(s) can we use for this problem? ____________________________
Missing Factors Game
1. Tear out the recording sheet in Unit 5 page 46 of the student book.
2. Spread out the Array Cards with the product side up.
3. When it is your turn, put your finger on a card. The card will have one
factor and the product. You must state the missing factor.
4. Turn the card over and check your answer. If you are correct, keep
the card. If you are wrong, place the card back on the table. For the
cards you collect, record the equation on your recording sheet.
5. When all the cards are collected, the player with the most cards wins.
Math 5: 4.5 Solving Multiplication and Division Problems
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.MD.7.a, 3.MD.7.B
SFO:
-I can use use multiplication combinations to solve division problems
-I can use the inverse relationship between multiplication and division to solve problems.
-I can use and understand multiplication and division notation.
Teacher Input:
-Begin the lesson by giving the students a story problem and asking them to determine whether it is multiplication or division and write an equation to solve the problem and
then solve it.
Problem 1: Six friends collected bottles and cans to bring to the redemption center. The cashier gave them $24 for all of the bottles and cans. The friends shared the money
equally. How much money did each friend receive?
Problem 2: Sarah bought a 48 pack of pencils to bring to school. She wanted to share the pencils equally among her friends. If she shared with 12 friends how many pencils
would each friend receive?
-Next give students multiplication and division equations and have them write a story problem to go with each. Use the problems 5x7, 7x3, 32/4, 36/6. Students may work
with partners.
-For independent practice have students create 2 multiplication and 2 division story problems on the left side of their math notebook.
-If students finish early have them play Dreambox or missing factors game
Assessment: Left side of interactive notebook
4.5 Solving Multiplication
and Division Problems
Objective(s):
-I can use multiplication combinations to solve division
problems
-I can use the inverse relationship between
multiplication and division to solve problems.
-I can use and understand multiplication and division
notation.
Solve this problem.
• Six friends collected bottles and cans
to bring to the redemption center. The
cashier gave them $24 for all of the
bottles and cans. The friends shared
the money equally. How much money did
each friend receive?
• Is it multiplication or division?
• How do you know?
Solve this problem.
• Sarah bought a 48 pack of pencils to
bring to school. She wanted to share
the pencils equally among her friends. If
she shared with 12 friends how many
pencils would each friend receive?
• Is it multiplication or division?
• How do you know?
Guided Practice
• Work with a partner. Create a story problem
for each of the following equations.
1.
5x7
2.
36 ÷ 6
Word Problem Match
• Hand out 1 index card per student.
• Assign half of the class with multiplication and half
with division.
• Students will work with their partner to create a
story problem based on the operation they were
assigned. They will write the word problem on one
index card without giving away the answer and the
equation to solve it on the other.
• Give students about 5 minutes to do this. When they
finish collect and mix up all the index cards.
• Pass them out to random students. When you say go,
students must get up and find their match. Once all
students have found their match go over all word
problems by having students read aloud to check for
correctness.
Independent Practice
• Option 1: Create a 4 tab foldable and write 2
multiplication and 2 division story problems.
• Challenge Option 2: Create a 4 tab foldable
and writ2 multiplication and 2 division story
problems using at least one 2 digit number.
Use the break apart strategy to help you.
• Challenge Option 3: Solve four of the 2 step
story problems on the next slide. Show your
work, solve the problem, and write the
equation.
2 Step Story Problems
1.
2.
3.
4.
Jerry was selling his old games. He started out with
forty-five but sold eighteen of them. He packed
the rest up putting nine games into each box. How
many boxes did he have to use?
A painter needed to paint 9 rooms in a building.
Each room takes 8 hours to paint. If he already
painted 5 rooms, how much longer will he take to
paint the rest?
Robin uploaded thirty-five pictures from her phone
and five from her camera to Facebook. If she
sorted the pictures into five different albums with
the same amount of pictures in each, how many
pictures were in each of the albums?
Sarah bought 6 packs of paper for $8.00 each. If
she gave the cashier a $100 bill, how much change
would she receive?
