Array Number Stories
Objectives To introduce everyday examples of rectangular
arrays;
and to provide experiences with solving multiplication
a
problems using multiplication diagrams and array models.
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Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Solve multiplication number stories using
rectangular arrays. [Operations and Computation Goal 4]
• Create multiplication number stories using
rectangular arrays. [Operations and Computation Goal 4]
• Write a number model that represents a
rectangular array. [Patterns, Functions, and Algebra Goal 2]
Key Activities
Children identify and describe familiar arrays,
create and solve number stories about arrays
using multiplication diagrams and array
models, and complete number models to
summarize solutions.
Family
Letters
Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Ongoing Learning & Practice
1 2
4 3
Playing the Fact Extension Game
My Reference Book, pp. 134 and 135
per partnership: 4 each of number
cards 0–9 (from the Everything Math
Deck, if available), 2 sheets of paper,
1 die, calculator
Children practice fact extensions.
Math Boxes 6 8
Math Journal 1, p. 152
Children practice and maintain skills
through Math Box problems.
Home Link 6 8
Math Masters, p. 183
Children practice and maintain skills
through Home Link activities.
Ongoing Assessment:
Recognizing Student Achievement
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Playing Simon Says
24 counters
Children practice making equal rows using
a concrete model.
ENRICHMENT
Creating Array Number Stories
Math Masters, p. 419
Children write number stories, draw an array
for the number story, and write a number
model to represent the story.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 142
Children add the term array to their Math
Word Banks.
Use journal page 151. [Operations and Computation Goal 4]
Key Vocabulary
multiplication diagram x-by-y array
Materials
Math Journal 1, pp. 150 and 151
Home Link 67
Math Masters, p. 182 (optional); pp. 183
and 438
transparency of Math Masters, p. 438
(optional) per partnership: 50 pennies or
other counters (optional) calculator
Advance Preparation
In Part 1, choose one of the following to display a multiplication diagram and its corresponding array:
• Make an overhead transparency of Math Masters, page 438.
• Draw and erase multiplication diagrams, arrays, and number models on the board as needed.
For an additional mathematics and literacy connection, obtain copies of Sea Squares by Joy N. Hulme (Hyperion
Books for Children, 1999) and Amanda Bean’s Amazing Dream by Cindy Neuschwander (Scholastic Inc., 1998).
Teacher’s Reference Manual, Grades 1–3 pp. 90–92
418
Unit 6
Whole-Number Operations and Number Stories
Mathematical Practices
SMP1, SMP2, SMP4, SMP5, SMP6
Content Standards
Getting Started
2.OA.4
Mental Math and Reflexes
Math Message
Pose number stories about multiples of equal groups.
Egg carton: 2 rows of 6 eggs. Use your calculator
to find how many eggs in all. 12 eggs
Suggestions:
Home Link 6 7 Follow-Up
Yuko has 2 boxes of crayons. There are 8 crayons in each
box. How many crayons in all? 16
Arlie can walk about 3 miles per hour. About how many
miles can he walk in 4 hours? About 12 miles
Review answers. Ask children to write number
models for each problem and to read them aloud.
6 × 3 = 18, 2 × 4 = 8, 8 × 10 = 80
Each apple costs 25 cents. Jenna bought 5. How much did
she pay? $1.25
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Masters, p. 438)
Have children share how they solved the problem on their
calculator.
For example:
I entered 6
+
6 on my calculator. (all calculators)
=
I entered 6
X
2
. (all calculators)
=
I entered 2
I entered 2
SL-450)
+
,
=
=
,
=
,
,
If children do not mention the 6
,
,
,
,
X
=
=
,
,
rows
eggs per row
2
6
eggs in all
12
?
Number model:
. (on the TI-108)
6 + 6 = 12 or 2 × 6 = 12
. (on the Casio
2 option, be sure to point it
out and have children solve the Math Message by entering
=
X
.
2
6
Explain that this key is the standard multiplication key and that
they will have an opportunity to use this key in later lessons.
Next, ask someone to draw the egg carton on the board. Remind
children that an array is a rectangular arrangement of objects in
rows and columns and point out that the eggs form an array.
There are 2 rows of eggs with 6 eggs in each row, so there are
12 eggs in all.
Display a multiplication diagram. (See Advance Preparation.)
