7EE-Use+properties+of+operations+to+generate+equivalent+expressions

7.MP.2. Reason abstractly and quantitatively. 7.MP.6. Attend to precision. 7.MP.7. Look for and make use of structure. 7.MP.2. Reason abstractly and quantitatively. 7.MP.6. Attend to precision. 7.MP.7. Look for and make use of structure. 7.MP.8. Look for and express regularity in repeated reasoning. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard**===
 * 7.EE.1.** Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
 * 7.EE.2**. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. //For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”// || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**===
 * 7EE 1**
 * 7EE 2**
 * || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== ||
 * 7.EE.1** **This is a continuation of work from 6th grade using properties of operations (table 3, pg. 90) and combining like terms. Students apply properties of operations and work with rational numbers (integers and positive / negative fractions and decimals) to write equivalent expressions.**

Solution: The Greatest Common Factor (GCF) is 2, which will be the width because the width is in common to both rectangles. To get the area 2a multiply by a, which is the length of the first rectangles. To get the area of 4b, multiply by 2b, which will be the length of the second rectangle. The final answer will be 2(a + 2b)
 * Example 1:** What is the length and width of the rectangle below?

Solution: 3x + 15 – 2 Distribute the 3 3x + 13 Combine like terms
 * Example 2:** Write an equivalent expression for 3(x + 5) – 2.

Solution: The expressions are not equivalent. One way to prove this is to distribute and combine like terms in the first expression to get 10a – 4, which is not equivalent to the second expression. A second explanation is to substitute a value for the variable and perform the calculations. For example, if 2 is substituted for a then the value of the first expression is 16 while the value of the second expression is 18.
 * Example 3:** Suzanne says the two expressions 2(3a – 2) + 4a and 10a – 2 are equivalent? Is she correct? Explain why or why not?

Solution: Possible solutions might include factoring as in 3(a + 4), or other expressions such as a + 2a + 7 + 5.
 * Example 4:** Write equivalent expressions for: 3a + 12.

Solution: 6w or 2(2w) Solution: 3(2x + 5), therefore each side is 2x + 5 units long.
 * Example 5:** A rectangle is twice as long as its width. One way to write an expression to find the perimeter would be w + w + 2w+ 2w. Write the expression in two other ways.
 * Example 6:** An equilateral triangle has a perimeter of 6x + 15. What is the length of each side of the triangle?


 * 7.EE.2** **Students understand the reason for rewriting an expression in terms of a contextual situation.**

For example, students understand that a 20% discount is the same as finding 80% of the cost (.80c). All varieties of a brand of cookies are $3.50. A person buys 2 peanut butter, 3 sugar and 1 chocolate. Instead of multiplying 2 x $3.50 to get the cost of the peanut butter cookies, 3 x $3.50 to get the cost of the sugar cookies and 1 x $3.50 for the chocolate cookies and then adding those totals together, student recognize that multiplying $3.50 times 6 will give the same total.


 * Example 1:** All varieties of a certain brand of cookies are $3.50. A person buys peanut butter cookies and chocolate chip cookies. Write an expression that represents the total cost, T, of the cookies if p represents the number of peanut butter cookies and c represents the number of chocolate chip cookies

Solution: Students could find the cost of each variety of cookies and then add to find the total. T = 3.50p + 3.50c

same total. T = 3.50(p +c)
 * Or** students could recognize that multiplying 3.50 by the total number of boxes (regardless of variety) will give the

expression?
 * Example 2:** Jamie and Ted both get paid an equal hourly wage of $9 per hour. This week, Ted made an additional $27 dollars in overtime. Write an expression that represents the weekly wages of both if J = the number of hours that Jamie worked this week and T = the number of hours Ted worked this week? What is another way to write the

Solution: Students may create several different expressions depending upon how they group the quantities in the problem. Possible student responses are:

number of hours Ted worked by 9. Add these two values with the $27 overtime to find the total wages for the week. The student would write the expression 9J + 9T + 27.
 * Response 1:** To find the total wage, first multiply the number of hours Jamie worked by 9. Then, multiply the

number of hours worked by 9. Add the overtime to that value to get the total wages for the week. The student would write the expression 9(J + T) + 27.
 * Response 2:** To find the total wages, add the number of hours that Ted and Jamie worked. Then, multiply the total

week. To figure out Jamie’s wages, multiply the number of hours she worked by 9. To figure out Ted’s wages, multiply the number of hours he worked by 9 and then add the $27 he earned in overtime. My final step would be to add Jamie and Ted wages for the week to find their combined total wages. The student would write the expression (9J) + (9T + 27).
 * Response 3:** To find the total wages, find out how much Jamie made and add that to how much Ted made for the

Given a square pool as shown in the picture, write four different expressions to find the total number of tiles in the border. Explain how each of the expressions relates to the diagram and demonstrate that the expressions are equivalent. Which expression is most useful? Explain. ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can use operations to generate equivalent expressions, equations, and inequalities.**===
 * Example 3:**


 * (7EE1) I can use operations to expand linear expressions.**
 * (7EE2) I can translate word phrases to mathematical symbols.**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**

 * peer tutoring, guided notes, blogs, grouping, foldables, justification of answers, inquiry learning to accelerate/remediate, create a table with all the words that mean (add, subtract, multiply, divide), use a large graph that students can manipulate**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/grade07/


 * Lining Up Dominoes--Distributive Property**
 * Writing Equations from Word Problems Dominoes**
 * Algebraic Expressions Square Puzzle**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== http://qta.quantiles.com/qtaxon/goal/29757/ http://qta.quantiles.com/qtaxon/goal/29758/
 * [|Writing Expressions and Combining Like Terms]**
 * Math Partners resources,**
 * large wall graph, poster paper**

http://kutasoftware.com/freeipa.html http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/grade07/ http://www.montgomery.k12.nc.us/18032092913393583/site/default.asp
 * http://www.mathgoodies.com,**
 * http://tinyurl.com/kwsrug,**

Algebra Expressions for Words Card Sort Variables and Expressions Study Guide

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===