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Unit 4: Family Letter
Multiplication and Division
Unit 4 focuses on the most common uses of multiplication and division—problems that
involve equal sharing and equal grouping. In Second Grade Everyday Mathematics,
children were exposed to multiplication and division number stories and multiplication
and division facts. To solve multiplication and division number stories, children will refer
to familiar strategies introduced in second grade:
Acting out problems using concrete objects,
such as counters (below)
Representing problems with
pictures and arrays (below)
3 4 12
2 7 14
Copyright © Wright Group/McGraw-Hill
Using diagrams to sort out quantities (below)
children
pennies
per child
pennies
in all
4
?
28
A sheet of stamps has 6 rows. Each row has
3 stamps. How many stamps are on a sheet?
6 3 18
Using number models to represent solution
strategies (below)
Problem:
Solution strategies:
Each child has 2 apples.
There are 16 apples. How
many children have apples?
2 ? 16, or I know that 16 2 8.
If there are 16 apples and each child
has 2, then there must be 8 children.
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Unit 4: Family Letter cont.
Vocabulary
Important terms in Unit 4:
multiples of a number The product of the
equal groups Sets with the same number of
number and a counting number. For example,
multiples of 2 are 2, 4, 6, and 8….
elements, such as tables with 4 legs, rows with
6 chairs, boxes of 100 paper clips, and so on.
multiplication/division diagram In Everyday
dividend The number in division that is being
Mathematics, a diagram used to represent problems
in which the total number of objects in several equal
groups is being considered. The diagram has three
parts: number of groups, number in each group,
and total number. For example, the multiplication/
division diagram here represents this number story:
There are 3 boxes of crayons. Each box has 8
crayons. There are 24 crayons in all.
divided.
boxes
3
crayons per box
8
crayons
24
rectangular array
A 2-by-6 array of eggs
quotient The result
of division.
In 28 4 7,
28 is the dividend,
4 is the divisor, and
7 is the quotient.
remainder An amount left over when one number
is divided by another number. In the division
number model 16 3 ∑ 5 R1, the remainder is 1.
The product of a
339
number multiplied by
The number 9 is a
square number.
itself; any number that
can be represented
by a square array of dots or objects. A square array
has the same number of rows as columns.
In 4 3 12,
4 and 3 are the factors,
and 12 is the product.
product The result
of multiplying two numbers.
Building Skills through Games
In Unit 4, your child will practice division and multiplication by playing the
following games. For detailed instructions, see the Student Reference Book.
Division Arrays
Players make arrays with counters. They use number cards to determine the
number of counters and a toss of a die to establish the number of rows.
Beat the Calculator
A Calculator (a player who uses a calculator) and a Brain (a player who
solves the problem without a calculator) compete to see who will be first
to solve multiplication problems.
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Copyright © Wright Group/McGraw-Hill
two or more numbers
in a product.
another number, the dividend.
square number
A group of objects
placed in rows and
columns.
factor Each of the
divisor In division, the number that divides
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Unit 4: Family Letter cont.
Do-Anytime Activities
To work with your child on concepts taught in this unit and in previous units,
try these interesting and rewarding activities:
1. Together with your child, sort objects into equal groups. Discuss what you could do
with any leftover objects.
2. Review multiplication-fact shortcuts:
turn-around facts The order of the factors does not change the product. Thus,
if you know 3 4 12, you also know 4 3 12.
multiplication by 1 The product of 1 and another number is always equal to
the other number. For example, 1 9 9; 1 7 7.
multiplication by 0 The product of 0 and another number is always 0. For
example, 4 0 0; 0 2 0.
square numbers Arrays for numbers multiplied by themselves are always
squares. For example, 2 2 and 4 4 are square numbers.
224
4 4 16
Copyright © Wright Group/McGraw-Hill
3. Use the , Fact Triangles (a set will be sent home later) to practice the basic facts.
Act as a partner by covering one number on the card and then asking your child to
create a multiplication or division number model using the other two numbers.
7 8 56
56
8 7 56
56 8 7
, 7
56 7 8
8
4. Write any number–for example, 34,056. Then ask questions like the following:
How many are in the thousands place? (4) What is the value of the digit 5? (50)
5. Ask questions like the following:
Is 467 518 more or less than 1,000? (less) Is 754 268 more or less than 500? (less)
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Unit 4: Family Letter cont.
3 410
As You Help Your Child with Homework
As your child brings home assignments, you might want to go over the instructions together, have your child
explain the activities, and clarify them as necessary. The answers listed below will guide you through this unit’s
Home Links.