Fill it in. Mark or draw a 2-by-6 array and write number models
as shown in the margin.
Lesson 6 8
419
Home Link Master
Name
Date
Time
▶ Identifying Familiar Arrays
Arrays
HOME LINK
68
Family
Note
(Math Masters, p. 183)
In this lesson, your child solved multiplication problems about arrays, which are rectangular
arrangements of objects in rows and columns. Encourage your child to use counters, such as
pennies or buttons, while working on the following exercises.
Please return this Home Link to school tomorrow.
Distribute Home Link 6-8. At the bottom it includes pictures of six
familiar arrays. For each array, ask children how many rows there
are and how many items there are in each row. Encourage them to
talk about x-by-y arrays. For example:
Tell someone at home what you know about arrays.
1. Look at the array
and fill in the
blank.
2. Draw an array of
3. Draw an array of
dots. Your array
should have
12 dots.
Sample
answers:
1-by-12;
2-by-6;
3-by-4;
4-by-3;
6-by-2;
12-by-1
5 rows of dots
7 dots in each row
That’s
in all.
4 rows of dots
35
dots
6 dots in each row
dots in all.
Telephone: 4 rows of keys, 3 keys in each row; a 4-by-3 array
Checkerboard: 8 rows of squares, 8 squares per row; an 8-by-8
array
py g
g
p
24
WHOLE-CLASS
ACTIVITY
Telephone:
a 4-by-3 array
Muffins:
a 3-by-2 array
Tic-tac-toe Grid:
a 3-by-3 array
2-by-6 arrays: 2 rows, 6 per row
Muffins:
a 3-by-4 array
Adjusting the Activity
Eggs:
a 2-by-6 array
Checkerboard:
an 8-by-8 array
Math Masters, p. 183
156-194_EMCS_B_G2_MM_U06_576949.indd 183
1/28/11 2:02 PM
Draw the 2-by-6 dot array on the board. Explain that there are different
ways to describe the array and write the following statements on the board.
2-by-6 Array
2 Rows and 6 Dots in each Row
2 Rows and 6 Dots per Row
To support English language learners, clarify that the word per can
replace the words in each.
A U D I T O R Y
NOTE Math Masters, page 182 is identical
to journal page 150. Make copies of this
master if children need more space to record
number stories involving arrays.
ELL
K I N E S T H E T I C
T A C T I L E
Creating and Solving Number
Stories about Arrays
V I S U A L
WHOLE-CLASS
ACTIVITY
PROBLEM
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SOLVING
SO
S
OL
O
LV
VING
VIN
ING
(Math Journal 1, p. 150; Math Masters, p. 182)
Student Page
Date
LESSON
6 8
Display a multiplication diagram.
Time
Array Number Stories
Array
Multiplication Diagram
rows
per row
in all
Solving Number Stories
Number model:
Array
Multiplication Diagram
rows
per row
in all
Number model:
Array
per row
1. Fill in the headings on the multiplication diagram on the
journal page. For example, if the story is about rows of keys,
fill in “keys” on the first line of the multiplication diagram.
2. Fill in the known numbers and write a question mark for
the number to be found.
Multiplication Diagram
rows
You or the children make up number stories involving arrays of
objects. (See the number-story suggestions on page 421.) For each
story, children work alone or with a partner to do the following:
in all
3. Make an array with counters to model the story.
Number model:
Array
Multiplication Diagram
rows
per row
in all
4. Show the array next to the multiplication diagram by
coloring the circles, drawing a ring around the circles, or
marking the circles with Xs.
5. Write the answer on the diagram and circle it.
150
ff
Number model:
6. Write an addition or multiplication number model.
Math Journal 1, p. 150
EM3MJ1_G2_U06_131_158.indd 150
420
1/29/11 10:57 AM
Unit 6 Whole-Number Operations and Number Stories
As children solve each problem, fill in the displayed diagram,
mark or draw an array picture, and ask for the answer. Help
children to summarize by writing a number model. A sample
solution is shown below.
Telephone: 4 rows of keys, 3 keys in each row. How many keys?
Adjusting
the Activity
ELL
First, children make the arrays with counters.
Then they record their arrays on the
journal page.
