Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 03:
Suggested Duration: 01
Unit 03: Multiplication (14 days)
Possible Lesson 01 (6 days)
Possible Lesson 02 (4 days)
Possible Lesson 03 (4 days)
POSSIBLE LESSON 01 (6 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students recall multiplication facts using mathematical properties, multiplication charts, area models/arrays, and various numerical strategies such as doubles and “add
one more set” in mathematical and real­life situations.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
4.4
Number, operation, and quantitative reasoning.. The student multiplies and divides to solve meaningful problems involving whole
numbers. The student is expected to:
4.4A
Model factors and products using arrays and area models.
Supporting Standard
4.4B
Represent multiplication and division situations in picture, word, and number form.
Supporting Standard
4.4C
Recall and apply multiplication facts through 12 x 12.
Supporting Standard
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4.6
Patterns, relationships, and algebraic thinking.. The student uses patterns in multiplication and division. The student is expected to:
4.6A
Use patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in
related multiplication and division number sentences (fact families) such as 9 x 9 = 81 and 81 ÷ 9 = 9). Supporting Standard
Underlying Processes and Mathematical Tools TEKS:
4.14
Underlying processes and mathematical tools.. The student applies Grade 4 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
4.14A
Identify the mathematics in everyday situations.
4.14C
Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic
guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
4.15
Underlying processes and mathematical tools.. The student communicates about Grade 4 mathematics using informal language. The
student is expected to
4.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
4.15B
Relate informal language to mathematical language and symbols.
Performance Indicator(s):
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Grade 4/Mathematics
Unit 03:
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Grade4 Mathematics Unit03 PI01
Determine the multiplication fact needed to solve two real-life situations such as the following:
Mandy needed 11 dozen cookies for the school bake sale. How many cookies did she need?
Jared washed 8 cars to raise money for the soccer team. If he received $7 for each car, how much money did he receive?
Use a graphic organizer for each problem to record: (1) the multiplication fact and solution represented by the situation, (2) a sketch of the area model, (3) the related fact family,
and (4) a justification of the preferred recall strategy.
Standard(s): 4.4A , 4.4B , 4.4C , 4.6A , 4.14A , 4.14C , 4.15A , 4.15B
ELPS ELPS.c.1C , ELPS.c.4I , ELPS.c.5G
Key Understanding(s):
Multiplication facts can be recalled using a variety of models and strategies including problems in context, patterns in fact families, area models, partial products,
and other known facts.
When observing and recording a variety of strategies and mathematical ideas to solve real-life multiplication problems, thinking processes are revised, refined, and
valued, all which sharpen mathematical understanding.
Misconception(s):
Some students may think that 3 x 6 with 6 x 3 can be represented with the same addition sentence and write the addition sentence incorrectly (e.g., 3 + 3 + 3 + 3
+ 3 + 3 = 18, instead of 6 + 6 + 6 = 18).
Some students may think that 3 x 6 with 6 x 3 can be represented with the same word sentence and write the word sentence as 6 groups of 3 instead of 3 groups
of 6.
Some students may think that for the multiples of 11, they can multiply digits by 1 (e.g., 11 x 3 = 33 because 1 x 3 = 3 and 1 x 3 = 3).
Underdeveloped Concept(s):
Some students may not recognize that they can use easier and/or known facts to help them find solutions to harder and/or unknown facts (e.g., 3 x 8 = 3 x 5 + 3
x 3).
Some students may not realize when multiplying a two-digit number by a one-digit number, they are multiplying by tens and ones (e.g., 24 x 3 = 20 x 3 + 4 x 3).
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Grade 4/Mathematics
Unit 03:
Suggested Duration: 01
Vocabulary:
area model
array
commutative property of multiplication
distributive property of multiplication
factor
identity property of multiplication
multiplication
partial product
product
square number
zero property of multiplication
Materials:
cardstock (4 sheets per 2 students)
cardstock (optional) (10 sheets per 2 students)
cardstock (optional) (15 – 18 sheets per teacher)
counter (transparent) (1 per teacher)
highlighter (1 per teacher, 1 per student)
marker (optional) (1 per teacher)
math journal (1 per student)
Multiplication Chart (previously created) (1 per teacher, 1 per student)
paper (8 ½” by 11”) (optional) (1 sheet per student)
paper lunch sack (optional) (3 per teacher)
plastic zip bag (sandwich sized) (2 per 2 students)
plastic zip bag (sandwich sized) (optional) (1 per 2 students)
scissors (1 per teacher)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Cupcake Arrangement KEY
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Grade 4/Mathematics
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Cupcake Arrangement
Cupcake Arrangement Problem Cards
Cupcake Arrangement Array Cards
Cupcake Arrangement Recording Sheet KEY
Cupcake Arrangement Recording Sheet
Multiplication on a Grid – Notes
Multiplication on a Grid KEY
Multiplication on a Grid
Van Travel Multiplication Model KEY
Van Travel Multiplication Model
Math Journal Directions (optional)
Centimeter Grid Paper
Multiplication Property Practice KEY
Multiplication Property Practice
Multiplication Chart
Blank Multiplication Chart
One Fact at a Time Sample KEY
One Fact at a Time
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Triangular Flash Cards
Square Number Dot Grid KEY
Square Number Dot Grid
Square Facts KEY
Square Facts
Centimeter Grid Work Paper
Multiple Logic
Multiple Logic Practice KEY
Multiple Logic Practice
Fact Concept Map Assessment Sample KEY
Fact Concept Map Assessment PI
Fact Cards PI
Fact Concept Map Alternate Assessment PI
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
Suggested Instructional Procedures
Notes for Teacher
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Topics:
Spiraling Review
Arrays to area models for multiplication fact families
Engage 1
Students connect arrays to area models for multiplication fact families.
ATTACHMENTS
Teacher Resource: Cupcake
Arrangement KEY (1 per teacher)
Instructional Procedures:
1. Prior to instruction create a card set: Cupcake Arrangement Problem Cards for every 2
students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag.
Additionally, create card set: Cupcake Arrangement Array Cards by copying on cardstock,
laminating, cutting apart, and placing in a plastic zip bag.
2. Place students in groups of 4. Explain to students that they may work either as a group or with a
partner.
3. Display page 1 of teacher resource: Cupcake Arrangement. Invite a student to read the problem
aloud. Model the problem using circles to represent the cupcakes.
Ask:
What is an array? (a set of items arranged in rows and columns)
How many cupcakes will be in the first row of the array? How do you know? (5,
Teacher Resource: Cupcake
Arrangement (1 per teacher)
Card Set: Cupcake Arrangement
Problem Cards (1 set per 2 students)
Card Set: Cupcake Arrangement Array
Cards (1 set per 2 students)
Teacher Resource: Cupcake
Arrangement Recording Sheet KEY (1
per teacher)
Handout: Cupcake Arrangement
Recording Sheet (1 per student)
MATERIALS
because the problem states that there are 5 cupcakes in each row.)
cardstock (4 sheets per 2 students)
How could the array be drawn to model this story? Answers may vary. Draw 6 rows with 5
scissors (1 per teacher)
cupcakes in each row; etc.
plastic zip bag (sandwich sized) (2 per 2
students)
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Notes for Teacher
4. Using page 1 of teacher resource: Cupcake Arrangement, explain to students that on the first
10 x 10 grid, each box represents a cupcake.
Ask:
How should these boxes be shaded to represent this array? Answers may vary. Shade 6
rows of boxes with 5 boxes in each row; etc.
Shade-in the appropriate boxes.
What number sentence could be used to represent this area model? (6 x 5 = 30)
5. Remind students that by multiplying the number of rows by the number of cupcakes in each row,
a total number of cupcakes can be quickly determined. Explain to students that they do not have
to tediously count each individual cupcake because they can multiply the number of rows of
symbols by the number of symbols in each row to find the total number of symbols. On the grid,
this total is equivalent to the area, in square units, of the rectangle.
Ask:
How is an area model like an array? Answers may vary. They both have rows and
columns and can be used to represent a multiplication situation; etc.
How is an area model different from an array? Answers may vary. The array’s rows and
columns are represented in separate pieces – creating gaps, whereas the area model’s rows
and columns are on a grid covering the entire area of the model; etc.
6. Using page 2 of teacher resource: Cupcake Arrangement, display the second 10 x 10 grid and
explain to students that the same product (in this case 30) can be represented on this grid by
shading-in a different number of shaded boxes in each row.
