5th Grade Math
Special Session
Objective 1: Number, Operation, and
Quantitative Reasoning
Multiplication and Division
Austin Independent School District
Elementary Mathematics Department
April 2010
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 1
TEKS: 5.3D
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(D) Identify common factors of a set of whole numbers
Verbs: solve, identify
Vocabulary:
array, dimensions, factors, factor pairs,
prime, composite, product, least, greatest
Guiding Questions: What is an array? How could you use arrays to determine the factors of a number? How could you
determine if you have made all of the possible arrays? What is a prime number? What is a composite number?
Materials Needed: Color Tiles (25 per student or pair), BLM 5.3D_1 (several per student), Mrs. Smith’s Problem BLM
5.3D_3 (1 per student), BLM 5.3D_4(1 per student), BLM 5.3D_5 (1 per student)
Math Tool: Transparency (BLM 5.3D_2), Arrays
Lesson:
1. Pose problem: (Transparency: BLM 5.3D_2)
Mrs. Smith is having a party. She wants to arrange 24 tables across the room in an array style. She can
arrange the tables 24 across the room. Using your square tiles, show different ways Mrs. Smith could arrange
the twenty-four tables across the room in rectangular arrays. Copy the arrays onto grid paper (BLM 5.3D_1)
and label them with the dimensions.
2. Today we are going to build rectangular arrays to determine whether a number is prime or composite.
3. Who remembers what prime numbers are? (Numbers that have only one pair of factors) What are composite
numbers? (Numbers that have more than one pair of factors.) Is the number 24 that you just built prime or
composite? (Composite) How do you know? (Because it has more than one factor pair: 1x24, 2x12, 3x8, 4x6.)
Now let’s practice. Instruct students to create as many rectangles as possible using the number of tiles indicated (BLM
5.3D_3). Record them on grid paper and label their dimensions. Also, record whether it is prime or composite. Have them
talk to a partner to proof their answer choices.
Look for the following:
 Can the student build rectangular arrays and identify the factor pairs?
 Does the student have a systematic method for finding all the factors of a number?
Listen for the following:
 Does the student’s model and explanation match his or her written work?
Debriefing questions:
 What patterns did you observe while building the arrays? (Some numbers have only one possible rectangle.
Some numbers have more than one possible rectangle. The dimensions of the rectangles are the same as the
factors of the number.)
 Which numbers have only one possible rectangle? Why? (13, 11, 7 because they only have two factors. They
are prime numbers.)
 Which numbers have more than one possible rectangle? Why? (21, 8, 12, 6 because they have more than
one pair of factors. They are composite numbers.)
Independent Practice:
Instruct students to fold another piece of grid paper in half lengthwise. Label one-half PRIME and the other half
COMPOSITE. Instruct students to find five examples of prime numbers and five examples of composite numbers (other
than the ones we just did). Test the answers using color tiles and by drawing the rectangles on the grid paper. Prove your
answers to a partner.
TAKS Connection:
 BLM 5.3D_4 (Answers: Problem #1: 24, Problem #2: A)
BLM 5.3D_1
BLM 5.3D_2
Mrs. Smith’s Party
Mrs. Smith is having a party. She wants to arrange
24 tables across the room in an array style. She
can arrange the tables 24 across the room.
24
Using your square tiles, show different ways Mrs.
Smith could arrange the twenty-four tables across
the room in rectangular arrays. Copy the arrays
onto grid paper and label them with the
dimensions.
BLM 5.3D_3
Number of
Arrays
Tiles
Factor Pair(s)
Prime or
Composite
1x24
24
1 by 24
2 by 12
3 by 8
4 by 6
2x 12
3x 8
4x6
21
8
12
Composite
BLM 5.3D_4
Number of
Tiles
Arrays
Factor Pair
Prime or
Composite
11
13
6
7
Page 6 of 64
BLM 5.3D_5 (TAKS Connection)
1
The list below shows the 8 factors of which number?
1, 24, 2, 3, 4, 8, 12, 6
Record your answer and fill in the bubbles. Be sure to use the correct place
value.
2
The factors for the numbers 31 and 12 are shown below.
31
12
1, 31
1, 2, 3,
4, 6, 12
According to the factors, which of the following statements is NOT true?
A 31 and 12 are prime numbers.
B 31 is a prime number
C 12 is a composite number.
D 1 is a factor of both 31 and 12.
Page 7 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 2
TEKS: 5.3D
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(D) Identify common factors of a set of whole numbers
Verbs: solve, identify
Vocabulary: factors, factor pairs, common factors, prime, composite, product, least,
greatest, array, Venn Diagram
Guiding Questions: How do you determine a factor of a number? How do you know if you have listed all the factors
of a number? What factor do all numbers have in common? How do you determine common factors of numbers?
Materials Needed: Color tiles, Sorting Circles to model Venn Diagram (can make out of yarn or use hula hoops), BLM
5.3D_7 (several per student), BLM 5.3D_8 (1 per student), BLM 5.3D_9 and 10 (several per student—you want them
to eventually be able to create for themselves on their own paper), pre-made cardstock games (BLM 5.3D_11 and 12),
BLM 5.3D_13 (1 per student)
Math Tool: T-chart, Venn Diagram, Transparency (BLM 5.3D_6),
Lesson:
1. What do you know about factors? Who can tell me what it means to find the factors of a number? (A
number that will divide into another number evenly with no remainder.) If you have something in common with
someone, what does this mean? (You share something with someone, or you and someone else have
something alike. For example, Josh and Kevin both have on Longhorn t-shirts so they have that in common.) Let’s
look at a Venn Diagram (Transparency of BLM 5.3_6). What does the Venn Diagram tell you? (Four beetles
are spotted, 3 beetles are striped, 1 beetle is both spotted and striped, 3 beetles are neither spotted nor striped.)
What does the Venn Diagram help you easily see? (What the beetles have in common.)
2. What do you think it means to find common factors of a set of numbers? (Common factors are factors that a
set of numbers share or numbers that will evenly divide each number in a set of numbers.)
3. Today we are going to identify common factors of a set of whole numbers. (Record vocabulary on an anchor
chart.)
4. What are the factors of 12? (Have students count out 12 color tiles and prove the factors of 12 using their color
tiles. Have students record their findings.) What process did you use to create the color tile arrays? How did
you make sure that you created all the possible arrays? (Start with width 1, width 2, and continue checking to
see which combinations create rectangular arrays.) What system did you use to record all of the factors?
(Look to see what strategies they use.) So what are the factors of 12? Record their findings on a T-chart (1x12,
2x6, 3x4). Explain the process you are using. (T-chart: Start with the factor “1”, factor “2: and use consecutive
numbers to check each to see if the factor works. Continue the table until factors reverse.)
12
1 12
2 6
3 4
Note: Factor pairs that repeat
themselves are only recorded
once. For example, 2 x 12
and 12 x 2 are the same factor
pairs so are only recorded one
time.
5. The arrays you built are the factor pairs of 12. Let’s list the factors of 12 in order from smallest to largest
using a T-Chart. (Add to class chart.)
12
1 12
2 6
3 4
Factors of 12:
(1, 2, 3, 4, 6, 12)
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2
6. Now with your partner using your color tiles (or grid paper) find all the factors for 18. Record your results
using a t-chart. (Students can also build their arrays on grid paper (BLM 5.3D_7) and record on Blackline Master
8.)
7. What are the factors of 18? What are the common factors of 12 and 18? (Model with students using Sorting
Circles (Venn Diagram Manipulative) and index cards with factors. Show students how to record on Venn Diagram.
Students can record on BLM 5.3D_8.)
Make a T-Chart for each factor
12
1
2
3
12
6
4
Factors of 12:
(1, 2, 3, 4, 6, 12)
Venn-Diagram
Model using Sorting Circles and then record results on a Venn
Diagram.
