#$&* course mth151 12/3/14 at 4:15 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `a** You have 20,000, represented by two pointing fingers, plus 3,000, represented by three lotus flowers, plus 100, represented by 1 scroll, 40, represented by four heel bones, and 5, represented by 5 sticks. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `qquery 4.1.30 lll sssss hhhh tt + ll sss sss hh ttt ttt Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the given sum. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: we can reorganize this first to find out how many of each symbol there is lll + ll + sssss + sss+ sss + hhhh + hh + tt+ ttt+ ttt llll + sssssssssss + hhhhhh + tttttttt there are 5 lotus flowers = 5*1000 there are 11 scrolls since 10 of those scrolls represent a lotus flower we can say that we have an extra lotus flower and just one scroll now there are 6 lotus flowers = 6*1000 = 6000 1 scroll = 1*100 = 100 6 heel bones = 6*10 = 60 8 tally sticks = 8*1 = 8 6000+100+60+8 =6,168 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** STUDENT SOLUTION USING THE WRONG METHODS: Pointing finger is 10,000 lotus flower is 1000 scroll is 100 heel bone is 10 tally stick is 1 So the first number is 3500 + 40 + 2 = 2542, the second number is 2626. Adding up 3542 + 2626 we get 6168. INSTRUCTOR COMMENT: This isn't how the Egyptians would have reasoned this problem out. They didn't have our decimal system, and you can't work the problem in our system unless they could do the same. We can use digits to refer to small numbers, understanding that they would also have had names for these digits, but we use our system any further than that. They would almost certainly have reasoned something like this: You have a total of tt ttt ttt, which we represent as 8 tally sticks. You have hhhh hh, which we represent as 6 heel bones. You have sssss sss sss, which is the same as l s or 1 lotus flower to be included in the next step with the other lotus flowers, and one scroll. You have lll ll in the original sum plus the l from the l ss you got in the previous step, for a total lll lll, which we see as six lotus flowers. So the sum is lll lll ss hhhh hh tt ttt ttt. 6 lotus flowers represents 6 * 1,000 = 6,000 in our decimal system. 1 scroll represents 1 * 100 = 100 in our decimal system. 6 heel bones represents 6 * 10 = 60 in our decimal system. 8 tally sticks represents 8 * 1 = 8 in our decimal system. The total is 6,000 + 100 + 60 + 8 = 6,168. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `qquery 4.1.30 ppp ll h ttt + pp l sssss hhhh hhhh tttt tttt YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: we can reorganize by grouping common symbols together ppp pp ll l h hhhh hhhh ttt tttt tttt sssss there are 5 pointing fingers 3 lotus flowers 9 heel bones 11 tally sticks 5 scrolls since 10 of those tally sticks equal a heel bone we add more more heel bone and are left with just one tally stick adding that heel bone now gives us 10 heel bones total and 10 heel bones equal one scroll so now we have 5 pointing fingers = 5*10,000= 50,000 3 lotus flowers = 3*1,000 = 3,000 6 scrolls = 6*100 = 600 1 tally stick = 1*1 = 1 53,601 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aCOMMON ERROR AND INSTRUCTOR RESPONSE: The numbers are 32,013 and 21,588. When we add these numbers we get 63,601. This is ppp ppp lll sss sss t. The Egyptians would have reasoned something like this: You have 11 tally sticks, which will be represented by a heel bone and a tally stick. You have nine heel bones in the sum, plus the one we get from the 10 tally sticks, so there are 10 heel bones. They will all be represented by a single scroll and no heel bones. You have five scrolls, which in addition to the one that now represents the 10 heel bones gives you six scrolls. There are three lotus flowers. There are five pointing fingers. So the sum is ppppp lll ssssss t. This can all be summarized as follows: ppp ll h ttt + pp l sssss hhhh hhhh tttt tttt = ppp pp ll l sssss hhhh hhhh h ttt tttt tttt = ppp pp ll l sssss hhhh hhhh hh t = ppp pp ll l sssss s t or ppppp lll ssssss t which stands for 5,168. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): im not sure where you are getting 5,168 as the total... pointing finger which are represented by p is 10,000 and we both argee that there are a total of 5 pointing fingers so at very lease you should have a total of 50,000 we both also agree that there are 3 lotus flowers. a lotus flower is 1000 so that should be 3,000 there are 6 scrolls according to both of our answers and a scroll represents 100. 6*100=600 since the heel bones became a scroll we are left with 0 for that spot which is the 10s after ten of the tally marks became a heel bone we were only left with 1 tally which represents the 1s your ending symbols are even right so you might want to check what you have down at the end ------------------------------------------------ Self-critique Rating:3
