Grade 6 Mathematics Curriculum Map

Grade 6 Mathematics Curriculum Map

Geometry

Ratios & Proportional

Solve real-world and mathematical problems involving area, surface area, and volume.

Focus: Understand ratio concepts and use ratio reasoning to solve problems.

Standards:

6.RP.1.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities

6.RP.1.2

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.

6.RP.1.3

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 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.

b. Solve unit rate problems including those

involving unit pricing and constant speed.

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 units appropriately

when multiplying or dividing quantities.

e. Understand the concept of Pi as a ratio of the

circumference of a circle to its diameter.

6.NS.3.6b-Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the number line and in the plane with negative number coordinates.

6.NS.3.8- Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

6.G.1.1- Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6.G.1.3.- Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

6.G.1.2- Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V=lwh and V=bh to find the volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

6.G.1.4- Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Statistics and Probability

• Develop understanding of statistical variability.
• Summarize and describe distributions.

The Number System

Expressions and Equations

• Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations and inequalities
• Represent and analyze quantitative relationships between dependent and independent variables

6.EE.1.1- Write and evaluate numerical expressions involving whole-number exponents.

6.EE.1.2- Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for numbers.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, coefficient); view one or more parts of an expression as a single entity.

c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-numbers exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

6.EE.1.3- Apply the properties of operations as strategies to generate equivalent expressions.

6.EE.1.4- Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

6.EE.2.6- 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 specified set.

6.EE.2.5- 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.2.7- 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.2.8- Write an inequality of the form x > c or x < c to represent a constaint 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.3.9- Use variables to represent two quantities in a real-world problem from a variety of cultural contexts that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

6.NS.1.1- Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

6.NS.2.2- Fluently divide multi-digit numbers using the standard algorithm.

6.NS.2.3- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.2.4- Find the greatest common factor of two who numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express the sum of two whole numbers 1 - 100 with a common factor as a multiple sum of two who numbers with no common factors.

6.NS.3.5- Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.3.6a and c- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

a. recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g. –(-3)=3 and that 0 is its own opposite.

c. find and position integers and other rational numbers on a horizontal or vertical number line diagram.

6.NS.3.7- Understand ordering and absolute value of rational

numbers.

a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

d. Distinguish comparisons of absolute value from statements about order.