Multiples
of Equal Groups
Objective To introduce multiplication as a way to find the total
number of things in several equal groups.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Practicing with +/- Fact Triangles
• Count the total number of objects in
several groups. +/- Fact Triangles in an envelope
Children use Fact Triangles to practice
addition and subtraction facts.
[Number and Numeration Goal 1]
• Make arrays to represent equal groups. [Operations and Computation Goal 4]
• Use various strategies to solve
equal-groups number stories. Math Boxes 6 7
Math Journal 1, p. 149
Children practice and maintain skills
through Math Box problems.
[Operations and Computation Goal 4]
Home Link 6 7
Key Activities
Children are introduced to diagrams to
identify the known and unknown quantities
in multiplication problems and to complete
number models to summarize the solutions.
Children also solve number stories about
equal groups of things.
Math Masters, p. 179
Children practice and maintain skills
through Home Link activities.
Ongoing Assessment:
Recognizing Student Achievement
Use the Math Message. [Operations and Computation Goal 4]
Key Vocabulary
equal groups multiplication times multiplied by
Materials
Math Journal 1, p. 148
My Reference Book, pp. 112 and 113
Home Link 66
Math Masters, p. 415
per group: 40 pennies or other counters 6 boxes or bags to hold pennies or other
counters (for demonstration) pennies or
other counters (for demonstration)
Advance Preparation
For the optional Extra Practice activity in Part 3, obtain the book Each Orange Had 8 Slices:
A Counting Book by Paul Giganti, Jr. (Greenwillow Books, 1992).
Teacher’s Reference Manual, Grades 1–3 pp. 90, 91
412
Unit 6
Whole-Number Operations and Number Stories
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Finding Totals for Equal Groups
Math Masters, p. 180
calculator
Children use their calculators and repeated
addition to solve equal-groups problems.
ENRICHMENT
Solving Equal-Groups Riddles
Math Masters, p. 181
Children create and solve equal-groups
number riddles.
EXTRA PRACTICE
Equal Groups in Literature
Each Orange Had 8 Slices: A Counting Book
Children identify and solve multiplication
problems found in literature.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 142
Children add the term multiplication to their
Math Word Banks.
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6
Content Standards
Getting Started
2.OA.2, 2.OA.4, 2.MD.5
Mental Math and Reflexes
Home Link
6 6 Follow-Up
Have children share strategies for solving comparison number stories like
the following:
Vivianna is 40 inches tall. Jennifer is 30 inches tall. How much taller is Vivianna than
Jennifer? 10 inches taller
Cecilia’s pencil was 19 centimeters when it was new. Now it is 9 centimeters shorter.
How long is Cecilia’s pencil now? 10 centimeters long
Josh caught a fish that was 15 inches long. Jackie caught a fish that was 7 inches
longer. How long was Jackie’s fish? 22 inches
Math Message
Children draw the
different arrays they made with 24
Xs. Be sure to include the following
arrays: 1 row of 24 Xs and 24 rows
of 1 X each. Show children any
other possible arrays that they do
not suggest.
Jane bought 3 packs of gum. There are 5 sticks of gum per pack. How many
sticks of gum did she buy? Show how you found your answer on an Exit Slip
( Math Masters, page 415).
5 + 5 + 5 = 15
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
ELL
Math Message Ongoing Assessment:
Recognizing Student Achievement
Use the Math Message to assess children’s understanding of combining equal
groups to find the total. Children are making adequate progress if they can find
the answer by counting by 1s, 5s, drawing a picture, creating tally marks, or
adding the equal groups. Some children may be able to write a multiplication
number model for the problem.
[Operations and Computation Goal 4]
Ask children to share their solution strategies. Expect a variety of
strategies: count by 1s; count by 5s; add 5s; double 5, and then
add 5. Some children might draw pictures or use tallies. (See
margin.)
