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Counting on the Pythabacus The triangular arrangement of beads on the Pythabacus displays rows of beads that demonstrate the progression of whole numbers from 1 to 10. Students can familiarize themselves with this progression by counting rows and combinations of these rows. Place the mouse arrow on a bead to see the number associated with it, when counting the beads in a row from left to right. Students can count up to 100, if they begin at the top row, count downward through each row , and then after counting the gold row, count upward through the rows until they reach the top again. In this way, students will count the brown beads twice and the gold beads once to reach a count of 100. |
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To Explore the Whole Numbers 0 to 9 Step1: Press enter until triangle is positioned against the right post. Step2: Left click the leftmost gold bead. Press Left Arrow (PLA). The number above the top most bead indicates the number of brown beads displaced with the gold bead. Step3: Left click the next leftmost bead. PLA Note the change in the number above and to the left. Step4: Left click the next bead, PLA and continue to the next bead. Note the finger counting method using the thumb to indicate 5. Numeral Formation |
Representing the Numbers 1 to 99 on Your Fingers and the Pythabacus Step1: Press enter until the triangle is positioned in the middle of the frame. A small pin clipped as shown will aide students. Step2: Left click the rightmost gold bead. PRA Left click the leftmost gold bead. PLA Step3: Left click the next rightmost gold bead. PRA Note the change in the number to the left and the associated hand that represent the 1's digits. Continue displacing the rightmost gold bead until the 1's digit is 4. Note that the number of brown beads in the diagonal column above the gold bead and leaning in the direction of displacement equal the 1's digit. Step4: Left click the leftmost bead of the triangle against the right post. PLA Continue displacing the leftmost gold beads of the triangle until the 1's digit is 9. |
Representing the Numbers 1 to 99 On Your Fingers And the Pythabacus Step5: Left click the 9 bead or rightmost gold bead PRA and it becomes the 0 bead. Then left click the next leftmost gold bead of the middle triangle. PLA Note that the left digit now displays the 10's. Step6: Repeat steps 3 through 5. Note the progression through the order of 10's. Step7: You can repeat steps until the digits display 99. Press escape to reset Pythabacus! |
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Adding And
Subtracting On The Centered Frame Step1: Click application and press enter until the triangle is positioned in the center of the frame. Step 2: Set up frame for representing numbers 1 to 99. See instruction above. Step 3: Represent a number such as 34 on the Pythabacus. |
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Addition Step 4: Place mouse over math sign to choose addition then click math sign. Every time you remove and place mouse over math sign the operation will change but only click math sign again to change the top digits, then to change bottom digit, you must return math sign to addition and click again. Step 5: Reposition beads on right or 1's side of frame to increase count of the bottom 1's. See counting above. The fingers below the equals bar will display the sum. Step 6: When push beads against the right post, the left side or 10's hand will disappear to indicate you must carry or increase the count of the beads on the left side of the frame by 1. When beads are repositioned correctly the 10's hand will reappear. Un-centered Method |
Subtraction Step 4: Place mouse over math sign to choose subtraction then click math sign. Every time you remove and place mouse over math sign the operation will change but only click math sign again to change the top digits, then to change bottom digit, you must return math sign to subtraction and click again. Step 5: Reposition beads on right or 1's side of frame to increase count by 10 minus the bottom 1's. The fingers below the equals bar will display the difference. Step 6: When you push beads on the right side against the center of the frame, the left side or 10's hand will disappear to indicate you must borrow or decrease the count of the beads on the left side of the frame by 1. When beads are repositioned correctly the 10's hand will reappear. |
Note 1: When you place mouse over math sign it will change to the
opposite sign. Note 2: In the problem above and to the left, to add on the centered frame you always reposition beads in turn to increase count by the bottom 1's digit. To subtract on the centered frame you always reposition beads in turn to increase count by 10 minus the bottom 1's digit. |