Math: 5:4.6 Solving Multiplication and Division problems continued & Division/Multiplication Story Problems Mini-Assessment
CCSS:
3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.MD.7.a, 3.MD.7.B
SFO:
-I can use use multiplication combinations to solve division problems
-I can use the inverse relationship between multiplication and division to solve problems.
-I can use and understand multiplication and division notation.
Teacher Input:
30 Minutes: Solving multiplication and division story problems
-LI: Complete pages in student activity book for review independently or with a partner
-TD & Advanced Learners in LI: Introduce long division and solving story problems that involve long division.
30 minutes: Multiplication/Division Story Problem Quiz
Assessment: Multiplication/Division Story Problems Mini-Assessment
FOR TD, GET THE SMART NOTEBOOK FROM GOOGLE DOCS
Area (CMS)
**Irregular Shapes
CCSS:
3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. (a) A square with a side length 1 unit, called “a unit square,” is said
to have “one square unit” of area, and can be used to measure area. (b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an
area of n square units.
3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
SFO:
I can measure the area of irregular shapes using square units.
Materials:
Shape set A-J
Square Tiles
Recording Sheet
Exit Ticket - Area Day 1
Before:
Have students complete the EOG Review problem of the day.
Say: If we want to know the size of a shape, we can cover it with squares to see how many squares it takes to cover the shape. When we use squares to measure a shape, we
call the squares “square units” because we are using them to measure size like we use the units inches and centimeters to measure length and pounds to measure
weight. The number of squares it takes to cover a shape is called the area.
Today, we are going to find the area of some shapes to see which shape is the biggest. Each shape is labeled with a letter. Begin by estimating the size and order of the
shapes. Then measure to see the actual size. Record the letter of your shape and how many square units it takes to cover the shape.
During:
Students use square tiles to measure the square units of shapes A-J. Student use the area to order the shapes by size.
After:
Say: Since we are measuring these shapes to see what size they are…the area, these squares are units of measure. Just like we use units such as inches to measure how long
something is, we use square units to see what size a flat shape is…to find its area. So, today when we talk about our shapes, let’s describe them in square units. The area of
shape (A) is (22) square units.
Ask students for the size of some of the shapes they measured (making sure that students describe the size in square units). Eventually determined the shape with the
greatest area.
Assessment:
What is the Area? Exit ticket
CMS Area Day 1
Objective: I can measure the area of irregular shapes using square units.
S
EOG Prep
Area
We already worked with perimeter, and importance of figuring
out the perimeter of a shape… for instance, to keep crazy
third graders on the playground, we may need to build a
fence around the playground. We would need to know the
length around the playground to buy enough fencing.
Sometimes it is important to know how much space we have
inside a 2D shape. Why might that be important?
We call the space inside of a 2D shape the area. We can
measure area by covering the shape with squares and
counting how many squares it took to cover the shape.
When we use squares to measure area, we call them square
units.
Finding Area using Square
Units
Drag Square
Units to measure
the shape.
What is the area
of this shape?
Independent
1.
Each table will get 10 shapes (A-J).
2.
As a group, estimate and list the order the shapes from
smallest to largest on your recording sheet.
3.
Each students needs to measure each shape using square
unit tiles (if there aren’t enough tiles, take turns measuring
the shapes.
4.
Record the area of each shape on your sheet.
5.
Reorder and list the shapes from smallest to largest on your
recording sheet.
Exit Ticket
Math 5: 3.1A What’s the Area
CCSS:
3.MD.C.5
3.MD.C.6
SFO:
I can use tiles to find the area of a rectangle.
I can find the area of a rectangle by multiplying the dimensions.
EQ: Why might you calculate area in the real world?
Materials:
Square inch tiles (investigations)
Teacher Input:
1. Remind the students that we have been working with arrays, and that we have been figuring out how many squares an array has by counting one-by-one, skip counting, or
multiplying the dimensions.
2. Explain that they, like yesterday, were finding the area of these shapes. Area is just the space inside of a 2-D shape, unlike the perimeter which is the length around a
shape.
