xii Introduction
Teach a total of fifteen lessons by repeating steps 2 through
4.
Program Structure
341
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multiplication & division 1
Unit 1: Beginning-of-Unit Assessment
1 4 4 4 4 4 4
2 6 6 6
3 Write a multiplication equation for 3 3 3 3 3 15.
4 Write a multiplication equation for the equal groups.
�The rectangles below are constructed with square tiles. Write a
multiplication equation for each one that shows the total number of
square tiles in each rectangle.
5
6
7
8
9 3 6
10 4 4
11 5 1
12 4 5
�Do your best at solving the problems below. Don’t worry if you
have difficulty—your answers will tell your teacher about what you
know and what you need to learn.
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1multiplication & division
13 6 3
14 5 6
15 0 11
16 3 0
17 10 8
18 7 10
19 Write a multiplication equation to solve.
There are 6 dogs. Each dog has 2 ears. How many ears are there
in all?
20 Write a multiplication equation to solve.
There are 5 cars. Each has 4 tires. How many tires are there in
all?
21 Write a word problem based on the equation below.
3 4 12
22 Write a multiplication problem for the addition problem
below. Explain how you know your answer is correct.
2 2 2 2 2
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Lesson 2Lesson 1PLANNER Lesson AssessLesson 4Lesson 3
Lessons 1–5
5
UNIT
1
Lesson Summary Students brainstorm things that come in equal
groups of twos, threes, fours, fives, and sixes.
Students write and solve equations for multiplication word
problems.
Students write and solve multiplication word problems for a
given equation.
Students compare two word problems with the same factors in
reverse order, learning that reversing the order of the factors
produces different word problems with the same answer.
Students demonstrate understanding of the objectives of Lessons
1–4 by completing WorkSpace pages independently.
Objectives Identify examples of equal groups. • Communicate
ideas with key math •vocabulary: equal.
Calculate products with factors 1 through 6.•
Write an equation for a multiplication •word problem.
Communicate ideas with key •math vocabulary: equal, equation,
multiplication, and times.
Write a multiplication word problem •for a given equation.
Calculate products with factors •1 through 6.
Introduce key math vocabulary: •equal, equation, multiplication,
and times.
Communicate ideas with key •math vocabulary: equal, equation,
multiplication, and times.
Write a multiplication word problem •for a given equation.
Calculate products with factors •1 through 6.
Communicate ideas with key •math vocabulary: equal, equation,
multiplication, and times.
Calculate products with factors •1 through 6.
Write an equation for a multiplication •word problem.
Write a multiplication word problem •for a given equation.
Communicate ideas with key math •vocabulary: equal and
multiplication.
Materials S Student Bag
Unit 1: Beginning-of-Unit Assessment
WorkSpace • pages 3 and 4chart paper•
WorkSpace• pages 5 and 6 Things that come in groups • charts
from Lesson 1
WorkSpace• pages 7, 8, 190 and 195–198 • Things that come in
groups charts from Lesson 1chart paper •blank paper •
WorkSpace• pages 9 and 10 • Things that come in groups charts
from Lesson 1 chart paper • from Lesson 3
•WorkSpace pages 11–15 • Things that come in groups charts from
Lesson 1Circles and Stars Capture• cards Additional Practice•
Built-in Differentiation
Writing the names of items that come in groups of given amounts
contributes to students’ vocabulary development.
Using symbolic representations of students’ figuring allows all
students to follow different methods of reaching a solution.
Writing equations on the board and then reading them aloud
reinforces the language of mathematics.
Solving problems presented using a graphic organizer gives
students introduction to reversing factors in a multiplication
problem following a familiar routine.
Assessing understanding through problems presented in a familiar
graphic organizer allows students to show their understanding
without having to approach the material in an unfamiliar
context.
Interactive Whiteboard Toolscontains all hands-on manipulatives
and WorkSpace pages for Unit 1, Lessons 1–5.
TeacherSpace CD-ROM contains Unit Assessments, Additional
Practice pages, and other reproducibles to support teaching these
lessons.
