Math Ed 305
Multiplication and Division Problems and Strategies
For each of the problems below,
A. State the problem type (i.e. multiplication, measurement division, partitive
division),
then describe how a child might attempt to solve them using:
B. A Direct Modeling Strategy
C. A Counting or Adding Strategy
D. Derived Facts
As a group, try to come up with as many alternative ways of approaching the problem as
possible.
1.
Nineteen children are going to the circus. Five children can ride in each car.
How many cars are needed so that all the children can go to the circus?
2.
I have 6 bags with 4 pencils in each bag. How many pencils do I have altogether?
3.
I have 16 marbles. I want to give them away to my three friends so that each of
my friends gets the same number of marbles. How many marbles will each friend
get?
Math Ed 305
Review of Problem Types
For each problem below, decide whether it is a Multiplication problem, a Measurement
Division problem, or a Partitive Division problem.
1.
Gerry has 3 zucchini plants. There are 12 zucchini on each plant. How many
zucchini does he have to give away?
2.
Cookies cost 654 each. How many can you buy for $3.25?
3.
Jake jogged 12 miles. (He=s getting ready for a marathon.) It took him 3 hours.
If he ran the same speed the whole way, how far did he run in one hour?
4.
My garter snake is 18 inches long. Mary=s is 6 inches long. My snake is how
many times longer than Mary=s?
5.
Jake jogs 4 miles in an hour. How many hours will it take him to jog 12 miles?
6.
Gerry has 3 zucchini plants. There are the same number of zucchini on each
plant. All together there are 36 zucchini. How many zucchini are on each plant?
7.
Cookies cost 654 each. How much do 5 cookies cost?
8.
My garter snake is 18 inches long. She is 3 times as long as Mary=s snake. How
long is Mary=s snake?
9.
Jake jogs 4 miles in an hour. How many miles will he jog in 3 hours?
10.
Gerry has some zucchini plants. There are 12 zucchini on each plant. All
together there are 36 zucchini. How many zucchini plants does Gerry have?
11.
My garter snake is 3 times as long as Mary=s. Mary=s snake is 6 inches long.
How long is my garter snake?
12.
Bill bought 5 cookies. He spent a total of $3.25. If each cookie costs the same
amount, how much did one cookie cost?
Math Ed 305
Homework #3
Multiplication and Division Problems and Strategies
1. For each of the following problems,
a) State the problem type (i.e. multiplication, measurement division, partitive
division),
then describe how a child might attempt to solve them using:
b) A Direct Modeling Strategy
c) A Counting or Adding Strategy
d) Derived Facts
A. Kim had 5 bags of candy with 7 pieces of candy in each bag. How many pieces
of candy did Kim have?
B. At Sally=s birthday party there were 15 children and 3 blankets. If the same
number of children sat on each blanket, how many children sat on each blanket?
C. Maria has 17 fish. If 3 fish can be put into one fish bowl, how many bowls does
she need to hold her fish?
D. Lee collects stamps. He has 45 stamps. If he sticks 9 stamps on each page, how
many pages would he fill with stamps?
E. Mr. Wong has 4 children. He wants his children to share 12 marbles so that they
each get the same amount. How many marbles should Mr. Wong give each child?
2. Using the division problem 23 ÷ 3 , write four different partitive division problems
for which the answers are:
a. 7
b. 8
c. 7 ⅔
d. 2
3. Repeat Problem 3 with measurement division problems.
A. Teen Girl Squad® bumper stickers cost $2.50
each. How many can I buy for $15?
B. It takes me 15 seconds to grade a quiz
question. If there are 6 questions on a quiz,
how long will it take me to grade a quiz?
C. I have 3 sport jackets, and 4 pairs of slacks.
How many outfits can I make (if I don’t worry
what clashes)?
D. Emily made a 4 foot volcano for the Science
Fair. Whilmer made a 12 foot volcano. How
many times taller is Whilmer's volcano than
Emily's?
E. In Mr. Phelps’ class there are 42 desks in 7
equal rows of equal size. How many desks are
in each row?
F. I have 75 cents in my pocket, which is 3 times
more than Dan has in his pocket. How much
does Dan have in his pocket?
G. Ms. Tingey bought 4 boxes of cupcakes. There
were 8 cupcakes in each box. How many
cupcakes did she buy altogether?
H. I can walk 3 miles in 24 minutes. How long
will it take me to walk 1 mile?
I. Baldrick had 6 turnips. Edmund Blackadder
had 3 times more turnips. How many turnips
did Edmund have?
J. I spent $32 on 2 “Rally Monkey” T-shirts.
How much did each shirt cost?
Measurement
Division
Partitive
Division
Multiplication
Combination
Array
Rate
Price
Problem
Multiplicative
Comparison
4. For each of the following problems, put an “X” in any column that accurately
describes that problem.
Children’s Multiplication and Division Solution Strategies
Measurement
Division
Partitive
Division
Grouping
Measuring
Partitioning
Dealing
Trial & Error
Repeated Addition
Repeated
Subtraction
Doubling
Halving
Skip Counting
Skip Counting
Multiplication
Direct Modeling
Counting
Trial & Error
Repeated
Addition/Subtraction
Trial & Error
Skip Counting