Not Just Math
- More Ideas, Gordon Scott, September, 1998.
Part 1. Math Related, p. 2 - 7.
(counting, number charts and lines, days of the week, months, practise
tests
and drills on basic facts, odd and even)
Part 2. Language Related, p. 8 - 12.
(syllables, vowels, spelling and story writing, activities for rhyming
words and
words with same beginnings, questioning)
Part 3. General, p. 13.
(left and right; north, south, east and west; jump turns with fractions
and
degrees)
Part 4. Science and More, p. 14 - 20.
(light and color, gravity and friction, balance, maps and story writing)
Part 5. Math Drill Tests (as in Part 1), p. 20, with map and
sample tests following p. 20.
Who might find this booklet useful?
Beginning and Experienced Teachers, Teachers of Teachers, Parents.
In this booklet I will try to describe more of what I used in my
classroom
that may be useful to you in teaching young children.
You may not wish to use the ideas as they are, but they could spark new
ideas of your
own that are better suited to you, and your teaching situation.
I’m including a set of speed tests for basic facts as I know they are
tedious to make up,
but I feel they are very useful to young children.
Some of what is here has been mentioned in my Games, Simple Math, and
Not So
Simple Math booklets.
The ideas in this booklet are not all mine. I’m sure many may have been
picked up
somewhere at sometime, and some I know I have modified from others.
Please contact me by mail or e-mail if you have any questions,
comments, or advice
for improvements.
As with my other booklets, my wife, Margaret, has also searched
carefully for errors
and poorly worded explanations. I’m sure we haven’t found them all.
My mailing and email addresses are on the home page.
1.
Part 1. Math Related:
Number Sense:
I can’t stress enough the importance of experiences with all kinds of
counting,
especially when it is related to a number line or chart. We want
children to be able to
count in a very simple sense, keeping track of what was already
counted, not skipping
numbers, and keeping them in order. But more than that we want children
to
appreciate the value of the number they count, and to relate it to all
the other numbers
they are familiar with.
I don’t intend to even try to tell all one might say about counting and
the development
of a sense of the value of numbers in relation to others. I’d just like
to offer a few more
ways of working with them that might give you a start.
When you look at two sets of randomly placed objects that are close in
number, and
over a certain size, say 35 and 37, you may not get a visual picture of
which is larger,
and by how much. Simple counting will tell you which is larger, but it
won’t show you.
Spotting the two numbers on a number chart from 0 to 100, or a number
line from 0 to
200+ will give a visual picture of the difference, and will reinforce
an understanding of
the ordered growth of numbers.
So will arranging the two groups in an ordered way so they can easily
be compared.
Lining up the two sets so that one can see that 37 has two more than 35
is a
worthwhile experience.
Placing the objects in groups of ten, with some left over is also
valuable.
I’ve described in my other booklets how I made much use of common egg
cartons, laid
out in two rows of 6. I cut off two egg places so the carton would hold
10 small objects
in two rows of 5. With these it is easy to compare two sets of objects
visually, and it
relates directly to the very important concept of place value.
Children can easily compare the sets of ten for most numbers they might
work with,
and if the amount of tens is the same in each number they need only
look into the
partially filled cartons, the ones, to compare the relative size of the
numbers.
Number lines and charts:
In my Simple Math booklet I’ve described the number line that I made
from 0 to 203 on
cash register roll paper. It ran all across the front of the classroom
and half way down
one side. From a stiff paper product I cut out some markers with
windows in them that
would slide along the line to show how many days we had been at school.
It was
simply a matter of leaving a flap that would fit behind the line, top
and bottom. The line
was stapled to the wall in the center so the the marker could slide all
along it, even
around the corner ( much to the delight of the children). I had to have
two markers,
one which served for the one and two place numbers, and another to
change to for the
three place numbers.
2.