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7. Instruct student groups to discuss how they think the grid can be shaded to represent the same
product. Facilitate a class discussion about how the grid could be shaded as a 3 x 10; 5 x 6; or
10 x 3.
Ask:
Can you show a 2 x 15 or a 15 x 2 area model? Why or why not? (Yes, I could if I had a
larger grid.)
8. Place students in pairs. Distribute handout: Cupcake Arrangement Recording Sheet to each
student and card sets: Cupcake Arrangement Problem Cards and Cupcake Arrangement
Array Cards to each pair.
9. Instruct student pairs to shuffle the cards from card set: Cupcake Arrangement Problem
Cards and place them in a pile.
10. Instruct student pairs to lay the cards from card set: Cupcake Arrangement Array Cards on
the desk so both students can see them.
11. Instruct student pairs to take turns selecting a problem card from card set: Cupcake
Arrangement Problem Cards, turning it over, and reading the problem aloud. Explain to
students that both students are to determine the array that matches the problem situation, record
the array card letter next to the problem card number on their handout: Cupcake Arrangement
Recording Sheet, work together to shade-in the area model for this array, write the number
sentence that corresponds to that model, and record the related fact families for each number
sentence. Allow time for students to complete the activity. Monitor and assess students to check
for understanding. Common errors will include shading the grids inappropriately (e.g., 3 x 4
shaded instead of 4 x 3). Facilitate a class discussion regarding student solutions.
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Notes for Teacher
Topics:
Spiraling Review
Grid area models for multiplication fact families
Explore/Explain 1
Students use grids to create area models for multiplication fact families.
ATTACHMENTS
Teacher Resource: Multiplication on a
Grid – Notes (1 per teacher)
Instructional Procedures:
1. Record the following question for the class to see: How is multiplication like addition? Instruct
students to record their answer in their math journal. Facilitate a class discussion about the
similarities of multiplication and addition to include how both are putting groups together to find an
amount.
2. Display teacher resource: Multiplication on a Grid – Notes with only the array showing.
Teacher Resource: Multiplication on a
Grid KEY (1 per teacher)
Handout: Multiplication on a Grid (1 per
student)
Teacher Resource: Van Travel
Multiplication Model KEY (1 per teacher)
Teacher Resource: Van Travel
Facilitate a class discussion about the array, revealing each portion that addresses the question.
Multiplication Model (1 per teacher)
Ask:
Teacher Resource: Math Journal
Directions (optional) (1 per teacher)
What would 4 rows of 3 look like on this grid? Answers may vary. Rows 1, 2, 3, and 4 with
3 boxes shaded in each row; etc.
MATERIALS
What are the factors for this grid? How do you know? (4 and 3) Answers may vary. They
are the numbers I am multiplying; etc.
math journal (1 per student)
How could you write an addition number sentence for this array? Answers may vary. 3
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+ 3 + 3 + 3 = 12; etc.
How could you write this number sentence in words? Answers may vary. 4 rows of 3
equal 12; 4 groups of 3 equal 12; etc.
What part of the model would represent the product of this problem? (The total or sum
of all the rows and columns.)
What is the product of this problem? (12)
What would this model look like as a multiplication sentence? (4 × 3 = 12)
Notes for Teacher
TEACHER NOTE
When recording an addition number sentence for
an array, some students may record the incorrect
representation (e.g., 4 groups of 3 as 4 + 4 + 4 =
12 instead of 3 + 3 + 3 + 3 = 12). Be sure to make
the distinction between the two representations: 4
groups of 3 and 3 groups of 4.
3. Display teacher resource: Van Travel Model Multiplication. Read the problem aloud to
students.
Ask:
RESEARCH
According to Marilyn Burns and Robyn Sibley
(2001), journal writing can be a valuable technique
How could this problem be modeled on the grid provided? How do you know?
to further develop and enhance mathematical
Answers may vary. Shade the first 6 rows with 6 boxes shaded in each row. The rows could
thinking and communication skills in mathematics.
represent the vans and the boxes could represent the people; etc.
How could this problem be written as an addition number sentence? (6 + 6 + 6 + 6 + 6
+ 6 = 36)
How could this number sentence be written in words? Answers may vary. 6 rows of 6
equal 36; 6 groups of 6 equal 36; etc.
What would this model look like as a multiplication number sentence? (6 × 6 = 36)
4. Distribute handout: Multiplication on a Grid to each student. Review the directions and instruct
students to complete the handout individually. Explain to students that they are to use their own
numbers to create original area models for numbers 5 and 6 on the handout. Facilitate a class
discussion about possible scenarios for creating a multiplication problem situation for numbers 9
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and 10.
Topics:
Zero property of multiplication
MATERIALS
math journal (1 per student)
Identity property of multiplication
Explore/Explain 2
TEACHER NOTE
Students use reasoning skills to model the zero property and identity property of multiplication with
The purpose of introducing and using the correct
pictorial representations.
terminology in naming the various properties of
multiplication is to identify these properties as
Instructional Procedures:
1. Record the following instructions for the class to see: Show me 3 groups of 0. Now, show me 1
group of 8. Instruct students to use their math journals to record the two models. Facilitate a
class discussion about the models.
tools that can be used to help recall multiplication
facts. If these properties are used on a word wall,
examples should be emphasized. (e.g., Zero
Property of Multiplication example 21 x 0 = 0; 455
x 0 = 0; etc.)
2. Record the following for the class to see: 4 x 0 = ___; 0 x 9 = ___; 21 x 0 = ____.
Ask:
What do you know about any number multiplied by zero? (The product is zero.)
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What is the product of each problem, and can you describe the pattern? (0; the
product is always zero.)
Explain to students that this is called the Zero Property of Multiplication and it states that the
product of any number and zero is 0. Record the property name and definition for the class to
see.
3. Instruct students to record “Zero Property of Multiplication,” the definition, and the list displayed
for the class as examples in their math journal.
Ask:
What would happen if you multiplied different numbers by 0? How do you know?
Answers may vary. I would get 0 because no matter how many groups I had, there would be
nothing, 0, in each group; etc.
4. Record the following for the class to see: 4 x 1 = ___; 1 x 9 = ___; 21 x 1 = ___.
Ask:
What is the product of each problem and can you describe the pattern? (The product is
the number itself; the product is always the number itself.)
Explain to students that this is called the Identity Property of Multiplication and it states that
the product of any number and one is that number. Record the property name and definition
for the class to see.
5. Instruct students to record “Identify Property of Multiplication” in their math journal and then list
the displayed class examples. Discuss with students how the number being multiplied by 1
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maintains its “identity.”
Ask:
What would happen if you multiplied different numbers by 1? How do you know?
Answers may vary. I would get the same number I multiplied by, because no matter how many
items I have in the group, there is only one group containing those items; etc.
What are the multiples of 1? (1, 2, 3, 4, etc.)
Remind students that a multiple is a number that is a product of a number and another number.
So if one of the numbers or factors is one, then the product is the other number or factor.
3
Topics:
Commutative property of multiplication models
ATTACHMENTS
Teacher Resource: Centimeter Grid
Paper (1 per teacher)
Explore/Explain 3
Teacher Resource: Multiplication
Students use pictorial representations to model the commutative property of multiplication.
Property Practice KEY (1 per teacher)
Handout: Multiplication Property
Instructional Procedures:
Practice (1 per student)
1. Record the following problem situation for the class to see: Find two ways to arrange 8 tables in
equal groups.
2. Instruct students to find two arrangements and write a number sentence for each arrangement in
their math journal. Allow time for students to complete the activity. Monitor and assess students
MATERIALS
math journal (1 per student)
to check for understanding. Facilitate a class discussion about student solutions.
Ask:
TEACHER NOTE
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How can 8 tables be arranged in equal groups? (2 rows of 4 tables, 2 groups of 4 tables,
2 fours, or 2 x 4 = 8; or 4 rows of 2 tables, 4 groups of 2 tables, 4 twos, or 4 x 2 = 8.)
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Notes for Teacher
If students struggle with this problem, suggest that
they draw pictures of the rows.
How are these number sentences alike? Different? (Same factors, same product; the
order is reversed.)
