Kindergarten

## 6th Grade Math Common Core State Standards and Curriculum

Sixth grade math standards present challenges not just in the mathematical area. The structure of your student’s schooling has likely changed and will present difficulties as well. If your student attends a traditional school, they will no longer remain in one classroom to learn. Instead, they switch between several. They may struggle with schooling overall as they transition and become familiar with their new surroundings. Math is no exception. Expectations of teachers and curriculum rise significantly as of this school year. Keeping up with 6th grade math Common Core standards can help you stay ahead and ensure your student is getting practice in the right areas.

Your student’s success in sixth grade depends heavily on their success in fifth grade. This is because there is a step-by-step concept development system built into Common Core standards. 6th grade math is no exception to this. Fifth grade created finalization on elementary math and prepared students for upcoming, more complex math concepts. By the end of their elementary school math journey, your student should be comfortable with:
• Addition, subtraction, multiplication, and division with fractions
• Students should have developed familiarity with fraction operations in the fifth grade. They should have methods prepared and practiced for simplifying fractions. Additionally, they should be competent in identifying equivalent fractions. Students should also understand the correlation between fractions and decimals, as well as how to transition from decimal form to fraction form.
• All four operations involving multiple digits
• Students should have practiced methods for solving equations involving multiple steps and digits reaching the thousands. They should incorporate the commutative property of multiplication to create efficiency with their solving in division. Students should have the ability to define operations and explain why the solving methods they use work.
• Defining and solving for volume in three-dimensional shapes
• Students exiting their fifth grade year should understand the definition of volume and correlate their skills in multiplication with identifying the volume of given examples.
• Students should also have practice with plotting points on a standard grid. They should be familiar with the x and y axes, along with different line drawings. These include rays, line segments, points, and lines.
• Peers should have plenty of practice measuring and identifying angles in two-dimensional shapes. They should be able to analyze and draw conclusions about the shapes based on their angle findings.
If your student is facing severe detriment in any of these subjects, they will undoubtedly face difficulties with 6th grade math standards. During the summer before sixth grade, ensure that their math skills remain sharp. ArgoPrep is the perfect platform for collecting high-quality summer study materials. They have an extensive selection of workbooks and online tutorials. To further benefit your student, their curriculum is carefully aligned with Common Core math standards. Grade 6 calls for as much practice as your student can get, and ArgoPrep has more than enough.

### 6th Grade Common Core Math Standards: Focus Areas Overview

Sixth grade students will focus their studies in four main areas. These draw on what they were taught in fifth grade. More flexible thinking and new utilization of numbers are called for in 6th grade standards. Math practice will also involve new types of expressions and find various ways to solve them. These four focus areas are:
• Area 1: Develop an understanding of ratio and rate
• Area 2: Expand methods for fraction division; define and practice with rational numbers
• Area 3: Introduce, identify, utilize, and solve for variables
• Area 4: Form familiarity and skills in statistical thinking
Most of these subjects are most likely completely new material to your student. Albeit they build on concepts previously established, there is a great deal of new vocabulary and ideas in 6th grade Common Core standards. Math progress can be difficult to regain once a student has fallen behind. Make sure your student is getting the help they require. If necessary, look into your student’s tutoring hours and programs. Even if they have a smooth experience in math, tutoring can make an important positive impact on your student’s success in math.

### 6th Grade CCSS Math: Focus Area Breakdown and Study Suggestions

#### Area 1: Develop an understanding of ratio and rate

In this focus area, students will recognize the correspondence between ratio and rate to multiplication and division. Sixth graders will create familiarity with thinking in terms of ratio and rate by examining real-world examples. They will express these with illustrations and by filling in tables.

#### Area 1 Study Suggestion

Ratio and rate create mathematical context to situations your student is likely already familiar with. For example, your student likely understands rates of speed, such as driving a car at 20 miles per hour. With this instance in mind, ask them how many miles you can drive in two hours going 20 miles an hour. ArgoPrep also has plenty of tutorials on ratio and rate that draw from real-world examples. Sign up for access to their helpful educational content.

#### Area 2: Expand methods for fraction division; define and practice with rational numbers

Sixth grade students have touched on fraction division in fifth grade Common Core math standards. 6th grade, however, will further these methods. Students will divide fractions involving mixed numbers and with varied denominators. They will also study the reasoning behind why fraction division methods provide accurate results.

#### Area 2 Study Suggestion

Fraction multiplication is simple: simply multiply straight across the fractions. An easy way to remember fraction division is to remember that it is the opposite of multiplication. Therefore, rather than multiplying numerators to numerators and so on, multiply numerators to denominators: the opposite of usual multiplication.

