order of operations - nova scotia department of …hrsbstaff.ednet.ns.ca/jsandford/math/super math...

Orderof

Operations

Susan Mercer

Unit Description

The NCTM standards contend that “... learning mathematics without understanding has

long been a common outcome of school mathematics instruction.” (page 20 NCTM standards) In

particular this is true for order of operations. Traditionally, textbooks have presented order of

operations as a convention, a cluster of rules to be followed and memorized in order to get the right

answer. For example, Mc Dougal Littell states, in the California Middle School Mathematics:

Concepts and Skills Course 1 textbook, “To make sure everyone gets the same result when an

expression is evaluated, mathematicians have established order of operations.” These rules do not

provide understanding; nor do they build on students’ prior knowledge of numbers and operations.

Students are expected to apply the rules without comprehending why they are doing what they are

doing. Furthermore, the NCTM standards argue that “Students who memorize facts of procedures

without understanding often are not sure when or how to use what they know, and such learning is

often quite fragile.” (page 20 NCTM standards) Mathematical expressions are presented to

students out of context, without any meaning attached to the numbers or operations. This leads to

mistakes primarily because students tend to solve mathematical expression from left to right

rather than looking at the problem as a whole. In my experience, students view mathematical

expressions as abstract and meaningless and tend to “decode” them in the same way as they

decode a sentence or paragraph, from left to right.

Also, many teachers encourage students to use the acronym “Please Excuse My Dear Aunt

Sally” (PEMDAS) to remember the order in which to evaluate mathematical expressions.

Unfortunately, PEMDAS does not provide an explanation and students tend to solve the

multiplication before the division rather than multiplication and division from left to right and

addition before subtraction rather than addition and subtraction from left to right.

The order of operation model described in this article requires students to represent

mathematical expressions in three different ways: 1) verbally; 2) using a drawing; and 3)

symbolically using addition and/or subtraction only. These representations help students “see” the

mathematical expressions and help them evaluate them by finding the number of objects in the

representation. By using this model students “…gain access to mathematical representations and

the ideas they represent, they have a set of tools that significantly expand their capacity to think

mathematically.” (page 37 NCTM standards) Modeling order of operations using different

representations helps students comprehend how to evaluate a mathematical expression by

making sense of the parts of the expression rather than applying memorized rules. In addition,

scaffolding methodologies are used throughout. The unit starts by reviewing what students

already know and build on that knowledge. Each new concept or idea is introduced one at a time

and layered upon the concepts already presented.

© S. Mercer - Order of Operations Description page - 2

This model was developed on addition and multiplication seeing that students learned these

two concepts in the primary grades. Addition is the operation of combining two or more elements

or groups of elements and multiplication denoting successive additions. For example: three times

seven is the same as three groups of seven and this is the same as 7 + 7 + 7. Further, exponents

can be expressed as successive multiplications and multiplications can be expressed as successive

additions. For example: three to the power of two is the same as three times three, which is the

same as three groups of three which can be written as three plus three plus three.

Mathematically: 32 = 3• 3 = 3 + 3 + 3.

Expression

A graphic organizer is used to help students appreciate the different representations of a

mathematical expression. The above example presents the graphic organizer. In the middle oval

students write the mathematical expression. In the top left box, students record the expression in

words as they “read” it from left to right. In the top right box, students represent the expression

using individual objects and/or groups of objects. In the bottom left box, students use the pictorial

representation to rewrite the mathematical expression using only addition and/or subtraction. In

the final box, students write the answer after evaluating the mathematical expression.

When using this model, it is very important not to provide students with the order of

operation rules as they are stated in the textbook. The hierarchies between the different

operations need to be “discovered” and generalized by the students as they move through the unit.

The teacher is a key element in guiding and facilitating student discussion in order for them to

make the needed connections and generalizations. It is crucial for the teacher to model how to

complete the graphic organizer. The teacher should model each example by asking probing

questions and recording the students’ answers on the graphic organizer.


The teacher introduces the graphic organizer by reviewing multiplication with a simple

problem such as three times seven. The above example shows the completed graphic organizer for

the problem three times seven. In the top left box, students represent the problem using words

“three groups of seven”; in the top right box students draw three circles to represent three groups

and inside each group they draw seven objects; in the bottom left box the students represent the

multiplication problem as successive additions, in this case seven plus seven plus seven. Students

might not remember or know the concept of multiplication as successive additions therefore it is

important for them to complete the bottom left box by observing their picture. Students need to

know that to evaluate an expression means, in this context, to find out how many objects they

have in total. This is easily accomplished by looking at the picture. The bottom right box shows

the total number of objects. If students are familiar with the representation of multiplication as

“groups of“ and successive additions, then they should evaluate one or two more multiplication

problems. If this is a new concept for them then more problems are necessary.