3. Record the following for the class to see: 4 + 5 = ___; 5 + 4 = ___.
4. Instruct the students to find each sum.
Ask:
TEACHER NOTE
A reminder that the purpose of introducing and
Which addition property does this show? (Commutative Property of Addition)
using the correct terminology in naming the
In the table problem you did something similar with multiplication. What do you think
various properties of multiplication is to identify
this property is called? (Commutative Property of Multiplication)
these properties as tools that can be used to help
recall multiplication facts.
5. Display teacher resource: Centimeter Grid Paper. Draw a rectangle showing 3 rows of 8
squares for the class to see. Label the lengths and sides as shown.
For the commutative property, examples in
addition, as well as, multiplication should help
students have a better understanding of the
numerical relationships involved.
6. Explain to students that the number of squares in each rectangle can be thought of as 3 rows of 8
squares, 3 groups of 8 squares, 3 eights, or 3 x 8 squares.
Ask:
How many squares are in the rectangle? (24)
It should be pointed out to students that although
the addends have been interchanged, the value is
the same. The same is true for multiplication. Do
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not say to students “3 x 6” is the same as “6 x 3”.
7. Invite a student to rotate the displayed rectangle 90 degrees for the class to see.
Ask:
Instead, let them know that their values are the
same, but the representations are different. For
example:
How would you describe the rectangle now? (8 rows of 3 squares, 8 groups of 3 squares,
8 threes, or 8 x 3 squares)
Has the total number of squares in the rectangle changed? (No, they both have a total
of 24 squares.)
RESEARCH
Automaticity is the goal for mastery of basic facts.
8. Remind students that because the number of squares in the rectangle did not change when you
rotated it, then it’s true that 3 x 8 = 8 x 3. Explain to students that in the Commutative Property
of Multiplication, order does not matter, and that it states that two numbers multiplied in any order
give the same product. Record the property name and definition for the class to see.
Benjamin Bloom (1986) states that automaticity is
the ability to perform a skill unconsciously with
speed and accuracy.
9. Facilitate a class discussion about the meaning of the word “commute” (e.g., When you
commute to work, you go back and forth from home and work, and the distance is the same both
ways.) and that “commuting” is like switching places. Write this property name and its definition
for the class to see. Instruct students to record the name of the property and the definition in their
math journal.
10. Place students in pairs and distribute handout: Multiplication Property Practice to each
student. Instruct student pairs to complete the handout. Allow time for students to complete the
multiplication practice. Monitor and assess students to check for understanding. Facilitate a
class discussion about student solutions.
Topics:
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Spiraling Review
Multiplication chart facts
Explore/Explain 4
ATTACHMENTS
Students use multiplication charts to determine which multiplication facts they already know and
Teacher Resource: Multiplication Chart (1
which ones they need to learn.
per teacher)
Handout: Multiplication Chart (1 per
Instructional Procedures:
1. Display teacher resource: Multiplication Chart. Place students in groups of 4 and distribute
handout: Multiplication Chart to each student.
student)
Handout (optional): Blank Multiplication
Chart (1 per student)
2. Using the displayed teacher resource: Multiplication Chart, demonstrate how to use a
multiplication grid by placing a transparent counter on 24 and moving over and up (or vice versa)
to find 3 and 8. Repeat the process again to find 8 and 3.
MATERIALS
counter (transparent) (1 per teacher)
paper (8 ½” by 11”) (optional) (1 sheet per
student)
TEACHER NOTE
For students who struggle with moving over and up
on the multiplication chart, use a half sheet of
paper to help them find products. For example, if a
student wanted to find the product of 7 and 6, you
would instruct them to use their piece of paper to
slide along their chart as follows:
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Instruct students to use their handout: Multiplication Chart to find the other multiplication
sentences of 24 (e.g., 2 x 12, 12 x 2, 4 x 6, 6 x 4, etc.).
Slide your piece of paper along the top of
the chart until it is right next to the column
3. Instruct student groups to examine their handout: Multiplication Chart and look for any patterns
with the 7 at the top.
they may see. Allow time for students to identify several patterns. Facilitate a class discussion
Next, slide the paper down so the bottom
about patterns in the multiplication table.
edge is just above the row beginning with
Ask:
the 6.
What patterns do you see in the multiplication table? Answers may vary. The products in
the 5’s row all end in either 5 or 0; the products in the 10’s row all end in 0; the products in the
9’s row and column all decrease by 1 in the ones place and increase by 1 in the tens place;
Look at the bottom right corner of the
paper. What number does the corner point
to? (42) This is the product of 7 and 6.
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Notes for Teacher
etc.
4. Facilitate a class discussion for students to identify which multiplication facts are easy for them.
Explain to students that the 0’s and 1’s should be easy. Using the displayed teacher resource:
Multiplication Chart, demonstrate crossing off the 0 and 1 multiplication facts. Instruct students
to replicate the model on their handout: Multiplication Chart.
TEACHER NOTE
To develop a firm foundation in multiplication,
Grade 4 students need to learn the multiplication
table. This can seem overwhelming and often
students are defeated even before they start. By
5. Explain to students that without the zeroes, there are 144 facts on a 12 x 12 multiplication chart.
Ask:
beginning with the multiplication chart and
demonstrating the facts that most students
already know, the task does not seem so
What other facts can you agree are easy? Answers may vary. 2’s, 5’s, and 10’s are easy;
etc.
daunting. In fact, many students should be
encouraged by how much they already know and
how little they have left to learn.
6. Using the displayed teacher resource: Multiplication Chart, demonstrate crossing off the 2, 5,
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and 10 multiplication facts. Instruct students to replicate the model on their handout:
Multiplication Chart.
Ask:
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Notes for Teacher
TEACHER NOTE
An online interactive Multiplication Table can be
found on the NCTM Illuminations website. This
table can be used for additional practice or set-up
as a computer center activity.
TEACHER NOTE
Square numbers will be defined and investigated
further in this lesson. Please note that there are
different interpretations as to whether zero is a
square number. Zero is highlighted as a square
number here because the definition for square
Can the elevens be crossed off as well? Explain Answers may vary. Yes, because of the
pattern of 11, 22, 33, 44, 55; etc.
numbers being used is, “A number that is the
product of a whole number and itself.” By this
definition, zero is indeed a square number,
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7. Using the displayed teacher resource: Multiplication Chart, demonstrate crossing off the 11
multiplication facts. Instruct students to replicate the model on their handout: Multiplication
Chart.
Notes for Teacher
because 0 = 0 x 0 and zero is a whole number.
However, another definition has more of a
“geometric” interpretation. In order to measure the
area of a square that is 0 units on a side, you
don’t really have a square to begin with, you have
nothing.
RESEARCH
John Van de Walle (2006) notes some alternate
methods for finding hard facts:
(1) Double and double again: 6 x 4; Double 6 is
12. Double again is 24.
(2) Double and one more set: 7 x 3; Double 7 is
14. One more 7 is 21.
Ask:
(3) Half then double (even factors only): 6 x 4; 3
How many facts are remaining? (49)
times 4 is 12. Double 12 is 24.
Are any of these facts commutative, like 3 x 4 and 4 x 3? (yes)
(4) Add one more set: 6 x 7; 5 sevens is 35 and
one more 7 is 42.
8. Using the displayed teacher resource: Multiplication Chart, circle the 12 for 4 x 3 and then draw
Note: Pay attention to how students add 35 and 7.
a line through its commutative fact (3 x 4) as shown below. Instruct students to circle the first
If you see finger counting, the idea of composing
commutative fact and then to draw a line through the other. Continue to model several other
and decomposing numbers needs to be
examples until students begin to see the pattern.
addressed.
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Notes for Teacher
ADDITIONAL PRACTICE
The handout (optional): Blank Multiplication
Chart is provided for additional practice of
multiplication facts. This practice consists of
students using various strategies to complete the
chart. The handout may be used as independent
practice or homework.
9. Place students in pairs. Instruct student pairs to find as many commutative facts as possible,
circle the first commutative fact and then draw a line through the other. Allow time for student
pairs to complete the activity. Monitor and assess students to check for understanding, pointing
out student’s examples they may or may not have found, and the usefulness of the commutative
property for eliminating 21 of the 42 commutative facts.
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Notes for Teacher
Ask:
How many facts are remaining on the multiplication grid? (7)
What do you notice about these facts? Do they follow a pattern? Answers may vary.
They follow a diagonal pattern on the chart; the factors for each are the same (e.g., 3 x 3 = 9,
4 x 4 = 16); etc.