With this permanent set of numbers
visible to all, and laid out in a line, we had a very
useful tool for a lot of different work. Together we did skip counting,
adding onto and
taking away from large numbers, multiplication, comparisons of value,
place value
work, and the concept of before, after and between. By thinking of the
line extending
around the room several times we could even get a sense of how really
big a
thousand would be.
Some teachers prefer to form the same kind of line as the days go by.
They start the
rolled up line at 0 and print on a new number each day, extending the
roll as they go.
The youngest children then have the advantage of seeing the numbers
printed out, but
the older children loose the advantage of having the full line to refer
to during the year.
I haven’t done this, or seen it used, but I believe that teachers who
aren’t able to have
a number line stuck up around the room could make a large number chart
to serve the
same purpose. It would have to go from 0 to beyond the normal school
year, and be
spaced out to allow up to three figures.
Some simple marker could be used to move along the chart if the numbers
were
already printed.
My classroom also had a 0 to 99 chart we used to see the regular
repeated patterns
the numbers form. It was especially useful to reinforce what always
came before and
after a number of tens. Some children have difficulty learning what
comes before
numbers like 40.
We also used it for place value work. The numbers in each of the ten’s
and one’s
places were printed with different colors. One’s place numbers were
black and ten’s
place numbers were red. 0 to 9 in the first row were written as 00, 01,
02, ... This
made it easy to see place value at work, and completed some interesting
patterns.
Each morning we started the day by moving the marker along the number
line. We
also added a 1in. snap together cube to a pile we kept on a high ledge.
Ones were
loose. Sets of ten snapped together in lines. Ten lines became a square
of 100.
On a steel chalkboard close to these blocks I first printed a column of
0 to 9, with 9 at
the top, and had a magnetic marker to place beside the number of days
at school.
I printed a second 0 to 9 column to the left to go beyond 9, and used a
different marker
to show the number of tens. Eventually a third column had to be added.
This activity clearly demonstrated the repeated movement through the
one’s place
numbers before a new ten’s place number could be used.
Along with this we learned the use of tally marks, four vertical lines,
one for each day,
and a diagonal line across them for the fifth day. When we had two sets
of 5 we
circled them and noted that we had a set of 10. Comparisons were made
with hands
and fingers.
We didn’t always use tally marks; just often enough to keep the
children familiar with
them since they are sometimes useful.
3.
Days of the week and Months of the Year:
Sitting on the chalk ledge of the classroom we had a board, about
the size of a large
calendar page, covered in colorful plastic, into which 5 rows of 7
screw hooks had
been placed. I had a set of round tags with holes in them so they could
be hung from
the hooks. The tags were used to show 1 to 31. Above each column of
hooks was a
label for each of the days of the week.
This way we could keep track of the days of the month by adding the
appropriate tag
under the day of the week. (I made some special tags for certain
holidays.)
A retiring teacher whose husband had made it for her gave me this
calendar, and I
passed it on when I retired.
Another way of doing this might be to make up and duplicate a calendar
page, withou
t the numbers or the month written on it. This way the children could
see the numbers
being formed and progressing through the weeks and the month.
For the youngest children I had a large chart with the days of the
weeks printed on it.
For all the children, I used a set of three stiff paper pockets set
along the chalk ledge.
‘Yesterday’, ‘Today’, and ‘Tomorrow’ were printed on the pockets. I
also had a set of 7
large strips on which were printed the days of the week.
Each day we moved these days of the week to the appropriate pocket. The
day of the
week strips moved from ‘Tomorrow’ to ‘Today’ to ‘Yesterday’. This
allowed us to
develop a sense of future, present, and past. We were also able to talk
about terms
such as the day after tomorrow, and the day before yesterday.
These pockets were simply formed by folding the bottom of a larger
sheet in accordion
(or pleated skirt) fashion and stapling the ends to make a durable
pocket.
