Multiplication Mountain |

With each fact you learn on the first level, you learn a fact you will find further up the mountain. For example, because 2 x 9 = 18, and 9 x 2 = 18, you learn a 2x fact and a 9x fact at the same time! Multiplication facts are easy to learn if you slowly but steadily climb the Multiplication Mountain. Start on the bottom and climb from left to right. With every step there is one less fact to learn, and by the time you’ve climbed the mountain and reached the sun... you only have one fact to learn: 12 x 12 is 144. Enjoy the climb! Each table has its own catchy song to help you memorize the facts. Lots
of musical styles are included to make the climb interesting and fun.
The times tables are presented in the order most students find easiest to learn. However, for some students, this exact order may not be the best. For example, some students may find the 4s easier than the 9s, or the 7s easier than the 8s. You can change the order to fit the needs of the student(s) with whom you are working. Numbers in parenthesis ( ) are versions with no answers. These fill-in-the-blanks versions can be used after the student has learned the particular time table or as a diagnostic test. Track 26 is an instrumental version of “Shake Up The Tables” where teacher and students can choose the facts and sing them with the musical accompaniment. You can use music in combination with other learning methods such as movement activities, pictures, and rhymes. This teaching guide presents activities to accommodate different learning styles. The ideas in this guide are suggestions. Feel free to adapt and change them to fit your environment and meet the needs of the students.
This song shows that multiplying by twos is the same as doubling a quantity. The melody is in the form of a 12 bar blues with a swinging shuffle beat. 2 x 1 is 2, 2 x 2 is 4, 2 x 3 is 6 The pattern stays stable through the whole twos table Repeat Tables Double three bees you get six bees buzzin’
The tens are among the easiest tables for children to learn. Multiplying by 10 is as easy as counting by 10s, and that’s how we open this reggae/calypso flavored tune.
The tens just trip right off of your tongue 10 x 1 is 10, 10 x 2 is 20, 10 x 3 is 30 Repeat Tables The tens just trip right off of your tongue The fives have a simple pattern that is easily learned. Here the facts are sung with a jazzy rhythm interspersed by improvised solos on piano, saxophone and trumpet. 5 x 1 is 5, 5 x 2 is 10, 5 x 3 is 15 Fives can be exciting Repeat Tables Fives can be exciting The elevens are another easy table to learn because of the double numbers that make up most of the answers. Only 3 facts need to be memorized: 11 x 10 = 110, 11 x 11 = 121, and 11 x 12 = 132. 11 x 1 is 11, 11 x 2 is 22, 11 x 3 is 33 Elevens have those doubles Repeat Verse One and Tables The rhythm of a waltz is a series of repeating 3 counts. It is an especially appropriate form for singing the threes table. The 3/4 time meter and a rich orchestral sound give a change of pace that helps achieve one of the important goals of this recording: to provide musical variety and make each table unique and memorable. 3 x 1 is 3, 3 x 2 is 6, 3 x 3 is 9 Repeat Verse One and Tables One, two, three, one, two, three The nines can be challenging, but when the pattern is recognized, the task becomes easy. With each answer, the tens digit goes up one and the ones digit goes down one – e.g. 18, 27, 36. Activities for showing this pattern are presented on page 11 of this guide. The musical style of the nines song is a fusion of rock and country - a form that is often called “rockabilly.” 9 x 1 is 9, 9 x 2 is 18, 9 x 3 is 27 The number nine is rolling down the line Repeat Tables and Verse 3 Got to keep on rollin’ so she won’t be late It’s easy to find things that come in groups of four: the legs on a chair, the paws on a bear, and the sides of a square. Couple this with the fact that most popular music is in 4/4 time and you have the theme of this song: fours are everywhere! With four counts to the bar 4 x 1 is 4, 4 x 2 is 8, 4 x 3 is 12 With four legs on a bed Repeat Verse 2 and Tables A guitar has six strings and is an ideal image to show multiplication by six. This song opens with the six strings of a guitar being plucked one at a time. More guitars are gradually added until six guitars (36 strings) are strumming. When the rest of the bluegrass band joins in, we’re ready to sing the six tables. 6 x 1 is 6, 6 x 2 is 12, 6 x 3 is 18 We’re learning multiples of six Repeat Tables and Last Verse This song is built around a series of electronic rhythm loops that combine to form a poly-rhythmic groove that motivates learners to memorize the 8s. It’s even more fun when you dance and sing along at the same time! 8 x 1 is 8, 8 x 2 is 16, 8 x 3 is 24 Repeat First Verse and Tables We shimmy, shimmy shake