AUDITORY
rows
keys per row
4
3
KINESTHETIC
TACTILE
VISUAL
keys in all
?
12
Number model: 3 + 3 + 3 + 3 = 12 or 4 × 3 = 12
NOTE Some children may write an addition
Number-story suggestions:
Carton of soup cans: 4 rows of cans, 6 cans per row. How many
cans? 24
number model to represent the number story.
Others may write a multiplication number
model. At this time both are acceptable.
Floor tiles: 5 rows of tiles, 9 tiles in each row.
How many tiles? 45
Tic-tac-toe: 3 rows of squares, 3 squares per row. How many
squares? 9
Math Boxes: 3 rows of problems, 2 problems in each row. How
many problems? 6
Calendar: 3 weeks, 7 days in each week. How many days? 21
Summary: Arrays are examples of equal groups of objects.
The total number of objects in an array can be found by using
repeated addition or multiplication.
Teaching Master
Name
LESSON
68
Date
Time
Array Number Stories
Array
Multiplication Diagram
rows
Adjusting the Activity
ELL
Pose problems like these:
per row
in all
Number model:
Array
Theater seats: 15 rows of seats, 10 seats per row. How many seats? 150
Multiplication Diagram
rows
per row
in all
Cases of soda: 10 cases of soda, 24 cans per case. How many cans? 240
Number model:
Imagine a 20-by-30 array of dots. How many dots in all? Use your calculator to
solve. 600
Array
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
Multiplication Diagram
rows
per row
in all
Number model:
Array
Multiplication Diagram
rows
per row
in all
Number model:
Math Masters, p. 182
156-194_EMCS_B_G2_MM_U06_576949.indd 182
1/29/11 12:23 PM
Lesson 6 8
421
Student Page
Date
Time
LESSON
6 8
Solving Array Multiplication
Multiplication Number Stories
For each problem:
Use Xs to show the array.
Problems
Answer the question.
Write a number model.
1. The marching band has 3 rows with
5 players in each row. How
many players are in the band?
(Math Journal 1, p. 151)
2. Mel folded his paper into 2
There are 15 players.
Number model: 5 × 3 =
rows of 4 boxes each. How
many boxes did he make?
He made 8 boxes.
Number model: 2 × 4
15
or 5 + 5 + 5 = 15
Partners work together to draw arrays, solve problems, and write
number models.
Ongoing Assessment:
Recognizing Student Achievement
=8
or 4 + 4 = 8
3. The sheet has 5 rows of stamps.
4. The orchard has 4 rows
There are 5 stamps in each row.
How many stamps are there?
PARTNER
ACTIVITY
Journal page 151
Problems
1 and 2
Use journal page 151, Problems 1 and 2 to assess children’s ability to show an
array. Children are making adequate progress if they can make the array and
count the total. Some children may be able to complete the number model.
of trees. Each row has 8
trees. How many trees are
there?
[Operations and Computation Goal 4]
There are 25 stamps in all.
Number model: 5 × 5 = 25
There are 32 trees.
or
Number model: 4 × 8 = 32
5 + 5 + 5 + 5 + 5 = 25 or 8 + 8 + 8 + 8 = 32
Math Journal 1, p. 151
EM3MJ1_G2_U06_131_158.indd 151
1/29/11 10:57 AM
2 Ongoing Learning & Practice
Playing the Fact Extension Game
PARTNER
ACTIVITY
(My Reference Book, pp. 134 and 135)
Children practice fact extensions through the Fact Extension
Game first introduced on page 292 in Lesson 4-8. Directions for
the game can be found on pages 134 and 135 in My Reference Book.
Math Boxes 6 8
(Math Journal 1, p. 152)
Student Page
Date
Time
LESSON
68
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 6-6 and 6-10. The skill in Problem
6 previews Unit 7 content.
Math Boxes
1. Choose the best answer. Be
INDEPENDENT
ACTIVITY
2. Draw the line of symmetry.
careful!
6 tens
NOTE After children complete journal page 152, you may want to have them
create a shape using their Pattern-Block Template. Then have them use their
shape to create a pattern that involves flipping, sliding, or turning the shape.
3 ones
8 hundreds
638
836
368
863
60
3. Use counters to solve.
4. This is a
5
-by-
4
array.
Home Link 6 8
$14.00 is shared equally.