We also had a large chart to show the months of the year in two columns
of 6 each,
with the number of the month printed beside each. At the bottom of this
chart was a
space to show ‘Last Month’, ‘This Month’, and ‘Next Month’. I simply
cut out two slits
after each so one of a set of 12 strips, each with a month printed on
it, could be tucked
into the slits to hold it in place for the month. Of course this
allowed us to discuss past,
present, and future again, as well as the month before last month, and
the month after
next month.
Tests and drills on basic facts:
The word “test” seems to bring out negative emotions in some
people.
The tests I refer to here are not those primarily used for reporting
purposes.
I do believe that the frequent use of tests on basic facts can have
positive results for
children. Arithmetic or math soon requires students to be both quick
and accurate.
Some children are not inclined to be one, or the other, or both. Tests
do give them a
reason to be quick and accurate. They can become a reality in their
lives. Children
can come to see in other children the results of trying hard, and learn
to be proud of
their best efforts.
4.
If you’ve ever taken part in a Kindergarten sports day you may have
seen children who
already are willing to put out a great deal of energy to do their best.
But many children
will only go through the motions of doing a task with the least effort.
Ask them to try to
jump far and they will just jump, where a few will surprise you.
The tests I used for basic facts were all of the same format, and they
were of different
degrees of difficulty. All the children soon became familiar with the
task, and it was
possible to give different tests that suited their ability, or grade
level, at the same time.
There was a column of 20 questions, such as 4 + 3 = ___ , on a narrow
sheet of paper,
all in horizontal form, and all with the missing number in the same
place. They would
be handed out, upside down, and all children would wait with their
pencils ready for
the signal to start. When I gave the signal to start I would note the
time.
The children would print their name at the top and start to print the
answers. Whether
they checked their work or not was up to them.
(Early on I might leave charts or chalkboard notes up that would allow
them to look up
at the answers. They soon found this was not the best thing to do since
it took more
time than searching one’s memory.)
I stayed at the front, watched for inappropriate behavior, and waited
for children to
bring their finished papers to me. There was a space at the bottom of
the test where I
could print the number of minutes they had finished in. After 5 minutes
I called in any
remaining papers and marked them as 5+ minutes.
The papers were easily marked over my lunch hour as I had an answer key
to set the
tests on top of, and I didn’t bother to mark correct answers. I just
drew a line through
incorrect answers. Numbers that were unclear were also marked wrong.
After lunch, and before the tests were returned, I wrote the names of
the children with
perfect scores on the chalkboard under the headings: 2 minutes, 3
minutes, 4 minutes,
5 minutes, indicating the amount of time it took them to finish. The
tests were then
handed back so they could be finished or corrected, and help was
available.
Some may feel this is very harsh treatment, but it gave us an
opportunity to discuss the
speed at which we all are able to do things. Foot races were a common
topic.
Children out on the playground soon learn who they can catch, and who
they can’t.
I also used it as a time to talk about the purpose of speed and
accuracy in math facts,
and how I knew from experience that we would be able to watch the whole
class
improve. Probably on the second day of this some children would hand in
a perfect
paper and take one minute less to do it. Then if their name were up,
say under the
heading “4 minutes”, I could erase their name and print it under “3
minutes”. There it
would stay, unless they could show that they could improve to under 2
minutes.
Names never came off the list, and never moved back to a slower time,
unless
someone was caught copying answers from others too often.
5.
Children who used their fingers, or
looked about the room for other aids, soon found
that memory was fastest.
I’ll always remember one very bright little lady who suddenly did
poorly when I
covered up some charts she had been using.
“Well, I guess I’ll have to learn those,” she said.
And I’ll always remember Betty, in Grade Two, who could get 20 correct
answers in
under a minute, faster that her teacher could ever hope to go.
I hope you can see these were not troublesome tests. They only took a
few minutes to
mark. The majority were perfect. Few corrections were required, and if
time were
short, then children with perfect scores were delighted to help others
and mark
corrections. Those doing well were eager to help others improve.
N.B: Sample drill tests on loose sheets will be given
at the end of this booklet.
