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Ever wondered how to teach multiplying rational numbers in an engaging way to your middle school students?

In this lesson plan, students will learn about multiplying fractions, integers, and decimals and their real-life applications. Through artistic, interactive guided notes, check for understanding, practice worksheets, and a color by number activity, students will gain a comprehensive understanding of multiplying rational numbers.

The lesson culminates with a real-life example that explores how multiplying rational numbers can be applied to picking a hotel when planning a trip.

- Standards: CCSS 7.NS.A.2, CCSS 7.NS.A.2.a, CCSS 7.NS.A.2.c
- Topics: Integers & Rational Numbers, Fractions, Decimals
- Grade: 7th Grade
- Type: Lesson Plans

$4.25

After this lesson, students will be able to:

Multiply rational numbers including fractions, integers, and decimals

Apply the concept of multiplication to solve real-life math problems involving rational numbers

Before this lesson, students should be familiar with:

Basic multiplication skills and fluency in multiplying whole numbers

Understanding of the concept of rational numbers and their representation on a number line

Basic understanding of fractions, including how to multiply fractions

Basic understanding of decimals and their relationship to fractions (optional, but helpful)

Pencils

Colored pencils or markers

Rational numbers

Fractions

Integers

Decimals

Multiply

As a hook, ask students why understanding how to multiply rational numbers, including fractions, integers, and decimals, is important in real-life situations. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the guided notes to introduce the concept of multiplying rational numbers. Walk through the key points of the topic, emphasizing the different strategies for multiplying fractions, integers, and decimals. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

**Check for Understanding**: Have students walk through the "You Try!" section in the guided notes. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching and have more advanced students begin work on the practice exercises.

Have students practice multiplying rational numbers including fractions, integers, and decimals using the practice color by code activity provided in the resource. Walk around the classroom to answer any student questions and provide support as needed.

Fast finishers can dive into the word problems included in the resource for extra practice. You can also assign these activities as homework for the remainder of the class.

Bring the class back together, and introduce the concept of rational number multiplication in real-life situations. Discuss with the students how multiplying rational numbers can be useful in various real-world scenarios, such as calculating distances, time, or money.

For example, explain to the students that when planning a road trip, they may need to calculate the total price of a hotel stay. In this case, they may encounter rational numbers, such as fractions or decimals, when multiplying the nightly rate by the number of nights. By understanding how to multiply rational numbers, they will be able to accurately determine the total price of the hotel stay.

Refer to the FAQ section of the resource for more ideas on how to further engage the students and explore different real-life applications of multiplying rational numbers.

If you’re looking for digital practice for multiplying rational numbers including fractions, integers, and decimals, try the Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here is an activity to try:

A fun, no-prep way to practice multiplying rational numbers including fractions, integers, and decimals is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here is an activity to try:

Rational numbers are numbers that can be expressed as the ratio (or fraction) of two integers. Examples of rational numbers include fractions, integers, and terminating or repeating decimals.

To multiply rational numbers, you simply multiply the numerators (the top part of the fraction) together and the denominators (the bottom part of the fraction) together. For example, to multiply two fractions, you multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator.

When multiplying a fraction by an integer, you can think of the integer as a fraction with a denominator of 1. Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

To multiply a decimal by a fraction, first convert the decimal into a fraction by writing it over a denominator of 1 followed by the appropriate number of zeros. Then, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

The process of multiplying fractions and decimals is similar. However, when multiplying fractions, you multiply the numerators and denominators directly. When multiplying decimals, you need to convert them into fractions before performing the multiplication.

Yes, there are rules for multiplying positive and negative rational numbers. When you multiply two numbers with the same sign (both positive or both negative), the result is always positive. When you multiply two numbers with different signs (one positive and one negative), the result is always negative.

Multiplying rational numbers is used in calculations involving time, price, and quantities:

**Price.**Let's say you are at a store and you want to buy 3 shirts, each costing $19.99. To find the total cost, you can multiply the number of shirts (3) by the cost per shirt ($19.99). This would involve multiplying a whole number (3) by a decimal ($19.99), resulting in the total cost.**Time**. If you're finding the total price of a stay at the hotel, you would multiply a the nightly rate, a decimal ($127.45/night) by the number of nights, a whole number (5).**Quantities**. If you're trying to double the size of a recipe, and the recipe involves 1/4 teaspoon of baking soda, you'd multiply a fraction (1/4 tsp) by a whole number (2).

Guided notes and doodles can be an engaging way to teach multiplying rational numbers. The structured notes provide a framework for students to follow along and take important notes. The doodles, sketches, and color coding can help students visualize and remember the steps and concepts involved in multiplying rational numbers.

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