No Series: Concept First, Notation Last
Math.Practice.MP4
 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.
Math.Practice.MP6
 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.
Math.7.EE.B.4b
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.
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Discussion and Supporting Materials
Thought starters
 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?
School Details
Martin Luther King Middle School1781 Rose Street
Berkeley CA 94703
Population: 1027
Data Provided By:
Teachers
Leah Alcala
Math / 7 8 / Teacher
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TCH Special
56 MIN
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45 MIN
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14 Comments
Harriette Huang Dec 21, 2019 2:20am
I love Ms. Alcala's approach. Every problem, she asks students to give a few numbers to test and try if they work. Then she asks Ss to plot and find the trend. At last, she guides Ss to use mathematical notations to describe the solution concisely and beautifully.
When students learn math this way, they are not learning for scores or for colleges. They are learning problemsolving that they can apply to their life the same day they go back home. How much sugar do we want in this cake? Try it and taste it. Find all the solutions that work and write down as a recipe.
Kathleen Taylor Mar 1, 2019 5:31am
The title of this lesson is what caught my attention first conceptual understanding is paramount, and something many teachers donâ€™t take the time to develop. TIME is the key here, and though I feel like there is never enough of it, I am committed to taking the time necessary to develop conceptual understanding. Thank you for this!!!
Carolynn Molleur Nov 10, 2018 9:14am
Thank you for this video! I work with a team of Algebra teachers who recently watched this video together, and it allowed us to teach inequalities in a way that engaged and made sense to students!
Melissa Fenner Apr 30, 2018 7:19pm
Bion Shelden Dec 16, 2017 10:20pm