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. Pass out activity sheets. Shade 9 parts of the tenths Decimal Square in #1 on the activity sheet and shade the second tenths Decimal Square in #1 with 3 parts. Determine how many times bigger the shaded amount for .9 is than the shaded amount for .3 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.

2. Shade the two Decimal Squares in #2 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 Decimal Square to show that .05 "fits into" or can be "subtracted from" .20 four times.

3. Using the blank Decimal Squares in #3, shade the tenths square for .6, and the hundredths square for .15, determine how many times bigger .6 is than .15, and write the division equation below the squares. Discuss student reasoning. Some students may see that .6 is 4 times bigger than .15, and that .6 ÷ .15 = 4. Others may visualize replacing the Decimal Square for .6 by a hundredths square for .60 and then divide the 60 shaded parts by the 15 shaded parts, that is, 60 ÷ 15 = 4, so .6 ÷ .15 = 4.

4. Shade the two Decimal Squares in #4 for .7 and .2 and determine how many times bigger the shaded amount of the .7 Decimal Square is than the shaded amount of the .2 Decimal Square. (3 and one-half or 3.5) Discuss student methods of obtaining this quotient. Some students may see that .2 "fits into" .7 three times and that the remaining .1 is half as big as .2. Others may divide 7 shaded parts by 2 shaded parts to obtain 3.5.

TEACHER MODELING/STUDENT COMMUNICATION

DIVISION 6.NS.3 Division of Decimals by Decimals

5. Shade the two Decimal Squares in #5 for .525 and .075 and determine how many times bigger the shaded amount of the .525 Decimal Square is than the shaded amount of the .075 Decimal Square. Discuss student methods of obtaining this quotient. Since we are comparing whole numbers of equal size parts, one approach is to divide 525 by 75. This can be done by using a calculator or by long division, as shown here; 525 ÷ 75 = 7, so .525 ÷ .075 = 7.)

Activity 2 Summarizing to See Patterns and Relationships

Look for patterns in our 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 by a whole numbers.

Activity 3 Approximating Quotients with Compatible Numbers

Approximate each quotient by finding convenient compatible number replacements. Answers may vary. a. .61 ÷ .2 ≈ .6 ÷ .2 = 3 b. .9 ÷ .4 ≈ .8 ÷ .4 = 2 c. .77 ÷ .23 ≈ .75 ÷ .25 = 3 d. .517 ÷ .48 ≈ .5 ÷ .5 = 1

Game In the game EXACT FITS, each player in turn takes two Decimal Squares of the same color (decimals with the same number of decimal places), selects the Decimal Square for the greater decimal, divides the number of shaded parts of this Decimal Square by the number of shaded parts of the other Decimal 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 6.NS.3 #27, #28 and #29 decimalsquares.com Laser Beams (In this game, mixed decimals are rounded to whole numbers, and if and their quotient can be computed in time, the asteroid will be destroyed before it passes out of view.)

INDEPENDENT PRACTICE AND ASSESSMENT