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… where kids learn a worldof math skills
Chris Biffle
Co-Founder, Whole Brain TeachingYucaipa, California
For free downloadsWholeBrainTeaching.com
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Introduction 4
Playing Smooth Bumper Planet 6
Handouts 21
Copyright b009, Chris Biffle.All rights reserved. Copies of this document may be reproduced for use byindividual teachers. However, no portion of this document may be sold, or offeredfor sale, without the written permission of the authors.
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In 1999 in the small town of Yucaipa, California, three
instructors met for a year to design the principles of a new teaching
system. Their goal was simple: create a method that was free,
effective and marvelously fun. In the last 10 years, over 8,000
educators representing a quarter of a million students have
attended Whole Brain Teaching (WBT) conferences. WBT has
spread across America and to more than 20 foreign countries.
Thousands of teachers have downloaded countless pages of free
ebooks from WholeBrainTeaching.com. WBT videos on YouTube and
TeacherTube have received over 1,00,000 views. The three
instructors, and their colleagues, are not done.
Originally designed to teach kindergarteners the remarkable
skill of counting to 1,000, Smoothy Bumper Planet developed into a
suite of techniques that teach new learners a host of math skills:
-- counting 1 to 1,000
-- counting by 10s to 1,000
-- counting by 100s to 1,000
-- skip counting to 100 by 2, 5, 9, 10
-- adding one and two digit numbers from 1 to 1,000
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-- subtracting one and two digit numbers from 1 to 1,000
-- using the concepts of more than and less than
-- understanding place value for 1s, 10s, and 100s
Many of the skills above are not learned until second or third
grade; our classroom experience indicates that a significant
percentage of kindergarten students playing Smoothy Bumper
Planet can master these concepts with remarkable speed.
In addition, Smoothy Bumper Planet provides a basis for a large
number of entertaining math games. Remarkably enough, all these
features can be provided to your kids on the front and back of one
sheet of paper. Not only is the Smoothy Bumper Planet exceedingly
versatile, but also it’s cheap!
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Playing Smoothy Bumper Planet
The current guide describes only two locations on Smoothy
Bumper Planet, the Number Wall and the Number Towers. Let’s
start with the Number Wall (a full size version is on page 20).
Note that some number blocks, the Smoothies, are flat to the
wall and some number blocks, the Bumpers, stick out.
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Smoothies are the easy numbers for kids to understand;
they all follow a simple pattern. Once your class learns to count
from 1 to 10, many of the rest of the numbers from 1 to 1,000 can
be easily understood. For example, 41 is simply a 4 and a 1; 962 is
simply a 9, a 6 and a 2, and so forth.
Bumpers, and there are only 7, are trickier. Think about it ...
fifteen should be “five-teen.” Thirty should be “three-ty.” The hard
numbers, the Bumpers that cause students the most difficulty, are:
11, 12, 13, 15, 20, 30, and 50.
We’ll begin by teaching your students to count to 30, and
then in the next few games, we’ll get them to 1,000.
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Counting 1 to 30
The first feature of the Number Wall to point out to students is
that there are two kinds of blocks, as I indicated above. Smoothies
are flat to the wall and Bumpers stick out.
Divide your class into pairs of weaker and stronger learners. If
you have an odd number of students, then you will pair with one of
your weaker learners. Proceed as follows (these lessons can be
spread over several weeks):
1. Explain the concept of the Smoothies and Bumpers and
then let students take turns pointing out Smoothies and Bumpers to
each other.
2. Name various Smoothies between 1 and 15 and ask the
groups to point at them.
3. Name various Bumpers between 1 and 15 and ask the
groups to point at them.
4. Tell your class that they should always begin counting
where the penguin sits on the 1 block.
5. When you are confident at least one kid in each group can
count to 15, have students take turns pointing at the numbers and
counting them aloud. When a child comes to a Bumper, she should
give it extra emphasis. Thus, counting should sound like “1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.” If you want to make this
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counting more energetic, and slightly crazed (we like slightly
crazed in WBT because it gives challenging students the opportunity
to be energetic, but on task), students can pound their fist on each
Bumper.
6. Repeat steps 2 to 5, adding additional numbers, until the
majority of your students can count to 30.
Counting 1 to 100
Next, teach your class to count by 10s to 100. Point out that
they should begin counting on the far right of the Number Wall
where the dog sits on 10 and count downward to where the monkey
is standing on the 100. (The dog and monkey were deliberately
included to give students visual reference points.)
Your class should pay special attention to the only Bumper left,
50.
When students can count 1 to 30 and by 10s to 100, use any
of the following games to get the majority of your class to 100:
--> Race Leader: Beginning at a random place on the Number
Wall, count aloud slowly; students repeat after you and follow along
with their fingers. Slowly, increase the cadence of your count, until
your class is racing to keep up. Let other students take the role of
Race Leader.