Next, an addition operation is added to the multiplication problem. It is crucial that the first

example shows the addition first when reading the problem from left to right because in this way

students do not make the erroneous assumption that expressions are evaluated as they are read

from left to right. It is very important for teachers to model on the board or overhead how to

complete the graphic organizer and model the different expressions, especially when a new

component or level of difficulty is added to the previous problems.

Expression

The above example displays a complete graphic organizer for the expression five plus two

times three. It is essential for the teacher to help students make connections between the

different representations and the idea that even though the five is first when the expression is read

from left to right, mathematically the number of objects in the groups is evaluated first.


In words Representation

Expression with addition only Answer

Expression

3 + 2 • 8 + 2Can you thinkof a shortcut to solve this

problems?

threeplus

two groups of eightplustwo

3 + 8 + 8 + 221

Emphasis should be placed on the number of objects.



Expression

2 • 6 + 4 • 4Can you thinkof a shortcut to solve this

problems?

two groups of sixplus

four groups of four

6 + 6 + 4 + 4 + 4 + 428


The above examples demonstrate the completed graphic organizer for different expressions

that include addition and multiplication. At this point it is important to challenge the students to

find “shortcuts”. For example, some students may ask “can’t we just write the number, instead of

drawing all the pictures”. Or they may suggest, writing directly twelve instead of “6 + 6” or writing

“16” instead of writing “4 + 4 + 4 + 4”. It is crucial for the teacher to challenge students to explain

why they are able to write their shortcuts and where in the different boxes or representations they

can find the short cut. For example: “6 + 6” is two groups of six in the verbal representation, it is 2

• 6 in the expression box, it is the two groups of six in the drawing and it is “6 + 6” in the expression

with addition only box. It is key to have students note that they are not really solving the problem

from left to right when using their shortcut but rather looking at the problem as a whole and

finding the “groups” to find out how many objects are in each group.

It is critical for the teacher to constantly ask probing questions such as: How many groups

do you have? How many objects are in each group? What part of the expression represents the

number of groups? What part of the expression represents the number of objects in each group?

What is outside of the groups? Are all the groups the same? Why? Why not?


Once students are able to represent and evaluate expressions that involve addition and

multiplication, parenthesis is incorporated into the expression. This is a new type of problem and

the teacher needs to model how to solve the first expression with the students, while asking

probing questions such as: How is this problem the same as the ones we did before? How is it

different? It is very important for students to make connections with what they learned previously

and realize that the logic that they applied before is still valid with the new concept.

Different shapes or colors can be used to represent what is inside each group but it is

important that students focus on the total number of objects in each group and not their shape or

color. Also, the teacher needs to ask students: What is inside the group? How many groups are

there?

Expression

4 (2 + 3)

Expression

The above examples display the graphic organizer completed for two problems that include

parenthesis. Next, students solve different problems that include addition, multiplication and

parenthesis.




Expression

3 • 2 • 4 Can you thinkof a shortcut to solve this

problems?

three groups of two groups of four

4 + 4 + 4 + 4 + 4 + 4

24


Subsequently, students apply what they have learned to problems involving successive

multiplications. The above example presents the expression three times two times four. The

picture represents three groups, each one containing two groups of four elements. During the

discussion time students are able to describe “shortcuts” such as six groups of four or three groups

of eight. This is an appropriate time to discuss the commutative and associative properties.

Next, students are presented with expressions including exponents. Students are introduced

to this concept with the expression three to the power of two. In words three to the power of two is

three times three, which is represented as three groups of three. Using an expression with addition

only, three to the power of two is three plus three plus three. The answer is nine. After modeling

one or two examples with exponents only, exponents and addition is presented to students. The

graphic organizer below shows a completed graphic organizer for the expressions using addition

and exponents.

Expression

4 2+ 3

Once students are familiar with the different types of expressions that involve addition,

multiplication, parenthesis and power of two, subtraction is introduced to the model.