3. Display a 5-inch by 7-inch rectangle on the board along with square-inch tiles(ppt, w/o dimensions).
4. Ask the students explain how they can use the tiles to find the area of the rectangle, and model the process.
5. Explain that the tile is a square with 1 inch sides. Since the rectangle holds 35 tiles, the area of the rectangle is 35 square inches, or 35 square units.
6. Have the students describe the rectangle, pretending that they are trying to tell someone who couldn’t see it how to build it. (Possible answers: They need 35 tiles, the
rectangle has 5 rows and each row is 7 tiles long, the dimension are 5 by 7, etc.)
7. Explain that they can describe a rectangle by the length of its sides. Have the students name the length of each side, and notate the dimensions on the rectangle.
8. Now that the students can see the dimensions of the rectangle, and the area of the rectangle, have the students explain how area relates to multiplication.
9. Demonstrate how a ruler can be used to measure dimensions and determine area.
Independent:
1. Pass out 40 square inch tiles to each student.
2. Have the students complete pages C22 and C24.
Homework:
C23 and C26 (students will need a ruler at home)
CMS Area Day 2
Objective:
I can use tiles to find the area of a rectangle.
I can find the area of a rectangle by multiplying the dimensions.
EQ:
Why might you calculate area in the real world?
S
EOG Prep - Day 4
Fill in the blanks to make the statement true.
a. 4 groups of five = _________
4 fives = _________
4 × 5 = _________
Finding Area Using Square
Units
Yesterday we worked on finding the area of shapes using
square units.
Remember, the area of a shape is just the amount of square
units that can fit inside of a shape.
How can you use
these square units to
measure this
rectangle?
What is the area
of this shape?
Specific Units
It just so happens that these squares that we are using to
measure have 1 inch sides. We can call these square inches.
So, this rectangle has an area of 35 square inches.
1 in.
1 in.
1 in.
1 in.
How Would You Describe It?
Let’s just pretend you were trying to explain to someone how
to build this particular rectangle. How would you describe
it?
Dimensions
Some of you described this rectangle using dimensions! What
are the length of the sides?
How is area related to multiplication?
A Ruler Works
You can also use a ruler to measure the side, then multiply to
figure out the area! (rotate the ruler by selecting it and using
the green button at the top of it).
What are the dimensions of this rectangle? What is the area?
Guided Practice
Independent
1. Option 1: Complete pages C22 and C24.
2. Option 2: Create a 4 tab foldable. Cut out
4 different regular shapes out of graph
paper. On the inside students must figure
out the area using 2 different methods
(multiplying & counting the arrays)
Area (CMS)
**Irregular Shapes
CCSS:
3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. (a) A square with a side length 1 unit, called “a unit square,” is said
to have “one square unit” of area, and can be used to measure area. (b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an
area of n square units.
3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
SFO:
I can use standard units to measure area
Materials:
4 rulers marked with centimeters (or cm cubes)
4 rulers marked with inches (or square tiles)
4-8 12 inch rulers
4-8 yard sticks
4-8 meter sticks
Tape or chalk shapes that can be measured in square centimeters, square inches, square feet, square yards, or square meters.
5 sheets of chart paper
Recording Sheet
How Big Is a Foot? By Rolf Myller (optional)
Before:
Have students complete the EOG Review problem of the day.
(Prior to this lesson, you might consider reading aloud the book How Big Is a Foot? By Rolf Myller. This book emphasizes the need for standard units).
We’ve been measuring area for two days using square tiles. Yesterday, we said that we could name the area in square inches since each tile is 1 inch on each side. So, when
we found the area of the rectangle that was 2 inches by 4 inches, we said it was 8 square inches. Mathematicians use different sized squares to measure area. We name the
unit by how long one side is. What is a square inch? What is a square foot? What is a square yard? (Tape together 4 rulers to make a square foot, 4 yard sticks to make a
square yard, and 4 meter sticks to make a square meter) What would you measure with a square inch? Foot? Yard?
Today, we are going to do a two-part activity. We are going to create a list of things we can measure using a square centimeter, inch, foot, yard, and meter. We have 5
posters around the room that we are going to use as a graffiti wall. We are going to rotate around the room and record things that we might measure using each of these
units. Then, we will measure some shapes/rectangles using these square units. (Some shapes will be very large and you may need to consider ways to arrange you
classroom to accommodate or use a hallway space with planned adult supervision or use side walk chalk on a safe, supervised outdoor black top area used for student play)
During:
·
Students create lists of things that might be measured with square units of different sizes.
