Purpose: To divide decimals by decimals Materials: Decimal Squares and Blank Decimal Squares for

Dividing Decimals by Decimals (attached)

Activity 1 Shading Blank Decimal Squares to Find Quotients Blank Decimal Squares for Dividing Decimals by Decimals

1. Use #1 on the activity sheet and shade the first square with 9 parts and the second square with 3 parts. Determine how many times bigger the shaded amount for .9 is than the shaded amount for .3, write the number (quotient) in the box, and complete the equation beneath the squares. Discuss that lines can be drawn on the .9 square to show that .3 "fits into" .9 three times. Use #2 on the sheet to illustrate .8 ÷ .2, write its quotient in the box, and complete the division equation.

2. Use #3 on the sheet and shade the two squares with 20 shaded parts and 5 shaded parts. Determine how many times bigger .20 is than .05, and write a division equation for .20 ÷ .05. (.20 ÷ .05 = 4) Draw lines on the .20 squares to show that .05 "fits into" or can be "subtracted from" .20 four times.

3. Use #4 on the sheet, and shade the first square for .60, and the second square for .15. Draw lines on the first square to show how many times .15 "fits into" .60, and write the division equation below the squares.

4. Use the squares in #5 to illustrate .30 ÷ .02. How many times bigger is .30 than .02? (15 times bigger) Write the division equation for this result. (.30 ÷ .02 = 15) Discuss that this example shows that dividing by small numbers can produce large numbers, a result that sometimes surprises students. Look at the .30 square to see that .30 ÷ .01 = 30.

TEACHER MODELING/STUDENT COMMUNICATION

DIVISION 5.NBT.7 DIVISION OF DECIMALS BY DECIMALS

5. Shade the squares in #6 for .40 and .16 and determine how many times bigger .40 is that .16 by marking off two groups of 16 on the .40 square. Explain how these squares can be used to show that .40 ÷ .16 = 2 ½ or 2.5 (.16 fits into .40 two times and the remaining 8 hundredths squares are half of 16, that is, .16 "fits into" .40 two and one-half times.) cc

Activity 2 Summarizing to See Patterns and Relationships

Look for patterns in the examples of dividing decimals by decimals and write a rule for dividing one decimal by another. Students may have noticed that these activities involved dividing whole numbers of shaded parts by whole numbers of shaded parts. This suggests the following rule for using long division. 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 whole numbers.

Activity 3 Approximating Quotients with Compatible Numbers

Approximate each quotient by finding convenient compatible number replacements. Your answers will vary. a. .61 ÷ .2 ≈ .6 ÷ .2 = 3 b. .9 ÷ .4 ≈ .8 ÷ .4 = 2 c. .77 ÷ .23 ≈ .75 ÷ .25 = 3

Decimal Squares

In the game EXACT FITS, each player in turn takes two red squares or two green squares (decimals with the same number of decimal places), selects the square for the greater decimal, divides the number of shaded parts of this square by the number of shaded parts of the other square, and rounds the quotient to the nearest whole number. This number is the player's score for the turn. The player with the greatest point total after 5 rounds win the game. In the example shown here, the player receives 3 points. Bonus Turn: If a player's quotient is a whole number and does not have to be rounded, the player has an "Exact Fit" and in addition to receiving the points for the turn, receives a bonus turn.

Worksheets 5.NBT.7 #27, #28 and #29 decimalsquares.com (Laser Beams In this game, mixed decimals are rounded to whole numbers, and if their quotient are computed in time, the asteroids will be destroyed before they pass out of view.)

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EXPANDING THE CONCEPTS

INDEPENDENT PRACTICE AND ASSESSMENT

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