Modeling Simple Equations

Work as a team to understand variables, coefficients, and constants by modeling and solving equations to find the mystery value of the cup!

Grades covered: 3 through 9
Curriculum Topics: Algebraic Terminology, Equations, Variables

Standards

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

Common Standards Click to View

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 3||Mathematical Practices|||3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1||Common Core Mathematics||Grade 3||Operations And Algebraic Thinking||Represent And Solve Problems Involving Multiplication And Division|||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 4||Mathematical Practices|||4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 ? 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Use The Four Operations With Whole Numbers To Solve Problems|||4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Use The Four Operations With Whole Numbers To Solve Problems|||4.OA.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Use The Four Operations With Whole Numbers To Solve Problems|||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 5||Mathematical Practices|||5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.||Common Core Mathematics||Grade 5||Operations And Algebraic Thinking||Write And Interpret Numerical Expressions|||5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “”add 8 and 7, then multiply by 2″” as 2 ? (8 + 7). Recognize that 3 ? (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.||Common Core Mathematics||Grade 5||Operations And Algebraic Thinking||Write And Interpret Numerical Expressions|||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.3. Apply the properties of operations to generate equivalent expressions.||Common Core Mathematics||Grade 6||Expressions And Equations||Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions|||6.EE.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.||Common Core Mathematics||Grade 6||Expressions And Equations||For Example, Apply The Distributive Property To The Expression 3 (2 + X) To Produce The Equivalent Expression 6 + 3X; Apply The Distributive Property To The Expression 24X + 18Y To Produce The Equivalent Expression 6 (4X + 3Y); Apply Properties Of Operations To Y + Y + Y To Produce The Equivalent Expression 3Y|||6.EE.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.||Common Core Mathematics||Grade 6||Expressions And Equations||Reason About And Solve One-Variable Equations And Inequalities|||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.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.||Common Core Mathematics||Grade 6||Expressions And Equations||Reason About And Solve One-Variable Equations And Inequalities|||6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.||Common Core Mathematics||Grade 6||Expressions And Equations||Reason About And Solve One-Variable Equations And Inequalities|||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.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.||Common Core Mathematics||Grade 7||Expressions And Equations||Use Properties Of Operations To Generate Equivalent Expressions|||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.||Common Core Mathematics||Grade 7||Expressions And Equations||Solve Real-Life And Mathematical Problems Using Numerical And Algebraic Expressions And Equations|||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|||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|||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

California Standards (Click to View)

1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).||CA Mathematics||Grade 4||02. Algebra and Functions||1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.|||1.2 Interpret and evaluate mathematical expressions that use parentheses.||CA Mathematics||Grade 4||02. Algebra and Functions||1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.|||1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.||CA Mathematics||Grade 4||02. Algebra and Functions||1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.|||1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.||CA Mathematics||Grade 4||02. Algebra and Functions||1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.|||2.0 Students know how to manipulate equations.||CA Mathematics||Grade 4||02. Algebra and Functions|||1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.||CA Mathematics||Grade 5||02. Algebra and Functions||1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.|||1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.||CA Mathematics||Grade 7||02. Algebra and Functions||1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs.

Categories include:
  • Grades 3-5
  • Grades 6-8
  • Math
Tags: Expressions & Equations
Subjects covered: ["Math"]