7.EE.2
Expressions Learning Cycle
GOAL:
Students will be able to recognize component parts of an expression and identify equivalency
Develop Activity:
Mystery Bag
Anticipate:
~students know the difference between bags and coins
~they would need to be prompted to write it as a numerical expression
~expect students to show the equivalency both numerically and pictorially
~students will identify a variable and what it represents
Vocabulary that will be brought out in the task:
*expression
*term
*constant
*equivalency
*co-efficient
*like terms
*variable
Teacher Helps for the Develop Activity:
*3 Posters – one with each model
*Have a group of students share their representations one on each poster
*Discuss as a group what the lists have in common…put stars by that
Story to Introduce the Activity:
Once upon a time long ago in a kingdom far far away, the king had built himself a brand new castle on the other side of the kingdom. He has a dilemma! He has to get his money to the new castle.
He decided to use his 3 most trusted knights: Sir Diego, Sir Daniel and Sir Dave. Each took a different amount of money. What they were entrusted with is shown in the models on your task.

Solidify Activity:
Work At the Music Store
Anticipate:
~On Question 2 the student will copy Patricia and Sun’s pictures and expressions and then put an addition sign between them
~On Question 3 students will simplify
~Students will be guided by giving them the variable
Hamburger Heaven
Anticipate:
~Coming up with their own variable and pictorial representation
~Students will go from a model to the expression
~Students will finish by thinking about equivalency
Practice Activity:
Practice with Expressions
Anticipate:
~Prompt students to re-arrange (distribute) to be able to simplify expressions.
~Refer back to the music store task when they combined Sun and Patricia’s hours
~Press students to persevere and simplify all 4 expressions when they are looking for the expression that is not equivalent
~For the final real world problem suggest they draw a picture
~Ask “What do you know that has a decimal?”
Learning Cycle created by:
Audrey Kearl ankearl@graniteschools.org
Carol Kaskel ckaskel@alpinedistrict.org
Kristy Stevens kstevens@alpinedistrict.org
Krystin Sanchez krysanchez@alpinedistrict.org

(This activity was adapted from Moving
Straight Ahead CMP Prentice Hall 2006…
Solving Equations 3.2 & 3.3)
Sir Diego
The money bags in each diagram have the same number of coins.
Using as many different models as you can, write down information that represents each diagram.
Sir Daniel
Sir Dave

1. Knowing that each bag contained the same number of coins, are there any situations that created
equivalent expressions? How do you know?
2. Using a picture and an expression how many ways
can you:
A. Make the other two diagrams equivalent to A.
B. Make the other two diagrams equivalent to B.
C. Make the other two diagrams equivalent to C.

Working at the Music Store
Patricia, Hugo and Sun work at a music store. Each week, Patricia works three more than twice the number of hours that Hugo works. Sun works 2 less than Hugo.
1. Let x represent the number of hours that Hugo works each week. The number of hours that Hugo, Patricia, and Sun work can be modeled is shown below. Write an expression that represents each person’s number of hours.
Patricia’s Hours Sun’s
Hours
Hugo’s Hours x
1
-1 x x
1
1 x
-1
Expression: _________________ Expression: _________________ Expression:
_________________
2. Model the total number of hours that Patricia and Sun work together.
Draw the result below. Then write an expression for the drawing.
Expression:
________________________
3. Like tiles are tiles that have the same shape. Using the model from question 2, group like tiles together and remove the zero pairs. Draw the result below. Then write an expression for your drawing.
Expression:
________________________

Dave, Lucy, and Frank love hamburgers. Dave ate as many hamburgers as he could. Lucy ate two more than Dave, and Frank ate twice as many as
Lucy. Frank was really hungry.
-Draw three pictorial representations of how many burgers Dave, Lucy, and Frank ate.
-From your pictures write three expressions.
-For each expression tell me how many terms you have and identify the variable.
-For each expression tell me your coefficient.
-Are your three expressions equivalent? If so prove it and if not explain why not.

Why are the expressions 3(y - 2) + 2(y – 2) and 5(y -2) equivalent? Justify your answer.
Write an expression that has three terms and simplifies to 9y –
11. Identify the coefficient(s) and constant(s) in your expression.
Which expression is not equivalent to the other three? Justify your reasoning.
-8 - 7n + 16n 9(n – 8) n – 8 + 8n
Which expression is not equivalent to the other three?
9n - 8
2(1 + 2b +
3a) 2(1+2a)+2(a+2b) 6a + 2 + 4b
Write a real world problem for the expression 5.75n + 25.
2(3a+1) +
4b+1