The 7th Grade Skills below are based on the Common Core Standards For Mathematics. You can find out more about the Common Core Standards here.

You will also find a listing of related math resources (worksheets, charts, etc.) here.

**Note: Math standards and curricula can vary by location or school. Check with your child’s school to determine what 7th grade math skills are expected in your location.**

## Ratios & Proportional Relationships

## Calculating unit rates based on ratios that include fractions. e.g. if cyclist travels 1/4 of a mile in 1/6 of one hour their speed can be calculated as 1½ miles/ hour.

## Identifying and showing proportional relationships

The listing of worksheets and other math resources below are related to the following standard extracted from the *Common Core Standards For Mathematics*:

Recognize and represent proportional relationships between quantities.

1. 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.

2. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

3. 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.*

4. 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.

### Worksheet

## Solving ratio and percentage problems with multiple steps. e.g. percentage increase, interest rates, etc.

The listing of worksheets and other math resources below are related to the following standard extracted from the *Common Core Standards For Mathematics*:

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.

### Example/Guidance

- Converting percents (to/from decimals & fractions)
- How to calculate percentages

### Lesson

- Calculating with Percent e.g. 35% of 180 is ?
- Calculating with Percent e.g. 16 out of 50 is what % & 12 is 40% of ?

### Worksheet

- Printable percentage worksheets
- Calculating Percentages in Two Steps e.g. Finding 10% of a value and then multiplying to find 40%
- Calculating Percentages in Steps e.g. Finding 10%, then 5% and adding to find 15%
- Changing Recipe Quantities (e.g. serves 4 so change quantities to serve 6 etc.)

## The Number System

## Adding and subtracting rational numbers. e.g. adding and subtracting with negative numbers.

The listing of worksheets and other math resources below are related to the following standard extracted from the *Common Core Standards For Mathematics*:

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.

1. 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.*

2. 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.

3. 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.

4. Apply properties of operations as strategies to add and subtract rational numbers.

### Example/Guidance

### Quiz

- Integer Rules Quiz (e.g. 5 – (-4) = 9

### Worksheet

- Comparing & Ordering Integers
- Adding Integers
- Subtracting Integers
- Adding & Subtracting Integers – 1
- Adding & Subtracting Integers – 2
- Temperature Changes Using Positive & Negative Numbers (1 of 4)
- Temperature Changes Using Positive & Negative Numbers (2 of 4)
- Temperature Changes Using Positive & Negative Numbers (3 of 4)
- Temperature Changes Using Positive & Negative Numbers (4 of 4)

## Multiplying and dividing rational numbers. e.g. with negative numbers.

*Common Core Standards For Mathematics*:

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

1. 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.

2. 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.

3. Apply properties of operations as strategies to multiply and divide rational numbers.

4. 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.

**Chart**

### Fraction Charts

- Decimal/ Fractions Equivalents Chart e.g. fractions to 1/64

### Worksheet

- Fractions to Decimals e.g. 3/25 = 0.12

## Adding, subtracting, multiplying, and dividing with rational numbers to solve real-world problems.

*Common Core Standards For Mathematics*:

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

### Worksheet

- Changing Recipe Quantities (e.g. serves 4 so change quantities to serve 6 etc.)

## Expressions & Equations

## Adding, subtracting, factoring, and expanding linear expressions that include rational coefficients.

## Recognizing that, if an expression is rewritten in a different form, it can better show the relationship between quantities. e.g. y + 0.25y = 1.25y shows that a 25% increase is the same as multiplying by 1.25.

*Solving multi-step real-world problems *involving positive and negative rational numbers in whole number, fractional, and/or decimal form and being able to mental estimate to determine if answers appear reasonable.