Answer

Problem

10 - 9

Expression with addition and/or subtraction only

ten minus nine

10 – 91

First students need to review the concept of subtraction as taking away. A simple

expression such as 10 minus 9 can be used as review. Students complete the graphic organizer for

subtraction. It is critical for the teacher to show students what notation will be used to represent

take away in order for all students to use the same visual aid.

Next, the teacher presents an expression such as 10 – 3 • 2. In words students write ten

minus three groups of two. When representing this expression students need to draw ten objects

and then take away three groups of two. Mathematically using addition and/or subtraction

students need to record 10 – 2 – 2 – 2. Ten represents the starting number of objects and two is

the number of objects the students need to take away three times in order to represent the

expression accurately.


Answer

Expression

6 • 3 - 4 • 4Can you thinkof a shortcut to solve this

problems?

Expression with addition and/orsubtraction only.

take awayfour groups of four

fromsix groups of three

3+3+3+3+3+3–4–4–4–4 2



Answer

Expression

4 ( 9 - 5)


four groupsof

nine minus five

9–5 + 9–5 + 9–5 + 9–516

The above example shows a completed graphic organizer that combines subtraction and

multiplication and the above example llustrates an expression that combines parenthesis and

subtraction. It is imperative to introduce each type of situation individually and model it for the

students. In this way students are able to “see” how to represent each expression and can

conceptually understand what is being done to solve each expression. Due to space constrains not

all the different examples can be presented.


Answer

Expression

Sabrina has six boxes of crayons, with eight crayons in each box. She uses ten crayons. How many crayons does she have left?

Expression with addition and/or subtraction only.

8+8+8+8+8+8 – 10 38 crayons

6 • 8 – 10

The graphic organizer can also be used to solve word problems. Using this model helps

students write expressions given a word problem. The above example illustrates a word problem

where students are asked not only to solve the problem but also to write a mathematical

expression to represent the problem. Representing problems visually helps students see the

groups and the objects that are added that are not in groups.


Once students are familiar with the different types of problems and their representations, it

is important for students to work in groups to discuss, draw conclusions and summarize in what

order expression are evaluated. To help this process students are asked to complete a summary

table that has three columns.

Evaluating Expressionswith the Representation

Evaluating Expressionswithout the Representations

Order the expression was evaluated10 + 3 • 4

ten plus

three groups of four

10 + 3 • 4

10 + 12

221) multiplication

2) addition10 4 4 4

5 + 3 ( 2 + 1)

fiveplus

three groups of two plus one

2+1 2+12+15

5 + 3 ( 2 + 1)

5 + 3 • 3

5 + 9

14

1) parenthesis

2) multiplication

3) addition

10 + 4 + 4 + 4 = 22

5 + 3 + 3 + 3 = 14

The above table illustrates this process. In the first column students evaluate an

expression using a picture. Next, they are asked: “How would you evaluate this expression without

the representation?” It has been my experience that many students when asked this question

revert to looking at the problem from left to right. But as soon as they realize that the answer they

get from evaluating the expression from left to right does not coincide with the answer they arrived

at by drawing the picture they self-correct. The graphic organizer provides students with

immediate feedback; they can check their answers by looking at the picture. Lastly students are

asked: “While evaluating the expression without the picture, what operation did you do first?

Why? What did you do next?” Students record in the last column the order they evaluated the

expression. After several examples, a pattern emerges that enables students to generalize the

order of operation rules. These generalizations can then be extended to expressions that are

difficult to represent with a picture such as expressions with fractions, decimals, and division.

At this point it is necessary to review with the students the importance of evaluating an

expression from left to right if it includes only addition and subtraction. This can be done by writing

the following expression on the board: 10 – 4 + 3 and asking students to represent it using words

and a picture. Students will write “ten minus four plus three” and will represent the expression by

drawing ten objects, taking away four and finally adding three leaving nine objects. Next, ask

students: “Do you get the same answer if you add four and three and then subtract the answer

from ten? Why not?” Students quickly realize that if they add first they are subtracting seven

from ten instead of subtracting four then adding three. Using several of these examples can be


used to reinforce and emphasize the importance of evaluating an expression from left to right if it

only includes addition and subtraction. After students are familiar with these types of problems,

the same type of activity can be used with multiplication and division.

Probing questions such as: How can you explain to a friend how to solve a problem if you

cannot draw a picture? Do you always solve problems from left to right? Is there an order in which

problems are solved? Is there a hierarchy? Students should be able to articulate the conclusion

they have found regarding order of operations. In my experience each student can arrive at two or

three conclusions, such as all multiplications can be expressed as additions but not vice versa.