////\ ////\ ////\
5
10
////\
1 pack
////\
1 pack
////\
1 pack
15
}
15 sticks
Some solution strategies for the Math Message
problem
Use the Math Message problem to lead into a discussion about
equal groups. Write equal groups on the board. Ask children to
name things that come in equal groups and write their responses
on the board. To support English language learners, draw pictures
of any unfamiliar contexts. In the Math Message problem, the
packs of gum are equal groups, because each pack has five sticks
of gum in it. Six-packs of soft drinks are another familiar example
of equal groups, because each six-pack has six cans or bottles in it.
Ask children to name things that do not come in equal groups.
Sample answers: Families, classroom sizes
Lesson 6 7
413
Tell children that they can find the total number of things in
several equal groups by multiplication. Emphasize that in a
multiplication situation, each group must have the same number
of things.
Show children some possible number models for the number
story: 5 + 5 + 5 = 15 or 3 × 5 = 15. Mention that 3 × 5 is read
“3 times 5” or “3 multiplied by 5.” To support English language
learners, review the meaning of times in this context.
Solving Number Stories
WHOLE-CLASS
ACTIVITY
about Equal Groups
ELL
PROBLEM
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
IIN
NG
Algebraic Thinking Divide the class into groups of 4 or 5. Display
several boxes of an item, such as pennies, paper clips, dominoes,
or crayons. Each box should contain the same number of the
item selected.
Example: Display five boxes and put four pennies in each one.
Tell the class that there are four pennies per box. Ask children to
find the total number of pennies in all the boxes by using counters
to act out a solution.
Suggested questions:
●
How many groups of pennies are there? 5, because there are
5 boxes
●
How many pennies are in each group? 4 Are they equal groups?
Yes, because there is an equal number of pennies in each box.
●
How many pennies are there in all? 20
●
What number model can we write for this problem?
5 × 4 = 20 or 4 + 4 + 4 + 4 + 4 = 20
Draw a diagram on the board that identifies the known and
unknown quantities. Point out that the numbers in the diagram
tell the quantities we know and that the question mark indicates
the quantity we are trying to find. Once children have found the
answer, erase the question mark, write in the answer 20, and
circle it. (See below.)
boxes
5
pennies per box
pennies in all
4
20
5 × 4 = 20
4 + 4 + 4 + 4 + 4 = 20
Make up other stories by changing the number of boxes and the
number of items per box. Emphasize the language of equal groups:
for example, three boxes with seven marbles per box and three
boxes with seven crayons in each box.
414
Unit 6 Whole-Number Operations and Number Stories
Student Page
Children should continue using counters, pictures, doodles, or
anything else that might help them find the total number of items.
As they share solution strategies, write number models on the
board and read the models aloud. For example:
Number Stories
You can use a diagram to help you solve
a number story about groups with equal
numbers of objects.
Mia has 4 packs of gum.
There are 5 sticks of gum in each pack.
How many sticks of gum are there in all?
5 + 5 + 5 = 15 5 plus 5 plus 5 equals 15.
3 × 7 = 21 3 times 7 is 21.
Number of
groups
Number of
objects in
each group
Total number
of objects
packs
sticks per pack
sticks in all
4
5
?
You know the
number of groups.
You know the
number of objects
in each group.
4 × 6 = 24 6 multiplied by 4 equals 24.
Continue to fill in a diagram for each of the problems on the
board. Write in the known quantities, and write a question mark
for the unknown quantity. Ask children to help you complete the
diagrams as you discuss problems, but do not expect children to
come up with diagrams on their own. Repeated exposure to such
diagrams will help children understand the meanings of
multiplication and division.
Next, make up several number stories that do not require boxes of
items as props. Fill in diagrams as before. As children share
solutions, write number models on the board. Suggestions:
Number model: 4
5
You don’t know
the total number
of objects.
?