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--> Crazy Race Leader: For extra fun (and learning), a Race
Leader (you or a student) can count forward and then backward ...
and then forward again! What a race!
--> Hyper Race Leader: Hyper Race Leaders can count
forward, backward, faster, slower, faster ... and then jump to new
place on the wall and start counting again. Oh, my goodness!
Where will that Racer go next???
--> Square Dancin’ Hyper Race Leader: To add even more
instructional value, you can call out, “Let’s go forward to the right ...
let’s go back to the left, now, let’s go up two rows” and so forth.
Call out various directions, in various combinations and your
students will be square dancin’ with their fingers!!!
--> Guesser: Call out two numbers and have students point at
the smaller or the larger number. (This introduces the important
more than/less than concept needed from second grade onward.)
--> Finger Bender: Call out two, three, then four numbers,
randomly spaced on the Number Wall; students have to figure out
how to use fingers on each hand to touch all of them
simultaneously.
--> Mind Reader: Pick two numbers that are one number
apart, say 24 and 26. Ask students to find the “number in the
middle that I’m thinking of.”
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Skip Counting 100 to 1,000
Show your class the row of numbers across the bottom of the
wall, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000. To skip
count by 100s, students simply start at the cat who sits next to the
100 block and continue to the scrawny flower bush in front of the
1,000 block (the cat and the bush were included to give students
reference points.)
Counting 1 to 1,000
When the techniques above have been mastered, teaching
students to count from 1 to 1,000 is easy. Show your class that
numbers above 100, like 141, are formed by pointing at a number in
the lower row, 100, and then pointing at a number above, say 41.
Thus, not only are they learning how to form 141, but they’re also
learning an important addition concept.
Use any of the games in Counting 1 to 100 to increase
students ability to count to 1,000.
Create an award wall for students who are mastering math
skills. The highest award should be the 1,000 club; given any
number from 1 to 1,000 students earn entry in the club by counting
forward for a minute without error.
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Skip Counting by 2s, 5s, 9s, 10s, 100s
When students can count to 1,000 they have already
mastered skip counting by 10s and 100s.
To skip count by 2s, kids follow the darker or lighter number
blocks. (Note that students can begin either with 2 or 1, to skip
count even or odd numbers.)
Skip counting by 5s simply involves beginning in the middle of a
row, say at the 5 block, and ending at the end of a row, 10 and so
on down the wall.
Skip counting by 10s, as your class has learned already, is
nothing more than naming the numbers at the end of each row.
Skip counting by 100s was mastered by counting from the cat
to the scrawny flower bush in Counting 1 to 1,000.
Skip counting by 9s is slightly trickier, but can be mastered by
kindergarteners. Show your students that counting by 9s forms a
diagonal pattern across the number wall, 9, 18, 27, etc.
With a bit of practice, students will also be able to skip count
by 3, 4, 6, 7, 8 and 9. We suggest after learning 2s, 5s, and 10s,
students go on to 4s, because they will always end on blocks that
are the same color.
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Addition and Subtraction
When students have mastered some of the skills above, you
can begin to introduce simple addition and subtracting skills by
asking them to “walk” their fingers on the wall. Proceed as follows:
1. Clapper: Call out a number and ask students to walk their
fingers forward two blocks. Then when you clap your hands, they all
shout the number they “walked” to simultaneously. Make the game
more challenging by having students add 3, 4, 5, etc. When
students can add small numbers, then you can have them begin
practicing subtraction by “walking back” on the number wall.
2. Jumper: Point out the ease with which students can add or
subtract 10 to a number. They simply go down or up one row on
the wall, for example, from 17 down to 27, or from 36 up to 26.
Instead of walking, when they add or subtract 10, students should
“jump” their fingers high in the air and then land (as hard or soft as
you wish) on the new number.
For an extra challenge, teach students that whenever they add
9 to a number, they end up with one less, in the next row, than the
number they began with. Thus, adding 9 to 25, they end up with
34. So, 9 becomes a “backward diagonal” number.
Adding 11 to a number becomes a “forward diagonal.” Thus,
adding 11 to 55, students go down one row and then forward one
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block. Older students can learn that adding or subtracting 8 or
7 to a number also creates a diagonal pattern.
The more time your students spend on the Number Wall,
walking their fingers back and forth, leaping from one row to
another, using backward or forward diagonals, the more the numbers
themselves become visual, even tactile, rather than mere
abstractions.
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SuperSpeed Number Wall
Over the last 10 years, we at Whole Brain Teaching have found
no learning activities more motivating than exercises that involve
students in setting and breaking personal records. Our suite of
games, SuperSpeed Letters, SuperSpeed Numbers, SuperSpeed 100,
SuperSpeed 1000 and SuperSpeed Math have proved to be, for
thousands of teachers, highly motivating learning aids.
