CECmath.45
TITLE: ESTIMATING WITH MONEY
AUTHOR: Louise Murphy, Scott Libby; Litchfield, AZ
GRADE LEVEL: 1-5
OVERVIEW:
Since I am not a classroom teacher it did not make
much "CENTS" to me to do a regular unit. This
mini-unit is to be used with Chapter I Students
(remedial students) in grades one through five. I
thought that it would be beneficial to intertwine the
same theme for all the grades at the same time since
many of the younger children have older family members
in our program also and this could lead to family math
discussions at home.
Many of the activities that the students would be
involved in would be an extension of the same skills
that children in the previous grades would be doing.
I chose estimation because it lends to developing
many different strategies to arrive at an answer. I
also feel that not enough time is spent on this
particular skill in the classroom. Another reason for
this choice is that sometimes it gives the less
mathematically inclined student a chance to shine and
this leads to a greater love of math. It is a fun unit
and the children enjoy learning the skills.
In using this mini-unit I would use a glass
container and pennies. The amount of pennies would be
determined by the grade level of the students. With
students in the first grade I would use just one guess
and this would be agreed upon by the team in the
cooperative groups. In the second and third grade I
would have a guess and a guesstimate. The guesstimate
would be a second guess based on some added information
or prompt. The fourth and fifth graders would give a
guess, a guesstimate, and an estimate. This would
provide additional data for use in the multi-faceted
activities in these upper grades.
This type of unit is non-threatening to the
students and everyone feels free to participate and
become totally involved. It also involves skills that
are needed in real-life situations.
GRADE ONE
The first graders would have a glass or plastic jar
containing between twenty and thirty pennies. Each
group would be told to put heads together and come up
with a guess. As the groups report their guess, the
group name and guess will be recorded by the teacher.
The information will be written down on a chart by the
teacher so that it can be used the following days.
ACTIVITIES AND PROCEDURES:
a) Show a one-to-one correspondence with unifix cubes
or blocks
b) Tell the number that comes before each team's
guess
c) Tell the number that comes after each team's guess
d) Find the guess on the big classroom number line
e) Find the guess on your own number line
f) Use the number line to show which number is
greater or less
g) Use heads and tails to show patterns
h) Make stacks of 5's and exchange for nickels
i) Use the pennies to show different ways to make a
number
j) Use pictures of things the children could buy for
those pennies and discuss prices
GRADE TWO
These students will work in six cooperative groups.
The number of pennies will be increased. The amount
should not exceed one hundred. The students will first
submit a group guess. The guesses will be recorded on
the board. Then the pennies will be arranged in piles
of about ten. The pennies will not be counted so the
number will fluctuate from eight to twelve. The groups
will then take a guesstimate. All this information
will be recorded on a large chart for use during the
activities.
ACTIVITIES AND PROCEDURES:
a) Order the numbers guessed
b) Tell if the numbers are odd or even
c) Use < and > to show comparisons
d) Tell how many tens and ones in each guess
e) Add ten to each guess
f) Discuss the range difference between the guess
column and the guesstimate column and discover why
the range is not so great
g) Make a large floor graph showing guesses
h) Find the sum of each group's guess and guesstimate
i) Find out how much the pennies weigh
j) Discuss what are reasonable and unreasonable
guesses not necessarily the groups' guesses
k) Decide what you could buy with those pennies
l) Show how you could make that amount with coins
other than pennies
m) Generate simple word problems using the data
recorded on the charts ( + and - )
GRADE THREE
The third graders could use an amount up to five
hundred pennies. They would first take group guesses.
Then about half of the pennies would be taken out of
the container and counted. It is necessary for the
class to decide on what looks like " about half". The
groups then make a guesstimate. All information is
recorded on a large chart for later use. It would be
beneficial at this grade level to make copies of the
charts for all the students.
ACTIVITIES AND PROCEDURES:
a) Order the numbers
b) Round the numbers to the nearest ten or hundred
c) Identify numbers by using place value
d) Express the guesses in different forms using the
cent sign and dollar sign
e) Show many ways to express the amounts using bills
and all kinds of coins
f) Find the difference between the guesses and
guesstimates
g) Write the guesses in Roman Numerals
h) Add 100 to each guess or guesstimate
i) Discuss what you could buy with that amount
j) Find the difference between the ranges in both
columns
k) Weigh the coins and discuss pounds and ounces
l) Generate words problems using the data
m) Make graphs on the computer using the data
GRADE FOUR
The fourth graders will use an amount of pennies up to
one thousand. The groups will make a guess. Then
about half of the pennies will be counted and weighed
and a group guesstimate will be given. Then one hundred
pennies will be counted and followed by a discussion of
the size of the pile. The remainder of the pennies
will be divided into piles of ABOUT one hundred. The
piles will be made by eye-balling and not counting.
ACTIVITIES AND PROCEDURES:
a) Ordering the numbers in all three columns
b) Find the range and find the differences in each
column
c) Identify numbers by place value
d) Round the numbers
e) Show the numbers in expanded notation
f) Find the multiples of 2,3,5, and 10
g) Multiply each guess by 10 or 100
h) Find the mean in each column
i) Find items in the newspaper that you could buy for
that amount of money
j) Write the amounts in words
k) Show half of the exact number of pennies
l) Tell how much of the real amount each of the six
groups would receive
m) Tell how much each group member would get
n) Generate problems using all four operations
o) Decide what you would buy if you had that money
GRADE FIVE
The initial activities for the guess, guesstimate and
estimate can be the same as those used with the fourth
grade classes, but you could increase the amount of
pennies being used. All the group activities that are
listed for fourth grade can be used and expanded upon
for the fifth graders.
ACTIVITIES AND PROCEDURES:
a) Show fractional parts of the whole group
b) Find the mean, mode and average
c) Use money to begin the study of decimals
d) Use scientific notation for expressing numbers
e) Use catalogs and newspapers to show what the money
could buy
f) Use a menu from a fast food restaurant and compute
your bill and find the change
g) Use calculators to work some word problems
h) Find out how many quarters you would have with
this amount of money
i) Find out how many dimes you would have
j) Explain good strategies for estimating.