Model putting on T-Chart:
12
18
1
2
3
18
9
6
18
4
12
Factors of 18:
(1, 2, 3, 6, 9, 18)
9
1
2
3
6
18
Table
Model putting in a table. List all the factors in order from least to greatest. Circle the common factors.
Factors of 12: 1 2 3 4 6 12
Factors of 18
1 2 3 6 9 18
ASK:
 What are the factors of the first number? (12: 1, 2, 3, 4, 6, 12)
 What are the factors of the second numbers? (18: 1, 2, 3, 6, 9. 18)
 What factors do they have in common? (1, 2, 3, 6)
 What is the greatest common factor of the two numbers? (6)
Page 9 of 64
8. What if we add another number? Let’s add the number 15. What are the common factors of 12, 15, and 18?
Make a T-Chart
Venn Diagram
Model using Sorting Circles and then record results on a
Venn Diagram.
Model putting on T-Chart.
15
15
1 15
3 5
15
Factors of 15:
(1, 3, 5, 15)
1
4
2
12
12
3
6
9
18
18
Table
Model putting in a table. List all the factors in order from least to greatest. Circle the common factors.
Factors of 12:
1
2
3
4
6
12
Factors of 18:
1
2
3
6
9
18
Factors of 15:
1
3
15
Check for understanding:
Let’s look at the Venn Diagram.
 What are the common factors of 12 and 18? (2)
 What are the common factors of 12 and 15? (1, 3)
 What are the common factors of 15 and 18? (1, 3)
 What are the common factors of 12, 15, and 18? (1, 3)
9. Now let’s practice. (Guided Practice: BLM 5.3D_9 and 10. Watch for students using strategies taught today: T-chart,
systematic recording method, Venn Diagram, Table.)
10. Teach Common Factor Game or Factor Pair Game (depending on your students’ needs, BLM 5.3D_11 and 12).
Practice playing the game until the students understand the game and are able to play during independent practice
time. Make sure students record and prove the factors for each number.
Look for the following:
 Can the student identify common factors of two or three whole numbers?
 Does the student use factor pairs when determining the factors of a whole number?
 Does the student have a systematic method for finding all the factors of a number?
Listen for the following:
 Does the student’s explanation match his or her written work?
Debriefing Questions:
 How do you determine a factor of a number? (It has to divide the number evenly with no remainder.)
 When you have found one factor of a number, how does this help you find another factor of that number?
(Factor pairs)
 How do you know if you have listed all of the factors of a number? (No other numbers will divide it.)
 What factor do all numbers have in common? (One)
 Which tool was easier for you to find the common factors: a Venn Diagram or a T-chart? (Answers will
vary.)
Page 10 of 64
Independent Practice:
Have students work in pairs to find common factors. Each student draws a number, finds the factors, records factor pairs
on T-Chart, on a Venn Diagram, and a table.
Students play Common Factor Game or Factor Pair Game (BLM 5.3D_11 and 12)
TAKS Connection:
 BLM 5.3D_13 (Answers: Problem #1: B, Problem #2: C, Problem #3: C )
Page 11 of 64
BLM 5.3D_6
Page 12 of 64
BLM 5.3D_7
Page 13 of 64
BLM 5.3D_8
T-Chart for factors of 12
Venn Diagram for Factors of:
Factors of 12:
T-Chart for factors of 18
Factors of 18:
Venn Diagram for the factors of:
12, 18, and 15
Page 14 of 64
BLM 5.3D_9
T-Chart for factors of ______
Venn Diagram for Factors of:
Factors:
T-Chart for factors of ______
Factors:
Table:
Page 15 of 64
BLM 5.3D_10
T-Chart for factors of ______
Venn Diagram for Factors of:
________, _________, and _________
Factors:
T-Chart for factors of ______
Factors:
T-Chart for factors of ______
Factors:
Table:
Page 16 of 64
BLM 5.3D_11
Common Factor Game
Players: Group of 4 (2 sets of partners)
Materials: BLM 5.3D_12 with numbers cut out (if made out of cardstock they are easier to pick up),
paper and pencils for student’s record work
Directions:
1. Put the cards face down in the middle of the players. Each person draws a number and
creates a T-Chart listing the factor pairs for their number and a table listing factors in
order.
2. Each set of partners finds the common factors for their drawn numbers.
1. Whichever team has the most common factors wins all of the cards. In the case of a tie,
place the cards face up in a separate pile (called the discard pile). The next time there is a
winner, the winner gets all the face up cards from the discard pile as well.
2. Play continues until all of the cards are gone. Then whoever has the most cards wins.
Factor Pairs Game
Players: 2 players
Materials: BLM 5.3D_12 with numbers cut out (if made out of cardstock they are easier to pick up),
paper and pencils for students record work
Directions:
3. Put the cards face down in the middle of players. Each person draws a number and creates
a T-Chart listing the factor pairs for their number and a table for factors in order.
4. Whoever has the most factors wins all of the cards. In the case of a tie, place the cards face
up in a separate pile (called the discard pile). The next time there is a winner, the winner
gets all the face up cards from the discard pile as well.
5. Play continues until all of the cards are gone. Then whoever has the most cards wins.
Page 17 of 64
BLM 5.3D_12
5
6
7
8
9
10 11 12 13 14
15 16 17 18 20
21 22 23 24 25
26 27 28 30 32
33 34 35 36 38
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40 42 44 45 46
48 49 50 60 80
Page 19 of 64
BLM 5.3D_13 (TAKS Connection)
1
What are the common factors of 16 and 24?
A 1, 2, 4
B 1, 2, 4, 8
C 1, 2, 3, 4, 8
D 1, 2, 3, 4, 6, 8, 12, 16, 24
2
Which group shows all the numbers that are common factors of 6, 12, 18, and
24?
A 1, 2
B 1, 2, 6
C 1, 2, 3, 6
D 1, 6
3
What are all the prime factors of 36?
A 1, 3, 9
B 2, 3, 9
C 2, 3
D 2, 3, 7, 11
Page 20 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 3
TEKS: 5.3B
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(B) Use multiplication to solve problems involving whole numbers (no more than three digits times two digits without
technology)
Verbs: solve, use
Vocabulary: multiply, multiplication, products, groups
Guiding Questions: How are multiplication and addition alike? How are multiplication and addition different? What do
you know about multiplication? What makes a situation a multiplication situation? What strategies can you use to solve a
multiplication problem?
Materials Needed: Sorting Circles, Dry Erase Boards or Communicators (optional), BLM 5.3B_2 (1 per student), BLM
5.2B_3 (1 per student), BLM 5.2B_4 (1 per student)
Math Tool: Transparency (BLM 5.3B_1), Multiplication Table (Show struggling students how to create and use to
remember facts and solve problems)
Lesson:
1. Today we will be looking at some problems and see how you might solve them.
2. Let’s look at this problem. Pose problem #1: (Transparency: BLM 5.3B_1). Read problem together. Cover problem.
What do you know about the problem? Do this several times until students can tell you what the problem is asking.
You are trying to get them to visualize the problem. (Research shows that students need to read the problem at least
3-5 times before they will understand the problem. Struggling students often don’t do this. They read the problem
once and then just do something with the numbers.)
3. Ok, now that we know what kind of problem it is, let’s solve it. Give students some time to think about the
problem and solve it. (You might have them solve on dry erase boards or communicators so they can hold up their
solutions and share.)
4. How did you solve this problem? (Multiplication) How did you know it was a multiplication problem? (Answers
will vary, but you are looking for students to realize they are looking for the total, and that because the bows come in
equal groups they can be multiplied.)
5. Label one sorting circle “Multiplication” and place a question inside the circle. Add post-it notes with big ideas of what
makes it a multiplication problem (Looking for the total, all sets must be equal (equal groups). These are key concepts
not key words. Students should look for key concepts rather than key words. After reading the problem they should
visualize the situation rather than focusing on a word or phrase. Understanding the key concepts for each operation
will help students make a thoughtful decision regarding the appropriate operation to use in solving the problem.)