Each child gets $5.00.
How many children are sharing?
2
children
4
dollars
16°C and 28°C
15°C and 43°C
20
dots
Home Connection Children describe arrays and solve
array problems.
88 89
5. Find the differences.
70°F and 57°F
(Math Masters, p. 183)
How many dots in all?
How many dollars are left over?
6. What comes next?
12
13
28
Math Journal 1, p. 152
EM3MJ1_G2_U06_131_158.indd 152
422
INDEPENDENT
ACTIVITY
1/28/11 9:06 AM
Unit 6 Whole-Number Operations and Number Stories
Home Link Master
Name
3 Differentiation Options
Date
HOME LINK
68
䉬
Family
Note
Time
Arrays
In this lesson, your child solved multiplication problems about arrays, which are rectangular
arrangements of objects in rows and columns. Encourage your child to use counters, such as
pennies or buttons, while working on the following exercises.
Please return this Home Link to school tomorrow.
READINESS
Playing Simon Says
SMALL-GROUP
ACTIVITY
5–15 Min
To provide experience with making equal rows using a concrete
model, have children play Simon Says where the directions are
about modeling numbers in rows. Distribute 24 counters to each
child. Give directions like the following:
●
Simon says, “Put your counters in 4 equal rows.”
●
How many counters are in each row? 6 counters
●
Simon says, “Put your counters in rows with 3 in each row.”
●
How many rows of counters are there? 8 rows
Be sure to discuss instances where children cannot make
equal rows.
ENRICHMENT
Creating Array Number Stories
Tell someone at home what you know about arrays.
1. Look at the array
2. Draw an array of
and fill in the
blank.
dots. Your array
should have
5 rows of dots
7 dots in each row
That’s
in all.
4 rows of dots
35
6 dots in each row
24
dots in all.
Telephone:
a 4-by-3 array
Tic-tac-toe Grid:
a 3-by-3 array
Muffins:
a 3-by-2 array
Checkerboard:
an 8-by-8 array
dots
3. Draw an array of
12 dots.
Sample
answers:
1-by-12;
2-by-6;
3-by-4;
4-by-3;
6-by-2;
12-by-1
Muffins:
a 3-by-4 array
Eggs:
a 2-by-6 array
183
Math Masters, p. 183
INDEPENDENT
ACTIVITY
15–30 Min
(Math Masters, p. 419)
To apply children’s understanding of array multiplication, have
them write multiplication-array number stories on Math Masters,
page 419. Children write the number stories in words, draw
an array for the number story, and write a number model to
represent the story.
Example:
Farmer Hannah planted 3 rows of corn. Each row had 9 corn
stalks in it. How many corn stalks were there in all?
Teaching Aid Master
Name
Date
Time
A Number Story
Unit
3 × 9 = 27 corn stalks
When children are finished writing their number stories,
encourage them to trade with a partner and solve.
ELL SUPPORT
Building a Math Word Bank
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 array, draw a picture
representing the term, and write other related words. See the
Differentiation Handbook for more information.
Math Masters, p. 419
Lesson 6 8
423
Name
LESSON
68
Date
Time
Array Number Stories
Array
Multiplication Diagram
rows
per row
in all
Number model:
Array
Multiplication Diagram
rows
per row
in all
Number model:
Array
Multiplication Diagram
rows
per row
in all
Array
Multiplication Diagram
rows
per row
Number model:
182
in all
Copyright © Wright Group/McGraw-Hill
Number model:
Measurement
You can cover a shape with unit squares to
find the area.
The area is the number of squares.
Count the squares to find the area.
3 ft
7 ft
1
4
7
10
2 3
5 6
8 9
11
1
4
7
10
13
16
19
2
5
8
11
14
17
20
The area of the front of this door is 21 square feet.
Try It Together
Draw a shape that has an area of 6 square centimeters.
Compare your shape with a partner’s shape.
69A
3
6
9
12
15
18
21
Measurement
You can draw unit squares on a shape to
find its area.
Tick marks along the edge can help you
draw the unit squares.
Draw and count squares to find the area.
1 2 3
4 5 6
7 8 9
10
11
The area of this shape is 11 square units.
Try It Together
Draw a shape with an area of 13 square inches.
Compare your shape with a partner’s shape.
69B