5. 5 4 20; 4 5 20;
20 5 4; 20 4 5
Home Link 4 1
1. 30 apples
6. 10 6 60; 6 10 60;
60 10 6; 60 6 10
Home Link 4 2
1. 24 counters
2. 24 counters
3. 24 counters
4. 358
5. 204
6. 428
Home Link 4 7
1. 5 6 30; 6 5 30;
30 6 5; 30 5 6
Home Link 4 3
1. 5 counters per person; 0 counters remaining
2. 2 counters per person; 5 counters remaining
3. 4 weeks in January; 3 days remaining
4. 4 teams; 2 children remaining
5. 2 pencils; 4 pencils left over
8. 31
3. 2 9 18; 9 2 18;
18 2 9; 18 9 2
4. 4 7 28; 7 4 28;
28 7 4; 28 4 7
5. 9 8 72; 8 9 72;
72 9 8; 72 8 9
6. 11 jelly beans; 0 jelly beans left over
7. 577
2. 8 3 24; 3 8 24;
24 3 8; 24 8 3
9. 801
6. 6 7 42; 7 6 42;
42 7 6; 42 6 7
Home Link 4 4
Home Link 4 8
1. 6 marbles; 0 marbles left over
2. 2 cookies; 1 cookie left over
1. 7; 5; 7 5 35; 35 square units
3. 4 complete rows; 6 stamps left over
2. 6; 7; 6 7 42; 42 square units
1. 10; 10
2. 15; 15
3. 20; 20
4. 9; 9
5. 90; 90
6. 365; 365
7. 0; 0
8. 0; 0
9. 0; 0
13. 14
10. 20
11. 20
14. 15
15. 50
12. 18
Home Link 4 6
4. 9 5 45
Home Link 4 9
The following answers should be circled:
1. more than the distance from Chicago to Dallas;
about 2,400 miles
1. 10; 10; 10; 10
2. 12; 12; 12; 12
3. 2 7 14; 7 2 14;
14 2 7; 14 7 2
4. 2 8 16; 8 2 16;
16 2 8; 16 8 2
84
2. about 600 miles;
less than the distance from Chicago to Denver
3. more than the distance from New York to
Chicago
4. less than the distance from Denver to Atlanta;
more than the distance from New York to
Portland; about 750 miles
Copyright © Wright Group/McGraw-Hill
3. 4 8 32
Home Link 4 5
Playing Everyday Math Games at
Home for Grades 3 and 4
All games require one deck of regular playing cards (with Jokers
removed) and can be played by 2-3 players or teams. If using the face
cards, remind everyone that J = 11, Q = 12, and K = 13.
Addition
Top-It
3 4 5
Practices addition
facts and
comparing sums
Subtraction
Top-It
3 4 5
Practices
subtraction facts
and comparing
differences
Use the cards from 1-10. Add more cards as the
players improve.
1. Shuffle the deck and place it face down in the center.
2. Each player turns over 2 cards and calls out the sum
of the numbers. Players should check each other’s
sums.
3. The player with the greatest sum takes all the cards.
In the case of a tie, each tied player turns over 2
more cards and calls out the sum. The player with
the greater sum takes all of the cards from both
plays.
4. Play ends when not enough cards are left for each
player to have another turn.
5. The player who collected the most cards wins.
Use the cards from 1-10. Add more cards as the
players improve.
1. Shuffle the deck and place it face down in the center.
2. Each player turns over 2 cards and subtracts the
smaller number from the larger number. He or she
then calls out the difference of the two numbers.
Players should check each other’s answers.
3. The player with the greatest difference takes all the
cards. In the case of a tie, each tied player turns
over 2 more cards and calls out the difference. The
player with the greater difference takes all of the
cards from both plays.
4. Play ends when not enough cards are left for each
player to have another turn.
5. The player who collected the most cards wins.
Multiplication
Top-It
Use the cards numbered 1-5. Add more cards as
players improve.
1. Shuffle the deck and place it face down in the center.
2. Each player turns over 2 cards and multiplies the two
numbers. He or she then calls out the product of the
two numbers. Players should check each other’s
Practices
answers.
multiplication facts
3. The player with the greatest product takes all the
and comparing
cards. In the case of a tie, each tied player turns
products
over 2 more cards and calls out the product. The
player with the greater product takes all of the cards
from both plays.
4. Play ends when not enough cards are left for each
player to have another turn.
5. The player who collected the most cards wins.
3 4 5
Name That
Number
3 4 5
Practices using the
four operations to
name numbers
1. Use all of the cards.
2. Place the deck face down in the center. Put five
cards face up to the left of the deck.
3. Turn over the top card on the deck. This is the
target number.
4. The first player tries to “name” the target number by
adding, subtracting, multiplying, or dividing the
numbers on as many of the 5 cards that are face up
as possible. If the player is successful, he or she
takes the target number and the other cards used to
name the target number. Those cards are replaced
by new cards from the deck.
5. If the player cannot name the target number, their
turn is over and the next card on the top of the deck
is turned over to be the target number.
6. The game is over when all of the cards in the deck
have been turned over. The winner is the player
who has collected the most cards.
Example: If the target number is 10 and the five cards
are 2, 3, 4, 7, and 8, some possible solutions are
3 + 7 = 10 (2 cards used)
(2 * 3) + 4 = 10 (3 cards used)
8 + (4/2) = 10 (3 cards used)
7 – 3 + 4 + 2 = 10 (4 cards used)