Understanding the M
eaning of M
ultiplication
2 Build a Foundation for Multiplication
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Understanding the M
eaning of M
ultiplication
Lessons 1–5
UNIT
1
FROM MaRilyn BuRns
Dear Colleague,The lessons that begin this unit develop and
reinforce students’ understanding by connecting multiplication to
real-world contexts. Lesson 1 begins by engaging students in
brainstorming things that come in equal groups. Students first
focus on things that come in equal groups of 3s—legs on stools,
sides on triangles, triplets, and so on. They then expand their
thinking to things that come in equal groups of 2s, 4s, 5s, and
6s.
Things that come in groups of 4
wheels on a carlegs on a tablesides on a square
Then, in Lessons 2 through 5, students write and solve
multiplication word problems. Writing multiplication word problems
helps reinforce for students the essential idea that defines
multiplication situations—combining equal groups. We’ve found that
having students write their own problems helps cement their
understanding of multiplication and increases their success with
solving word problems.
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The Teacher Guide is organized into five units of fifteen
lessons each.
Every fifth lesson is an assessment that provides an opportunity
to monitor student progress. Beginning-of-Unit and End-of-Unit
Assessments measure student understanding.
2
Beginning-of-Unit AssessmentStudents complete the assessment as
a pre-unit snapshot of what they know (see pages 341 and 342 for an
example).
Prepare The Unit Overview offers a summary of the content and
instruction of the following fifteen lessons. Planners are provided
before each set of five lessons, as is a letter from Marilyn Burns
explaining the context and goals of the upcoming lessons.
1
UN
IT 1
CONTENTS
Build a Foundation for MultiplicationAlthough students may have
previous experience with multiplication, we take a step back in
this unit and deepen students’ conceptual understanding of the
meaning of multiplication by drawing on real-world contexts and
rectangular arrays. Playing Multiplication Bingo engages students’
interest while giving them practice with multiplication facts.
Students will…• Use visual models to represent multiplication of
whole numbers.
• Calculate products for factors 0, 1–6, and 10.
• Write and solve multiplication word problems.
• Communicate ideas with key math vocabulary: equal, equation,
factor, multiplication, multiply, product, and times.
LESSONS 1–5
Understanding the meaningof multiplication . . . . . . . . . . .
. . 1–22Identifying everyday objects that come in equal groups . .
. . . . . . . . . . . .4
Solving problems with equal groups. . . .8
Writing and solving word problems. . . .12
Comparing equations for word problems . . . . . . . . . . . . .
. . . . . . . . . . 16
Assessing student understanding. . . . . 20
LESSONS 6–10
Practicing multiplicationfacts . . . . . . . . . . . . . . . . .
. . . . . . . . . . .23–44Calculating problems with factors 1
through 6 . . . . . . . . . . . . . . . . . . . 26
Practicing facts with Multiplication Bingo. . . . . . . . . . .
. . . . . . . . 30
Calculating products when one factor is zero. . . . . . . . . .
. . . . . . . . . . . . . . . . 34
Multiplying with 10 as a factor . . . . . . . 38
Assessing student understanding. . . . . 42
LESSONS 11–15
Connecting multiplication to arrays, rectangles, and the
multiplication chart . . . . . . . 45–66Writing multiplication
equations for equal rows . . . . . . . . . . . . . . . . . . . . .
. . . 48
Relating equal rows of tiles to multiplication. . . . . . . . .
. . . . . . . . . . . . . .52
Practicing facts with Tiles Capture . . . . 56
Relating rectanglesto multiplication. . . . . . . . . . . . . .
. . . . . . . . 60
Assessing student understanding. . . . . 64
Measuring StudentUnderstanding With theEnd-of-Unit Assessment .
. . . . . . . . . . 67
UNIT
1Lessons 1–15
Tiles Capture
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xiii
Each unit follows the same progression of steps 1 through 5.
Lesson SummaryStudents brainstorm things that come in equal
groups of twos, threes, fours, fives, and sixes.
AssessAdminister the Unit 1: Beginning-of-Unit Assessment before
beginning today’s instruction.
ObjectivesIdentify examples of equal groups. •Communicate ideas
with key math •vocabulary: equal.
MaterialsWorkSpace• pages 3 and 4chart paper•
Interactive Whiteboard Tools
WorkSpace pages and manipulatives for Lesson 1 are provided on
the Interactive Whiteboard Tools CD-ROM.
PreparationUnit 1: Beginning-of-Unit AssessmentMake 1 copy of
the assessment for each student from pages 341–342 or the
TeacherSpace CD-ROM.
