Rational Numbers

Topic: working with rational numbers

Objectives & Outcomes

• By the end of this lesson, students will be able to subtract, add, and multiply rational numbers.

Materials

• Rational numbers cards (one for each student)
• Cardboard cutouts of circles for manipulatives (one for each student)

Warm-up

• Ask students if they have ever seen a fraction before. Ask them to give an example of a fraction they have seen before.
• Introduce the concept of a rational number as a fraction that has a finite number of fractions in its denominator (e.g. 3/4, 2/3, 1/4, etc.).
• Ask students if they can think of a way to show a fraction as a decimal. Ask them to give an example of how they would do this.

Direct Instruction

• Introduce the concept of a decimal as a way to represent a fraction as a number.
• Explain that when we want to subtract or add rational numbers, we need to make sure that the denominators match up.
• Show examples of how to subtract and add rational numbers, making sure to check the denominators as we go.
• Explain that when we want to multiply rational numbers, we need to make sure that the denominators match up and that the numerators are multiplied together.
• Show examples of how to multiply rational numbers, making sure to check the denominators and to multiply the numerators as we go.

Guided Practice

• Give the students a set of rational numbers to work with and have them work in pairs to complete the following problems:
• Subtracting: make sure the denominators match and that the numbers are correctly written as fractions.
• Adding: make sure the denominators match and that the numbers are correctly written as fractions.
• Multiplying: make sure the denominators match and that the numerators are multiplied together.

Independent Practice

• Have the students work in groups to create their own set of rational numbers to add, subtract, and multiply.
• They should make sure their numbers match the criteria for being rational (i.e. the numerator must be a multiple of the denominator) and that they are correctly written as fractions.
• Encourage the students to be creative and have fun with this activity.

Closure

• Review the rules for adding, subtracting, and multiplying rational numbers.
• Ask the students to share any interesting or surprising results they got while working on their groups project.

Assessment

• Observe the students during the independent practice to assess their understanding of the material.
• Collect and review the projects to assess the students ability to apply the material learned in the lesson.
• Administer a brief quiz at a later date to assess the students retention of the material.