It is time to review how to write expressions with addition, subtraction, multiplication, and division.
The situation  The model  The answer 
Two sticks are joined together with tape. One stick is 5 centimeters long and the other is x centimeters long. What is the total length of the two sticks  The total length of the two sticks is centimeters. 

A stick is x centimeters long. It is cut into two pieces. If the shorter piece is 5 centimeters long, what is the length of the longer piece  The length of the longer piece is centimeters. 

A stick is x centimeters long. If it is cut into 5 equal pieces, what is the length of each piece  The length of each piece is 

Five identical sticks are taped together to form one long stick. If each of the smaller sticks is x centimeters long, what will be the total length of the combined stick  The total length of the sticks will be 
Assuming x stands for a number that is larger than 1, there are four things we can say about the above algebraic expressions:
 Adding and multiplying typically make the answer LARGER.
 Subtracting and dividing typically make the answer SMALLER.
and
 Adding and subtracting typically involve things that are NOT EQUAL in length, size, weight, etc.
 Multiplying and dividing typically involve things that are EQUAL in length, size, weight, etc.
These four statements can be arranged into a grid to help you know whether a situation involves addition, subtraction, multiplication, or division.
The objects get bigger or smaller  
Bigger  Smaller  
The objects in the situation are equal of NOT equal in size.  Not equal 
Addition Two sticks are joined together with tape. One stick is 5 centimeters long and the other is x centimeters long. What is the total length of the two sticks? The total length of the two sticks is centimeters. 
Subtraction A stick is x centimeters long. It is cut into two pieces. If the shorter piece is 5 centimeters long, what is the length of the longer piece? The length of the longer piece is 
Equal 
Multiplication Five identical sticks are taped together to form one long stick. If each of the smaller sticks is x centimeters long, what will be the total length of the combined stick? The total length of the sticks will be 
Division A stick is x centimeters long. If it is cut into 5 equal pieces, what is the length of each piece? The length of each piece is 
Remember x must represent a number larger than 1 in order for these statements to be true!.
EXPLORE!


SelfCheck
Question 1 You have m marbles. You separate them into 4 equal piles. How many marbles are in each pile?

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Question 2 Two pieces of wood are laid endtoend. What is the total length of the wood?

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Question 3 Two pieces of wood are laid endtoend. Their total length is 18 cm. If the shorter piece of wood is n cm, what is the length of the longer piece?

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Question 4 These five stamps cost a total of m cents. How much does each stamp cost?

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Question 5 David has 9 bags. He places x coins in each bag. How many coins does he have total?

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Question 6 Anna and Brian's combined weight is 140 pounds. If Brian weighs h pounds, how heavy is Anna?

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Question 7 Jenny has d dolls. If she buys 5 more dolls, how many will she have altogether?

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Question 8 There are m apples in each bag. If you buy 5 bags, how many apples will you have?

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Question 9 At a movie cinema, adult tickets cost p dollars and child tickets cost k dollars. If 3 adults and 5 children go to the movies, how much is the total price for tickets? (Write a variable expression.)

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