Multiplicatio
Alice was given 14 cards of
bows for her birthday. Each
card had 5 bows on it. How
many bows did Alice get for
her birthday?
This would be a
good anchor of
support to begin
using.
6. Present problem 2 (Transparency: BLM 5.3B_1). Give students some time to read and solve it.
7. How did you solve this problem? (It’s an addition problem.) How do you know it’s an addition problem? (Look
for the total but it doesn’t have equal groups.)
Page 21 of 64
8. Now label another sorting circle “Addition” and place a question inside the circle. Have students add post-it notes with
big ideas of what makes it an addition problem. (Look for the total, sets don’t have to be equal (not equal groups).)
Addition
Add to anchor
of support.
Alice sent through her box of
bows. She had 5 blue bows,
12 pink bows, 8 yellow bows,
3 red bows, and 7 purple
bows. How many bows did
she have altogether?
9. How are these problems alike? (They are both looking for a total.) How are these problems different? (In a
multiplication problem there must be equal groups. In addition there needn’t be equal groups.)
Multiplication
Alice was given 14 cards of
bows for her birthday. Each
card had 5 bows on it. How
many bows did Alice get for
her birthday?
Addition
Alice sent through her box of
bows. She had 5 blue bows,
12 pink bows, 8 yellow bows,
3 red bows, and 7 purple
bows. How many bows did
she have altogether?
Guided Practice:
Now let’s practice. Pass out a set of problem cards (BLM 5.3B_2) to each student. Have them sort them by their
operation (Addition or Multiplication).
Answers:
 Problem 2, 3, and 5 are addition problems
 Problems 1, 4, and 6 are best solved with multiplication.
Have students justify their answers.
Look for the following:
 Can the student recognize multiplication and addition situations?
 Can the student explain why it is a multiplication or addition problem?
Independent Practice:
Students solve problems they just sorted.
Answer Key:
1.
$192 on the tickets
2.
$3.53 spent on supplies
3.
430 puppies
4.
72 more votes
5.
41 saves
6.
450 minutes on science assignments
Multiplication Tic-Tac-Toe (BLM 5.3B_3): This is for students who finish early or for students who have already passed
TAKS.
Look for the following:
 Can the student identify the information necessary to solve the problem?
 Can the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Can the student talk about the reasonableness of his or her solution?
Page 22 of 64
Probe further with:
 Explain the steps you used to solve this problem.
 Justify your answer.
 How did you decide on the equation (number sentence) you used to solve this problem? Was there
another equation that would have also worked?
 Can you solve the problem another way?
 Is your solution reasonable? How do you know?
TAKS Connection:
 Transparency: BLM 5.3B_4 (Answers: Problem #1: C, Problem #2: D, Problem #3: B)
Page 23 of 64
BLM 5.3B_1
1. Alice was given 14 packets of bows for her birthday.
Each packet had 5 bows in it. How many bows did
Alice get for her birthday?
2. Alice went through all of her of bows. She had 5 blue
bows, 12 pink bows, 8 yellow bows, 3 red bows, and 7
purple bows. How many bows did she have
altogether?
Page 24 of 64
BLM 5.3B_2
1 Anna bought 12 tickets to a
concert. Each ticket cost $16.
How much did she spend on
the tickets?
2 Luis bought a poster for $0.59,
a box of paints for $2.19, and a
brush for $0.75. How much
money did Luis spend for his
supplies?
3 Mrs. Barksdale started a puppy
training program three years
ago. Each year, the number of
puppies in the program has
increased. In the first year,
there were 41 puppies. In the
second year, there were 173
puppies, and in the third year,
there were 216. How many
puppies have been in the
program altogether?
4 In an election, Mr. Jones
received 3 votes for every 1
vote that Mr. Smith received. If
Mr. Smith received 24 votes,
then how many votes did Mr.
Jones receive?
5 In the championship hockey
series, the goalie made 3 saves
in the first match, 8 saves in the
second match, 11 saves in the
third match, 6 saves in the
fourth match, and an incredible
13 saves in the fifth and final
match. How many saves did the
goalie have in the series?
6 It takes Will about 25 minutes to
complete each of his science
assignments and 20 minutes to
complete his history
assignments. If he had 18
science assignments this
grading period, what was the
total time spent on science?
Page 25 of 64
BLM 5.3B_3
Multiplication Tic-Tac-Toe
Choose and complete one activity in each row.
Draw a picture that shows a
Your brother multiplied 64 x
model of 7 x 35. Make
8 and got the answer
connections between your
4,832. What could you
drawing and how you use
show and tell your brother
paper and pencil to find the
to help him understand why
product. Discuss your ideas
his answer is wrong?
with a friend.
Place the numbers: 3, 4, 6,
15, 20, and 30 in the
triangle so that the product
of each side is 360.
Place a multiplication sign
to make a number
sentence that is true.
6_3_9_4_5 = 31,970
Write one more problem
like this one and trade it
with a classmate.
Make a collage of items
that come in equal groups.
Write two more problems
like this one and trade them
with a classmate.
Interview a classmate
about what he or she
knows about multiplication.
Find out as much as you
can in three minutes. Write
a report with suggestions
for teaching this concept.
Use a pencil and paper to
write directions for two
different ways to find the
product of 92 and 24.
Which two numbers should
you exchange so that the
product of the numbers on
each card is the same?
120
85 6
3 17
8 3
30 2
4
102
Write two more problems
like this one and trade with
a classmate.
Your friend solved a word
problem by multiplying 3 by
24 and then subtracting 9.
Write two interesting word
problems that your friend
could have used to
solve it this way.
From Math for All: Differentiating Instruction, Grades 3-5, by Linda Dacey and Jayne Banford Lynch
Solutions Publications
. 2007 Math
Page 26 of 64
BLM 5.3B_4 (TAKS Connection)
1
A restaurant has 52 tables. Each table can seat 6 people. If every table is
full, how many people are seated in the restaurant at the same time?
A 58
B 300
C 312
D 314
2
Jennifer is 5 feet tall. Her teacher told her that the Statue of Liberty in
New York City is 13 times as tall as she is. How tall is the Statue of
Liberty?
A 18 ft
B 50 ft
C 55 ft
D 65 ft
3
There are 52 fifth graders at Sunset Valley Elementary. If each student in
fifth grade has 8 insects in his or her insect collection, what is the total
number of insects the fifth grade has collected?
A
60
C
318
B
416
D
400
Page 27 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 4
TEKS: 5.3B
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(B) Use multiplication to solve problems involving whole numbers (no more than three digits times two digits without
technology)
Verbs: solve, use
Vocabulary: multiply, multiplication, factors, product
Guiding Questions: What do you know about multiplication? What makes a situation a multiplication situation? What
strategies can you use to solve a multiplication problem?
Materials Needed: Sorting Circles, BLM 5.3B_7 and 8 (1 per student)
Math Tool: Transparency (BLM 5.3B_5), Multiplication Table (Show struggling students how to create and use this
table to remember facts and solve problems.)
Lesson:
1. Yesterday we looked at some problems and what makes a situation an addition or multiplication situation.
Who can remember what we learned about addition? (Looking for the total, groups do not have to be equal.)
What did we learn about multiplication? (Looking for the total, groups have to be the same size.)
2. Let’s look at this problem. Pose problem (Transparency: BLM 5.3B_5): Read together, giving time for students to
think about problem and think-pair-share what they know about the problem.
3. What kind of problem is this? (Multiplication) How do you know? (Think-Pair-Share: Looking for the total number
of cars, there are equal groups of 24 cars in each row.)
