Standard 2: Add, subtract, multiply and divide rational numbers.

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Type: Formative Assessment

Students are asked to add, subtract, multiply, and divide positive and negative fractions.

Type: Formative Assessment

Students are asked to solve a word problem involving division of fractions.

Type: Formative Assessment

Students are given a numerical expression to evaluate.

Type: Formative Assessment

Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.

Type: Formative Assessment

Students are asked to assess the reasonableness of answers using estimation strategies.

Type: Formative Assessment

Students are asked to assess the reasonableness of an answer using mental computation and estimation strategies.

Type: Formative Assessment

Students are asked to combine rational numbers, including fractions and decimals, and use the properties of operations to simplify calculations.

Type: Formative Assessment

Students are asked to explain why the product of a positive and a negative rational number is negative.

Type: Formative Assessment

Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.

Type: Formative Assessment

Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.

Type: Formative Assessment

Students will use percentages and states' apportionment of representatives in the House to determine how much funding should be allocated to each state, in this integrated lesson plan.

Type: Lesson Plan

Use data from U.S. Census Bureau that shows Apportionment Population, Resident Population, and Overseas Population for 2020 & 2010 Census to create and compare ratios in this integrated lesson plan.

Type: Lesson Plan

In this lesson, students will be presented with the same scenario as lesson 1. Now there are additional taxes revenues that came in due to new developments in the area. The budget has a 12.5% increase but due to the new developments, there are allocation constraints to the budget. After dispersing their new funds students will compare their results with their original analysis. This is lesson 2 of 3 in a mini-unit integrating math and civics.

Type: Lesson Plan

In this lesson, students will peer review their assignments from lessons 1 and 2 to compare their solutions and determine the validity of the classmate’s process according to the provided rubric. This is lesson 3 of 3 in a mini-unit integrating math and civics.

Type: Lesson Plan

In this lesson, students will be re-introduced to ratios and percentages and explain how we use them for budgeting and taxes. Students will get information on tax income funds and use the information to allocate funds for providing the different services in a community (Police, Fire, Schools, Hospitals, Roads, etc.) This is lesson 1 of 3 in a mini-unit integrating civics and math.

Type: Lesson Plan

Students will work collaboratively to rank civic duties and responsibilities needed to keep a constitutional republic. They will utilize mathematical strategies to convert measurements of time as they calculate costs using the four operations with decimals and create an effective schedule for the ads within a budget in this model eliciting activity.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students will analyze the mathematical accuracy of fictitious political messages to explain bias in media.

Type: Lesson Plan

In this MEA, students will take on the role as a member of the Sunshine County Budget Committee. Members will collaborate to determine the optimal sales tax rate, use that rate to calculate how much money can be used for special projects, then decide which special projects to include in the budget proposal. Students will use percentages to problem-solve in context while considering citizen input and constraints on spending.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Student will use geoboards to decompose composite figures and polygons into squares, rectangles, and triangles in order to find the total area.

Type: Lesson Plan

In this Model Eliciting Activity (MEA), students must use their knowledge of radioactive dating and geologic time to select an effective elemental isotope to be used to date three rare specimens. This decision requires an understanding of the concept of a half-life and the benefits and limitations of radiometric dating. Students must complete mathematical calculations involving equations and operations with fractions and percentages. Students completing this MEA must develop two essays that respond in a professional manner to a client in the scientific industry.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Students investigate how the pedal and rear wheel gears affect the speed of a bicycle. A GeoGebra sketch is included that allows a simulation of the turning of the pedal and the rear wheel. A key goal is to provide an experience for the students to apply and integrate the key concepts in seventh-grade mathematics in a familiar context.

Type: Lesson Plan

During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.

Type: Lesson Plan

Students will apply skills from the Geometry Domain to build graduation caps for themselves using heavyweight poster paper. They will also apply some basic mathematical skills to determine dimensions and to determine minimum cost. Some of the Geometric skills reinforced in Building Graduation Caps: Cooperative Assignment are finding area, applying the concept of similarity, and the application of the properties of parallelograms. Other skills also involved in this application are measuring, and statistical calculations, such as finding the mean and the range. In addition to the hands-on group project that takes place during the lesson, there is the Prerequisite Skills Assessment: Area that should be administered before the group activity and a home-learning activity. Building Graduation Caps: Individual Assignment is the home-learning assignment; it is designed to reinforce the skills learned in the group activity.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students will research a list of companies to invest in through purchasing stocks. Students will calculate the amount invested and readjust their investment choices.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

The student explores several strategies for selecting a sample population to support making inferences about the population.

Type: Lesson Plan

Students explore variation in random samples and use random samples to make generalizations about the population.

Type: Lesson Plan

In this lesson students will use candy to find the probability of independent compound events, determining the sample space from a tree diagram. They will then conduct an experiment to test the theoretical probability. Once the experiment is complete, the students will compare the theoretical and experimental probability.

Type: Lesson Plan

This resource provides a Lesson Plan for teaching students how to apply the Product of Powers Property of exponents. They will be able to write equivalent exponential expressions and evaluate them when possible.

Type: Lesson Plan

In this lesson, students will complete proof tables to justify the steps taken to solve multi-step equations. Justifications include mathematical properties and definitions..

Type: Lesson Plan

This lesson allows students to apply the area of triangles, quadrilaterals, and trapezoids to composite figures, and gives students a chance to work with classmates to find the area by taking measurements and making the necessary calculations. Students will also see the relationship between the area formulas for rectangles, triangles, trapezoids, and polygons. 

Type: Lesson Plan

Students will explore how percentages, proportions, and solving for unknowns are used in important jobs. This interactive activity will open their minds and address the question, "When is this ever used in real life?"

Type: Lesson Plan

Students will review the properties used in solving simple equations through a quiz-quiz-trade activity. As a class, they will then associate these properties with individual steps in solving equations. The students will then participate in a Simultaneous Round Table to practice their justifications. Finish the lesson with a discussion on the different methods that students could use to acquire the correct answer. The following day, students will take a short quiz to identify misconceptions.

Type: Lesson Plan

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Evaluate numerical expressions with rational numbers expressed as fractions using the order of operations and properties of operations in this interactive tutorial.

This is part 1 in a two-part series. 

Type: Original Student Tutorial

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What is fluency? What are the ingredients required to become procedurally fluent in mathematics? Dr. Lawrence Gray explores what it means for students to be fluent in mathematics in this Expert Perspectives video.

Type: Perspectives Video: Expert

Why is it important to look beyond whether a student gets the right answer? Dr. Lawrence Gray explores the importance of understanding why we perform certain steps or what those steps mean, and the impact this understanding can have on our ability to solve more complex problems and address them in the context of real life in this Expert Perspectives video.

Type: Perspectives Video: Expert

Unlock an effective teaching strategy for making connections with absolute values to graphing in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

In this task, students answer a question about the difference between two temperatures that are negative numbers.

Type: Problem-Solving Task

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Type: Problem-Solving Task

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

In this video, you will work through an example to correctly use the order of operations.

Type: Tutorial

Explore negative numbers to represent real world situations in this tutorial.

Type: Video/Audio/Animation