Consequently a class discussion where all the conclusions are presented, recorded and summarized

is critical. This dialogue allows students to thoroughly understand how to evaluate mathematical

expressions. By the end of this unit students should be able to answer the following key questions:

Why are addition and subtraction done last? What are parentheses used for in an expression?

Why were the rules of order of operations established? Why were they selected? Are the rules

arbitrary or is there a reason for them?

Extension

Using the same reasoning process, this model can be used with variables to introduce the

distributive property. The first expression should be “3a” represented as three groups of “a” which

is the same as “a + a + a”. The graphic organizer below shows how this model can be used to teach

distributive property by changing only the last box from “Answer” to “Expression without

Parenthesis.” It is crucial for the teacher to continually ask students: How many groups are

there? What is in each group? What part of the expression is not part of the group? What part of

the expression denotes the number of groups? What part of the expression indicates the number

of objects in each group?


Expression with addition only

Expression

5 + 2 ( a + 3b + 4 )

five plustwo groups of

a plus three b plus four

5 + a + b + b + b + 4

+ a + b + b + b + 4

Expression without parenthesis

2a + 6b + 13

a bbb 4

a bbb 4

5


Conclusion

This model is not magical. It requires the teacher to plan and prepare the examples

carefully and to continually ask probing questions that help students make the connections

between the mathematical expression and its representations. Furthermore, the teacher needs to

assess the needs of his/her students and determine the pace and number of examples each type of

problem requires before introducing the next level difficulty. Is the time and effort worthwhile?

Absolutely! By using this unit students deepen their understanding of number and operation and

improve their number sense


Orderof

Operations

Susan Mercer

Answer Key

Multiplication



Expression



Expression

4 • 5

3 • 7

three groups of seven

7 + 7 + 7 21

four groups of five

5 + 5 + 5 + 5 20



© S. Mercer - Order of Operations Answer Key page - 1



Expression



Expression

1 • 9

3 • 3

three groups of three

3 + 3 + 3 9

one group of nine

9 9




Multiplication and Addition



Expression



Expression

9 + 3 • 4

5 + 2 • 3

fiveplus

two groups of three

5 + 3 + 3 11

nine plus

three groups of four

9 + 4 + 4 + 4 21






Expression



Expression

10 + 6 • 2

7 • 4 + 2Can you thinkof a shortcut

to evaluate this expression?



Expression



Expression

10 + 6 • 2



Can you thinkof a shortcut


seven groups of fourplus two

4+ 4+ 4+ 4+ 4+ 4 +4 +230

ten plus

six groups of two

10+ 2+ 2+ 2+ 2+ 2 +2 22






Expression



Expression

3 + 2 • 8 + 2

2 • 6 + 4 • 4





threeplus

two groups of eightplustwo

3 + 8 + 8 + 221

two groups of sixplus

four groups of four

6 + 6 + 4 + 4 + 4 + 428






Expression



Expression

5 + 2 • 4 + 1

4 • 1 + 5 • 2





fiveplus

two groups of fourplusone

5 + 4 + 4 + 114

four groups of oneplus

five groups of two

1+ 1+ 1+ 1+ 2 + 2+ 2+ 2+ 214






Expression



Expression

10 • 4 + 9

5 • 2 + 7 • 2





ten groups of fourplusnine

4+4+4+4+4+4+4+4+4+4+949

five groups of twoplus

seven groups of two

2+2+2+2+2 + 2+2+2+2+2+2+2 24




Multiplication, Addition and Parenthesis



Expression



Expression

2 ( 3 + 1)

4 ( 2 + 3)

two groups of three plus one

3 + 1 + 3 + 18

four groups oftwo plus three

2+3 + 2+3 + 2+3 +2+320






Expression



Expression

3 ( 3 + 2) + 6

6 + 4 (1 + 1)


to evaluate this problems?



three groups of three plus two

plussix

3+2 + 3+2 + 3+2 + 621

six plus

four groups ofone plus one

6 + 1+1 + 1+1 + 1+1 +1+114






Expression



Expression

4 • 2 + 2 ( 6 + 2)