Drills are also important. Drills are activities children might
do as a class activity, but
probably more often as a individual or group activity. They might be
oral, or written.
The purpose of a drill activity is for children to attempt to get the
correct answer, and if
their answer is incorrect, to see or hear the correct answer as soon as
possible.
In a drill, having the answer given to you is, in a sense, more
valuable than getting the
correct answer. Being given the correct answer tells children two
things, what is
correct and what is not correct.
Long ago my school district made up sturdy cards with about 50
questions on each, all
in vertical format. Under each was a hole where the answer should be. A
child placed
the card on a blank sheet of the same size, printed the answer in the
space created by
the hole, and, when finished, turned the card over, keeping it the same
way up.
On the back of the card, above each hole, was written the question as
well as the
answer. This meant the children could mark and correct their own
answers which
appeared in the holes. Even children more inclined to do things the
easiest way were
forced to look at the question and its correct answer.
I have seen a number of similar drill cards, each card being graded as
to difficulty and
number operation.
Another type of drill I used required papers similar to that used for
speed and accuracy
tests. This time there were two spaces after each incomplete number
sentence. The
first was for the child’s answer. The second was for the child to write
the answer I gave
if the child had not written his/hers yet, or had written an incorrect
answer.
eg. 6 + 3 = _____ (child’s) _____ (teacher’s)
This drill had the advantage of a very quick reinforcement for the
correct answer, and
correction for wrong answers.
It also forced a certain speed as the teacher read out the question,
paused a short
time, then reread the question and filled in the answer.
6.
There was then a pause while some
wrote in the teacher’s space before going on. At
the end the children could count up the number of answers they got on
their own.
Even those who wrote the teacher’s answer in their own space had the
benefit of
seeing, hearing, and writing the correct answer to the question.
There are many commercially available drill cards and they come in many
forms.
Some drill cards are very easy to make or have made by parents or older
children.
If you’ve read my Simple Math booklet you know my approach to basic
math facts was
based on a very simple format. “Part + Part = Whole” and “Whole - Part
= Part”
covered all the basic addition and subtraction situations. “Factor x
Factor = Whole”
and “Whole -:- Factor = Factor” covered all the basic multiplication
and division
situations. ( -:- is the closest I can come to a division symbol.)
For this reason I made up drill cards that had a triangular form, with
the “Whole” at the
top and the “Part” or “Factor” on each side at the bottom. I didn’t,
but I could have,
made the drill cards out of triangular pieces.
A drill card would contain 2 of the 3 related numbers on one side, with
the third as a
blank or question mark. On the other side the full three were given so
children could
be challenged by others to come up with the third number in the set, or
could work on
their own.
I know now that I should have made similar cards, but with all three
numbers on one
side. On the other would have been the four (or two) number sentences
the three
related numbers on the other side could make. A child would be
challenged to come
up with those four (or two) sentences.
Odd and Even Numbers (those made with sets of two):
Paying attention to this distinction between numbers early on can
be very useful later.
(Even numbers are also easily related to multiplication.)
Children can learn to make an easy check of answers to simple or
complex questions.
At a glance one can tell this answer is incorrect: 4187 + 2948 = 7134.
You don’t even
have to know 7 + 8 = 15. You just have to see that it is an ‘odd + even
= odd’ situation,
and the 4 in the one’s place of the answer isn’t odd.
Children can soon work out the statements about even and odd numbers
that always
will be true for the whole numbers they work with.
I believe it is good for children to know that math has such simple
ideas that always
are true.
Using ‘o’ for odd and ‘e’ for even, you can soon discover that:
o + o = e, o + e = o, e + o = o, e + e = e, and o - o = e, o - e = o, e
- o = o, e - e = e.
o x o = o, o x e = e, e x o = e, e x e = e, and o -:- o = o, e -:- o =
e.
It can help to think of odd numbers as being an even number, plus one
more.
7.