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Grade 7:  The Learning Equation Math

12.01 Exploring Decimals and Multiplication of Decimals

 Number Operations Decimal Explorer Refresher pp 20-21 Activity 12.01 Refresher pp 22-23
Learning Outcomes:

The student will:

## Area of a Rectangle

Area of a rectangle can be calculated by multiplying the length and width of the rectangle.  Any product can be shown as the area of a rectangle. The length and width are the factors and the product is the area.  Let's look at an interactive example where we can change the length and width of the rectangle and the area created. In this model the dimensions are natural numbers. A similar model could be created that included decimal numbers for the dimensions of the rectangle.

We will need some blocks to illustrate decimal products.   You will need to understand the value of each type of block:

## TLE Exploring Decimals

If you are using The Learning Equation math program, the directions for using Exploring Decimals is on pages 20 and 21 of the Refresher accompanying the CD resources.

The explorer features decimal tiles(blocks).

## Decimal Block Values

1

0.1

0.01

To illustrate the product:

3.2 x 2.4

we will need to combine blocks together

 length = 3.2 units width = 2.4 units

becomes

 3.2 units 2.4

Product = Area = 6x1 + 16 x 0.1 + 8 x 0.01 = 7.68

The following internet site(s) will give you the opportunity to build more rectangles to demonstrate decimal multiplication.

Base 10 Blocks: Exploring Whole Decimal Numbers with Blocks

or

Base 10 Blocks: Exploring Whole Decimal Numbers with Blocks

You have had an opportunity to visualize multiplication of decimals with rectangles.  Now it is time to learn how to multiply decimal numbers without a visual aid.

## Multiplying Decimals

Example Explanation

4.36 x 6.2

 4.36   6.2 872 26160 27.032 There will be 3 digits after the decimal in the answer, because there are 3 numbers after the decimal in the factors.
Line up the numbers as if there were no decimals.

Multiply as usual.

Count the total number of digits after the decimals in the factors.

The number of digits counted equals  the number of digits after the decimal in the quotient.

Enter your name, then click enter.  You will be given multiplying decimal questions to complete!   You will have to work the question out on paper, then enter the answer.  The applet will show you the steps if you need them.

After practicing making the multiplication rectangles, try these sites to see if you have started to visualize decimal products.

Review:

A+ Math Flash Cards - Choose multiplying

Enrichment:

 Key Terms: A-E F-J K-O P-R S-Z

integer, positive, negative, signed number, magnitude, direction, addend, sum, difference, zero model, absolute value

Prerequisite Skills:

Introduction to Integers:  Grade 7 Lesson 11.09

Introduction to Integers:  Grade 7 Lesson 11.09

Introduction to Integers:  Grade 7 Lesson 11.09

Scientific Calculator

Introduction to Integers:  Grade 7 Lesson 11.09

Introduction to Integers:  Grade 7 Lesson 11.09

Activities Example Explanation

A+ Math Flash Cards -  adding

6.1 + 23 = 6.3 + 23.0

 6.1 23. --> 6.1 23.0 29.1
If no decimal, place one on the far right (Think money:  \$2 = \$2.00).

Add zeros after the decimal to fill "empty" spaces.

Enter your name, then click enter.  You will be given adding decimal questions to complete!

## Subtracting Decimals

Activity Example Explanation

Subtracting Decimals

A+ Math Flash Cards - subtracting

23.4 - 6.97

 23.4  6.97 --> 23.40 6.97 16.43
If no decimal, place one on the far right (Think money:  \$2 = \$2.00).

Add zeros after the decimal to fill "empty" spaces.

Subtract as usual.

Enter your name, then click enter.  You will be given subtracting decimal questions to complete!

linked source:  Subtraction of Decimal Numbers

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