Math 15 Operations on Whole Numbers
Name ________________________
Goal: Investigate the many different representations for addition, subtraction, multiplication, and
division. Make connections between symbolic representations and a word problem.
1. Read each word problem listed below. For each problem A. Write the symbolic
representation that most directly matches the action in the problem (i.e. write the equation such
as 8 – 3 = 5). There may be more than one. B. Note whether you need to find the whole amount
or a part to answer the question. C. Draw a picture to represent the problem.
a. Clinton had 8 balloons. Then some of them popped. Now he has 3 balloons. How many
balloons popped?
b. Laurel has 3 red balloons and 5 green balloons. How many balloons does Laurel have all
together?
c.
Clinton had some balloons. Then he bought 3 more balloons. Now he has 8 balloons.
How many balloons did Clinton have to begin with?
d. Clinton had 8 balloons. Three of them are blue and the rest are yellow. How many of
Clinton’s balloons are yellow?
e. Laurel had three balloons. Then Clinton gave her some more balloons. Now she has 8
balloons. How many balloons did Clinton give her?
f. Laurel had some balloons. Then 3 of her balloons popped. Now she has 5 balloons.
How many balloons did she have to begin with?
2. We have talked about three different models for subtraction: Take-Away Model, Comparison
Model and Missing Addend Model. For each of the following problems: A. Write the symbolic
representation for the problem. B. Determine which of the three subtraction models is
represented. (There can be more than one). C. Draw a diagram for the problem.
a. There are 7 chairs and 5 people in the room. If each person sits on a chair, how many
extra chairs are there?
b. Alice has $5 and Tanisha has $8. How many more dollars does Tanisha have than Alice?
c. Terry has 9 strawberries in her bowl. If she eats 3 of them, how many strawberries are
left?
3. There are four models for multiplication: Repeated Addition, Area, Array, and Cartesian
Product. For each model: A. Create a problem. B. Draw a diagram or model for the problem.
C. Write the number sentence for the problem (i.e. 3 x 4 = 12).
4. Division situations often occur when you know the total amount and you want to find either
the number of items in each group or the number of groups. There are two ways this usually
occurs. (1) The Repeated Subtraction involves repeatedly subtracting equivalent parts, as in “If
you have 20 apples, how many packages of 4 apples each can you make?” (2) The Partition
Model involves sharing objects to form equivalent parts, as in “If I distribute 20 apples among
my 4 friends, how many apples will each friend receive?” Indicate below which diagram
represents the Repeated Subtraction Model and which represents the Partition Model.
A
B
C
_______________
@ @ @ @ @/@ @ @ @ @/@ @ @ @ @/
D
@ @ @ @ @
_______________
(A, B, C, D are 4 friends)
@@@@  1 @@@@  2 @@@@  3
@@@@  4 @@@@  5
5. For each problem below, draw a diagram and indicate whether the situation involves the
Repeated Subtraction Model or the Partition Model. Then write the equation for the problem.
a. A club sandwich requires 3 slices of bread. If Marcus has 18 slices of bread, how many
club sandwiches can he make?
b. Cory, Andre, Ryan, and Jodie ate a pizza. The pizza cost $12. How much does each
person need to pay if they share the cost?
c. Skyler made a batch of 36 maple sugar cookies. He is going to put them in bags with 4
cookies each and pass them out during his study group. How many bags of cookies will
Skyler have to distribute?
6. Reflection ( 1 – 3 paragraphs): Compare the ideas presented in this lab with the way you
remember learning addition, subtraction, multiplication, and division. Also, what is the biggest
take-away point you’ve learned about the connections between addition/subtraction and
multiplication/division from this assignment or our class discussions and reading Section 3.2.