My Reference Book, p. 112
6 children have wet shoes, 2 shoes per child. How many wet
shoes? 12
3 children took 4 crackers each. How many crackers? 12
4 packs of juice, 6 cans per pack. How many cans? 24
2 weeks, 7 days per week. How many days? 14
Adjusting the Activity
Pose problems using larger numbers. For example:
• 3 hours, 50 miles per hour. How many miles? 150
• 5 toys, 99 cents per toy. Total cost? $4.95
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Student Page
Date
Solving Number Stories
about Equal Groups
LESSON
6 7
PARTNER
ACTIVITY
Time
Multiplication Stories
Solve each problem. Draw pictures or use counters to help.
How many cans are in
three 6-packs of juice?
Example:
PROBLEM
PR
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
L
LV
VING
VI
VIN
V
IN
IN
NG
G
(Math Journal 1, p. 148; My Reference Book,
pp. 112 and 113)
Algebraic Thinking You may wish to read about number stories
with equal groups in My Reference Book, pages 112 and 113 with
your class. Partners act out and solve the multiplication stories on
the journal page. Ask them to show how they solved the problems.
Children might draw pictures or use counters.
///
///
6
///
///
12
Answer:
18
///
///
18
cans
1. Mr. Yung has 4 boxes of
2. Sandi has 3 bags of marbles.
markers. There are 6 markers
in each box. How many
markers does he have in all?
Answer:
24
Each bag has 7 marbles in it.
How many marbles does she
have in all?
markers
3. Mrs. Jayne brought
Answer:
30
marbles
4. After the picnic, 5 boys each
5 packages of buns to
the picnic. Each package
had 6 buns in it. How many
buns did she bring in all?
Answer:
21
buns
picked up 4 soft-drink cans to
recycle. How many cans did
the boys pick up all together?
Answer:
20
cans
Math Journal 1, p. 148
EM3MJ1_G2_U06_131_158.indd 148
1/29/11 9:44 AM
Lesson 6 7
415
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Math Boxes
67
1. Write the number.
2. Make ballpark
Unit
estimates. Write a
number model for
each estimate.
32 + 59 Sample estimates.
325
30
+
60
=
90
30
=
80
51 + 27
50
10 11
9
+
How many?
cm
Have children work with a partner using the Fact Triangles as
flash cards. Remind children that when their partner misses a
fact, they should flash the other fact problems on the triangle and
then return to the fact that was missed.
51
Cross out 23 cubes.
How many are left?
Draw a line segment 3 cm
shorter.
28
Write a number model.
51
-
23
=
Math Boxes 6 7
28
31
5. Lauren’s birthday is on the
6. Double.
tenth day in the shortest month
of the year. In what month is
her birthday?
2
4
February
10
50
85
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 149)
Unit
4
8
20
100
+/- Fact Triangles
PARTNER
ACTIVITY
92–94
4.
3. Measure the line segment.
Practicing with
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-9. The skill in Problem 6
previews Unit 7 content.
Math Journal 1, p. 149
EM3MJ1_G2_U06_131_158.indd 149
1/29/11 10:57 AM
Writing/Reasoning Have children draw, write, or
verbalize their answers to the following: In Problem 5, if
Lauren was born the same year as you, is she older or
younger? What strategy did you use to solve the problem?
Sample answer: She is older than me; I was born in June, so she
would turn 8 years old first. She is younger than me, I was born in
January, so I would turn 8 years old first.
Home Link 6 7
INDEPENDENT
ACTIVITY
(Math Masters, p. 179)
Home Connection Children can use objects, draw
pictures, count, or use any other helpful device to solve
problems about equal groups.
Home Link Master
Name
Date
HOME LINK
Time
How Many?
67
In today’s lesson, your child learned that multiplication is an operation used to find the total
number of things in several equal groups. As you help your child solve the following
problems, emphasize that each group has the same number of things. Your child can use
objects, draw pictures, count, or use any other helpful devices to find the answers.
Family
Note
Please return this Home Link to school tomorrow.
How many apples in 4 packages?