To play Superspeed Number Wall, arrange your class in groups of
two. If you have an odd number of students, you will pair with the
extra student. Without telling your pupils, be sure that a weaker
learner is always paired with a stronger learner.
Begin by saying something like the following, “We’re going to
play SuperSpeed Number Wall, a game you’ll love! When I say ‘go!’,
one person on your team reads the first number, then the other
person on the team reads the next number, and so on. Keep taking
turns. If your partner doesn’t know a number, ‘helpsies’ is allowed.
Say the number for him or her. Keep taking turns, counting as fast
as you can. I’ll say ‘stop!’ after a minute. Mark your team’s record on
the page and then I’ll give you another try for a minute. Start over
with the first number you read, but whoever started goes second
and whoever went second, now goes first. You’ll be trying to beat
your previous record. Tell your teammate right now how badly the
two of you want to keep breaking your record!”
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It doesn’t matter how many numbers your class has
mastered. You can limit the game to having students count from 1
to 20 as many times as possible in a minute, or, for advanced
students they can count as high as possible in a minute. For these
students, only one additional rule needs to be added. Whenever an
advanced team breaks their record they can start one row down the
next time they play. For example, Juan and Tasha start counting at
1, with Juan beginning. The two of them get to 92 in a minute.
Then Tasha starts the next time and the team reaches 104 after a
minute. Juan and Tasha have broken their own record. The next
time they play they can start 11, one row down, from 1. Thus,
advanced teams will climb upward through the number sequence.
Whenever students break a team record, and they will
frequently, you should encourage them to give themselves a merry
cheer.
Now, here is a very important point. Students love to play
SuperSpeed games because they love to set and break personal
records. It should be pointed out that teams are never competing
against each other, but against their own previous best effort.
Thus, the learning goal is set at exactly the right level, no matter
your students’ ability. The only standard they must exceed is the
one they set for themselves the last time they played the game.
Until you try SuperSpeed in class, you won’t believe the enthusiasm
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your students will have while playing. Students love the feeling
of being record breakers, and the unique structure of SuperSpeed
gives them this feeling over and over.
If you have gifted students who are not entirely happy working
with a slower partner, then set up two games, doubles and singles.
In doubles, two students work together to set and break records. In
singles, each students tries to break his or her personal record.
Place Value, 1s, 10s, 100s
The concept of place value is so important, and difficult, that
we created a second location of Smoothy Bumper Planet to help
early learners.
On the following page are the Number Towers (a full size
version is on page 21):
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The Number Tower on the right stands for 1s, the Number
Tower in the middle stands for 10s and the Number Tower on the
left stands for 100s. On the far left is a block with a 1 that will be
used, as you will see, to form 1,000.
Just as students begin counting on the block the penguin sat
on above the Number Wall, students begin counting on the block
the penguin sits on in the 1s Tower.
Students can form any number from 1 to 999 by pointing at
numbers in the appropriate Tower.
To form 19, a student would point at a 1 in the 10s Tower (in
the middle) and 9 in the 1s Tower (on the right).
To form 232, a student would point at a 2 in the 100s Tower,
a 3 in the 10s Tower and a 2 in the 1s Tower.
Students would count on the Number Towers by pointing at 1
in the 1s Tower and continuing to form numbers using the 3 Towers
until they reached 999.
To form 1,000, a student points at the 1 on the block on far
left, where the bear is standing, and then points at the zeros in the
three towers.
The great advantage to early learners of the Number Towers is
that they are not merely repeating a sequence, but creating
numbers. They will begin to learn that in a number like 463, each
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digit stands for a different value. This is a strange concept
which the Number Tower clarifies. In 463, 4 stands for 400, 6
stands for 60 and 3 stands for 3. Very strange! Once this concept
is understood, fundamental properties of numbers are less of a
mystery.
The easiest way to check your students’ understanding of
place value, is simply to call out a number and have students point
at the appropriate digits on the Number Towers. Thus, if you called
out 139, your students would point at a 1 in the 100s Tower, a 3 in
the 10s Tower and a 9 in the 1s Tower. Any student who can do
this correctly 10 times in a row, can become a teacher who will call
out numbers for a group of students.
You can also use the directions for SuperSpeed Number Wall on
the Number Towers. This will involved more advanced skills because
students will be making selections the involve place value, 1s, 10s
and 100s.
The next two pages contain full size versions of the NumberWall and Number Towers. (For extra fun, we’ve put a “hiddennumber” on both diagrams … your students will enjoy searching forthe “backwards 200.”)We’d love to hear about your students’experiences on Smoothy Bumper Planet. Write to me, Chris Biffle,directly at [email protected]. For more free downloads, or to postquestions about our methods or materials, go toWholeBrainTeaching.com.
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