Solve two-step word problems using the four operations. 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.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.
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.
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.
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.
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.
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.
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.
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.
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?
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.
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Grade: 09, 10, 11, 12
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Grade: 09, 10, 11, 12
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Grade: 09, 10, 11, 12
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
What are those letters inside of algebra equations? They’re not just runaways from your English class--they’re variables! In this BrainPOP movie, Tim and Moby find themselves in a bind: how to build a ladder to get to their new treehouse. Using a simple one-variable equation, Tim will walk you through the process of simplification and show you how to isolate the variable on one side of the equals sign. You’ll learn how to substitute numbers you don’t know for letters, and how to figure out what numbers those letters actually stand for. Cool! Watch this movie, and you’ll know what to do the next time you have to solve for x. Or y. Or a. Or d. You get the point!
In this lesson plan which is adaptable for grades 2-7, students will explore authentic contexts for measurement skills. Students will use a free online math game to take on the role of a carpenter who needs to cut planks of wood. Younger students will practice equal grouping in early levels of the game, while older students practice measurement, factoring, division, and algebra as they cut slabs of wood in the advanced game levels. Students then work collaboratively to create math word problems that include real world measurement scenarios. This lesson plan is aligned to Common Core State Standards. See more »
In this lesson plan, which is adaptable for grades 6 through 8, students use BrainPOP resources to explore mathematical concepts. They will describe, represent, and apply numbers using mental strategies, paper/pencil and technology through an online game. Students will also evaluate algebraic expressions. This lesson plan is aligned to Common Core State Standards. See more »
In this lesson plan, which is adaptable for grades 6, 7, and 8, students use BrainPOP resources to to explore mathematical concepts. They will describe, represent, and apply numbers using mental strategies, paper/pencil and technology through an online game. Students will also identify, describe, extend, and create numeric patterns and functions, and interpret and write a rule for a one operation function table. This lesson plan is aligned to Common Core State Standards. See more »
In this lesson plan, which is adaptable for grades 4-8, students use BrainPOP resources to practice applying knowledge of distance, rate, and time to real-world problem solving. Students will also graph linear equations, demonstrate knowledge of slope and intercept, and solve two step equations. See more »
In this lesson plan which is adaptable for grades 3-12, students work collaboratively to research selected math skills. Students then create, play, and assess a math game that is designed to apply and reinforce their selected math concept. This lesson plan is aligned to Common Core State Standards. See more »