Example:
////\
////\
////\\
////\\
char style: G1_MM Prob Num bol
style sheet: No Style
1 pica to top rule
1 pica to left rule
5 5 5 5 20
There are 20 apples in 4 packages.
1.
3
How many sides on each triangle?
How many sides in all?
18
sides
8
2
wheels
wheels
How many fingers for each person?
10
fingers
How many fingers in all?
80
fingers
Math Masters, p. 179
156-194_EMCS_B_G2_MM_U06_576949.indd 179
416
Finding Totals for Equal Groups
INDEPENDENT
ACTIVITY
5–15 Min
sides
How many wheels on each bike?
3.
READINESS
(Math Masters, p. 180)
2.
How many wheels in all?
3 Differentiation Options
To provide experience with solving equal-groups problems, have
children use their calculators and repeated addition. Some
children may want to program the calculator to skip count, while
others may want to enter + repeatedly. When they have
finished solving the problems, have them compare their answers.
They should rework problems on which they don’t agree. Have
volunteers share their strategies for solving the problems.
Consider having children record addition number sentences to
show how they solved problems.
1/26/11 3:45 PM
Unit 6 Whole-Number Operations and Number Stories
Teaching Master
ENRICHMENT
▶ Solving Equal-Groups Riddles
SMALL-GROUP
ACTIVITY
Name
LESSON
67
15–30 Min
Date
Time
Finding Totals for Equal Groups
You may use your calculator to help you solve the problems.
Answers vary.
(Math Masters, p. 181)
1. How many people are in my group?
How many hands do the people in my group have
all together?
To further explore the concept of equal groups, have children use
Math Masters, page 181 to create and solve equal-groups riddles.
How many fingers do the people in my group have
all together?
2. How many tables are in the classroom?
EXTRA PRACTICE
▶ Equal Groups in Literature
SMALL-GROUP
ACTIVITY
15–30 Min
Read the following book to groups of children, or have
children read the book themselves.
Each Orange Had 8 Slices: A Counting Book by Paul
Giganti, Jr. (Greenwillow Books, 1992) Summary: Multiplication
concepts are explored in the full-color book. In the first
presentation, 3 red flowers are seen; each flower has 6 petals,
and each petal has 2 black bugs. Questions are posed about the
number of flowers, the number of petals, and the number of bugs.
Have children answer the questions posed in the book.
ELL SUPPORT
▶ Building a Math Word Bank
How many legs do the tables have?
3. One flower has 5 petals.
How many petals do 6 flowers have?
4. Make up your own problem like the ones above. Draw a
picture to help someone solve your problem.
Math Masters, p. 180
156-194_EMCS_B_G2_MM_U06_576949.indd 180
1/26/11 3:45 PM
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook, p. 142)
To provide language support for multiplication, have children
use the Word Bank template found on Differentiation Handbook,
page 142. Ask children to write the term multiplication, draw a
picture representing the term, and write other related words. See
the Differentiation Handbook for more information.
Teaching Master
Name
Planning Ahead
Have children copy their Beat the Calculator results from Math
Journal 1, page 24 to Math Journal 2, page 311. Children
will continue to record the facts for which they can beat the
calculator. The Fact Power Table on journal page 311 will become
a cumulative record of children’s progress toward addition fact
power during Beat the Calculator game situations.
Date
LESSON
67
Time
Equal-Groups Riddles
What Number Am I?
1. If you put me into 7 equal groups with 3 in each group and
5 are left over, what number am I?
26
Draw a picture of what you did.
Sample answer:
2. I am a number between 20 and 30. When you put me into
6 equal groups, there is an even number in each group
and 1 is left over.
What number am I?
25
Draw a picture of what you did.
Sample answer:
3. Try writing your own equal-groups riddle.
Answers vary.
Math Masters, p. 181
156-194_EMCS_B_G2_MM_U06_576949.indd 181
1/26/11 3:45 PM
Lesson 6 7
417