4. Give students time to solve problem and time to share their strategies.
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
Begin anchor chart for
Multiplication
Strategies. (See sample
BLM 5.3B_6)
5. Ok, now let’s look at a 2nd problem. Pose problem: Transparency: BLM 5.3B_5
6. Read the problem together until everyone can visualize the problem. Pair-share what they are going to do to solve
the problem and then have students solve it.
Page 28 of 64
7. Today we are going to use what we have learned to love some problems? What tools can we use to help solve
problems like the ones we solved today? (Answers will vary: Strategy chart, Multiplication table)
8. Now let’s practice. Pass out a set of problem cards (BLM 5.3B_7) to each student.
Independent Practice: Students practice solving problems (BLM 5.3B_7).
Answer Key:
1.
C
2.
C
3.
C
4.
A
5.
A
6.
B
Multiplication Tic-Tac-Toe (BLM 5.3B_3): This is for students who finish early or for students who have already passed
TAKS.
Look for the following:
 Can the student identify the information necessary to solve the problem?
 Did the student show their work? Are their strategies clear?
 Can the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Can the student talk about the reasonableness of his or her solution?
TAKS Connection:
 Blackline Master 5.3B_8 (Answers: Problem #1: D, Problem #2: C, Problem #3: D)
Page 29 of 64
BLM 5.3B_5
The parking lot at the mall is full! All 35 rows of
parking spots are filled and each row has 24
cars. How many cars are parked in the parking
lot?
Mrs. Chi’s students are setting up chairs for the
school play. They need 500 chairs. So far, they
have set up 16 rows with 24 chairs in each row.
How many chairs must they set up?
Page 30 of 64
BLM 5.3B_6
Multiplication Strategies
The parking lot at the mall is full! All 35 rows of parking spots are filled
and each row has 24 cars. How many cars are parked in the parking
lot?
Area Model
Clusters

How can 35 be written into an easier number to
work with? (30 + 5)

How can 24 be written into an easier number to
work with? (20 + 4)
20
30
5
600
100
4
35 x 4 = 140
=700
=140
120
20
+
720 +
120
840
Tower
3 5
35 x 20 = 700
504
Related Set
30 x 24 = 720
x 2 4
5 x 24 = 120
2 0
(4 x 5)
1 2 0
(4 x 30)
1 0 0
(20 x 5)
720 +120 = 840
6 0 0 (20 x 30)
8 4 0
Page 31 of 64
BLM 5.3B_7
1 There
are 328 bricks in the 2 If a supermarket shelf holds 266
fireplace. If 51 identical fireplaces
cans of vegetables, how many
are built, how many bricks are
cans will 19 of these shelves hold?
used in all?
A 14
A 379
B 285
B 1968
C 5,054
C 16,728
D 5,154
D 164,328
3 Johnson
Elementary
School 4 Angelo has 15 crates of apples.
bought 15 cases of pencils. Each
He has 25 times as many apples
case contains 144 pencils. How
as crates. How many apples does
many pencils did they buy in all?
Angelo have?
A 129
A 375
B 159
B 350
C 2,160
C 300
D 3,000
D 275
5 Al sold 127 tickets to his school 6 Melanie’s classes are 50 minutes
play. Each ticket cost $7. How
much money did Al collect in all?
A $889
long. She attends 32 classes each
week. What is the total number of
minutes Melanie is in class each
week?
B $829
C $704
A 1,465 min
D $134
B 1,600 min
C 1,355 min
D 360 min
Page 32 of 64
BLM 5.3B_8 (TAKS Connection)
1
2
3
A farmer is planting tomatoes in rows with 32 plants in each row. His
field is big enough for 27 rows. If he plants the entire field, how many
plants will there be?
A 59
C 600
B 614
D 864
Juan’s fifth-grade class has 25 boxes of crayons and 15 packs of
markers. Each box contains 12 crayons. How many crayons are in his
class?
A 180
C 300
B 375
D 480
There is a new long-range jet that carries 11 fuel tanks. The jet can fly
about 880 miles on each tank. How many miles can the jet fly if it uses
the fuel in all of its tanks?
A 21,861 mi
C 19,600 mi
B 11,880 mi
D 9,680 mi
Page 33 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 5
TEKS: 5.3B
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(B) Use multiplication to solve problems involving whole numbers (no more than three digits times two digits without
technology)
Verbs: solve, use
Vocabulary: multiply, multiplication, products, groups
Guiding Questions: What do you know about multiplication? What makes a situation a multiplication situation? What
strategies can you use to solve a multiplication problem?
Materials Needed: Chart Paper, Markers
Math Tool: Multiplication Table (Show struggling students how to create and use to remember facts and solve problems)
Lesson:
1. Today we are going to review and practice using your multiplication strategies. What do you know about
multiplication? (Answers will vary.) How do you know a problem is a multiplication situation? (Want to find the
total, have equal groups or sets.)
2. What are some things that already come in equal groups? (2’s? Eyes, ears, shoes…3’s? Wheels on a tricycle…)
Keep brainstorming and add to anchor chart. You do not need to complete the chart, you are just trying to jump start
students’ thinking of things that come in groups.) See BLM 5.3B_9 (Things that Come in Groups)
2’s
3’s
4’s
5’s
Things that Come in Groups
6’s
7’s
8’s
9’s
10’s
Eyes
Ears
Shoes
11’s
12’s
Hot Dog
Buns
3. What are some things that come in 10’s? 11’s? 12’s? Can you think of things that come in groups of larger
numbers? (Number of teams in a baseball league - number can vary. Number of players on each baseball team numbers can vary)
4. Let’s see if we can write a two-digit x two-digit multiplication story problem together. What ideas could we
use for things that come in groups? (Answers will vary—record ideas on chart paper)
5. With students, write a problem such as: (Keep the wording simple since this will be a model for students to write their
own problems.)
A baseball league has 32 teams, and each team has 18 players. How many
players are in the league?
Or
Mrs. Frizzle bought 32 packages of hot dog buns for the school carnival. Hot dog
buns come 12 to a package. How many hot dogs could they make?
6. Ask students to share how they would solve the problem.
Independent Practice with Partner:
7. Assign students to work in pairs to create their own two-digit x two-digit multiplication problems.
8. Have students write their problems on chart paper.
9. Have students solve their problems two ways and make an answer sheet.
Students Trade Problems:
10. Have pairs of students exchange story problems to solve and compare answers.
11. Have students share their strategies.
12. Have students explain their multiplication strategies to the group.
Page 34 of 64
Look for the following (when writing problems):
 Can the student identify real-world problems that can be solved using multiplication?
 Can the student pose a problem that can be solved by multiplying whole numbers?
 Can the student pose a problem that is clear and easily interpreted by his or her partner?
Look for the following (when solving problems):
 Can the student identify the information necessary to solve the problem?
 Can the student use multiplication to solve problems involving whole numbers?
 Does the student select manipulatives or draw a picture to help solve the problem?
 Does the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Is the student able to discuss the reasonableness of her or solution?
