Kindergarten

## 7th Grade Math Common Core State Standards and Curriculum

By the 7th grade, math standards have become more demanding and more complex. It’s important to maintain focus and keep up with Common Core math standards. Grade 7 students can expect new terminology, additions to their understanding of the number system, and more. Creating a 7th grade math Common Core standards checklist can help you and your student stay on track. Knowing what to expect is important. Additionally, as the year progresses, the ability to pinpoint weaknesses among math subjects will prove useful. With these in mind, parents, tutors, educators, and students alike can list key areas to focus and improve on come finals.

### 7th Grade CCSS Math: What Your Student Should Already Know

In order to succeed in 7th grade math, Common Core standards from the previous year must be achieved. This is because there is a step-by-step system of education built into Common Core standards. 7th grade math is built upon what was learned in 6th grade math, and so on. By the arrival of 7th grade, your student should be able to:
• Define rate and ratio and solve problems involving them.
• Peers exiting 6th grade should identify and connect ratio and rate to real-world examples. They should apply multiplication and division strategies to solve problems involving these examples. Students should recognize the correlation between fractions and ratios and use this to their strategic advantage.

• Comfortably multiply, divide, add, and subtract fractions.
• Students should be able to explain why strategies for solving fraction division problems provide accurate results. They should be fluent in simplifying and expanding fractions for the sake of operations with fractions.

• Identify and solve for variables in equations.
• Students should have practice with varied methods for solving for a variable in an equation. They should have practice using tables and plotting points to represent patterns with variable and solutions.

• Represent statistical data in various forms.
• Students entering 7th grade should be able to utilize various forms of representation to draw conclusions in statistics. These include scatter plots, tables, and more. They should also have the fluent ability to find median and mean of sets of data. They should be able to draw from real-world examples to create these representations and solve problems in this area.

• Recognize rational numbers.
• Students should have a thorough understanding of negative numbers. They should also have an understanding of properties associated with negative numbers and strategies developed for solving problems with them.
Seventh grade math standards require competence and a firm grasp of the above concepts. To ensure preparation for 7th grade, create a study plan for the summer. This way, your student will be ready for the math to come. For high-quality, comprehensive curriculum, ArgoPrep is the solution. Their online content is aligned with 7th grade Common Core standards. Math workbooks available in their online store are no different. Their physical and online materials correlate for an interactive, expertly crafted educational experience.

### CCSS 7th Grade Math: Four Focus Areas

7th grade Common Core math standards aim to create competence and understanding in four main areas. Rather than introducing entirely new concepts, the curriculum of this year deepens and expands subjects studied in the previous year. The four focus areas are:
• Area 1: Expand and apply ratio knowledge to more complex examples and problems.
• Area 2: Recognize relationships between fractions, decimals, and percents.
• Area 3: Expand and practice with volume and surface area
• Area 4: Further distribution of data among populations
During the sixth grade, the basics for these concepts were practiced with the objective of creating a strong basis for which to be built upon. Not dissimilarly, math concepts taught in the seventh grade will form the grounds for eighth grade math. If you’re on the hunt for excellent study materials for the four focus areas, ArgoPrep provides thorough and detailed math curriculum designed with the success of your student in mind.

### CCSS Math: 7th Grade Focus Area Breakdowns and Study Suggestions

#### Area 1: Expand and apply ratio knowledge to more complex examples and problems.

In this focus area, students will continue their study of rates and ratios by moving towards multi-step equations. They will create further fluency with real-world examples of ratio. Some of these include percentages, such as tipping problems and tax-related equations. Others include examples of lowering or heightening percentages, such as monetary worth (like that of a car) or speed (i.e. a train moving at 56% of its previous speed, a bike slowing down by 17%, etc). Students will develop an understanding of relationships in proportion and use various methods of representing these relationships.

#### Study Suggestion for Area 1

Ratio problems most often relate to real-world situations. Physical examples, such as the aforementioned car or train, can help your student apply methods and strategies to concrete concepts. This, along with the visuals created by graphs and tables, can help with overall comprehension of these concepts and strengthen the methods.

#### Area 2: Recognize relationships between fractions, decimals, and percents.

Prior to seventh grade, students have worked with all three of these number forms. Now, they will ascertain the inherent relationship between them. They will develop methods with the aim of fluently interchanging between each form. Students should also discern and explain why these methods work, as well as incorporating these strategies to better and more efficiently solve math problems involving these three number forms.

