Purpose: To divide mixed decimals by mixed decimals Materials: Decimal Squares, Decimal Squares Grid (attached)

Activity 1 Rectangular Model for Division by Mixed Decimals Decimal Squares Grid

1. Use your Decimal Squares Grid to mark off a 1.4 by 1.7 rectangle and compute 1.4 × 1.7. (Some students may need help marking off the dimensions.) What is the number of whole squares and parts of a square contained in the rectangle? (2 whole squares and 38 parts out of 100. Discuss student methods of determining the number of whole squares and parts of a square. Some students may see the whole 10 by 10 square and count the columns and rows of 10 hundredths to obtain a second whole square. Others may compute 1.4 × 1.7 = 2.38 to obtain 2.38 whole squares.) Note: A transparency or projection of the grid is convenient for student/teacher demonstrations.

2. Suppose a rectangle has been formed with

one dimension of 1.8, and it contains 4 whole squares and 14 parts out of 100, that is, 4.14 square units. What is the missing dimension of this rectangle? (2.3. Discuss student reasoning. Some students may use the grid to form a rectangle that has one dimension of 1.8 and then extend the rectangle so that it contains 4 whole squares and 14 parts out of 100. Others may obtain the missing dimension by division, that is, 4.14 ÷ 1.8 = 2.3.) Discuss the relationship between multiplication and division. In the first example above, the area of a rectangle was found by multiplying the two dimensions. In the second example, the area of a rectangle and one dimension were given, and the missing dimension was found by dividing the area of the rectangle by the given dimension.

Activity 2 Long Division Algorithm

1. Show students the two diagrams at the right. The rectangle with one missing dimension is similar to the form shown below the rectangle that is used for long division. The quotient in long division may be thought of as the missing dimension of a rectangle. Notice that suggests part of a rectangle.

TEACHER MODELING/STUDENT RESPONSE

DIVISION 6.NS.3 DIVISION BY MIXED DECIMALS

2. Consider the following statement from the previous lesson on dividing decimals by decimals. This rule also holds for dividing a mixed decimal by a mixed decimal: Move the decimal point in both numbers to the right the same number of places to make the divisor a whole number and then divide as though dividing by a whole number. It is interesting that when using long division to divide by decimals or mixed decimals, the decimal or mixed decimal is always changed to a whole number by moving the decimal point.

Activity 3 Solving Word Problems Involving Division of Mixed Decimals Decimal Squares Grid

The information in the following word problems can be modeled by using the grid for help in finding a solution.

A rectangular countertop with one dimension of 2.6 feet is tiled with 5.46 square feet of tiles. What is the missing dimension of this rectangle? (2.1 feet, since 5.46 ÷ 2.6 = 2.1)

A rectangular flower garden has one dimension of 2.4 yards and

an area of 6.48 square yards. a. What is the missing dimension of the garden? (2.7 yards) b. If a fence is placed on the four sides of the garden, what is the length of the fence? (10.2 yards)

Activity 4 Approximating Quotients by Rounding Mixed Decimals

Approximate the following quotients by first rounding each mixed decimal to the nearest whole number. a. 15.3 ÷ 4.8 ≈ 15 ÷ 5 = 3 b. 40.4 ÷ 9.6 ≈ 40 ÷ 10 = 4 c. 20.73 ÷ 6.27 ≈ 21 ÷ 6 = 3.5

Game: In the game APPROXIMATE QUOTIENTS, each player in turn takes any two Decimal Squares and rolls the die twice. The player uses the two whole numbers from the die and the two decimals from the squares to form two mixed decimals, and then rounds the mixed decimals to the nearest whole numbers and computes the quotient of the larger whole number divided by the smaller. The quotient is then rounded to the nearest whole number for the player's score. In the example here, the player's score is 4 ÷ 3 ≈ 1. The first player to score 10 points wins the game. Worksheets 6.NS.3 #30, #31 and #32 decimalsquares.com Laser Beams Mixed decimals are rounded whole to numbers for computing quotients, products, differences, and sums.

INDEPENDENT PRACTICE AND ASSESSMENT

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