Get independent practice solving equations with rational numbers. Each incorrect response gets a text box explanation and another try. Correct responses are confirmed.

Brush up on your math skills relating to comparing rational numbers then try some practice problems to test your understanding.

This task requires students to determine whether a number is rational or irrational. The task assumes that students are able to express a given repeating decimal as a fraction.

The CyberSquad tries to rescue the Cyberchase Council, which is being held captive by Hacker in this video segment from Cyberchase.

In this interactive, use logic to solve riddles involving a wallaby jumping contest. Add two consecutive jumps and place them on a number line, finding equivalent fractions and common denominators to do so. Backward jumps represent negative numbers, and forward jumps represent positive numbers. Numbers are randomized so that riddles can be answered and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet handout to support the online work.

In this interactive, use logic to solve riddles involving a flea-jumping contest. Place each contestant's jump, represented by either a fraction or a decimal in both feet and inches, at the correct point on the vertical number line. Numbers are randomized so that riddles can be solved and fleas placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to accompany the online work.

In this interactive, use logic to solve three riddles involving a jumping frog competition. Then, using knowledge of inequalities and rational numbers, place the frogs in the correct range from 0 to 5 on a number line. The fractions, mixed numbers, and decimals (in feet and inches) are randomized so that the range on the number line is different each time the riddles appear. The accompanying classroom activity includes a concept review and a response sheet handout to support the online work.

In this interactive, use logic to solve three riddles involving high-jump performers in a flea circus. Then, using knowledge of inequalities, place the fleas in the appropriate range on a vertical number line. Numbers are randomized so that the range on the vertical number line is different each time one of the three riddles appears. The accompanying classroom activity includes a fraction/decimal concept review and response sheets to support the online work.

In this interactive, use logic to solve three riddles involving a jumping wallaby competition. Then, using knowledge of inequalities and rational numbers, place the wallabies on the correct range from -5 to 5 on the number line. Numbers are randomized so that the range on the number line is different each time the riddles appear. The accompanying classroom activity includes a concept review and response sheets to support the online work.

In this interactive, use logic to solve riddles involving a wallaby jumping contest. Then, place each contestant's jump-a fraction, mixed number, or decimal between -5 and +5-at the correct point on the number line. Backward jumps are represented by negative numbers and forward jumps by positive numbers. Numbers are randomized so that riddles can be solved and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to accompany the online work.

In this interactive, use logic to solve riddles involving a wallaby jumping contest.

In this interactive, use logic to solve riddles involving a wallaby jumping contest. Then, place each contestant's jump -- a fraction, mixed number, or decimal between -5 and +5 -- at the correct point on the number line. Backward jumps are represented by negative numbers and forward jumps by positive numbers. Numbers are randomized so that riddles can be solved and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to accompany the online work.

Working With Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Compare and order positive and negative numbers and place them on a number line.
Understand the concepts of opposites absolute value.

Lesson Flow

The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents adding or subtracting positive integers, and adding or removing weight represents adding or subtracting negative integers.

Students then move from the balloon model to a number line model for adding and subtracting integers, eventually extending the addition and subtraction rules from integers to all rational numbers. Number lines and multiplication patterns are used to find products of rational numbers. The relationship between multiplication and division is used to understand how to divide rational numbers. Properties of addition are briefly reviewed, then used to prove rules for addition, subtraction, multiplication, and division.

This unit includes problems with real-world contexts, formative assessment lessons, and Gallery problems.

Lesson OverviewStudents learn the definition of rational number, and they write rational numbers as ratios of integers and as repeating or terminating decimals.Key ConceptsStudents have been working with rational numbers throughout this unit, but the term rational number is formally defined in this lesson. A rational number is a number that can be written in the form pq, where p and q are integers. All the integers, fractions, decimals, and percents students have worked with so far in their math classes are rational numbers. Following are some rational numbers written as ratios of integers:36=361−1.2=−12105%=5100 −12=−12Any rational number can also be written as a decimal that terminates or that repeats forever in a regular pattern. For example, 35 = 0.6 and 711 = 0.63636363… Repeating decimals are often written with a bar over the digits that repeat. For example, 0.63636363… can be written as 0.63¯.There are numbers that are irrational. These numbers include π and the square root of any whole number that is not a perfect square, such as 2. The decimal form of an irrational number does not terminate, and the digits do not follow a repeating pattern. Students will study irrational numbers in Grade 8.Goals and Learning ObjectivesUnderstand the definition of rational number.Write rational numbers as ratios of integers.Write rational numbers as terminating or repeating decimals.SWD: Students with disabilities may have difficulty working with decimals and fractions, especially moving between the two. If students demonstrate difficulty to the point of frustration, provide direct instruction on the basics for finding equivalent fractions and decimals.ELL: Target and model key language and vocabulary. Specifically, focus on the term rational, as well as terms such as terminate. As you’re discussing the key points, write the words on the board or on large sheets of paper and explain/demonstrate what the words mean. Since these are important points that students will be using throughout the module, write them on large poster board so that students can use them as a reference. Have students record new terms, definitions, and examples in their Notebook. 

Here is a site that clearly and thoroughly explains multiplying and dividing radical expressions. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to students who have been absent or who need additional instruction on this or many other topics.

Here is a site that clearly and thoroughly explains rational and irrational numbers as subsets of the real number system. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to students who have been absent or who need additional instruction on this or many other topics.

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. What will the results be in 2012? This slightly more challenging activity encourages children to examine data and consider different kinds of influencing factors, and is designed to be accessible to primary pupils at Key Stage 2.

Compare numbers from 1 to 40 using inequality symbols and equal sign with this interactive game.

In this lesson on irrational numbers, students explore how to identify and plot irrational numbers.