6.1 Math standards that we will continue in January

The student will be able to reason about and solve one-variable equations and inequalities.

MGSE6.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.

MGSE6.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.

MGSE.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 non-negative rational numbers.

MGSE.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. Represent and analyze quantitative relationships between dependent and independent variables.

MGSE6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. a. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. b. 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. Understand ratio concepts and use ratio reasoning to solve problems.

MGSE.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems utilizing strategies such as tables of equivalent ratios, tape diagrams (bar models), double number line diagrams, and/or equations.

MGSE.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

MGSE.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.

MGSE.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); given a percent, solve problems involving finding the whole given a part and the part given the whole.

MGSE.6.RP.3d Given a conversion factor, use ratio reasoning to convert measurement units within one system of measurement and between two systems of measurements (customary and metric); manipulate and transform units appropriately when multiplying or dividing quantities. For example, given 1 in. = 2.54 cm, how many centimeters are in 6 inches?

BIG IDEAS 
• Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
• Relate and compare different forms of representation for a relationship.
• Use values from specified sets to make an equation or inequality true.
• Develop an initial conceptual understanding of different uses of variables.
• Graphs can be used to represent all of the possible solutions to a given situation.
• Many problems encountered in everyday life can be solved using proportions, equations or inequalities.
• Students will solve one-step equations.

ESSENTIAL QUESTIONS
• How is an equation like a balance? How can the idea of balance help me solve an equation?
• What strategies can I use to help me understand and represent real situations using proportions, equations and inequalities?
• How can I write, interpret and manipulate proportions, equations, and inequalities?
• How can I solve a proportion and an equation?
• How can I tell the difference between an expression, equation and an inequality?
• How are the solutions of equations and inequalities different?
• What does an equal sign mean mathematically?
• How can proportions be used to solve problems?
• How can proportional relationships be described using the equation y = kx?
• How can proportional relationships be represented using rules, tables, and graphs?
• How can the graph of y = kx be interpreted for different contexts?
• How does a change in one variable affect the other variable in a given situation?
• Which tells me more about the relationship I am investigating, a table, a graph or a formula?