Language DevelopmentKey Math VocabularyENGLISH SPANISH
equal igual
Academic VocabularyENGLISH SPANISH
car auto
finger dedo
group grupo
insect insecto
stool banquete
wheel rueda
LessonLesson
4 Build a Foundation for Multiplication
Lesson 1 Students brainstorm things that come in equal
groups.
Next Lesson Students write and solve equations for
multiplication word problems.
Guide students to brainstorm things that come in groups of
2.
1 Introduce the lesson.h It always helps to connect ideas to
real-world examples
when learning math. Here we’re going to focus on the basic idea
of multiplication by thinking about things in the world that come
in equal groups. I’ll start us with some simple examples and then
you’ll come up with your own examples.
2 List things that come in groups of 2.Post a piece of chart
paper and write on it as shown.
Things that come in groups of 2
ears
Ask a student to read the title.
h Who can explain why I wrote ears on this chart paper? (People
have 2 ears.)
What other things can we write on the list?
List students’ suggestions. (Possibilities include shoes,
chopsticks, legs, feet, hands, etc.)
3 Students write the list.Have students turn to WorkSpace page
3.Choose a student to read the list and then have students list
additional things that come in twos from the chart paper.
Guide students to brainstorm things that come in groups of
3.
1 List things that come in groups of 3.h I wouldn’t write legs
on a stool on our list of
things that come in twos. Who can explain why?
Ask a student to explain.
h On what list does legs on a stool belong? (Things that come in
groups of 3)
Post a piece of chart paper and write on it as shown.
Things that come in groups of 3
legs on a stool
Ask a student to read the title.
h What other things can we write on the list?
List students’ suggestions. (Possibilities include wheels on a
tricycle, colors on a traffic light, legs on a tripod, etc.)
2 Students write this list on WorkSpace page 3.Have a student
read the things listed for groups of 3 on page 3. Then have them
list additional things from the chart paper.
Language DeveLopmentSome of the words on the Things that come in
groups lists may be unfamiliar to your students. This activity is a
great way to build vocabulary; just knowing that bicycles have two
wheels and tricycles have three is helpful. Also, it may help to
show pictures. You might also draw a simple sketch of items on the
list.
Students brainstorm things that come in groups of 4.
1 List things that come in groups of 4.h What about wheels on a
car? On what list does
wheels on a car belong? (Things that come in groups of 4)
Post a piece of chart paper and write on it as shown.
Things that come in groups of 4
wheels on a car
Ask a student to read the title.
h What other things can we add to the list?
List students’ suggestions. (Possibilities include legs on a
chair, edges of a picture frame, legs on a cow, etc.)
2 Students write this list on WorkSpace page 4.Have a student
read the things listed for groups of 4 on page 4. Then have them
list additional things from the chart paper.
whoLe group whoLe group
1Step 2Step 3StepIdentifying everyday objects that come in equal
groups1
whoLe group
Things That Come in Groups
Workspace page 3 Things That Come in Groups
Workspace page 4
Continue
5UNIT 1 Lesson 1
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4Step Students brainstorm things that come in groups of 5 and
6.1 List things that come in groups of 5.h What about fingers on a
hand? On what list does
fingers on a hand belong? (Things that come in groups of 5)
Post a piece of chart paper and write on it as shown.
Things that come in groups of 5
fingers on a hand
Ask a student to read the title.
h What other things can we add to our list?
Have students think, pair, share. (Possibilities include toes on
a foot, petals on a violet, sides on a pentagon, etc.)
2 List things that come in groups of 6.Follow the same procedure
as for groups of 2, 3, 4, and 5.
3 Students write lists for 5 and 6 on WorkSpace page 4.
SUPPORTING INSTRUCTIONThink, pair, share is a routine that will
be used throughout this program. Having students talk in pairs
provides them a “safe” way to share ideas that they may not be
quite sure of, think of words to articulate their ideas,
brainstorm, and practice what they will say when they share with
the larger group.
Explain the routine to students: they think first and then share
their thoughts with their partners, take turns listening and
speaking, and finally discuss what they will say when they share
with the whole group.
Partners brainstorm things that come in equal groups.
1 Students work in pairs to complete WorkSpace pages 3 and
4.Have students work together to add more items to the lists on
pages 3 and 4.