Students measure rectangles using square units of different sizes..
After:
Why would you use one unit to measure one size shape, but another unit to measure a different size shape? How do you decide which unit to use? Why is it important to
know the length of the side of the square unit you are using to measure?
Evaluation:
Using Standard Units to
Measure Area
Objectives:
-I can measure the area of shapes using
standard units of measure
-I can estimate which unit of measure would be
best for a given space.
Class Discussion
We’ve been measuring area using square tiles. Yesterday, we said
that we could name the area in square inches since each tile is 1
inch on each side. So, when we found the area of the rectangle
that was 2 inches by 4 inches, we said it was 8 square inches.
Mathematicians use different sized squares to measure area.
They might use: (Show these to class so they understand the size)
•
•
•
•
•
square
square
square
square
square
centimeter (centimeter tile)
inches (inch tile)
feet (tape four 12 inch rulers together)
yard (tape 4 yard sticks together)
meter (tape 4 meter sticks together)
Carousel Activity
• We are going to create a list of things we can
measure using centimeter, inch, foot, yard,
and meter. We have 5 posters around the
room that we are going to use as a graffiti
wall. We are going to rotate around the room
and record things that we might measure
using each of these units. You will only be
given 2 minutes at each station!
Get Ready… Get Set… GO!
Activity Part 2
• Next, we will go on a scavenger hunt and
measure the area of some objects around
our classroom. We will work in groups of 3.
Each group will receive 1 ruler and 1 yard
stick. You will measure the length and
height of objects A-J listed on the next
slide using the appropriate unit of
measure. You will measure the length and
width of each object and then multiply to
get the area. Record your findings on your
recording sheet.
Recording Sheet
Objects to Measure
A = Textbook
B = Reading Book
C = Hallway space from our classroom door to Ms.
Watson’s classroom door
D = Desk
E = Smart board
F = Post it Note
G = Sheet of white printer paper
H = Tissue
I = Classroom Door
J = Choose your own object
Exit Ticket
Directions: Complete on a post it note or half
sheet of lined paper.
1. What is the area of your recording sheet
in centimeters?
2. Fold your recording sheet in half. What is
the area of half of your recording sheet
in centimeters?
3. Fold your recording sheet in half a second
time. What is the area of your recording
sheet now in centimeters?
Area of Irregular Shapes
Objectives:
• I can calculate the area of irregular
shapes.
• I can find the area of shapes that are
partially covered.
Let’s Review Area and Perimeter
of
Regular
Shapes!
10 cm
4 cm
A=
P=
5 in
A=
P=
9 cm
7 cm
A=
P=
Example: How to find the
area of irregular shapes
1. Find any unknown sides
2. Divide the irregular shape into squares or rectangles
3. Find the area of each square or rectangle
4. Add the areas together to find the total area of the shape
9cm
See next slide for
example!
6cm
5cm
10cm
How to find the area of irregular shapes
1. Find any unknown sides
2. Divide the irregular shape into squares or rectangles
3. Find the area of each square or rectangle
4. Add the areas together to find the total area of the shape
4 cm
A=lxw
16 + 50 = 66
4 cm
(the sum of the area
of the square and
rectangle)
A=4x4
9cm
A = 16
6cm
A=lxw
A = 10 x 5
A = 50
10cm
5cm
Area = 66 square cm.
Problem # 1
2m
7m
2m
4m
12m
Problem # 2
11cm
4cm
6cm
10cm
4cm
7cm
Problem # 3
Example
Work out the area shaded in each of the following diagrams
6 cm
4 cm
2 cm
8 cm
Extra Practice
This problem is not in your notebook!
9m
5m
7m
5m
5m
34m
Find the Area of the Rectangle
Problem # 4
Extra Practice
This problem is not in your notebook!
Left Side (Independent Practice)
Create a triple T chart like the one below and solve.
Irregular Shape
Show Your Work
Area