7 (4 +1) + 4 • 3





four groups of twoplus

two groups of six plus two

2+2+2+2 + 6+2+6+224

seven groups offour plus one

plusfour groups of three

4+1+4+1+4+1+4+1+4+1+4+1+4+1 + 3+3+3+3 47





Expression



Expression

3 • 2 • 4

6 • 2 • 3





three groups of two groups of four

4 + 4 + 4 + 4 + 4 + 4

24

six groups oftwo groups of three

3 + 3 + 3+ 3 + 3 + 3 +3 + 3 + 3+ 3 + 3 + 3 36






Expression



Expression

3 • 3 • 3

4 + 3 • 2 • 5

three groups of three groups of three

3+3+3+3+3+3+3+3+3

27

four plusthree groups of

two groups of five

4 + 5+5+5+5+5+534





33 33

33 33

33 33

35 5 35 5 35 54




Expression



Expression

5 2

3 2

five times fivetherefore

five groups of five

5+5+5+5+5

25

three times threetherefore


3 + 3 + 39

3 3 3

5 55 5

5




Expression



Expression

4 2 + 10

3 2 + 3 • 5





four groups of fourplusten

4+4+4+4 + 10

26

three groups of threeplus

three groups of five

3 + 3 + 3 + 5 + 5 + 524

104 4 44

3 3 53 5 5




Expression



Expression

1 + 6 2 + 2 • 3

2 2 + 3 ( 3 + 1)





one plussix groups of six

plustwo groups of three

1 + 6+6+6+6+6+6 + 3+343

two groups of twoplus

three groups ofthree plus one

2+2 + 3+1 + 3+1 + 3+116

1 6 6 3636 6 6

22

3 13 13 1




Expression



Expression

3 + 6 2 + 3 2

9 2 + 5 ( 4 + 7)





threeplus

six groups of sixplus


48

nine groups of nineplus

five groups of

four plus seven

9+9+9+9+9+9+9+9+9+4+7 + 4+7 + 4+7 + 4+7 + 4+7

136

3 + 6+ 6+ 6+ 6+ 6+ 6+ 3+ 3 + 3

9 4 7 4 7

4 7 4 7

4 799

999

999

3 3 336 66 6

66




Expression



Expression

Sabrina has five nickels and tendimes. How much money doesSabrina have?

Sabrina has ten nickels, five quarters and three pennies.How much money doesSabrina have?





125 cents or $1.25

178

5+5+5+5+5 +10+10+10+10+

10+10+10+10+10+10

5 • 5 + 10 • 10

10 • 5 + 5 • 25 + 3 • 1

5+5+5+5+5+5+5+5+5+5+25+25+25+25+25+

1+1+1

5 5 55 5

10 10 10 1010 10 10

1010

10

1115 5 5

5 525

555

25 252525

5 5




Expression



Expression

Sabrina has seven eggs in her refrigerator. She buys three more dozens eggs. How many eggs does she have?

Sabrina has three boxes of crayons with eight crayons in each box. She buys six more boxes with ten crayons in each box. How many crayons does she have?





43 eggs

64 crayons

7 + 12 + 12 + 12

7 + 3 • 12

3 • 8 + 6 • 10

8 + 8 + 8 +10 +10 +10 +10 +10 +10

10

1010

10

10

108 crayons

8 crayons

8 crayons


Subtraction


Expression with addition and/or subtraction only Answer

Expression


Answer

Expression

10 - 9

12 - 5


take away fivefrom

twelve

twelve minus five

12 – 5 7

take away ninefromten

ten minus nine

10 – 91



Answer

Expression



Answer

Expression

10 - 2 • 4

2 • 3 - 5


take away fivefrom

two groups of three

3 + 3 – 51

take awaytwo groups of four

fromten

10 – 4 – 42



Answer

Expression


Answer

Expression

6 • 3 - 4 • 4

7 • 2 - 5 • 2Can you thinkof a shortcut






take away five groups of two

from seven groups of two

2+2+2+2+2+2+2–2–2–2–2–2 4

take awayfour groups of four

fromsix groups of three

3+3+3+3+3+3–4–4–4–4 2



Answer

Expression


Answer

Expression

4 ( 9 - 5)

2 ( 7 - 3)



two groupsof

seven minus three

7 – 3 + 7 – 38

four groupsof

nine minus five

9–5 + 9–5 + 9–5 + 9–516



Answer

Expression


Answer

Expression

Sabrina has six dimes and ten quarters. She spends fifty cents. How much money does Sabrina have left?

Sabrina has ten nickels, one quarter and ten dimes. She spends 75 cents. How much money does Sabrina have left?