Explain to students that these numbers are called square numbers.
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10. Instruct students to count the circled and highlighted facts on their handout: Multiplication
Chart. (28) Explain to students that these are the facts that they will spend most of their time
attempting to learn and recall.
Ask:
If you didn’t know how to solve the multiplication problem 6 x 8, how could you
figure it out by using something you did know? Answers may vary. I could use 5 x 8 and
add one more 8; etc.
Explain to students that their method should include some mental computation and should
not rely on repeated addition only.
11. Instruct student pairs to identify a method for finding the x4 facts and share their ideas with
another pair of students. Allow time for student pairs to develop their method. Monitor and assess
students to check for understanding. Facilitate a class discussion about the identified strategies.
page 24 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
Ask:
What strategies do you know for finding the x4 facts? Answers may vary. You can double
a number twice or use the x2 fact and double it; etc.
12. Invite a student to demonstrate, for the class to see, and explain how they might solve a x4
problem. If students need more time with alternate strategies for remembering hard facts,
continue questioning using the x3, x6, and x8 facts.
Instruct students to keep their handout: Multiplication Chart for further instruction.
4
Topics:
Spiraling Review
Multiplication facts
Explore/Explain 5
Students use one fact at a time graphic organizers to assist in recalling difficult multiplication facts.
ATTACHMENTS
Teacher Resource: One Fact at a Time
Sample KEY (1 per teacher)
Instructional Procedures:
1. Distribute a copy of handout: One Fact at a Time to each student.
2. Display teacher resource: One Fact at a Time. Record the multiplication fact 3 x 4 = 12 in the
Teacher Resource: One Fact at a Time (1
per teacher)
Handout: One Fact at a Time (15 per
student)
center and demonstrate how to complete the remainder of the handout using the example shown
Class Resource (optional): Triangular
below. Instruct students to replicate the model on their handout: One Fact at a Time.
Flash Cards (1 set per 2 students)
Ask:
page 25 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
MATERIALS
Multiplication Chart (previously created) (1
per teacher, 1 per student)
cardstock (optional) (10 sheets per 2
students)
scissors (optional) (1 per teacher)
plastic zip bag (sandwich sized) (optional)
(1 per 2 students)
TEACHER NOTE
The facts in this lesson are normally identified as
facts that are difficult for students. However, you
may choose to substitute other facts according to
the needs of the students in your classroom.
How could you describe this multiplication equation in words? (3 groups of 4 is 12.)
How is multiplication like addition? Answers may vary. Both addition and multiplication put
things together or show grouping of items; etc.
ADDITIONAL PRACTICE
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Is there more than one way to draw an array or area model of this fact? How do you
know? (Yes, because the fact is commutative, therefore the array or area model can be
displayed two different ways.)
For the Area/Array Model, instruct students to label each side to clarify the dimensions being
used.
What is a related fact family? (A set of related addition and subtraction facts or
multiplication and division facts.)
What would a related fact family sentence look like for this problem? How do you
know? (4 x 3 = 12; 12 ÷ 3 = 4; 12 ÷ 4 = 3; because changing the order of the factors does
Notes for Teacher
Class resource (optional): Triangular Flash
Cards is provided for additional practice of the
recall of multiplication facts.
Prior to instruction, create a set for every 2
students by copying on cardstock, laminating,
cutting apart, and placing in plastic zip bag. These
flash cards may be used for basic facts mastery.
Each card shows a family of four facts. Cover the
not change the product; and multiplication and division are related.)
shaded number with your hand and you have two
How are multiplication and division related? Answers may vary. Multiplication and
multiplication problems. Cover each un-shaded
division are inverse operations. The factors and product of a multiplication problem are part of
number and you have a division problem.
a fact family from which a division problem can be derived. Both operations use groups or
The relationship between multiplication and
sets; etc.
division facts is emphasized. Students will
How can fact families and multiplication facts help you solve division problems?
become familiar with this relationship, learn
Answers may vary. Fact families include 2 multiplication and 2 division facts. So,
families of facts, and gain efficiency in
multiplication facts can be used to solve division problems because the factors of the
memorizing. These cards can be used as a quick
multiplication problem are the divisor and the quotient in the division problem; etc.
daily review of fact families or can be sent home
What are some of the elements needed to create a multiplication word problem?
for review.
Answers may vary. An essential element would be a problem that involved grouping or equal
groups; etc.
3. Display the previously created Multiplication Chart for the class to see. Instruct students to
examine their previously created Multiplication Chart.
Ask:
page 27 of 99 Enhanced Instructional Transition Guide
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How many other facts do you need to practice? (27) Note: Some students may say “28”
because that is how many facts are circled on their Multiplication Chart.
Explain to students that they have just completed one of the facts (3 x 4 = 12) as an example
on their handout: One Fact at a Time.
4. Record the following multiplication facts for the class to see.
5. Place students in pairs and distribute 7 additional copies of handout: One Fact at a Time to
each student. Instruct student pairs to complete a handout for each of the displayed multiplication
facts. Allow time for students to complete the 7 multiplication facts. Monitor and assess students
to check for understanding, noting the strategies they use to find the various solutions on the
maps.
6. Invite several student volunteers to demonstrate/explain their solutions/strategies for each of the
displayed multiplication facts to the class.
Ask:
How many other facts do you need to practice? (20)
7. Record the following multiplication facts for the class to see.
page 28 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
8. Distribute 7 additional copies of handout: One Fact at a Time to each student. Instruct students
to complete a handout for each of the displayed multiplication facts. Allow time for students to
complete the 7 multiplication facts. Monitor and assess students to check for understanding,
noting the strategies they use to find the various solutions on the maps.
Topics:
Square numbers
ATTACHMENTS
Teacher Resource: Square Number Dot
Grid KEY (1 per teacher)
Explore/Explain 6
Teacher Resource: Square Number Dot
Students use dot arrays to investigate multiplication facts that result in square numbers.
Grid (1 per teacher)
Handout: Square Number Dot Grid (1 per
Instructional Procedures:
1. Display square dot arrays for 4, 9, and 16 for the class to see.
student)
Teacher Resource: Square Facts KEY (1
per teacher)
Handout: Square Facts (1 per student)
MATERIALS
Multiplication Chart (previously created) (1
Ask:
What might the next array in this pattern look like? How do you know? Answers may
per teacher, 1 per student)
highlighter (1 per teacher, 1 per student)
vary. It would have 5 rows and 5 columns of dots, because each row and column pattern is 2by-2 (2 x 2), 3-by-3 (3 x 3), and 4-by-4 (4 x 4). So the next number should be 5-by-5, creating
page 29 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
a 5 x 5 dot array; etc.
2. Explain to students that square numbers can be formed by multiplying a number by itself, and
that each square number can be represented as an array square of dots.
3. Display teacher resource: Square Number Dot Grid. Distribute handout: Square Number Dot
Grid to each student.
Ask:
What is 1 x 1? (1)
4. Using the displayed teacher resource: Square Number Dot Grid, model recording the fact and
bracket a single dot in the upper left-hand corner of the grid. Instruct students to replicate the
model on their handout: Square Number Dot Grid.
Ask:
What would be the next square number? How do you know? (4, because a 2-by-2 dot
array contains 4 dots.)
How could you model this square number on the grid? Answers may vary. You could
draw a line to show each row and column; etc.
page 30 of 99 Enhanced Instructional Transition Guide
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5. Using the displayed teacher resource: Square Number Dot Grid, invite a student to
demonstrate recording the fact and bracket for 4.
6. Place students in pairs. Instruct student pairs to continue recording each fact and bracket for all
the square numbers on their handout: Square Number Dot Grid. Allow time for student pairs to
complete the activity. Monitor and assess students to check for understanding. Facilitate a class
discussion about the arrays created.
Ask:
Look at the arrays drawn above, why do you think these numbers are called square
numbers? Answers may vary. Each row and column have the same number of dots; each
has the same length and width; each array of dots forms a square; etc.
7. Display the previously created Multiplication Chart. Instruct students to refer to their previously
created Multiplication Chart.
Ask:
What numbers are square numbers on this chart? How do you know? (1, 4, 9, etc.;
because each factor is the same e.g., 1 x 1; 2 x 2; etc.)
8. Distribute a highlighter to each student.
page 31 of 99 Enhanced Instructional Transition Guide
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9. Using the displayed Multiplication Chart, model highlighting the 1, 4, 9, and 16. Instruct students
to replicate the model on their Multiplication Chart.
