Download MULTIPLICATION 4.NF.4 Multiplication of Whole Numbers Times

MULTIPLICATION 4.NF.4
of Whole Numbers Times Unit Fractions
01*
Multiplication
Purpose:
Materials:
To illustrate and compute products of whole numbers times unit fractions
Fraction Bars and "Blank Bars Race Tracks" (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Using visual fraction models
1. Give the following information:
pencils
and paper
Fraction Bars
 Armari wants to make a batch of chocolate chip cookies and needs 1/3 cup of
chocolate chips.
a. How can the information in the problem be represented by a visual fraction
model? (One possibility is to use a bar with three equal parts to represent 1/3 cup. In
general, the model could be any diagram with three equal parts.)
b. If Armari makes two batches of chocolate chip cookies, what fraction of a cup of
chocolate chip cookies will be needed? (2/3 cup.)
c. If Armari decides to make four batches of chocolate chip cookies, what
amount of chocolate chips will be needed? (4/3 cups or 1 1/3 cups.)
d. How can this information be represented by an addition equation? (1/3 + 1/3 + 1/3 +
1/3 = 1 1/3. By a multiplication equation? (4 × 1/3 = 1 1/3.) Discuss that repeated
addition can be represented by multiplying by a whole number.
e. How can your visual fraction model help to show that 4 × 1/3 = 1 1/3? ) Discuss the
following two methods with the bars. Method 1: Using two blank bars with 3 equal
parts, each part can be labeled with one of the numbers #1, #2, #3, and #4 for the 4
batches of cookies to show the total is 1 whole bar and 1/3 of a bar.
pencils
and paper
Method 2: Placing the shaded amount of four copies of the 1/3 bar end-to-end shows that
the total shaded amount is 1 1/3 bars. Discuss the similarity between illustrating the
product of a whole number times a whole number and the product of a whole number
times a fraction. In both cases we use multiplication in place of repeated addition. For
example, 7 + 7 + 7 + 7 = 4 × 7; and 1/3 + 1/3 + 1/3 + 1/3 = 4 × 1/3. In both examples, the
first factor 4 in the product indicates the number of times the second factor should occur.
1 whole bar
1
3
+
1
3
+
1
3
+
1
3
=1
1
3
Blank
Bars Race
Tracks
pencils
and
paper
2. Distribute copies "Blank Bars Race Tracks" and ask each student to complete activity #1.
Discuss results.
3. Activities 2, 3, and 4 on this sheet involve race tracks for eighths bars, fifths bars, and thirds
bars. It is best if students work in pairs or small groups and each student uses their own copy
of the Blank Bars Race Track. Students will need some method of randomly selecting one of
the numbers from 1 through 6, and this can be done by rolling a die.
Each student in turn rolls a die for a number, writes one type of letter on the parts of the
bar for the number they obtained, writes the number from the die in a box beneath the
bars, and then completes the equation. For each new turn, a different letter should be
used in the parts of the bars as a record for checking the equations. Continue taking turns
until someone reaches the End or goes beyond.
After completion of each racetrack, discuss the results. You might ask questions, such as:
What is the fewest number of turns for finishing the race track? (Eighths Track, 5 turns; Fifths
Track, 3 turns; and Thirds Track, 2 turns.) Will a race usually be faster on the eighths track or
the fifths track? (Fifths Track.) etc. Students might want to design a racetrack that uses a
variety of different types of zero bars.
Activity 2 Solving word problems
1. If Peyton practices on the drums for 1/5 hour each day for 4 days, what is the total
amount of time spent practicing?
2. At a construction site, each hole being dug for posts requires 1/4 ton of dirt. If each hole is
the same size, how much dirt is required to fill 7 holes?
3. If one-tenth of each day at a summer camp is spent in boating activities, how much time is
spent in boating activities for each 7-day week?
4. Jamie runs around a racetrack, and each lap of the track is 1/8 mile. To remember how
many times she has run around the track, Jamie picks up a small pebble for each lap
completed. One day she picked up 25 pebbles. What was the distance Jamie ran on the track
for that day?
Activity 3 Computing products
Here are some products for practice. If the product is greater than 1, write the answer as a
mixed number.
1.
4×
5. 8 ×
1
3
2. 15 ×
1
12
3.
1
5
6. 11 ×
1
4
7. 20 ×
9×
1
2
1
14
INDEPENDENT PRACTICE and ASSESSMENT
Worksheet 4.NF.4 #1
10 ×
1
6
8. 12 ×
1
8
4.
4.NF.4 Name:
Date:____________________
Blank Bars Race Tracks
1. Leighton uses
1
4
of a pound of butter in making one batch of popcorn. Shade parts of the following bars
to represent the amount of butter for making 5 batches of popcorn and write the fraction for the total
amount to the right of the bars.
____
a. Complete the addition equation to show the amount of butter used for making 5 batches of popcorn.
1
4
+
1
4
+
1
4
+
1
4
+
1
4
=
b. Write a multiplication equation to show the total amount of butter Leighton used for making 5
batches of popcorn.
2. Three racetracks are shown in parts a, b, and c. Roll a die, and beginning at the Start, write the letter B
in each part of the bar for the number you obtained on your die. On your second turn, write the letter C in
the parts of the bar, and so forth, until you reach the End of the bar. After each of your turns, complete the
multiplication to show the results of your turn.
a. Eighth Race Track:
Start
End
Turn #1:
×
1
8
=
Turn #2:
×
1
8
=
Turn #3:
×
1
8
=
Turn #4:
×
1
8
=
Turn #5:
×
1
8
=
Turn #6:
×
1
8
=
b. Fifths Race Track:
Start
End
Turn #1:
×
1
5
=
Turn #2:
×
1
5
=
Turn #3:
×
1
5
=
Turn #4:
×
1
5
=
Turn #5:
×
1
5
=
Turn #6:
×
1
5
=
c. Thirds Race Track:
Start
Turn #1:
End
×
1
3
=
Turn #2:
×
1
3
=
Turn #3:
×
1
3
=
Turn #4:
×
1
3
=