Concept First, Notation Last
Common Core State Standards
Math 
Math 
7 
Grade 7 
EE 
Expressions & Equations 
B 
Solve reallife and mathematical problems using numerical and algebraic expressions and equations 
4b 
Use variables to represent quantities in a realworld 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. 
Download Common Core State Standards (PDF 1.2 MB) 
Common Core State Standards
Math 
Math 
Practice 
Mathematical Practice Standards 
MP4 
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, twoway tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. 
Download Common Core State Standards (PDF 1.2 MB) 
Common Core State Standards
Math 
Math 
Practice 
Mathematical Practice Standards 
MP6 
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 
Download Common Core State Standards (PDF 1.2 MB) 

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 Lesson Objective
 Develop a conceptual understanding of inequalities
 Length
 11 min
 Questions to Consider
 How does the dotting of solutions help students build conceptual understanding?
 How does Ms. Alcala build off of her students' prior knowledge?
 What might you do after this lesson to move from conceptual understanding to procedural skill and application?
 Common Core Standards
 Math.7.EE.B.4b, Math.Practice.MP4, Math.Practice.MP6
Teacher & School Info

Leah Alcala
 School Details
 Martin Luther King Middle School Berkeley, CA
 Population
 957 students
 District Spending
 $11,289
Supporting Materials

Concept First, Notation Last Transcript

Lesson Plan: Linear Equalities.PDF