10. Instruct student pairs to identify and highlight the remaining square numbers on their
Multiplication Chart. Allow time for students to complete the activity. Monitor and assess student
pairs to check for understanding. Invite a student volunteer to display their results for the class to
see.
Ask:
Do you see a pattern with these numbers? Explain. (Yes, the numbers form a diagonal
on the multiplication chart.)
Why do you think they form a pattern? Answers may vary. The dot arrays for each of
these numbers creates a square; etc.
What do you call these numbers? (square numbers)
page 32 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
11. Distribute handout: Square Facts to each student to complete as independent practice or
homework.
5
Topics:
Spiraling Review
Area models for multiplication
Distributive property of multiplication
ATTACHMENTS
Explore/Explain 7
Teacher Resource: Centimeter Grid
Students use area models to investigate the distributive property of multiplication and more difficult
Paper (1 per teacher)
multiplication facts.
Handout: Centimeter Grid Paper (1 per
student)
Instructional Procedures:
1. Explain to students that even though the 11’s were crossed­off as “easy” on their Multiplication
Handout: Centimeter Grid Work Paper (8
per student)
Chart, there are patterns when multiplying by 11’s and 12’s. Display the first 3 multiples of 11 for
the class to see: 1 x 11 = 11; 2 x 11 = 22; 3 x 11 = 33.
TEACHER NOTE
Ask:
Typically students will break 12 apart using 10 +
What is the next product? (44) and the next? (55)
2. However,
Continue until students get through 9 x 11.
What is the product of 10 x 11? How do you know? (110) Answers may vary. Because
TEACHER NOTE
any whole number multiplied by 10 is that number with a zero in the one’s place; etc.
The Distributive Property can be used to solve
What is the product of 11 x 11? How do you know? (121) Answers may vary. Use the
multiplication problems. Remind struggling
known fact of 11 x 10 and adding 11; etc.
students that to distribute something means to
hand it out to each member of the group. If you
page 33 of 99 Enhanced Instructional Transition Guide
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2. Display the following problem situation for the class to see: A baker receives 7 orders for a dozen
Notes for Teacher
distribute a test paper to your class, you give a
cupcakes. How many cupcakes does the baker need to make to fill the 7 orders?
test to each person in the class.
Ask:
When students use the distributive property, they
are using the following process:
How many cupcakes are in a dozen? (12)
How could you find the total number of cupcakes the baker needs to make? (7 x 12)
Breaking a number into parts: 12 = 10 + 2
Multiplying the parts separately: 7 x 10 =
3. Display teacher resource: Centimeter Grid Paper. Distribute handout: Centimeter Grid Paper
70; 7 x 2 = 14
to each student. Explain to students that they are going to use centimeter grid paper to represent
Putting the parts back together: 70 + 14 =
the cupcakes in the problem situation.
84
4. Place students in pairs. Instruct student pairs to use their handout: Centimeter Grid Paper to
The Distributive Property of Multiplication states
create an area model of 7 rows with 12 in each row, recording 7 to the left of the figure and 12 at
that you can multiply the addends of a number and
the top of the figure.
then add the products.
Ask:
Is there a way you can break-up the 12 to make it easier to multiply? Explain. (yes)
Answers may vary. You could break it into 10 + 2 because 10 and 2 are easier numbers to
multiply; etc.
Are there any other ways to break-up the 12 besides 10 + 2? Explain. (yes) Answers
page 34 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
may vary. Use the 5 facts twice and then use the 2; etc.
Why is it convenient to use 10 + 2 instead of a different way? Answers may vary.
Multiplication by 10 or a multiple of 10 is easy. Just write a zero at the end of the number that
is being multiplied by 10; etc.
5. Instruct students to shade-in the last two columns of the rectangle created on their handout:
Centimeter Grid Paper and record 10 + 2 at the top of the area model.
Ask:
How can you find the total? (Multiply and then add.)
6. Demonstrate how to find the total number of squares for this problem as follows:
Ask:
page 35 of 99 Enhanced Instructional Transition Guide
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Notes for Teacher
What is the total number of small squares in this area model? (84)
What do you notice about the product of the area model and the total number of
squares in the area model? (They are the same.)
7. Explain to students that by shading-in the last two columns of the area model, they broke up the
12 into 10 + 2. The area model then showed 7 x (10 + 2) = (7 x 10) + (7 x 2). This is an example
of the Distributive Property meaning the factor 12 is decomposed into (10 + 2), with 7 being
distributed to both the 10 and the 2. This is also an example of using partial products to find the
product for a multiplication sentence.
Ask:
Why do you think this method is called “partial products”? Answers may vary. I am
finding the products of parts of the problem and then adding them together to get the
complete product; etc.
Could you use this method to find 11 x 12? (yes)
Instruct student pairs to use the partial products method to discuss how to find the product of
11 x 12.
8. Distribute a copy of handout: Centimeter Grid Work Paper to each student. Instruct students
to record the fact 11 x 12 in the blank box in the upper left-hand corner of the handout and then
model the product of 11 x 12 with an area model. Allow time for students to complete their model.
Monitor and assess students to check for understanding. Facilitate a class discussion about the
models for 11 x 12 which might include 11 x 12 = 11 (10 + 2); (11 x 10) + (11 x 2) = 110 + 122 =
132; 11 x 12 = (10 x 12) + (1 x 12) = 120 + 12 = 132.
page 36 of 99 Enhanced Instructional Transition Guide
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Grade 4/Mathematics
Unit 03:
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Notes for Teacher
Example of one possible 11 x 12 area model:
9. Record the following multiplication facts for the class to see:
10. Distribute 7 additional copies of handout: Centimeter Grid Work Paper to each student.
Instruct students to use each handout to create an area model for each problem. Explain to
students that they may choose how to decompose or “break apart” the given factors to model the
product. Remind students to record each multiplication fact in the blank box in the upper left-hand
corner of each handout. Monitor and assess students to check for understanding. Students may
complete this activity, if not completed in class, as homework.
Topics:
Use understanding of multiplication to identify numerical similarities and differences
ATTACHMENTS
Teacher Resource: Multiple Logic (1 per
teacher)
Elaborate 1
Teacher Resource: Multiple Logic
page 37 of 99 Enhanced Instructional Transition Guide
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Grade 4/Mathematics
Unit 03:
Suggested Duration: 01
Suggested Instructional Procedures
Notes for Teacher
Students use appropriate vocabulary and understanding of multiplication to identify numerical
Practice KEY (1 per teacher)
similarities and differences.
Handout: Multiple Logic Practice (1 per
student)
Instructional Procedures:
1. Display teacher resource: Multiple Logic.
Ask:
State Resources
What do these numbers have in common? (They are all odd; they are all multiples of 5;
they all end in 5.)
Does 30 belong in this group? How do you know? (No; even though it is a multiple of 5, it
is even.)
Does 100 belong in this group? How do you know? (No; even though it is a multiple of 5,
it is even.)
Explain to students that they can apply what they know about multiplication and the multiples
of numbers to determine the characteristics a set of numbers have in common.
MTC 3 – 5: Multiplication-Division
MTR 3 – 5: Are We Related?
TEXTEAMS: Rethinking Elementary
Mathematics Part I: Go Figure!; The
Greatest Product Wins; How long? How
many?; 4 In a Row may be used to
reinforce these concepts.
2. Distribute handout: Multiple Logic Practice to each student. Instruct students to complete the
handout. Monitor and assess students to check for understanding. Students may complete this
activity, if not completed in class, as homework.
6
Evaluate 1
Instructional Procedures:
ATTACHMENTS
Teacher Resource: Fact Concept Map
Assessment Sample KEY (1 per teacher)
1. Assess student understanding of related concepts and processes by using the Performance
Handout: Fact Concept Map Assessment
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Suggested Instructional Procedures
Indicator(s) aligned to this lesson.
2. Distribute handout: Fact Concept Map Assessment PI to each student. Instruct students to
complete each concept map independently.
Notes for Teacher
PI (1 per student)
Card Set (optional): Fact Cards PI (5 – 6
sets per teacher)
Handout (optional): Fact Concept Map
Performance Indicator(s):
Alternate Assessment PI (3 per student)
Grade4 Mathematics Unit03 PI01
Determine the multiplication fact needed to solve two real-life situations such as the following:
Mandy needed 11 dozen cookies for the school bake sale. How many cookies did
she need?