Page 35 of 64
5.3B_9 (Things that Come in Groups)
2
3
arms, legs, ears, eyes, nostrils, hands, feet, knees, etc
on a person
horns on triceratops
days in a weekend
months in a season
earrings in a pair
number of sides/angles/vertices in a triangle
shoes/ socks in a pair
number of triplets
wheels on a bicycle
number of twins
number of dwarf planets in solar system (Pluto, Ceres
and Eris)
number of moons around Mars
number of primary colors
number of cups in a pint
number of feet in a yard
number of pints in a quart
number of teaspoons in a Tablespoon
wheels on tricycle
3 bears/ pigs
3 wishes
leaves on clover
4
4
wheels on a car
number of mathematical operations
legs on a dog, cat, etc.
number of babies in a set of quadruplets
seasons in a year
number of suites in a deck of cards (hearts, clubs,
spades, diamonds)
number of sides/angles/vertices in a square, rectangle,
trapezoid, parallelogram or quadrilateral
number of cardinal directions
number of rocky planets in solar system (Mercury,
Venus, Earth, Mars)
number of quarters in one dollar
number of gas giants in solar system (Jupiter, Saturn,
Uranus, Neptune)
number of laps around track in a mile
number of wings on a butterfly or a dragonfly
legs on a table or chair
number of quarts in a gallon
number of strings on a violin, viola or cello
Page 36 of 64
5
5
fingers on hand
number of sides/angles/vertices in a pentagon
toes on a foot
appendages on a starfish
pennies in a nickel
number of oceans in the world
vowels in the alphabet
number of senses
number of even digits
number of babies in a set of quintuplets
number of odd digits
number of nickels in a quarter
players from team on basketball court
number of rings in Olympics symbol
days in a school week
6
7
half-dozen
days in week
wheels on truck
number of continents
number of sides/angles/ vertices in a hexagon
number of spots on a ladybug
number of strings on a standard guitar
number of sides/angles/vertices in a septagon
number of cans of soda in a "six-pack"
wonders of the world
number of sides in a cube
legs on an insect
number of babies in a set of sextuplets
number of players on Ice from a hockey team
Page 37 of 64
8
9
legs on a spider
planets in solar system
number of sides/angles/vertices in an octagon
judges on the U.S. Supreme Court
tentacles on an octopus
lives of a cat
number of Neptune's moons
10
11
number of angles, sides in a decagon
players on field from a soccer team or a football team
number of tens in one hundred
number of dimes in a dollar
number of pennies in a dime
10 Commandments
number of mm in a cm
number of cm in a dm
number of dm in a meter
Page 38 of 64
12
13
months in year
Baker's dozen
things in a dozen
number of original colonies
signs in the zodiac
number of months in a lunar calendar
number of hours in a.m.
number of hours in p.m.
number of inches in a foot
Page 39 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 6
TEKS: 5.3C
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(C) Use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends
without technology) including interpreting the remainder within a given context
Verbs: solve, use, interpreting
Vocabulary: divide, division, quotient, divisor, division
equation
Guiding Questions: How are division and subtraction alike? How are division and subtraction different? What do you
know about division? What makes a situation a division situation? What strategies can you use to solve a division
problem?
Materials Needed: Sorting Circles, 5.3C_2 and 4 (1 per student), 5.3C_3 (optional)
Math Tool: Transparency (BLM 5.3C_1), Multiplication Table
Lesson:
1. Today we will be looking at some more problems and see how you might solve them.
2. Let’s look at this problem. Pose problem: (Transparency: BLM 5.3C_1). Read problem together. Cover problem.
What do you know about the problem? Do this several times till students can tell you what the problem is asking.
You are trying to get them to visualize the problem. (Research shows that students need to read the problem at least
3-5 times before they will understand the problem. Struggling students often don’t do this. They read the problem
once and then just do something with the numbers.)
Alice was given 70 bows for her birthday. They came in 14 packets.
How many bows were in each packet?
3. Ok, now that we know what kind of problem it is, let’s solve it. Give students time to think about the problem and
time to solve it. (You might have them solve on dry erase boards or communicators so they can hold up their solutions
and share.)
4. How did you solve this problem? (Division) How did you know it was a division problem? (Answers will vary, but
you are checking to see if students know the total (number of cars) and that, since there are equal groups of cars in
each row, they can divide. How is this problem similar to a multiplication problem? (Both have to have equal
groups.) How is this problem different from a multiplication problem? (In multiplication you are trying to find the
total. In division you already know the total.)
5. Label one sorting circle “Division” and place a question inside the circle. Add post-it notes with big ideas of what
makes it a division problem. (You are looking for the total, all sets must be equal (equal groups). These are key
concepts not key words. Students should look for key concepts rather than key words. After reading the problem they
should visualize the situation rather than focusing on a word or phrase. Understanding the key concepts for each
operation will help students make a thoughtful decision regarding the appropriate operation to use in solving the
problem.)
Division
Add to anchor chart
previously created
for addition and
multiplication
6. Present problem 2 (Transparency: BLM 5.3C_1). Give students some time to read and solve the problem.
Page 40 of 64
7. How did you solve this problem? (Subtraction) How do you know it’s a subtraction problem? (Look for the total
but you don’t have equal groups)
8. Now label another sorting circle “Subtraction” and place a question inside the circle. With students, add post-it notes
with big ideas of what makes it an addition problem (know the total, sets don’t have to be equal (not equal groups).
Subtraction
Add to anchor
of support chart
9. How are these problems alike? (You know the total in both.) How are these problems different? (In a division
problem there have to be equal groups. In subtraction there doesn’t have to be equal groups.)
Division
Subtraction
Guided Practice:
Now let’s practice. Pass out a set of problem cards (5.3C_2) to each student. Have them sort them by their operation
(Addition or Multiplication).
Answers:
 Problem 2, 3, and 6 are subtraction problems
 Problems 1, 4, and 5 are best solved with division.
Have students justify their answers.
Look for the following:
 Can the student recognize subtraction and division situations?
 Can the student explain why it is a subtraction or division problem?
Independent Practice:
Students should solve problems (5.3C_2) that they just sorted.
Answer Key:
1.
C
2.
B
3.
A
4.
D
5.
A
6.
D
Division Tic-Tac-Toe: This is for students who finish early or for students who have already passed TAKS.
Look for the following:
 Can the student recognize division situations?
 Can the student identity real-world problems that can be solved by division?
 Can the student identify the information necessary to solve the problem?
 Can the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
Page 41 of 64
Listen for the following:
 Does the student’s explanation match his or her written work?
 Does the student talk about the reasonableness of his or her solution?
Probe further with:
 How are you solving the problem? Why?
 How do you know it is a division problem?
 What number sentence can you write to show your problem?
 Can you solve the problem another way?
 Is your solution reasonable? How do you know?
 Is there a remainder? What does it mean?
TAKS Connection:
 BLM 5.3C_4 (Answers: Problem #1: C, Problem #2: B, Problem #3: A )
Page 42 of 64
BLM 5.3C_1
1. Alice was given 70 bows for her birthday. They came in
14 packets. How many bows were in each packet?
2. Alice went through her box of bows. She had 35 bows.
Nine of the bows were pink. How many bows did she
have that were not pink?
Page 43 of 64
BLM 5.3C_2
1 April’s family of 4 went to dinner. The 2 Over a six-month period the Akins
bill was $72. If each person’s meal cost
Orchestra grew from 118 to 146
the same amount, how much did each
musicians. What was the increase in
meal cost?
size of the orchestra over this time
period?
A $14
A 38 musicians
B $17
B 28 musicians
C $18
C 21 musicians
D $288
D 14 musicians
3 Kylie has $27.18. She and Tina have 4 Hunter and his family went to Florida
$49.27 altogether. How much money
on their summer vacation. He wants to
does Tina have?
put the 192 snapshots that they took
into a photo album. If he can put 4
A $22.09
photos on a page, how many pages
B $28.50
does he need?
C $50.29
D $76.45
A 50
B 38
C 32
D 48
5 Mrs. Smith’s class bought a gift that 6 Bar-None Ranch had 230 sheep and
cost $84. Each student contributed $3.
1,522 longhorn cattle. After losing
How many students were in the class?
some of the cattle in a stampede, the
ranch still had 1,153. How many
A 28
longhorn cattle were lost in the
B 27
stampede?
C 26
D 26
A 552
B 833
C 422
D 369
Page 44 of 64
BLM 5.3C_3
Division Tic-Tac-Toe
Choose and complete one activity in each row.
Draw a picture that shows a
model of 245 ÷ 35. Make
Your sister divided 935 by
connections between your 17 and got 51. What could
drawing and how you use
you do to help your sister
paper and pencil to find the understand why her answer
quotient. Discuss your
is wrong?
ideas with a friend.
Write directions for two
different ways to find the
remainder of 314 ÷ 15
using paper and pencil.
