# Grade 6 Common Core Math Curriculum

## Grade 6 Common Core Math Curriculum

#### Listed below are Math quizzes for 6th grade students based on the Common Core Math State Standards.

For grade level assignments, we adhere to the Common Core State Standards Initiative's curriculum for the most part, in addition to considering other course curriculums such as GCSE(UK), Singapore Math, Australian and Indian Math curriculums. These courses will also help you to perform well in local and major international competitions such as the Science Bee, Math Olympiad, American Mathematic Competition and so on.

In grade 6, the focus is on four critical areas, namely

1) ratios, rates and the multiplication and division of whole numbers

2) division of fractions. rational numbers including negative numbers

3) using expressions and equations

4) statistical thinking concepts

Some of the mathematical principles that will be covered are:

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.

### Grade 6: Ratios and Proportional Relationships

Here, you will solve a wide variety of problems involving ratios and rates. You will use reasoning around multiplication and division to solve ratio and rate problems about quantities.

By learning more about equivalent ratios and rates, and by using multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, you will be able to connect your understanding of multiplication and division with ratios and rates.

We hope that this will expand the scope of problems for which you can use multiplication and division to solve problems, and how you are able to connect ratios and fractions

6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Basic ratios

Equivalent ratios

6.RP.A.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.

Comparing rates

Rate problems

Unit rates

6.RP.A.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.

Convert decimals to percents

Convert fractions to percents

Convert percents to decimals

Convert percents to fractions

Equivalent ratio and rates word problems

Finding percents using decimals method

Finding percents using fractions method

Finding percents using ratio method

Real world ratio problems

6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Measurement conversion and ratios

### Grade 6: The Number System

Here, you will use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense.

You will use these operations to solve problems. You should be able to extend your previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers.

You should be able to reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.

6.NS.A.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.

Divide mixed numbers

Divide Fractions

Dividing fractions related word problems

6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

Long division of large numbers by 2 digits

6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Dividing Decimals

Dividing Decimals Level 2

Dividing Decimals - Hundredth levels

Multiplying Decimals

Multiplying Decimals Level 2

Multiplying Decimals Level 3

Subtracting Decimals

Subtracting Decimals Level 2

6.NS.B.4 Find the greatest common factor of two whole 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 a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Greatest Common Factor and Least Common Multiples

Greatest Common Factor

Least Common Multiple

Greatest Common Factor and Least Common Multiples

Greatest Common Factor

Least Common Multiple

6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Interpreting Negative Numbers

6.NS.C.6 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.

Representing Negative Numbers

6.NS.C.6a 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.

Understand Rational Number as a Point

6.NS.C.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Understand Ordered Pairs

6.NS.C.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Find and Position Numbers in Graph

6.NS.C.7 Understand ordering and absolute value of rational numbers.

Order and Absolute Value of Numbers

6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Find Inequalities and the Number Line

6.NS.C.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Comparing Rational Numbers in Real World

6.NS.C.7c 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

Finding Absolute Value

Solving Absolute Value

6.NS.C.7d Distinguish comparisons of absolute value from statements about order.

Interpreting Absolute Value

6.NS.C.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.

Using Coordinate Planes to Solve Real World Problems

### Grade 6: Expressions and Equations

Here, you will understand the use of variables in mathematical expressions. You will write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems.

You will understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. You will know that the solutions of an equation are the values of the variables that make the equation true.

You will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. You will construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.

6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.

Evaluate Exponents

6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.

Evaluate Expressions with Variables

6.EE.A.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

Identify Expression Parts

6.EE.A.2c 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-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Evaluate Expressions

6.EE.A.3 Apply the properties of operations to generate equivalent expressions.

Write Equivalent Expressions

6.EE.A.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).

Identify Equivalent Expressions

6.EE.B.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.

Solving Equations and Inequalities

6.EE.B.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.

Model Problems Using Expressions

6.EE.B.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.

Solve Real World Problems Using Equations

6.EE.B.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 Inequalities

6.EE.B.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.

Using Equations to Show Relationships

In this section, you will build on your work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume.

You will find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, you should be able to discuss, develop, and justify formulas for areas of triangles and parallelograms.

You will find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area you can determine. You will reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths.

You can prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.

6.G.A.1 Find the 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.

Find the Area of Shapes

6.G.A.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 = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Finding the Volume

6.G.A.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.

Drawing Polygons in the Coordinate Plane

6.G.A.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.

Identify Shapes and Areas using Net

### Grade 6: Statistics and Probability

In this section, you will be building on and reinforcing your understanding of number, and begin to develop your ability to think statistically.

You will recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point.

You will be able to recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.

6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.