#### Area 3: Introduce, identify, utilize, and solve for variables

Students have had some practice with solving for unidentified values. Working for variables is not much different. Now, students will solve for a more concrete symbol and practice efficient methods for doing so. They will exercise these methods by solving equations involving variables, as well as creating their own based on given circumstances.

#### Study Suggestion for Area 3

Begin variable practice with small values. Try addition and subtraction problems with an unknown value marked with a letter, such as x. Starting with lesser values will help ease your student into using variables and help them become comfortable with them.

#### Area 4: Form familiarity and skills in statistical thinking

Similarly to ratio and rate, students will study statistical problems by observations of real-world examples. Students will represent statistical information in the form of various types of graphs and plots on coordinate planes. Students will also define and solve for mean and median of groups of numbers originating from a collection of characteristics or facts.

#### Area 4 Study Suggestion

Using illustrative representations of statistical data as a tool for understanding statistics is an excellent method. Try using scatter plots or other graphing methods to help your student understand and visualize the “shapes” that the trends create.

## Ratios & Proportional Relationships

### Understand ratio concepts and use ratio reasoning to solve problems.

#### CCSS.MATH.CONTENT.6.RP.A.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."

#### CCSS.MATH.CONTENT.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. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid \$75 for 15 hamburgers, which is a rate of \$5 per hamburger."1

#### CCSS.MATH.CONTENT.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.
##### CCSS.MATH.CONTENT.6.RP.A.3.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.
##### CCSS.MATH.CONTENT.6.RP.A.3.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?
##### CCSS.MATH.CONTENT.6.RP.A.3.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.
##### CCSS.MATH.CONTENT.6.RP.A.3.D
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

## The Number System

### Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

#### CCSS.MATH.CONTENT.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. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

### Compute fluently with multi-digit numbers and find common factors and multiples.

#### CCSS.MATH.CONTENT.6.NS.B.2

Fluently divide multi-digit numbers using the standard algorithm.

#### CCSS.MATH.CONTENT.6.NS.B.3

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

#### CCSS.MATH.CONTENT.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. For example, express 36 + 8 as 4 (9 + 2)..

### Apply and extend previous understandings of numbers to the system of rational numbers.

#### CCSS.MATH.CONTENT.6.NS.C.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.

#### CCSS.MATH.CONTENT.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.
##### CCSS.MATH.CONTENT.6.NS.C.6.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.
##### CCSS.MATH.CONTENT.6.NS.C.6.B
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.
##### CCSS.MATH.CONTENT.6.NS.C.6.C
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.

#### CCSS.MATH.CONTENT.6.NS.C.7

Understand ordering and absolute value of rational numbers.
##### CCSS.MATH.CONTENT.6.NS.C.7.A
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
##### CCSS.MATH.CONTENT.6.NS.C.7.B
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.
##### CCSS.MATH.CONTENT.6.NS.C.7.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. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
##### CCSS.MATH.CONTENT.6.NS.C.7.D
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

#### CCSS.MATH.CONTENT.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.

## Expressions & Equations

### Apply and extend previous understandings of arithmetic to algebraic expressions.

#### CCSS.MATH.CONTENT.6.EE.A.1

Write and evaluate numerical expressions involving whole-number exponents.

#### CCSS.MATH.CONTENT.6.EE.A.2

Write, read, and evaluate expressions in which letters stand for numbers.
##### CCSS.MATH.CONTENT.6.EE.A.2.A
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
##### CCSS.MATH.CONTENT.6.EE.A.2.B
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. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
##### CCSS.MATH.CONTENT.6.EE.A.2.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-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

#### CCSS.MATH.CONTENT.6.EE.A.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

#### CCSS.MATH.CONTENT.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). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..

### Reason about and solve one-variable equations and inequalities.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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 and analyze quantitative relationships between dependent and independent variables.

#### CCSS.MATH.CONTENT.6.EE.C.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 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.

## Geometry

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

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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.

#### CCSS.MATH.CONTENT.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.

## Statistics & Probability

### Develop understanding of statistical variability.

#### CCSS.MATH.CONTENT.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. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

#### CCSS.MATH.CONTENT.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

#### CCSS.MATH.CONTENT.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

### Summarize and describe distributions.

#### CCSS.MATH.CONTENT.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

#### CCSS.MATH.CONTENT.6.SP.B.5

Summarize numerical data sets in relation to their context, such as by:
##### CCSS.MATH.CONTENT.6.SP.B.5.A
Reporting the number of observations.
##### CCSS.MATH.CONTENT.6.SP.B.5.B
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
##### CCSS.MATH.CONTENT.6.SP.B.5.C
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
##### CCSS.MATH.CONTENT.6.SP.B.5.D
Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

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