Multiplying Decimals and Mixed Numbers

Abstract

This lesson is designed to reinforce skills associated with multiplying decimals and mixed numbers and allow students to visualize the effects of multiplying by a decimal or mixed number.

Objectives

Upon completion of this lesson, students will:

• have practiced multiplying decimals and/or mixed numbers.
• have explored the effects of multiplying decimals and mixed numbers.
• have practiced predicting the effects of multiplying a number by a decimal or mixed number.

Standards

The activities and discussions in this lesson address the following NCTM Standards:

Numbers and Operations

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

• work flexibly with fractions, decimals, and percents to solve problems

• understand the meaning and effects of arithmetic operations with fractions, decimals, and integers
• understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems

• select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods
• develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use

Analyze change in various contexts

• use graphs to analyze the nature of changes in quantities in linear relationships

Links to other standards.

Student Prerequisites

• Arithmetic: Students must be able to:
  • multiply whole numbers.
  • recall some knowledge regarding multiplication of mixed numbers and decimals.
  • It will also prove helpful if students have the skills needed to interpret a line graph.
• Technological Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• Access to a browser
• Pencil and paper
• Access to a calculator (optional)
• Copies of supplemental materials for the activities:
  • Multiplying Decimals Worksheet
  • Multiplying Mixed Numbers Worksheet

Lesson Outline

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • Can someone tell me what a decimal/mixed number is?

   • If I multiply the number 1 by a decimal, will the result be larger or smaller than 1? OR If I multiply 1 by a mixed number, will the result be larger or smaller than 1?

   • Entertain a discussion on decimals and mixed numbers, including how to multiply these types of numbers.

2. Objectives

   Let the students know what it is they will be doing and learning today. Say something like this:

   • Today, class, we will be talking about multiplying decimals and mixed numbers.

   • We are going to use the computers to look at the effect of multiplying a number by a decimal or mixed number, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about this program first.

3. Teacher Input

   Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use the computer applets on the Project Interactivate site.

   • Open your browser to The Sequencer in order to demonstrate this activity to the students.

   • Show the class that there is a box where they may enter a starting number, in other words, the number that will be multiplied by a decimal or mixed number.

   • Show the class the box where they will enter the multiplier, or the number that our starting number will be multiplied by.

   • Explain to the class that they should enter a "0" into the add-on box as this lesson is about multiplying decimals, not adding them. Show students where to enter the zero.

4. Guided Practice
   • After answering all questions that the students might have regarding the use of The Sequencer, pass out the Multiplying Decimals Worksheet.

   • Walk the students through the worksheet, having all of the students in class use the same numbers, for example: 3 for the whole number and 0.43 for the decimal number. For each question, ask two different students what they think the answer is. Ask the students to settle any disputes on what the answers are.

5. Independent Practice
   • Allow students to work independently or in groups to complete the worksheet and circulate the room to offer help where necessary.

   • When the students are finished with the Decimal worksheet, pass out the Multiplyi ng Mixed Numbers Worksheet and have them work through it independently.

6. Closure

   You may wish to bring the class back together for a discussion of the findings. Allow students to describe what steps are needed and how they differ when numbers are multiplied by a decimal or a mixed number.

Alternate Outlines

This lesson can be rearranged in several ways.

• You may choose to allow students to work in cooperative groups to make predictions about the effects of multiplying two particular number together and then check them as a class.

• You may invent your own way of using this lesson to suit the needs of your students.

Suggested Follow-Ups or Extensions

This lesson can be followed by:

• Fraction Facts: A lesson which introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.

• Ideas that Lead To Probability: which is an introduction to concepts about probability.