Place a division sign in one
of the blanks to make a
number sentence that is
true.
Fill in the blanks to make
these equations true
Fill in the blanks to make
these equations true
96 ÷ ____ = 8 r 1
648 = 2 × 3 × ____× 18
____ ÷ 21 = 9 r 3
4_8_6_1_8 = 27
720 = 3 × ____ × 5 × 12
____ ÷ ____ = 12 r 2
Write 3 division problems
that have remainder 7.
Write two more problems
like this one and trade them
with a classmate.
828 = 23 × ____× 2
Interview a classmate
about what he or she
knows about division. Find
out as much as you can in
three minutes. Write a
report with suggestions for
teaching division.
Your friend solved a word
problem by dividing 968 by
44 then adding 8. Write two
interesting word problems
that your friend could have
solved this way.
Page 45 of 64
BLM 5.3C_4 (TAKS Connection)
1
2
3
David’s music club put on a concert. There were 500 people in the audience. Each
ticket to the concert cost $5. The audience was seated in 4 sections. If each
section had the same number of people in it, how many people were in each
section?
A 25
C 125
B 100
D 150
Monica won 486 tennis matches during 9 years. She won the same number of
matches each year. How many matches did Monica win each year?
A 46
C 50
B 54
D 65
While cleaning out his closet, Edgar discovered his old collection of comic books.
The comic books were stored in 8 boxes, each containing the same number. If
Edgar had 376 comic books in storage, how many were in each box?
A 47
C 51
B 49
D 53
Page 46 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 7
TEKS: 5.3C
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(C) Use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends
without technology) including interpreting the remainder within a given context
Verbs: solve, use, interpreting
Vocabulary: divisor, dividend, quotient, division equation
Guiding Questions: How are division and subtraction alike? How are division and subtraction different? What do you
know about division? What makes a situation a division situation? What strategies can you use to solve a division
problem?
Materials Needed: BLM 5.3C_7 and 8 (1 per student)
Math Tool: Transparency (BLM 5.3C_5), Multiplication Table
Lesson:
1. Yesterday we looked at some problems and determined whether they were subtraction or division. Today we
are going to look at some similar problems. Who remembers what made a situation a subtraction situation?
Who remembers what makes a situation a division situation? How are the alike? How are they different?
2. Pose Problem: Put up transparency (BLM 5.3C_5). Read together, giving students time to think about the problem and
think-pair-share what they know about the problem.
3. What kind of problem is this? (Division) How do you know? Think-Pair-Share (We know the total number of cars
(840), making equal groups of 24 cars in each row, so we can divide.)
4. Give students time to solve problem and time share their strategies.
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
Begin anchor chart
for Division
Strategies.
5. Ok now let’s look at a 2nd problem. Pose problem: (Transparency: BLM 5.3B_5)
6. Read the problem together until everyone can visualize the problem. Think-Pair-Share what they are going to do to
solve the problem and then have students solve it.
7. Give students time to solve problem and time share their strategies.
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
Add any new strategies
to Division Strategies
anchor chart
Guided Practice:
8. Now let’s practice. Pass out a set of problem cards (5.3C_7) to each student.
Debriefing Questions:
 What kind of problem is this? (Division)
 How do you know? (First problem: We know the total number of cars (840) and they are already in equal rows of
24 cars in each row. Second problem: We know the total number of chairs (608), and we are putting the chairs
into equal groups in 16 rows)
Page 47 of 64

How is it different from the first problem we solved? (The first problem we knew the size of each group (24
cars) and we needed to find out how many equal-sized groups we had (35 rows of cars). In the second problem
we knew the number of equal-sized groups (16 rows) and we needed to find out how many were in each group
(38 chairs).)
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
Look for the following:
 Can the student identify the information necessary to solve the problem?
 Can the student show their work? Are their strategies clear?
 Can the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Can the student talk about the reasonableness of his or her solution?
TAKS Connection:
 Blackline Master 5.3C_8 (Answers: Problem #1: B, Problem #2: D, Problem #3: C)
Page 48 of 64
BLM 5.3C_5
The parking lot at the mall is full! There are 840
cars in the parking lot. Each row has 24 cars in it.
How many rows of cars are in the parking lot?
Mrs. Chi’s students are setting up chairs for the
school play. They need 608 chairs. They want to
set up 16 rows. How many chairs must they set
up in each row to have an equal number of chairs
in each row?
Page 49 of 64
BLM 5.3B_6
Division Strategies
Forgiving Method
(Partial Quotients)
5
10
10
First
create
a bank
24 840

240
(10 x 24 = 240)
1 x 24 = 24
2 x 24 = 48
360
5 x 24 = 120
240
(10 x 24 = 240)
20 x 24 = 480
120
120
10 x 24 = 240
10’s are
easy! Then
think about
halving and
doubling
that number
(5 x 24 = 120)
0
Page 50 of 64
BLM 5.3B_7
1 An afterschool fitness program has 252 2 A supermarket needs to put 875 cans
students. They want to form teams that
of vegetables on 25 shelves. If each
have 12 students on each team. How
shelf has the same number of cans,
many teams can they form?
how many cans should be on each
shelf?
A 21
A 25
B 30
B 30
C 35
C 35
D 3,024
D 40
3 A toymaker can assemble one toy in 3 4 A river boat travels 280 miles when
completing 4 round trips. It takes a car
hours. How many toys can he
300 miles to complete 4 round trips.
assemble in 126 hours?
How many miles does the boat travel in
A 24
one round trip?
B 32
C 40
D 42
A 35
B 75
C 70
D 145
5 If there is 1 computer for every 20 6 If Sandy needs 1 cup of sugar to make
students at Allan Elementary, how
15 cookies, how much sugar will she
many computers do they have for 440
need to make 720 cookies?
students attending school?
A 48 c
A 11
B 12 c
B 22
C 64 c
C 40
D 180 c
D 220
Page 51 of 64
BLM 5.3C_8 (TAKS Connection)
1
2
3
Fifteen children walked through an orchard gathering pecans. They gathered a
total of 915 pecans. Each child took home an equal number of pecans. How many
pecans did each child take home?
A 90
C 60
B 61
D 183
The ivy grew 140 inches up the wall in 10 months. If the ivy grew at a fairly
constant rate, how many inches did it grow each month?
A 30 in
C 19 in
B 21 in
D 14 in
A football league had 16 teams. Each team had the same number of players.
There were 512 players in the league. How many players were on each team?
A 36
C 32
B 34
D 28
Page 52 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 8
TEKS: 5.3C
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(C) Use division to solve problems involving whole numbers (no more than two digit divisors and three-digit
dividends without technology) including interpreting the remainder within a given context
Verbs: use, solve, interpreting
Vocabulary: divisor, dividend, quotient, division equation,
remainder
Guiding Questions: What do you know about division? What makes a situation a division situation? What strategies can
you use to solve a division problem? What do you do with the remainder?
Materials Needed: Sorting Circles, BLM 5.3C_11 (1 set per student)
Math Tool: : Transparency: BLM 5.3C_9 and 1 copy per student, Multiplication Table
Lesson:
1. Yesterday we solved some problems and looked at what makes a situation a division situation and what
strategies you could use to solve division problems.
2. Who can tell me what division is? (Division means separating something—one thing or a collection of things—into
equal-sized groups.) How do you know that the problem can be solved by division? (In a division problem, you
know the whole amount and either the number of equal-sized groups or the size of each of the groups)
3. Today, we are going to look at remainders in division problems. Sometimes you get a remainder because you
have leftovers. What you do with the remainder depends on the situation. Can anyone think of some examples
of where you might have leftovers in a division problem? (Answers will vary.)
4. Let’s look at this problem. Pose problem (Transparency: BLM 5.3C_9): Read together, giving time for students to
think about the problem and think-pair-share what they know about the problem.
