Build increasingly larger square pools with a single tile border to look for patterns in the number of tiles needed. Develop a general tile formula for any size square pool.

**Grades covered:**6 through 12

**Curriculum Topics:**Patterns, Variables, Functions, Graphing, Algebra

### Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices|||6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers.||Common Core Mathematics||Grade 6||Expressions And Equations||Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions|||6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.||Common Core Mathematics||Grade 6||Expressions And Equations||Reason About And Solve One-Variable Equations And Inequalities|||6.EE.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.||Common Core Mathematics||Grade 6||Expressions And Equations||Represent And Analyze Quantitative Relationships Between Dependent And Independent Variables|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices|||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.||Common Core Mathematics||Grade 7||Expressions And Equations||Solve Real-Life And Mathematical Problems Using Numerical And Algebraic Expressions And Equations|||7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.||Common Core Mathematics||Grade 7||Geometry||Solve Real-Life And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices|||8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1||Common Core Mathematics||Grade 8||Functions||Define, Evaluate, And Compare Functions|||8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.||Common Core Mathematics||Grade 8||Functions||Define, Evaluate, And Compare Functions|||8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.||Common Core Mathematics||Grade 8||Functions||Use Functions To Model Relationships Between Quantities|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||High School||Mathematical Practices

1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.||CA Mathematics||Grade 6||02. Algebra and Functions|||1.0 Students make decisions about how to approach problems.||CA Mathematics||Grade 6||05. Mathematical Reasoning|||1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.||CA Mathematics||Grade 6||05. Mathematical Reasoning||1.0 Students make decisions about how to approach problems.|||1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.||CA Mathematics||Grade 6||05. Mathematical Reasoning||1.0 Students make decisions about how to approach problems.|||3.0 Students investigate geometric patterns and describe them algebraically.||CA Mathematics||Grade 6||02. Algebra and Functions|||3.1 Use variables in expressions describing geometric quantities(e.g., P = 2w + 2l, A = 1/2 bh, C = pd–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).||CA Mathematics||Grade 6||02. Algebra and Functions||3.0 Students investigate geometric patterns and describe them algebraically.|||1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs.||CA Mathematics||Grade 7||02. Algebra and Functions|||1.0 Students make decisions about how to approach problems.||CA Mathematics||Grade 7||05. Mathematical Reasoning|||1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represent a verbal description (e.g., three less than a number, half as large as area A).||CA Mathematics||Grade 7||02. Algebra and Functions||1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs.|||1.1 Analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.||CA Mathematics||Grade 7||05. Mathematical Reasoning||1.0 Students make decisions about how to approach problems.|||1.2 Formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed.||CA Mathematics||Grade 7||05. Mathematical Reasoning||1.0 Students make decisions about how to approach problems.|||1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph.||CA Mathematics||Grade 7||02. Algebra and Functions||1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs.|||2.1 Use estimation to verify the reasonableness of calculated results.||CA Mathematics||Grade 7||05. Mathematical Reasoning||2.0 Students use strategies, skills, and concepts in finding solutions.|||2.2 Apply strategies and results from simpler problems to more complex problems.||CA Mathematics||Grade 7||05. Mathematical Reasoning||2.0 Students use strategies, skills, and concepts in finding solutions.|||2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.||CA Mathematics||Grade 7||05. Mathematical Reasoning||2.0 Students use strategies, skills, and concepts in finding solutions.|||2.4 Make and test conjectures by using both inductive and deductive reasoning.||CA Mathematics||Grade 7||05. Mathematical Reasoning||2.0 Students use strategies, skills, and concepts in finding solutions.|||2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.||CA Mathematics||Grade 7||05. Mathematical Reasoning||2.0 Students use strategies, skills, and concepts in finding solutions.|||3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.||CA Mathematics||Grade 7||05. Mathematical Reasoning|||16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.||CA Mathematics||Grade 8 – 12||01. Algebra I|||17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.||CA Mathematics||Grade 8 – 12||01. Algebra I

**Categories include:**

- Grades 6-8
- Math

**Tags:**Geometry, Expressions & Equations, Functions

**Subjects covered:**["Math"]