10+10+10+10+10+1025+25+25+25+25+25+2

5+25+25+25 – 50260 cents or $2.60

6 • 10 + 10 • 25 – 50

10 1010 1010 10

25 25

25 25 25

25

25

25

25 25

5+5+5+5+5+5+5+5+5+5+25+10+10+10+10+10+10

+10+10+10+10 – 75100 cents or $1.00

10•5 + 1•25 + 10•10 –75

5

101010

1010

25

10

101010

10

55 55 5 5 5

5

5



Answer

Expression


Answer

Expression


Sabrina bought two dozen eggs and uses eight to do an omelette. How many eggs does she have left?



8+8+8+8+8+8 – 10 38 crayons

6 • 8 – 10

12 + 12 – 8 16 eggs

2 • 12 – 8



Answer

Expression


Answer

Expression

Sabrina has 10 cans of soda. She buys seven 6-packs of soda. She drinks two sodas. How many sodas does she have left?

Sabrina has five dozen pens. She gives away two dozen to her friends. How many pens does she have left?



10 + 6 + 6 + 6 + 6 +6 + 6 + 6 – 2 50 cans

10 + 7 • 6 – 2

12 + 12 +12 +12 +12 – 12 – 12 36 pens

5 • 12 – 2 • 12

6 cans

6 cans

6 cans

6 cans

6 cans

6 cans

6 cans

12pens

12pens

12pens

12pens

12pens


Orderof

OperationsName: ____________________

Period: ________

Date: ______________________

Multiplication



Expression



Expression

4 • 5

3 • 7

© S. Mercer - Order of Operations page - 1



Expression



Expression

1 • 9

3 • 3


Multiplication and Addition



Expression



Expression

9 + 3 • 4

5 + 2 • 3




Expression



Expression

10 + 6 • 2





Expression



Expression

10 + 6 • 2








Expression



Expression

3 + 2 • 8 + 2

2 • 6 + 4 • 4








Expression



Expression

5 + 2 • 4 + 1

4 • 1 + 5 • 2








Expression



Expression

10 • 4 + 9

5 • 2 + 7 • 2






Multiplication, Addition and Parenthesis



Expression



Expression

2 ( 3 + 1)

4 ( 2 + 3)




Expression



Expression

3 ( 3 + 2) + 6

6 + 4 (1 + 1)








Expression



Expression

4 • 2 + 2 ( 6 + 2)

7 (4 + 1) + 4 • 3








Expression



Expression

3 • 2 • 4

6 • 2 • 3








Expression



Expression

3 • 3 • 3

4 + 3 • 2 • 5








Expression



Expression

5 2

3 2




Expression



Expression

4 2 + 10

3 2 + 3 • 5








Expression



Expression

1 + 6 2 + 2 • 3

2 2 + 3 ( 3 + 1)








Expression



Expression

3 + 6 2 + 3 2

9 2 + 5 ( 4 + 7)








Expression



Expression

Sabrina has five nickels and tendimes. How much money doesSabrina have?

Sabrina has ten nickels, five quarters and three pennies.How much money doesSabrina have?








Expression



Expression

Sabrina has seven eggs in her refrigerator. She buys three more dozens eggs. How many eggs does she have?

Sabrina has three boxes of crayons with eight crayons in each box. She buys six more boxes with ten crayons in each box. How many crayons does she have?






Subtraction


Expression with addition and/or subtraction only Answer

Expression


Answer

Expression

10 - 9

12 - 5




Answer

Expression



Answer

Expression

10 - 2 • 4

2 • 3 - 5




Answer

Expression


Answer

Expression

6 • 3 - 4 • 4

7 • 2 - 5 • 2Can you thinkof a shortcut








Answer

Expression


Answer

Expression

4 ( 9 - 5)

2 ( 7 - 3)





Answer

Expression


Answer

Expression

Sabrina has six dimes and ten quarters. She spends fifty cents. How much money does Sabrina have left?

Sabrina has ten nickels, one quarter and ten dimes. She spends 75 cents. How much money does Sabrina have left?





Answer

Expression


Answer

Expression


Sabrina bought two dozen eggs and uses eight to do an omelette. How many eggs does she have left?





Answer

Expression


Answer

Expression

Sabrina has 10 cans of soda. She buys seven 6-packs of soda. She drinks two sodas. How many sodas does she have left?

Sabrina has five dozen pens. She gives away two dozen to her friends. How many pens does she have left?




order of operations - nova scotia department of …hrsbstaff.ednet.ns.ca/jsandford/math/super math...

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