7EE-Solve+real-life+&+mathematical+problems+using+numerical+&+algebraic+expressions+&+equations

7.MP.1. Make sense of problems and persevere in solving them. 7.MP.2. Reason abstractly and quantitatively. 7.MP.3. Construct viable arguments and critique the reasoning of others. 7.MP.4. Model with mathematics. 7.MP.5. Use appropriate tools strategically. 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. **7EE 4** 7.MP.1. Make sense of problems and persevere in solving them. 7.MP.2. Reason abstractly and quantitatively. 7.MP.3. Construct viable arguments and critique the reasoning of others. 7.MP.4. Model with mathematics. 7.MP.5. Use appropriate tools strategically. 7.MP.6. Attend to precision. 7.MP.7. Look for and make use of structure. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">7.MP.8. Look for and express regularity in repeated reasoning. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standards**===
 * 7.EE.3.** Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. //For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.//
 * 7.EE.4.**Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
 * a.** Solve word problems leading to equations of the form //px// + //q// = //r// and //p//(//x// + //q//) = //r//, where //p//, //q//, and //r// are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. //For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?//
 * b.** Solve word problems leading to inequalities of the form //px// + //q// > //r// or //px// + //q// < //r//, where //p//, //q//, and //r// are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. //For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.// || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**===
 * 7EE 3**
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== ||
 * 7.EE.3** **Students solve contextual problems and mathematical problems using rational numbers. Students convert between fractions, decimals, and percents as needed to solve the problem. Students use estimation to justify the reasonableness of answers.**


 * Example 1:** Three students conduct the same survey about the number of hours people sleep at night. The results of the number of people who sleep 8 hours a nights are shown below. In which person’s survey did the most people sleep 8 hours?

• Susan reported that 18 of the 48 people she surveyed get 8 hours sleep a night • Kenneth reported that 36% of the people he surveyed get 8 hours sleep a night • Jamal reported that 0.365 of the people he surveyed get 8 hours sleep a night

Solution: In Susan’s survey, the number is 37.5%, which is the greatest percentage.

Estimation strategies for calculations with fractions and decimals extend from students’ work with whole number operations. Estimation strategies include, but are not limited to:

• __front-end estimation__ with adjusting (using the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts),

• __clustering__ around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate),

• __rounding and adjusting__ (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values),

• using __friendly or compatible numbers__ such as factors (students seek to fit numbers together - i.e., rounding to factors and grouping numbers together that have round sums like 100 or 1000), and

• using __benchmark numbers__ that are easy to compute (students select close whole numbers for fractions or decimals to determine an estimate).


 * 7.EE.4** **Students solve multi-step equations and inequalities derived from word problems. Students use the arithmetic from the problem to generalize an algebraic solution.**
 * Students graph inequalities and make sense of the inequality in context. Inequalities may have negative coefficients. Problems can be used to find a maximum or minimum value when in context.**


 * 7.EE.4a**
 * Students solve multi-step equations derived from word problems. Students use the arithmetic from the problem to generalize an algebraic solution.**


 * Example 1:** The youth group is going on a trip to the state fair. The trip costs $52. Included in that price is $11 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes cost the same price. Write an equation representing the cost of the trip and determine the price of one pass.


 * Example 3:** Amy had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost including tax?

Solution: x = number of pens 26 = 14.30 + 10x Solving for x gives $1.17 for each pen.


 * Example 4:** The sum of three consecutive even numbers is 48. What is the smallest of these numbers?

Solution: x = the smallest even number x + 2 = the second even number x + 4 = the third even number x + x + 2 + x + 4 = 48 3x + 6 = 48 3x = 42 x = 14

-2 Solution: x = 7
 * Example 5:** Solve: __x + 3__ = -5


 * 7EE4b**
 * Students solve and graph inequalities and make sense of the inequality in context. Inequalities may have negative coefficients. Problems can be used to find a maximum or minimum value when in context.**


 * Example 1:** Florencia has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 dollars and spend the rest on t-shirts. Each t-shirt costs $8. Write an inequality for the number of t-shirts she can purchase.

Solution: x = cost of one t-shirt 8x + 22 ≤ 60 x = 4.75  4 is the most t-shirts she can purchase


 * Example 2:** Steven has $25 dollars to spend. He spent $10.81, including tax, to buy a new DVD. He needs to save $10.00 but he wants to buy a snack. If peanuts cost $0.38 per package including tax, what is the maximum number of packages that Steven can buy?

Solution: x = number of packages of peanuts 25 ≥ 10.81 + 10.00 + 0.38x x = 11.03  Steven can buy 11 packages of peanuts


 * Example 3:** 7 – x > 5.4

Solution: x < 1.6


 * Example 4:** Solve -0.5x – 5 < -1.5 and graph the solution on a number line.

Solution: x > -7

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can use operations to generate equivalent expression, equations, and inequalities.**===


 * (7EE3) I can solve multi-step real-like problems with rational numbers.**
 * (7EE3) I can use estimation to justify answers.**
 * (7EE4) I can construct algebraic expressions from word problems.**
 * (7EE4) I can graph the solution of inequalities.**
 * **(7EE4a) II can write and solve equations from word problems.**
 * **(7EE4b) I can write and solve inequalities from word problems.**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**

 * expressions, equations, inequalities, combining like terms, is no more than, is at least, at most, at least, coefficient, factor, distributive property**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**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/


 * Inequalities Match**
 * Solving 2-Step Equations Square Puzzle**
 * Solving Inequalities Square Puzzle**

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== http://qta.quantiles.com/qtaxon/goal/29759/ http://qta.quantiles.com/qtaxon/goal/29760/ http://qta.quantiles.com/qtaxon/goal/29761/
 * large wall graph, poster paper,**
 * Math Partners resources,**

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,**
 * [],**

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