If 240 students and adults are
scheduled to go on a field trip by
minibus, how many minibuses
will be needed if each minibus
holds twenty passengers?
5. What kind of problem is this? (Division) How do you know? Think-Pair-Share (Know the total and have equal
groups.)
Begin creating an anchor
6. Give students time to solve problem and time to share their strategies.
chart with students for
 How did you solve the problem?
remainders. (BLM
 Did anyone solve it a different way?
5.3C_10)
 Is there another way we could have solved this problem?
 Is there a remainder? (Yes) What does it mean? What did you do with the remainder? (Dropped and the
Quotient is rounded up)
 Put problem in a sorting circle with a label, “Remainder dropped and the Quotient is rounded up”. BLM
5.3C_11 (Sorting Labels)
Remainder dropped
and the Quotient is
If 245 students and adults are
scheduled to go on a field trip by
minibus, how many minibuses will
be needed if each minibus holds
twenty passengers?
7. Ok, now let’s look at a 2nd problem. Pose problem: (Transparency: BLM 5.3C_9)
There are 200 books in the
bookcase. If I wanted to give
away 15 books per student, how
many students would get 15
books?
Page 53 of 64
8. What kind of problem is this? (Division) How do you know? Think-Pair-Share (Know the total and have equal
groups.)
9. Give students time to solve the problem and time to share their strategies.
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
 Is there a remainder? (Yes.) What does it mean? What did you do with the remainder? (Dropped and the
Quotient remains the same.)
 Put problem in a sorting circle with the label, “Dropped and the Quotient remains the same”. BLM 5.3C_11
(Sorting Labels)
Dropped and the
Quotient is remains the
same
There are 200 books in the
bookcase. If I wanted to give
away 15 books per student,
how many students would
get 15 books?
10. Ok now let’s look at another problem. Pose problem: (Transparency: BLM 5.3C_9)
11. What kind of problem is this? (Division) How do you know? Think-Pair-Share (Know the total and have equal
groups.)
If there are 150 cookies to be
shared between 12 students,
how many cookies will each
student receive?
12. Give students time to solve the problem and time to share their strategies.
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
 Is there a remainder? (Yes.) What does it mean? What did you do with the remainder? (Write as a
fraction.)
 Put problem in a sorting circle with the label, “Written as a Fraction”. BLM 5.3C_11 (Sorting Labels)
13. Ok, now let’s look at another problem. Pose problem: (Transparency: BLM 5.3C_9)
Linda had 65 pieces of candy to
give out on Valentine’s Day. She
gave the same number of
candies to each of her 9 best
friends. How many candies were
left over?
14. What kind of problem is this? (Division) How do you know? Think-Pair-Share (Know the total and have equal
groups.)
15. Give students time to solve problem and time share their strategies.
 How did you solve the problem?
 Did anyone solve it a different way?
 Is there another way we could have solved this problem?
 Is there a remainder? (Yes) What does it mean? What did you do with the remainder? (The remainder is
the answer)
 Put problem in asorting circle with a label, “The Remainder is the Answer”. BLM 5.3C_11 (Sorting Labels)
Page 54 of 64
Look for the following:
 Does the student use division to solve problems involving a whole number?
 Can the student identify the information necessary to solve the problem?
 Can the student show their work? Are their strategies clear?
 Can the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
 Does the student correctly interpret the remainder?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Can the student talk about the reasonableness of his or her solution?
 Can the student talk about the remainder and what it means?
Debriefing:
 Lay out all the sorting circles to compare remainder problem types. (Or use the anchor chart you just created with
the students.)
Dropped and the
Quotient is rounded
If 245 students and adults are
scheduled to go on a field trip by
minibus, how many minibuses will
be needed if each minibus holds
twenty passengers?
Dropped and the
Quotient remains the
same
There are 200 books in the
bookcase. If I wanted to give
away 15 books per student,
how many students would
get 15 books?
Remainder is written
as a fraction
The remainder is the
answer
If there are 150 cookies to be
shared between 12 students,
how many cookies will each
student receive?
Linda had 65 pieces of candy
to give out on Valentine’s
Day. She gave the same
number of candies to each of
her 9 best friends. How many
candies were left over?
Debriefing Questions:
 What do you do with the remainder? (It depends on the problem. Sometimes the remainder was dropped and
the quotient stayed the same or was rounded up. Sometimes the remainder was written as a fraction. And
sometimes the question is asking for the left over so the remainder is the answer.)
 What do you notice about the type of problem where the “remainder is dropped and the quotient is
rounded”? (Answers will vary.) Can you think of other types of situations that you would need to do this
with the quotient? (Answers will vary but look for people fitting in cars, boats, buses, etc., where you can’t cut to
give a fraction of it.)
 What do you notice about the type of problem where the “remainder is dropped and the quotient remains
the same”? (Answers will vary.) Can you think of other types of situations where you would need to do this
with the quotient? (Answers will vary but look for something where you only have a certain amount and you want
to share things equally like candies, books, toys, etc. and you can’t cut to give a fraction.)
 What do you notice about the type of problem where the “remainder is written as a fraction”? (Answers will
vary.) Can you think of other types of situations that you would need to do this with the quotient? (These
problems will usually be food that is easy to cut into pieces.)
Page 55 of 64
BLM 5.3C_9
If 245 students and
adults are scheduled
to go on a field trip by
minibus, how many
minibuses will be
needed if each
minibus holds twenty
passengers?
If there are 150
cookies to be shared
between 12 students,
how many cookies will
each student receive?
There are 200 books
in the bookcase. If I
wanted to give away
15 books per student,
how many students
would get 15 books?
Linda had 65 pieces of
candy to give out on
Valentine’s Day. She
gave the same
number of candies to
each of her 9 best
friends. How many
candies were left
over?
Page 56 of 64
BLM 5.3C_10 (Sample Anchor Chart—your class Anchor Chart should be created with your students in class)
What about the Remainder?
Sometimes you get a remainder because you have leftovers.
What you do with the remainder depends on the situation.
Dropped and the Quotient is rounded up
Dropped and the Quotient remains the same
If 245 students and adults are scheduled to go
on a field trip by minibus, how many
minibuses will be needed if each minibus
holds twenty passengers?
There are 200 books in the bookcase.
If I wanted to give away 15 books per
student, how many students would get
15 books?
Record a student’s strategy (a good
one) here showing all the steps they
used to solve the problem.
Record a student’s strategy here
showing all the steps they used to
solve the problem.
Model writing each
answer in complete
sentences and
boxing answer.
Thirteen mini-buses will need to
hold all twenty passengers.
Written as a Fraction
If there are 150 cookies to be shared
between 12 students, how many cookies
will each student receive?
Record a student’s strategy here
showing all the steps they used to
solve the problem.
1
Each student will receive 12 cookies.
2
Each student will bet 13 books.
The remainder is the answer
Linda had 65 pieces of candy to
give out on Valentine’s Day. She
gave the same number of candies
to each of her 9 best friends. How
many candies were left over?
Record a student’s strategy here
showing all the steps they used to
solve the problem.
Two candies were left over.
Page 57 of 64
BLM 5.3C_11 (Sorting Labels)
The remainder is…
The remainder is…
Dropped and the Quotient is
rounded up
Dropped and the Quotient
remains the same
The remainder is…
The remainder is…
Written as a Fraction
the answer
Page 58 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 9
TEKS: 5.3C
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(C) Use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends
without technology) including interpreting the remainder within a given context
Verbs: use, solve, interpreting
Vocabulary: divisor, dividend, quotient, division equation,
remainder
Guiding Questions: What do you know about division? What makes a situation a division situation? What strategies can
you use to solve a division problem? What do you do with the remainder?
Materials Needed: BLM 5.3C_12 (1 per student)
Math Tool: Multiplication Table
Lesson:
1. Yesterday we solved division problems with remainders.
2. What do you do with the remainder? (It depends on the problem. Sometimes the remainder was dropped and the
quotient stayed the same or was rounded up. Sometimes the remainder was written as a fraction. And sometimes the
question is asking for the left over so the remainder is the answer.)
