Teaching Algebra with Manipulatives

Chapter
12
Probability and Statistics
Teaching Notes and Overview
Algebra Activity
Recording Sheet
Area Diagrams
(p. 291 of this booklet)
Use With the activity on page 651 in Lesson
12-4 of the Student Edition.
Objective Model the probability of two events
occurring at the same time using an area
diagram.
Materials
none
This activity involves using an area diagram to
model the probability of the two events, namely,
colored clips and metallic clips, at the same
time. Explain how the area diagram is
constructed. The 1 red and three blue clips
represent the colored clips. The probability of
drawing a red clip (1) from the colored clips
(4) is 1 , and drawing a blue clip (3) from the
4
colored clips (4) is 3 . The probability of drawing
4
a gold clip (1) from the metallic clips (3) is 1 3 ,
and drawing a silver clip (2) from the metallic
clips (3) is 2 .Point out that rectangle A
3
represents drawing 1 silver clip and 1 blue clip,
that is, 2 3 by 3 .Before you separate the class
4
into groups to complete the exercises, you may
want to go over what rectangles B, C, and D
represent.
Answers
See Teacher Wraparound Edition p. 651.
Algebra Activity
Probability
(pp. 292–293 of this booklet)
Use With Lesson 12-4.
Objective Find the probability of a compound
event.
Materials
classroom set of Algebra Activity worksheets
transparency master of Algebra Activity
3 coins per group of students
Pass out the Algebra Activity worksheets and 2
coins to each group. Ask the groups of students
to complete Exercise 1 on the worksheet. Then
record each group’s results on the transparency
master.
Compare the total number of HHs to the total
number of tosses. Use ratios and percents for
this comparison and record the results on the
transparency.
Make a scatter plot of each group’s results on
the transparency. Draw a line that is suggested
by the points.
Use the tree diagram on the transparency to
illustrate possible outcomes from the toss
of two coins. Have students complete
Exercises 2 and 3.
As an extension, ask students to predict
outcomes for the toss of 3 coins and perform a
similar experiment. Have students compare
their experimental results to this theoretical
value.
Answers
1. See students’ work.
2a. 1 4
9
2b.
2 0
2c. males 30 and over
3
3a.
1 0
9
3b.
4 0
3c. tells where or where not to concentrate
their efforts
© Glencoe\McGraw-Hill 288 Teaching Algebra with Manipulatives