Things That Come in Groups
Groups of 2 Groups of 3
WORkSPaCe PaGe 3
Things That Come in Groups
Groups of 5Groups of 4
Groups of 6
WORkSPaCe PaGe 4
Students share items they added to their lists.
1 Choose a pair to report one item they added to a list.Leave
about five minutes before the end of class for students to report
examples from their Things that come in groups lists. As the pair
you chose reports the item, write it on the appropriate chart and
have students write it on the corresponding list in their
WorkSpaces.
2 Have other pairs report their items for the rest of the
available time.
SUPPORTING INSTRUCTIONKeep the class charts posted; students
will use them when they write and solve word problems in Lessons
2–5.
Step5 Step6whole group partners whole group
1 Identifying everyday objects that come in equal
groupslessoncontinued
Stop
6 Build a Foundation for Multiplication 7UNIT 1 Lesson 1
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Assessing student understandingcontinued
Lesson
additionaL practice
CheckPoint
55
All students could benefit from additional practice. For your
convenience, the reproducible of the Additional Practice for
Lessons 1–5 is available on the TeacherSpace CD-ROM. This
Additional Practice gives students more opportunities to write and
solve equations for multiplication word problems.
For Students Ready for a Challenge
Some students may like the challenge of greater •numbers as it
makes them feel good about their ability to solve “hard” problems.
If a student is constantly choosing very easy numbers, it is most
likely that those are the numbers he or she is most comfortable
using; however, some students may not have thought to choose
greater numbers. If you think a particular student needs a
challenge, pose a problem such as: There are 6 scorpions. Each
scorpion has 8 legs. How many legs are there in all?
For Students Who Need More Support
Ask the student if he or she prefers to draw •pictures, use
numbers, or use words to show how he or she figured a problem. Then
model a solution to a word problem using the student’s preferred
method. This will help him or her feel more comfortable and solve
the problem with more confidence.
Play • Circles and Stars Capture one-on-one with the student.
This allows you to guide the student through figuring the total
number of stars without counting them, while reinforcing the
language of multiplication. For example:
There are 3 groups with 2 stars in each –circle.
There are 3 equal groups of 2 stars.–
3 groups of 2 equals 6.–
3 times 2 equals 6.–
Have the student play a solitaire version of •Circles and Stars
Capture. The student turns over two cards, figures the total for
each, and decides which has the greater number of stars. Encourage
the student to record an equation for each card and draw a star
next to the one with the greater product.
Monitor Progress and Differentiate InstructionUse the Annotated
WorkSpace to assess pages 11 and 12. Although these lessons are
carefully paced and scaffolded, there may be instances when
students need additional support or challenges.
22 Build a Foundation for Multiplication
343
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multiplication & division 1
Name: Date:
Unit 1: End-of-Unit Assessment
1 3 3 3 3 3 3
2 5 5 5
3 Write a multiplication equation for 4 4 4 4 4 20.
4 Write a multiplication equation for the equal groups.
�The rectangles below are constructed with square tiles. Write a
multiplication equation for each one that shows the total number of
square tiles in each rectangle.
5
6
7
8
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1
9 2 6
10 3 3
11 6 1
12 3 4
13 5 2
14 6 5
15 0 9
16 5 0
17 12 10
18 10 9
19 Write a multiplication equation to solve.
There are 4 cats. Each cat has 2 ears. How many ears are there
in all?
20 Write a multiplication equation to solve.
There are 5 salads. Each has 3 tomatoes. How many tomatoes are
there in all?
21 Write a word problem based on the equation below.
4 6 24
22 Write a multiplication problem for the addition problem
below. Explain how you know your answer is correct.
2 2 2 2 2 2
multiplication & division
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3 5 4
Teach the LessonsEach lesson begins with a sidebar containing
the Lesson Summary, Objectives, Materials, Interactive Whiteboard
Tools, Preparation, and Language Development, followed by
step-by-step instruction.
Assess Student UnderstandingEvery fifth lesson is an opportunity
to monitor student progress with Show What You Know WorkSpace
pages. The CheckPoint page provides ideas for differentiating
instruction and offers additional practice.
End-of-Unit AssessmentThis assessment measures student growth
when compared with the results of the Beginning-of-Unit Assessment.
Use the Objectives Tracker (see page 339 for an example) to record
student achievement for each unit.
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