TITLE: Bean toss
AUTHOR: Elinor H. Crecelius, Wyoming Girls School;
Sheridan, Wyoming
GRADE LEVEL: Appropriate for General Math, Pre-Algebra,
and Algebra I levels.
OVERVIEW: This is a hands-on way to introduce students to
addition of integers. The materials used are concrete
representations of positive and negative numbers. I use
lima beans which have been spray painted on 'one side only'
with a color like red. Each bean has a red and a white side
which will represent a positive and a negative side in the
following activity. One red paired with one white makes a
zero. (+1) + (-1) = 0.
PURPOSE: Many of my students are not abstract thinkers.
Using lima beans which have been spray painted on one side
to represent positive and negative numbers is a concrete
reference for the concept. The students then discover the
rules themselves which, I believe, leads to increased
comprehension and retention.
OBJECTIVE: Students will arrive at a verifiable rule, or
set of rules, to handle all addition situations with signed
numbers.
MATERIALS: 10 painted lima beans, 1 dixie cup for storing
and tossing the beans from, 1 sheet of paper, and 1 pencil
for each student.
ACTIVITIES AND PROCEDURES:
First students decide which color stands for negative
and which will be positive. For example, the white side is
positive, the red side is negative. The students are then
paired up and each tosses her beans while the other records
the score. This score is obtained by pairing the white and
red beans to make zeros and counting what is left. eg.
Toss=6 whites and 4 reds. The 4 reds pair up with 4 of the
whites to make zeros and 2 whites are left alone. The score
is +2 since white represents positive. (+6 + -4 = +2). I
have required varying time lengths for this part of the
activity. Those students who are in higher levels of math
tend to begin predicting the correct outcomes relatively
sooner than others, but at least 15 rounds of the toss game
should give enough material to see some patterns and arrive
at the set of rules.
After enough rounds of the game have occurred, we
discuss and record on the blackboard several examples as
equations. I emphasize that we are adding the numbers
together. The students are encouraged to look for patterns
and state a rule that we can use for all the examples that
would enable us to predict the outcome correctly. One
example would be: you can subtract the numbers and take the
sign of the largest.
TYING IT ALL TOGETHER:
To conclude this lesson, I discuss the real-life application
of addition of signed numbers by making word problems about
them. For example, I receive $4 in incentive pay. I owe
Holli $5 from last month when she bought me some yarn to
make Christmas gifts. What does my account look like now?
(+4) +(-5) = -1. I am $1 "in the red".
An extension of this activity would be to subtract,
multiply and divide using the lima beans. For subtraction,
I emphasize the ideas that opposites yield zero and that
subtraction means to "take away". For example, 7-3=? Start
with 7 white beans. Take away 3 white beans to leave as an
answer, (+4). another example would be: (-7) - (+3) =?
Start with 7 red beans. We want to take away 3 white ones,
but we have no white beans. We must add zeros in the form
of pairs of white and red beans until we have enough to take
3 whites away. We add 3 white and 3 red beans and take away
the 3 whites. There are a total of 10 red beans left which
represent (-10). The benefit of the beans in subtraction is
that the student can see that a negative sign and the
subtraction sign are 2 different things. Seeing the (-5) as
being red beans, and the -(-5) as meaning to take away 5 red
beans helps clarify the symbology that can stump students so
easily.
Click here to return to OFCN's Academy Curricular Exchange
Click here to return to OFCN's Academy
Click here to return to OFCN's Main Menu
John Kurilecjmk@ofcn.org