Math Topics Outline 2nd quarter:
Unit 3: Equations Inequalities Applications
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.
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.
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.
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.
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 aproblem 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.Unit 4: Rates, Ratios, Proportionality
6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
Expectations for unit rates in this grade are limited to non-complex fractions.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratio 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.
b. Solve unit rate problems including those involving unit pricing and constant
speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many
lawns could be mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means
30/100 times the quantity); solve problems involving finding the whole, given a
part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform unitsappropriately when multiplying or dividing quantities