*Common Core Standards For Mathematics*:

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.*

**Worksheet**

### Simple Equations

- Equations with subtraction e.g. x – 4 = 2
- Equations with division e.g. n/2 = 12
- Subtraction & addition equations (1 of 2) e.g. a + 3 = 7 and x – 9 = 11
- Subtraction & addition equations (2 of 2) e.g. a + 3 = 7 and x – 9 = 11
- Multiplication & division equations (1 of 2) e.g. 3n = 12 and a/7 = 3
- Multiplication & division equations (2 of 2) e.g. 3n = 12 and a/7 = 3
- Addition, subtraction, multiplication & division equations
- Addition, subtraction, multiplication & division equations
- Solving equations in two steps (1 of 4) e.g. 5n + 4 = 29
- Solving equations in two steps (2 of 4) e.g. a/4 + 3 = 7
- Solving equations in two steps (3 of 4) e.g. 7n – 3 = 18
- Solving equations in two steps (4 of 4) e.g. b/9 – 4 = 6

## Writing simple equations and inequalities to help solve real-world problems using variables to represent quantities.

*Common Core Standards For Mathematics*:

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.

1. 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?*

2. 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.*

### Example/Guidance

### Worksheet

- Inequalities on a Number Line (2 pages)
- Inequalities for word problems (2 pages)

## Geometry

## Calculating full dimensions from scale drawings and redrawing these at a bigger or smaller scale.

## Drawing figures from specified attributes including by hand, with a straight edge, with a protractor, and with other technology.

## Describing the 2-D shapes that are generated by slicing through 3-D shapes in a plane.

## Recalling and using the formulas for the area and the circumference of a circle.

i.e. A = πr^{2} and C = πd

*Common Core Standards For Mathematics*:

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.

**Worksheet**

### Area

- Area of a Circle
- Calculating Compound Areas (with circles, semi-circles, etc.)

### Shapes and Figures

### Similarity, Congruence and Transformations

- Circles e.g. Identifying radii, diameter and center

## Finding missing angles in a figure by writing and solving equations using knowledge of supplementary, complementary, and adjacent angles.

*Common Core Standards For Mathematics*:

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.

**Example/Guidance**

### Lines and Angles

### Worksheet

- Angle Relationships
- 360° in a Quadrilateral Activity (Activity: Cutting & Rearranging Corners)
- Angles: Supplementary, Corresponding & Alternate (1 of 2)
- Angles: Supplementary, Corresponding & Alternate (2 of 2)
- Angles: Supplementary

## Solving real-world problems that include calculating area, volume, and surface area a 2-D and 3-D objects.

*Common Core Standards For Mathematics*:

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.

**Worksheet**

### Volume

- Calculating Volumes e.g. of triangular prisms and cylinders

## Statistics & Probability

## Recognizing that statistics use a representative sample of the population to make generalizations about the whole population and knowing that randomly picked samples are usually best for this purpose.

## Reasoning about an unknown characteristic by examining a random sample of data. e.g. predicting the mean age of the siblings of an entire class from a random sample of students.

## Assessing the visual overlap of two numeric data sets with similar variability and expressing the difference in centers as a multiple of a measure of variability.

## Using measures of center and of variability from random samples to compare two populations. e.g. find whether sentences in non-fiction books are longer or shorter than those in fiction books.

*Common Core Standards For Mathematics*:

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. *For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.*

### Worksheet

## Recognizing how a scale of 0 to 1 can be used to indicate the likelihood an event happening. e.g. the closer to 0 the less likely an event is, the closer to 1 the more likely an event is, and 1/2 (or 0.5) indicates that the chance of the event happening are the same as the chance of it not happening.

*Common Core Standards For Mathematics*:

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

### Example/Guidance

### Worksheet

## Gauge the probability of an event by making observations and collecting and analyzing data to predict the number of times the event is likely to happen. e.g. if a dice is thrown 60 times, predict the number 4 will be thrown around 10 times.

*Common Core Standards For Mathematics*:

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. *For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.*

### Worksheet

## Finding the probability of an event by generating and using a probability model, comparing forecast and actual frequencies, and explaining reasons for any differences.

## Finding the probability of compound events occurring.

*Common Core Standards For Mathematics*:

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

1. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

2. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

3. Design and use a simulation to generate frequencies for compound events. *For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?*

### Worksheet

Browse for skills and worksheets at other grade levels by clicking in the table below.