The sevens are placed at the top of the mountain because they are often the hardest to learn. The melody gradually modulates upward to give the feeling of climbing a mountain. The style is “cool jazz” and the tempo is not too fast, providing ample response time to sing the answer. 7 x 1 is 7, 7 x 2 is 14, 7 x 3 is 21 Repeat First Verse and Tables Oh we’ve made it to the top of Multiplication Mountain When you’ve climbed the Multiplication Mountain, you’re ready to reach for the sun and do the twelves. Best of all, you’ve already learned the twelves on your journey up the mountain. Just reverse the multipliers with each fact you hear. The answer stays the same. For example, if you hear “2 x 12 is 24,” say, “12 x 2 is 24.” There is only one new fact you need to learn: 12 x 12 is 144. 1 x 12 is 12, 12 x 1 is 12 4 x 12 is 48, 12 x 4 is 48 7 x 12 is 84, 12 x 7 is 84 10 x 12 is 120, 12 x 10 is 120 The twelves are the tables This is another way of looking at the fours. It’s one of the two song ideas I had for presenting the fours tables. I couldn’t decide which approach I preferred so I polled the students and teachers. The vote came out almost even, so I decided to keep both and include this one as a bonus song. 4 x 1 is 4, 4 x 2 is 8, 4 x 3 is 12 Multiplication by four reveals Repeat Tables Multiplication by four reveals
The challenge with this song is to call out the answers when the facts are presented in a random order. This version has 24 of the easier facts. There are only 6 answers for all 24 facts: 12 18 20 24 30 40. You can easily put out number cards and play the game “Point To The Product”. The first goal of this song is to show that you can reverse the multipliers and the answer remains the same. Students listen to each problem then reverse the multipliers and sing it back. They call out the answer in the short instrumental break which follows. 2 x 6, 6 x 2, 10 x 4, 4 x 10, 2 x 9, 9 x 2 Repeat First Verse 2 x 12, 12 x 2, 10 x 3, 3 x 10, 5 x 4, 4 x 5
Students receive both visual and
auditory input as they read the lyric and sing
along with the music.Activity:All tablesBest for: Hang answers on the walls around
the room.Setting: Students listen to each multiplication
problem, then face and point to the product.Activity: Twos, Threes, Sevens, Eights, Nines,
and "Shake Up The Tables".Best for: 12 students seated on the floor, or in
chairs. Each student has a number card.Setting: Direct the students to: “Stand up
when the card you are holding answers aActivity:multiplication problem.” To make this an individual activity,
place the cards in a circle on the floor. The
student stands inside the circle of number
cards and holds up the card that answersVariation:each problem. All tables.Best for: The number cards are placed on the
floor in a random order in an open area.
One student stands by each number card.Setting: In this activity there are 12 HAND
WAVERS and 1 – 3 RUNNERS. The hand
wavers take turns waving hands when they are
standing by a number that answers a multi-plication problem. Aided by the hand wavers,
the runners run to the number that answers
each multiplication problem.Activity: This activity can be done individually
by placing the numbers in a line and having the
student run up and down the line standing by
the answer to each multiplication problem.
Place the numbers in order or mix them up to
make the challenge appropriate.Variation:All tablesBest for: 12 students in a line or circle. Each
student stands behind a number card.Setting: Students begin moving when the
answer they are standing by is called. Each
student moves the number of body parts that
corresponds to the number being multiplied
(multiplicand).Activity:For example, with the twos, each student shakes 2 hands. 2 x 1 is 2 – The student standing by the numeral 2 shakes 2 hands. 2 x 2 is 4 – The student behind the numeral 4 joins in so now 4 hands are moving. 2 x 3 is 6 – The student behind the numeral 3 joins in. Now there are 3 students, each shaking 2 hands for a total of 6 hands moving. This continues in order until 2 x 12, where 12 students are each shaking 2 hands for a total of 24 hands shaking. This creates a concrete visual of what 2 x 12 looks like. Twos: Shake hands. Fours: Run in
place and circle arms to symbolize the 4
wheels of a race car. This activity works well with
the song “Twelve Race Cars”. Fives: Nod head
and shake 2 hands while bouncing or jumping
on 2 feet. Tens: WiggleBest for:10 fingers. Children can also make spiders using 2 styrofoam balls (a large one for the abdomen and a smaller one for the head), and pipe cleaners for the legs. For ideas for making spiders go to: www.happalmer.com Cards with multiples of 8 are
placed on the floor in order: 8, 16, 24, 32, etc.
Each child stands behind a multiple of 8 and
holds a picture of a spider.Setting: Students are given the direction: "When the answer you are standing behind is
called, hold up your spider". The observers
see that each spider has 8 legs and view the
number of legs increasing until finally 12
spiders have 96 legs. During the chorus of the
song, the students wiggle their spiders and
make them "shimmy and shake".Activity: Threes: Tricycle (3 wheels);
Triangle (3 points or sides)
Fours: Horse (4 legs); Car (4 wheels)
Fives: Starfish (5 points)
Sixes: Guitar (6 strings)
Eights: Spider (8 legs);
Octopus (8 arms)
Tens: Set of 10 bowling pins
Twelves: Dozen donuts.Best for:
Two circles of number cards 0 – 9 are
arranged side by side. One person stands
inside each circle facing the front of the room.