Jared washed 8 cars to raise money for the soccer team. If he received $7 for each
car, how much money did he receive?
MATERIALS
cardstock (optional) (15 – 18 sheets per
teacher)
scissors (optional) (1 per teacher)
paper lunch sack (optional) (3 per teacher)
marker (optional) (1 per teacher)
Use a graphic organizer for each problem to record: (1) the multiplication fact and solution represented
by the situation, (2) a sketch of the area model, (3) the related fact family, and (4) a justification of the
preferred recall strategy.
TEACHER NOTE
Standard(s): 4.4A , 4.4B , 4.4C , 4.6A , 4.14A , 4.14C , 4.15A , 4.15B
ELPS ELPS.c.1C , ELPS.c.4I , ELPS.c.5G
If time permits, in addition to the Performance
Indicator assessment, card set (optional): Fact
Cards PI and handout (optional): Fact Concept
Map Alternate Assessment PI may be used as
an additional assessment tool.
page 39 of 99 Enhanced Instructional Transition Guide
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Suggested Duration: 01
Notes for Teacher
Create 5 – 6 sets of card set: Fact Cards PI by
copying on cardstock and cutting apart.
Additionally, label 3 paper lunch sacks as (1) Hard
Facts, (2) Square Facts, and (3) Multiply by 12
Facts. Place the appropriate cards from card set:
Fact Cards PI in each bag. Instruct each student
to select 2 fact cards from each bag, and use the
6 facts to complete each of the 3 copies of
handout: Fact Concept Map Alternate
Assessment PI.
04/01/2013
page 40 of 99 Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement KEY
A baker is arranging cupcakes in a box for a party. She placed the cupcakes in 6 rows with 5
cupcakes in each row. How many cupcakes did the baker put in the box?
Draw a diagram that shows the cupcakes in an array.
Use the grid below to create an area model that represents the cupcake array shown above.
Number Sentence: 6 x 5 = 30 cupcakes
©2012, TESCCC
04/01/13
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement KEY
Use the grid below to create another area model that represents the same number of cupcakes.
Sample arrays include: 1 x 30; 30 x 1; 3 x 10; 10 x 3; or 5 x 6
©2012, TESCCC
04/01/13
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement
A baker is arranging cupcakes in a box for a party. She placed the cupcakes in 6 rows with 5
cupcakes in each row. How many cupcakes did the baker put in the box?
Draw a diagram that shows the cupcakes in an array.
Use the grid below to create an area model that represents the cupcake array shown above.
Number Sentence: _____________________________________
©2012, TESCCC
08/10/12
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement
Use the grid below to create another area model that represents the same number of cupcakes.
©2012, TESCCC
08/10/12
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Problem Cards
1
2
The baker is arranging cupcakes in a
The baker’s assistant is placing
box for a graduation party. She put the
cupcakes in boxes for a birthday party.
cupcakes in 8 rows with 9 cupcakes in
He put the cupcakes in 6 rows with 8
each row. How many cupcakes are
cupcakes in each row. How many
boxed for this party?
cupcakes are boxed for this party?
4
3
The baker is arranging cupcakes in a
The baker’s assistant is placing
box for a reception. She put the
cupcakes in boxes for an open house.
cupcakes in 5 rows with 8 cupcakes in
He put the cupcakes in 7 rows with 7
each row. How many cupcakes are
cupcakes in each row. How many
boxed for this party?
cupcakes are boxed for this open
house?
5
6
The baker is arranging cupcakes in a
The baker’s assistant is placing
box for a concert. She put the cupcakes
cupcakes in boxes for a school fair. He
in 9 rows with 4 cupcakes in each row.
put the cupcakes in 9 rows with 7
How many cupcakes are boxed for this
cupcakes in each row. How many
concert?
cupcakes are boxed for this school fair?
©2012, TESCCC
08/10/12
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Problem Cards
7
8
The baker is arranging cupcakes in a
The baker’s assistant is placing
box for a newcomer’s party. She put the
cupcakes in boxes for an award
cupcakes in 6 rows with 4 cupcakes in
ceremony. He put the cupcakes in 2
each row. How many cupcakes are
rows with 9 cupcakes in each row. How
boxed for this party?
many cupcakes are boxed for this
ceremony?
10
9
The baker is arranging cupcakes in a
The baker’s assistant is placing
box for a magic show. She put the
cupcakes in boxes for a luncheon. He
cupcakes in 4 rows with 5 cupcakes in
put the cupcakes in 4 rows with 4
each row. How many cupcakes are
cupcakes in each row. How many
boxed for this party?
cupcakes are boxed for this luncheon?
11
12
The baker is arranging cupcakes in a
The baker’s assistant is placing
box for a meeting. She put the cupcakes
cupcakes in boxes for a conference. He
in 3 rows with 6 cupcakes in each row.
put the cupcakes in 8 rows with 4
How many cupcakes are boxed for this
cupcakes in each row. How many
meeting?
cupcakes are boxed for this conference?
©2012, TESCCC
08/10/12
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Array Cards
A
B
C
D
E
F
©2012, TESCCC
08/10/12
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Array Cards
G
H
I
J
K
L
©2012, TESCCC
08/10/12
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Recording Sheet KEY
Card
Number
Array Letter
Area Model
Number
Sentence
Related Fact
Families
9 x 8 = 72
1
8 x 9 = 72
B
72 ÷ 8 = 9
72 ÷ 9 = 8
8 x 6 = 48
2
6 x 8 = 48
A
48 ÷ 8 = 6
48 ÷ 6= 8
8 x 5 = 40
3
D
5 x 8 = 40
40 ÷ 8 = 5
40 ÷ 5 = 8
4
E
7 x 7 = 49
49 ÷ 7 = 7
4 x 9 = 36
5
J
9 x 4 = 36
36 ÷ 4 = 9
36 ÷ 9 = 4
7 x 9 = 63
6
H
9 x 7 = 63
63 ÷ 9 = 7
63 ÷ 7 = 9
©2012, TESCCC
04/01/13
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Recording Sheet KEY
Card
Number
Array Letter
Area Model
Number
Sentence
Related Fact
Families
4 x 6 = 24
7
6 x 4 = 24
I
24 ÷ 6 = 4
24 ÷ 4 = 6
9 x 2 = 18
8
2 x 9 = 18
F
18 ÷ 2 = 9
18 ÷ 9 = 2
5 x 4 = 20
9
G
4 x 5 = 20
20 ÷ 5 = 4
20 ÷ 4 = 5
10
L
4 x 4 = 16
16 ÷ 4 = 4
6 x 3 = 18
11
C
3 x 6 = 18
18 ÷ 6 = 3
18 ÷ 3 = 6
4 x 8 = 32
12
K
8 x 4 = 32
32 ÷ 8 = 4
32 ÷ 4 = 8
©2012, TESCCC
04/01/13
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Recording Sheet
Card
Number
Array Letter
Area Model
Number
Sentence
Related Fact
Families
1
2
3
4
5
6
©2012, TESCCC
08/10/12
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Cupcake Arrangement Recording Sheet
Card
Number
Array Letter
Area Model
Number
Sentence
Related Fact
Families
7
8
9
10
11
12
©2012, TESCCC
08/10/12
page 2 of 2
Grade 04
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid – Notes
Row 1
Row 2
Row 3
Row 4
Row 5
Addition Number Sentence
____________________________
Number Sentence in Words
_________rows of _________ equals _________
Multiplication Number Sentence
________________________
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid KEY
(1)
Shade 3 squares in rows 1, 2,
and 3.
2)
Shade 4 squares in rows 1,
2, 3, 4, and 5.
Row 1
Row 1
Row 2
Row 2
Row 3
Row 3
Row 4
Row 4
Row 5
Row 5
Addition Number Sentence
Addition Number Sentence
3+3+3=9
4 + 4 + 4 + 4 + 4 = 20
Number Sentence in Words
Number Sentence in Words
3 rows of 3 equals 9
5 rows of 4 equals 20
Multiplication Number
Sentence
Multiplication Number
Sentence
3x3=9
5 x 4 = 20
©2012, TESCCC
08/27/12
page 1 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid KEY
(3) Shade 5 squares in rows 1, 2,
and 3.
(4) Shade 2 squares in rows 1, 2, 3, 4,
and 5.