3. Today, we are going to solve more division problems with remainders. Sometimes you get a remainder
because you have leftovers. As we learned yesterday what you do with the remainder depends on the
situation.
Guided Practice: (It will probably take 2 days to finish all the problems.)
4. Students solve problems (BLM 5.3C_12).
5. As students are working on problems, check for understanding.
 Was there a remainder?
 What did you decide to do with the remainder? Why?
 Is your answer reasonable? Having students show their work and label their answers should help them
determine if their answer is reasonable.
 How can you check the answer using the inverse operation?(Multiplication)
Answer Key:
Dropped and the Quotient is
rounded up
Dropped and the Quotient
is remains the same
Remainder written as a
fraction
The remainder is the
answer.
#3. A
#1. C
#4 C
#2. B
#5. D
#8. D
#12 B
#6. D
#7. B
#11. C
#9. A
#10. B
Look for the following:
 Does the student use division to solve problems involving a whole number?
 Can the student identify the information necessary to solve the problem?
 Can the student show their work? Are their strategies clear?
 Can the student solve the problem in more than one way?
 Does the number sentence match the student’s explanation?
 Does the student correctly interpret the remainder?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Can the student talk about the reasonableness of his or her solution?
Debriefing Questions:
 How do you know what to do with the remainder? (It depends on the problem. Sometimes the remainder was
dropped and the quotient stayed the same or was rounded up. Sometimes the remainder was written as a
fraction. And sometimes the question is asking for the leftover so the remainder is the answer.)
Page 59 of 64
BLM 5.3C_12
1 Gabby has a new kitten. The kitten eats 2 Victor opened a bag of pretzels and
3 ounces of cat food each day. How
counted 87. He gave each of 7 friends
many days can Gabby feed the kitten
an equal number of pretzels. How
from a 1-pound bag of cat food? (Hint:
many pretzels were left for himself?
There are 16 ounces in one pound.)
A 1
A 1
B 3
B 4
C 12
C 5
1
2
D 13
D 6
3 Delicious Bagels received an order for
80 doughnuts. If 1 box can hold 6
bagels, how many boxes will be
needed for 80 bagels?
4 Maria is wrapping packages. She has
76 feet of ribbon to make 8 bows. She
wants to use all of the ribbon. How
much ribbon does she have for each
bow?
A 14
A 8 feet
B 13
C 13
D 2
1
2
B 9 feet
C 9
1
feet
2
D 10 feet
5 On the day before the field trip, the final 6 Gus gave pencils to 12 of his friends.
He gave each friend an equal number
count turned out to be 360 students
of stickers and had some left over. If
and 12 adults. If a medium sized bus
Gus started with 190 stickers, what is
holds thirty-six passengers, how many
the greatest number of stickers he
medium sized buses would be needed?
could have given to each friend?
A 10
A 10
B 11
B 16
C 12
C 14
D 30
D 15
Page 60 of 64
BLM 5.3C_12 (continued)
7 Stephen had a birthday party and 8 Daniel’s book has 463 pages. If he
wanted to give out party favors. He had
reads 20 pages a day, how many days
65 toy cars to give out. He gave the
will it take him to read the entire book?
same number of toy cars to each of his
A 23 days
9 best friends. How many toy cars were
left over?
B 24 days
A 2
B 4
C 25 days
D 26 days
C 7
D 8
9 Mrs. Frizzle picked pecans over the 10 Mr. Fox made brownies for the 5th
weekend. She gave pecans to all 25 of
grade teachers at his school. He made
her students. She gave each student
15 brownies for the 6 teachers. He
an equal number of pecans and had
wants to give all of the brownies away
some left over. If Mrs. Frizzle started
to the 6 teachers. How many brownies
with 927 pecans, what is the greatest
will each teacher get?
number of pecans she could have
A 2
given to each student?
A 2
B 36
C 37
D 38
B 2
1
2
C 3
D 3
1
2
Page 61 of 64
Objective 1: Number, Operation, and Quantitative Reasoning
Lesson 10
TEKS: 5.3C
The student adds, subtracts, multiplies, and divides to solve meaningful problems.
(C) Use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends
without technology) including interpreting the remainder within a given context
Verbs: use, solve, interpreting
Vocabulary: divisor, dividend, quotient, division equation,
remainder
Guiding Questions: What do you know about division? What makes a situation a division situation? What strategies can
you use to solve a division problem? What do you do with the remainder?
Materials Needed: Sorting Circles (4 per pair), BLM 5.3C_12 (1 per student), BLM 5.3B_13 (1 set per student), BLM
5.3B_14 (1 per student)
Math Tool: Multiplication Table
Guided Practice:
 If students did not finish problems from yesterday, have them finish them today.
Lesson:
1. Yesterday we solved division problems with remainders.
2. What do you do with the remainder? (It depends on the problem. Sometimes the remainder was dropped and the
quotient stayed the same or was rounded up. Sometimes the remainder was written as a fraction. And sometimes the
question is asking for the leftover so the remainder is the answer.)
3. Today, you are going to work with a partner to check your answers and sort the problems that you solved by
what you did with the remainder.
Guided Practice:
4. Put students in pairs. Each pair will need 4 sorting circles, the problems they already solved (BLM 5.3C_12) and
Sorting Cards (BLM 5.3C_13)
5. Students work in pairs to make sure they agree with each others answers (correct if necessary). As they are checking
them, they will talk about what they did with the remainder and why. Then they will sort the problems accordingly.
Dropped and the
Quotient is
Dropped and
the Quotient
Remainder
written as a
The remainder
is the answer.
Debriefing Questions:
 How do you know what to do with the remainder? (It depends on the problem. Sometimes the remainder was
dropped and the quotient stayed the same or was rounded up. Sometimes the remainder was written as a fraction.
And sometimes the question is asking for the leftover so the remainder is the answer.)
Answer Key:
Dropped and the
Quotient is rounded up
Dropped and the
Quotient is remains the same
Remainder
written as a fraction
The remainder is
the answer.
#3. A
#1. C
#4 C
#2. B
#5. D
#8. D
#12 B
#6. D
#7. B
#11. C
#9. A
#10. B
Look for the following:
 Does the student correctly interpret the remainder?
 Can the student self-correct any errors?
Listen for the following:
 Does the student’s explanation match his or her written work?
 Can the student talk about the reasonableness of his or her solution?
TAKS Connection:
 Blackline Master 5.3C_14 (Answers: Problem #1: B, Problem #2: D, Problem #3: C)
Page 62 of 64
BLM 5.3B_13 (Sorting Labels)
The remainder is…
The remainder is…
Dropped and the Quotient is
rounded up
Dropped and the Quotient
remains the same
The remainder is…
The remainder is…
Written as a Fraction
the answer
The remainder is…
The remainder is…
Dropped and the Quotient is
rounded up
Dropped and the Quotient
remains the same
The remainder is…
The remainder is…
Written as a Fraction
the answer
Page 63 of 64
BLM 5.3B_14 (TAKS Connection)
1
Monica had a party and invited 7 of her best friends. She gave each friend an
equal number of small toy dolls and had some left over. If Monica started with
86 small toy dolls, what is the greatest number of toy dolls she could have
given to each friend?
A 2
B 12
C 12
1
2
D 13
2
A group of students needs to make at least $850 by washing cars this
Saturday to earn enough money to go to the State Drama Championship. They
are going to charge $16 to wash each car. How many cars will they need to
wash in order to make at least $850?
A 45
B 50
C 53
D 54
3
Trina opened a bag of pretzels and counted 128. She gave each of 13 friends
an equal number of pretzels. How many pretzels were left for herself?
A
9
C
11
B
10
D
12
Page 64 of 64