#### Study Suggestion for Area 2

Ensure that your student has complete mastery of place value. Place value is vital in converting numbers from form to form. Additionally, make sure your student has an excellent sense in factors and simplifying fractions. Try using flashcards to practice switching from percent and decimal form. Practice with all conversions between the three. Keep a calculator handy! They’ll be especially useful for conversions from fractions.

#### Area 3: Expand and practice with volume and surface area

In this area, students will explore volume of three-dimensional shapes. These shapes will not be limited to rectangular objects as of this year. Additionally, students will expand their knowledge and strategies with area to circles. Students will use inferences and area strategies to find total surface areas of three-dimensional objects. They will also solve real-world example problems involving volume and area, such as identifying the amount of liquid in a container.

#### Study Suggestion for Area 3

Not unlike rate and ratio, volume and area utilize physical examples quite often. (If it weren’t for physical examples, volume wouldn’t even exist!) Try using three-step multiplication flashcards for practicing volume fluency. For surface area, use different objects in your home, preferably rectangular objects. Illustrations can work well in a pinch. Measure sides and draw conclusions about the shapes together.

#### Area 4: Further distribution of data among populations

Students will examine random samples of statistical data in populations. By representing them in various ways, they will draw conclusions based on the represented results. Students will come to understand probability of events and express probability with numerical representation.

#### Study Suggestion for Area 4:

Probability can be easily expressed with physical objects around the home. For example, pulling from a bag with five marbles and five buttons has a ½ or 50% chance of being either a marble or a button. Try this exercise with different marble to button ratios. Keep track of each probability percentage as you go along. Tutorials may also prove useful in this area. The ones provided by ArgoPrep are colorful, engaging, and thorough. Sign up for access to their educational platform today.

## Ratios & Proportional Relationships

### Analyze proportional relationships and use them to solve real-world and mathematical problems.

#### CCSS.MATH.CONTENT.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

#### CCSS.MATH.CONTENT.7.RP.A.2

Recognize and represent proportional relationships between quantities.
##### CCSS.MATH.CONTENT.7.RP.A.2.A
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
##### CCSS.MATH.CONTENT.7.RP.A.2.B
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
##### CCSS.MATH.CONTENT.7.RP.A.2.C
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
##### CCSS.MATH.CONTENT.7.RP.A.2.D
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

#### CCSS.MATH.CONTENT.7.RP.A.3

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

## The Number System

### Apply and extend previous understandings of operations with fractions.

#### CCSS.MATH.CONTENT.7.NS.A.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
##### CCSS.MATH.CONTENT.7.NS.A.1.A
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
##### CCSS.MATH.CONTENT.7.NS.A.1.B
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
##### CCSS.MATH.CONTENT.7.NS.A.1.C
Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
##### CCSS.MATH.CONTENT.7.NS.A.1.D
Apply properties of operations as strategies to add and subtract rational numbers.

#### CCSS.MATH.CONTENT.7.NS.A.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
##### CCSS.MATH.CONTENT.7.NS.A.2.A
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
##### CCSS.MATH.CONTENT.7.NS.A.2.B
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
##### CCSS.MATH.CONTENT.7.NS.A.2.C
Apply properties of operations as strategies to multiply and divide rational numbers.
##### CCSS.MATH.CONTENT.7.NS.A.2.D
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

#### CCSS.MATH.CONTENT.7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.1

## Expressions & Equations

### Use properties of operations to generate equivalent expressions.

#### CCSS.MATH.CONTENT.7.EE.A.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

#### CCSS.MATH.CONTENT.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

### Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

#### CCSS.MATH.CONTENT.7.EE.B.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making \$25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or \$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

#### CCSS.MATH.CONTENT.7.EE.B.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
##### CCSS.MATH.CONTENT.7.EE.B.4.A
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
##### CCSS.MATH.CONTENT.7.EE.B.4.B
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions.

## Geometry

### Draw construct, and describe geometrical figures and describe the relationships between them.

#### CCSS.MATH.CONTENT.7.G.A.1

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

#### CCSS.MATH.CONTENT.7.G.A.2

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

#### CCSS.MATH.CONTENT.7.G.A.3

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

### Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

#### CCSS.MATH.CONTENT.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

#### CCSS.MATH.CONTENT.7.G.B.5

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

#### CCSS.MATH.CONTENT.7.G.B.6

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

## Statistics & Probability

### Use random sampling to draw inferences about a population.

#### CCSS.MATH.CONTENT.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

#### CCSS.MATH.CONTENT.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.Draw informal comparative inferences about two populations.e equations for an unknown angle in a figure.

#### CCSS.MATH.CONTENT.7.G.B.6

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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