Row 1
Row 1
Row 2
Row 2
Row 3
Row 3
Row 4
Row 4
Row 5
Row 5
Addition Number Sentence
Addition Number Sentence
5 + 5 + 5 = 15
2 + 2 + 2 + 2 + 2 = 10
Number Sentence in Words
Number Sentence in Words
3 rows of 5 equals 15
5 rows of 2 equals 10
Multiplication Number Sentence
Multiplication Number Sentence
3 x 5 = 15
5 x 2 = 10
©2012, TESCCC
08/10/12
page 2 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid KEY
Answers may vary.
(6) Shade ___squares in row(s)
______________
(5) Shade ___ squares in row(s)
________________
Row 1
Row 1
Row 2
Row 2
Row 3
Row 3
Row 4
Row 4
Row 5
Row 5
Addition Number Sentence
Addition Number Sentence
Number Sentence in Words
Number Sentence in Words
_______rows of _________ equals
_______rows of _________ equals
_________
_________
Multiplication Number Sentence
Multiplication Number Sentence
_____________
_____________
©2012, TESCCC
08/10/12
page 3 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid KEY
(7)
Mr. Perry has 6 vans scheduled for a class field trip. Each van will carry 4 people. How
many people altogether will the vans carry for this field trip?
Row
Row
Row
Row
Row
Row
Row
1
2
3
4
5
6
7
Addition Number Sentence: 4 + 4 + 4 + 4 + 4 + 4 = 24
Number Sentence in Words: 6 rows of 4 equals 24
Multiplication Number Sentence: 6 x 4 = 24
================================================
(8)
Mr. Perry has 6 vans scheduled for a class field trip. Each van will carry 5 people. How
many people altogether will the vans carry for this field trip?
Row
Row
Row
Row
Row
Row
Row
1
2
3
4
5
6
7
Addition Number Sentence: 5 + 5 + 5 + 5 + 5 + 5 = 30
Number Sentence in Words: 6 rows of 5 equals 30
Multiplication Number Sentence: 6 x 5 = 30
©2012, TESCCC
08/27/12
page 4 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid KEY
(9)
Create your own multiplication word problem in the space below.
Answers may vary.
(10)
Use this grid to model the solution to your problem above. Then write an addition, word,
and multiplication sentence in the spaces provided below.
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10
Addition Number Sentence: _______________________________________
Number Sentence in Words: _______rows of _________ equals _________
Multiplication Number Sentence: ___________________________________
©2012, TESCCC
08/27/12
page 5 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid
(1)
Shade 3 squares in rows 1, 2, and 3.
(2) Shade 4 squares in rows 1, 2, 3,
4, and 5.
Row 1
Row 1
Row 2
Row 2
Row 3
Row 3
Row 4
Row 4
Row 5
Row 5
Addition Number Sentence
Addition Number Sentence
Number Sentence in Words
Number Sentence in Words
_______rows of _________ equals
_______rows of _________ equals
_________
_________
Multiplication Number Sentence
Multiplication Number Sentence
_____________
_____________
©2012, TESCCC
08/01/10
page 1 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid
(3) Shade 5 squares in rows 1, 2,
and 3.
(4)
Shade 2 squares in rows 1, 2, 3,
4, and 5.
Row 1
Row 1
Row 2
Row 2
Row 3
Row 3
Row 4
Row 4
Row 5
Row 5
Addition Number Sentence
Addition Number Sentence
Number Sentence in Words
Number Sentence in Words
_______rows of _________ equals
_______rows of _________ equals
_________
_________
Multiplication Number Sentence
Multiplication Number Sentence
_____________
_____________
©2012, TESCCC
08/01/10
page 2 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid
(5) Shade ___ squares in row(s)
________________
(6)
Shade ___squares in row(s)
______________
Row 1
Row 1
Row 2
Row 2
Row 3
Row 3
Row 4
Row 4
Row 5
Row 5
Addition Number Sentence
Addition Number Sentence
Number Sentence in Words
Number Sentence in Words
_______rows of _________ equals
_______rows of _________ equals
_________
_________
Multiplication Number Sentence
Multiplication Number Sentence
_____________
_____________
©2012, TESCCC
08/01/10
page 3 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid
(7)
Mr. Perry has 6 vans scheduled for a class field trip. Each van will carry 4 people.
How many people altogether will the vans carry for this field trip?
Row
Row
Row
Row
Row
Row
Row
1
2
3
4
5
6
7
Addition Number Sentence: _______________________________________
Number Sentence in Words: _______rows of _________ equals _________
Multiplication Number Sentence: ___________________________________
================================================
(8)
Mr. Perry has 6 vans scheduled for a class field trip. Each van will carry 5 people.
How many people altogether will the vans carry for this field trip?
Row
Row
Row
Row
Row
Row
Row
1
2
3
4
5
6
7
Addition Number Sentence: _______________________________________
Number Sentence in Words: _______rows of _________ equals _________
Multiplication Number Sentence: ___________________________________
©2011, TESCCC
08/10/12
page 4 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication on a Grid
(9) Create your own multiplication word problem in the space below.
(10) Use this grid to model the solution to your problem above. Then write an addition,
word, and multiplication sentence in the spaces provided below.
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10
Addition Number Sentence: _______________________________________
Number Sentence in Words: _______rows of _________ equals _________
Multiplication Number Sentence: ___________________________________
©2011, TESCCC
08/10/12
page 5 of 5
Grade 4
Mathematics
Unit: 03 Lesson: 01
Van Travel Multiplication Model KEY
Mr. Perry has 6 vans scheduled for a class field trip. Each van will carry 6 people. How many
people altogether will the vans carry for this field trip?
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Addition Number Sentence: 6 + 6 + 6 + 6 + 6 + 6 = 36
Number Sentence in Words: 6 rows of 6 equals 36
Multiplication Number Sentence: 6 x 6 = 36
©2012, TESCCC
04/01/13
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Van Travel Multiplication Model
Mr. Perry has 6 vans scheduled for a class field trip. Each van will carry 6 people. How many
people altogether will the vans carry for this field trip?
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Addition Number Sentence: ________________________________________
Number Sentence in Words: _________rows of _________ equals _________
Multiplication Number Sentence: ___________________________________
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Math Journal Directions
1. Fold 2 or 3 sheets of 8.5 x 11 paper in half.
2. Mark all folds about one inch from the outer edges.
3. Set aside one sheet of paper. Take the rest of the sheets of paper,
keeping them stacked together and cut a one-inch slit along the fold
from either end toward the middle.
fold
cut
cut
4. Take the page you set aside and cut it along the fold IN BETWEEN
the two one-inch marks you made previously.
fold
cut
fold
5. Roll the sheet(s) you cut in Step 3 lengthwise and slip them through the cut in the middle of the
single page. Fit the slits together to make the booklet.
Adapted from TEXTEAMS Rethinking Elementary Mathematics Series Part I, p. xv.
©2012, TESCCC
04/01/13
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Centimeter Grid Paper
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication Property Practice KEY
Solve each problem and then use the commutative property to write a different multiplication
sentence.
(1)
3 x 6 = 18
(2)
6 x 3 = 18
(3)
7 x 5 = 35
5 x 7 = 35
6 x 8 = 48
8 x 6 = 48
(4)
4 x 9 = 36
9 x 4 = 36
Solve and label each solution.
(5)
There are 5 cookies in a bag. How many cookies are in 4 bags?
4 x 5 = 20; 4 bags with 5 cookies in each bag = 20 cookies
(6)
Kindra had 3 model boats that were red, 3 model boats that were blue, and 3 model boats that
were white. What is the total number of Kindra’s boats?
3x3=9
(7)
Harold has 4 packages with 3 pencils in each package. He has 5 packages with 6 pens in
each package. How many pencils and pens does Harold have?
4 x 3 = 12 (pencils) 5 x 6 = 30 (pens) 12 + 30 = 42 pencils and pens
(8)
Jackie is using beads to make 6 bracelets. She puts 7 large beads on 4 bracelets and then
puts 8 beads on 2 bracelets. How many beads did Jackie use?
4 x 7 = 28; 2 x 8 = 16; 28 + 16 = 44 beads used
(9)
Mark has 4 boxes with 7 balls in each box. Ron has 7 boxes with 4 balls in each box. Who
has more balls? How do you know?
They have the same number of balls because 4 x 7 = 7 x 4.