The observers are seated behind also facing
the front of the room.Setting: The partners work together to display
the answer to each problem. The person on the
left picks up the tens digit and holds it overhead
and between the two circles. The person on the
right picks up the ones digit and holds it over
head and next to the tens digit.
For example, to answer 6 x 7, the person on
the left would hold up the 4 card and the
person on the right would hold up the 2 card.Activity:For one digit answers, the person on the left holds up the 0 number card. For example, to answer 3 x 2, the person on the left holds up the 0 card and the person on the right holds up the 6 to show the answer 06 like a digital watch. The fives are a good table to start with because the pattern is easy to recognize. The person on the left (tens digit) stands inside a circle of the numbers 0 – 6. This person will hold up each card once or twice and then go in order to the next number. The person on the right (ones digit) needs only 2 cards 0 and 5. This person will answer every fact by alternately holding up the 5 and 0 card. For the nines table, a
group of 18 students stand in 2
lines of 9 and face each other.
Each person holds a number card
0 – 9. The students come together
in pairs in the center to show the
answers. This is a good activity
for showing the patterns in the
9s table. One line goes up the
numbers in order and the other
goes down the line in order.
Three students need to come
out to make the last answer:
9 x 12 is 108.Variation: Fours, Fives, Sixes,
Sevens, Eights, and Nines.Best for: Number cards placed in a circle 3 – 5
feet in diameter.Setting:The student stands inside the circle
of numerals.
• For a one digit answer, stand by the
answer on one foot.
• For a two digit answer, place one foot by
the ones digit, and the other foot by the
tens digit.
• For a three digit answer, place one foot by
the ones digit, the other foot by the tens
digit and a hand by the hundreds digit.Activity: One person stands inside the circle
and the other person stands outside the circle.
The person inside the circle stands by the tens
digit and the person outside the circle stands
by the ones digit.*Variation:*Activity suggested by Alan Cononico, former supervisor
of Health and Physical Education, West Virginia.
Example: 2 x 3 = 6, 3 x 2 = 6 – The inverse of multiplication.Division – Any of the numbers that when multiplied together form a product.Factor – A mathematic operation by
which any number or quantity may be added
to itself any number of times. Multiplication is
repeated addition. 6 x 4 means 6 added
together 4 times or 6 + 6 + 6 + 6.Multiplication – A multiplication problem
with two factors and its answer. A multiplication
fact contains the multiplicand, multiplier and
product. 2 x 8 = 16.Multiplication Fact – A number that is to be multiplied
by another number. In the problem 2 x 8, 2 is
the multiplicand.Multiplicand – The number by which you multiply
another. In the problem 2 x 8, 8 is the multiplier.Multiplier – The result of multiplying two
numbers or factorsProduct – The same number multiplied by the numbers 1 – 12. For example, the
six times table family would be 6 x 1, 6 x 2,
6 x 3, 6 x 4, 6 x 5, all the way to 6 x 12.Times Table Family
Among the 0 through 10 times tables, these are the multiplication facts that cause most difficulty. 6 x 7 = 42, 6 x 8 = 48, 4 x 12 = 48, 7 x 7 = 49 6 x 9 = 54, 7 x 8 = 56, 7 x 9 = 63, 8 x 8 = 64, 8 x 9 = 72, 6 x 12 = 72, 9 x 9 = 81 Source: www.bbc.co.uk/skillswise Use the instrumental version
of “Shake Up The Tables” to sing these
challenging facts.Suggestion:
Megan Schulze,Bass: Hap Palmer Jim Garafalo, Hap PalmerAcoustic Guitars: Hap Palmer,
Larry GiannecchiniElectric Guitar, Mandolin: Larry GiannecchiniSaxophone, Flute: Hap PalmerTrombone: Claralyse PalmerPiano: Dean MoraHorn Section: West Valley HornsHorns Recorded at Tedesco StudioArranged and Produced by Hap Palmer and Miriam MayerEngineers: Hap Palmer,
Miriam MayerMix Engineer: Joe BelamyEducational Consultants: Susan Diblasio, Angelia Leung,
Kevin North, Angela Sandoval, Kelly SchulzeCo-lyricist of "Number Nine Rollin' Down The Line": Daniel PalmerGuide Book Editors: Paula Benjamin Little, Miriam Mayer,
Betty WilliamsDesigned and Illustrated by Carole Schumacher OnaitisGuide Layout: Stan Onaitis For more information, including a larger print version of this guide. Back to Top |