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Given Solution: `a** We use the Egyptian algorithm. The first column will represent the numbers 1, 2, 4, 8 and 16. The second column will contain 81, 162, 324, 648 and 1296. Written out this looks like 1 81 2 162 4 324 8 648 16 1296 32 2592. These numbers would of course have been written by the Egyptians using their notation. Doubling a number is done by doubling the number of tally sticks, heel bones, scrolls, etc., then regrouping if there are more than 10 in any group. Keeping our numbers in the first column, but understanding that they would have used their own notation, they would have written their second column as follows: 1 hhhh hhhh t 2 s hhh hhh tt 4 sss hh tttt 8 sss sss hh hh tttt tttt 16 l ss hh hh hh hh h ttt ttt 32 ll ss ss s hhhh hhhh h tt To make up the number 36 on the left we need to use the third and sixth rows (4 and 32). This means that we will add the corresponding numbers sss hh tttt and ll ss ss s hhhh hhhh h tt, which will give us ll ss ss s sss s h tttt tt, standing for 2916. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q4.1.36 Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the product 21 * 44. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 t 44 hhhh tttt 2 tt 88 hhhh hhhh tttt tttt 4 tttt 176 s hhhh hhh ttt ttt 8 tttt tttt 352 sss hhh hh tt 16 h ttt ttt 704 sss ssss tttt we can add 16+4+1 = 21 we must add the cooresponding rows hhhh tttt s hhhh hhh ttt ttt sss ssss tttt s sss ssss hhhh hhhh hhh tttt ttt ttt tttt 8 s 11 h = 1 s + 1h 14 t = 1 h + 4 t ssss ssss s h h tttt 9s = 9*100 = 900 2h = 2*10 = 20 4t = 4*1 = 4 924 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**The first column will represent the numbers 1, 2, 4, 8 and 16. The second column will contain 44, 88, 176, 352, and 704. Written out this looks like 1 44 2 88 4 176 8 352 16 704 These numbers would of course have been written by the Egyptians using their notation. Doubling a number is done by doubling the number of tally sticks, heel bones, scrolls, etc., then regrouping if there are more than 10 in any group. Keeping our numbers in the first column, but understanding that they would have used their own notation, we would have 1 hhhh tttt 2 hhhh hhhh tttt tttt 4 hhhh hhhh hhhh hhhh tttt tttt tttt tttt OR s hhh hhh h ttt ttt 8 ss hhh hhh hhh hhh hh ttt ttt ttt ttt OR sss hhhh h tt 16 sss sss hhhh h hhhh h tt tt OR sss sss s tt tt. To make up the number 21 on the left we need to use the first, third and fifth rows. This means that we will add the corresponding numbers 44, 176, 704. 44 is represented by hhhh tttt 176 is represented by s hhh hhh h ttt ttt }704 is represented by sss sss s tt tt. This gives us a total of sss sss s s hhh hhh h hhhh tt tt ttt ttt tttt, which is regrouped as sss sss s s s hh tttt. This represents 924. ** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q4.1.36 Using p, l, s, h, t for pointing finger, lotus flower, scroll, heel bone and tally stick explain how you obtained the product 21 * 44. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 1 t 44 hhhh tttt 2 tt 88 hhhh hhhh tttt tttt 4 tttt 176 s hhhh hhh ttt ttt 8 tttt tttt 352 sss hhh hh tt 16 h ttt ttt 704 sss ssss tttt we can add 16+4+1 = 21 we must add the cooresponding rows hhhh tttt s hhhh hhh ttt ttt sss ssss tttt s sss ssss hhhh hhhh hhh tttt ttt ttt tttt 8 s 11 h = 1 s + 1h 14 t = 1 h + 4 t ssss ssss s h h tttt 9s = 9*100 = 900 2h = 2*10 = 20 4t = 4*1 = 4 924 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**The first column will represent the numbers 1, 2, 4, 8 and 16. The second column will contain 44, 88, 176, 352, and 704. Written out this looks like 1 44 2 88 4 176 8 352 16 704 These numbers would of course have been written by the Egyptians using their notation. Doubling a number is done by doubling the number of tally sticks, heel bones, scrolls, etc., then regrouping if there are more than 10 in any group. Keeping our numbers in the first column, but understanding that they would have used their own notation, we would have 1 hhhh tttt 2 hhhh hhhh tttt tttt 4 hhhh hhhh hhhh hhhh tttt tttt tttt tttt OR s hhh hhh h ttt ttt 8 ss hhh hhh hhh hhh hh ttt ttt ttt ttt OR sss hhhh h tt 16 sss sss hhhh h hhhh h tt tt OR sss sss s tt tt. To make up the number 21 on the left we need to use the first, third and fifth rows. This means that we will add the corresponding numbers 44, 176, 704. 44 is represented by hhhh tttt 176 is represented by s hhh hhh h ttt ttt }704 is represented by sss sss s tt tt. This gives us a total of sss sss s s hhh hhh h hhhh tt tt ttt ttt tttt, which is regrouped as sss sss s s s hh tttt. This represents 924. ** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!