(10)
How do you know that 27 x 4 = 4 x 27 without finding the products?
The product is the same regardless of the order in which it is multiplied. (The
Commutative Property of Multiplication)
(11)
What is the missing factor in 678 x ____= 678? How do you know?
1, Any number multiplied by 1 is that number. (The Identity Property of Multiplication)
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication Property Practice
Solve each problem and then use the commutative property to write a different multiplication
sentence.
(1)
3x6=
(2)
6x8=
(3)
7x5=
(4)
4x9=
Solve and label each solution.
(5)
There are 5 cookies in a bag. How many cookies are in 4 bags?
(6)
Kindra had 3 model boats that were red, 3 model boats that were blue, and 3 model boats that
were white. What is the total number of Kindra’s boats?
(7)
Harold has 4 packages with 3 pencils in each package. He has 5 packages with 6 pens in
each package. How many pencils and pens does Harold have?
(8)
Jackie is using beads to make 6 bracelets. She puts 7 large beads on 4 bracelets and then
puts 8 beads on 2 bracelets. How many beads did Jackie use?
(9)
Mark has 4 boxes with 7 balls in each box. Ron has 7 boxes with 4 balls in each box. Who
has more balls? How do you know?
(10)
How do you know that 27 x 4 = 4 x 27 without finding the products?
(11)
What is the missing factor in 678 x ____= 678? How do you know?
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiplication Chart
x
0
1
2
3
4
5
6
7
8
9
10 11 12
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10 11 12
2
0
2
4
6
8
10 12 14 16 18 20 22 24
3
0
3
6
9
12 15 18 21 24 27 30 33 36
4
0
4
8
12 16 20 24 28 32 36 40 44 48
5
0
5
10 15 20 25 30 35 40 45 50 55 60
6
0
6
12 18 24 30 36 42 48 54 60 66 72
7
0
7
14 21 28 35 42 49 56 63 70 77 84
8
0
8
16 24 32 40 48 56 64 72 80 88 96
9
0
9
18 27 36 45 54 63 72 81 90 99
10
0
10 20 30 40 50 60 70 80 90
100 110 120
11
0
11 22 33 44 55 66 77 88 99
110 121 132
12
0
12 24 36 48 60 72 84 96
120 132 144
©2012, TESCCC
08/10/12
108
0
0
108
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Blank Multiplication Chart
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
One Fact at a Time Sample KEY
(1) Word Sentence
(2) Addition Sentence
(3) Area/Array
Model
4 + 4 + 4 = 12
4
3 groups of
4 is 12
3
3 x 4 = 12
Fact
Kevin had 3
bags with 4
marbles in each
bag. How many
marbles did he
have
altogether?
(6) Word Problem
©2012, TESCCC
Doubles
4 x 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
I know that
3 x 2 = 6, so
double 6 is
12.
(5) Your Strategy for Remembering
this Fact
04/01/13
(4) Related Fact
Family
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
One Fact at a Time
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
3
5
5
1
6
1
1
4
4
9
9
08/10/12
8
1
8
1
©2012, TESCCC
6
1
2
2
1
7
1
7
1
1
1
3
page 1 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
2
8
16
2
2
14
7
18
9
6
3
4
10
5
6
2
2
2
©2012, TESCCC
2
2
8
4
08/10/12
2
12
page 2 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
6
12
84
8
10
7
72
12
9
96
12
24
12
12
©2012, TESCCC
12
5
3
1
120
48
12
2
12
108
12
4
36
12
08/10/12
12
60
page 3 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
12
4
9
18
6
7
5
3
3
3
3
15
3
3
21
27
9
24
3
8
3
©2012, TESCCC
08/10/12
page 4 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
20
5
16
28
7
8
6
4
4
4
4
24
4
4
32
9
36
4
©2012, TESCCC
08/10/12
page 5 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
30
6
40
8
25
9
7
5
5
5
5
35
5
42
7
8
6
6
©2012, TESCCC
54
9
36
45
5
6
6
48
6
08/10/12
page 6 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
56
7
49
9
8
7
7
63
7
72
9
64
81
8
8
©2012, TESCCC
8
9
08/10/12
9
page 7 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
6
10
70
8
10
7
60
10
9
80
10
20
10
10
©2012, TESCCC
10
5
3
1
100
40
10
2
10
90
10
4
30
10
08/10/12
10
50
page 8 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
6
11
77
8
11
7
66
11
9
88
11
22
11
11
©2012, TESCCC
11
5
3
1
121
44
11
2
11
99
11
4
33
11
08/10/12
11
55
page 9 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Triangular Flash Cards
12
11
12
11
11
10
©2012, TESCCC
108
12
132
110
9
144
12
08/10/12
12
132
page 10 of 10
Grade 4
Mathematics
Unit: 03 Lesson: 01
Square Number Dot Grid KEY
1x1=1
2x2=4
3x3=9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
11 x 11 = 121
12 x 12 = 144
©2012, TESCCC
04/01/13
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Square Number Dot Grid
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Square Facts KEY
Square Number – When you multiply a number by itself, the product is called a square number.
Complete the table below. The first row has been done for you.
©2012, TESCCC
Factors
Product
1x1
1
2x2
4
3x3
9
4x4
16
5x5
25
6X6
36
7x7
49
08/10/12
Model
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Square Facts KEY
©2012, TESCCC
Factors
Product
8X8
64
9x9
81
10 x 10
100
11 X 11
121
12 x 12
144
08/10/12
Model
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Square Facts
Square Number – When you multiply a number by itself, the product is called a square number.
Complete the table below. The first row has been done for you.
Factors
Product
1x1
1
Model
2x2
3x3
16
6X6
49
©2012, TESCCC
08/10/12
page 1 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Square Facts
Factors
Product
Model
8X8
100
11 X 11
©2012, TESCCC
08/10/12
page 2 of 2
Grade 4
Mathematics
Unit: 03 Lesson: 01
Centimeter Grid Work Paper
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiple Logic
What characteristics do these numbers have in common?
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiple Logic Practice KEY
Use the numbers in each box below to answer the questions.
(1)
What characteristics do these numbers have in common?
All multiples of 3
All odd numbers
Could 6, 18, or 27 belong to this group of numbers? Explain.
6 – No, multiple of 3, but even
18 – No, multiple of 3, but even
27 – Yes, multiple of 3 and odd
(2)
What characteristics do these numbers have in common?
All multiples of 4
All even numbers
Could 11, 121, or 132 belong to this group of numbers? Explain.
11 – No, multiple of 11, but odd
121 – No, multiple of 11, but odd
132 – Yes, multiple of 11 and even
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Multiple Logic Practice
Use the numbers in each box below to answer the questions.
(1)
What characteristics do these numbers have in common?
Could 6, 18, or 27 belong to this group of numbers? Explain.
(2)
What characteristics do these numbers have in common?
Could 11, 121, or 132 belong to this group of numbers? Explain.
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Fact Concept Map Assessment Sample KEY
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Fact Concept Map Assessment PI
©2012, TESCCC
08/10/12
page 1 of 1
Grade 4
Mathematics
Unit: 03 Lesson: 01
Fact Cards PI
Hard Fact Cards
©2012, TESCCC
3 x 4 = 12
3 x 6 = 18
3 x 7 = 21
3 x 8 = 24
3 x 9 = 27
4 x 6 = 24
4 x 7 = 28
4 x 8 = 32
4 x 9 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
08/10/12
page 1 of 3
Grade 4
Mathematics
Unit: 03 Lesson: 01
Fact Cards PI
Hard Fact Cards (Continued)
7 x 8 = 56
7 x 9 = 63
8 x 9 = 72
Square Fact Cards
©2012, TESCCC
3x3=9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
08/10/12
page 2 of 3
Grade 4
Mathematics
Unit: 03 Lesson: 01
Fact Cards PI
Square Fact Cards - continued
11 x 11 = 121
Multiply by 12 Fact Cards
3 x 12 = 36
4 x 12 = 48
5 x 12 = 60
6 x 12 = 72
7 x 12 = 84
8 x 12 = 96
9 x 12 = 108
11 x 12 = 132
12 x 12 = 144
©2012, TESCCC
08/10/12
page 3 of 3
Grade 4
Mathematics
Unit: 03 Lesson: 01
Fact Concept Map Alternate Assessment PI
©2012, TESCCC
\03/02/12
page 1 of 1