Count backwards in step of 5, starting at 31. What is the first negative number you come to?

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Jignesh77

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Good evening,

I hope someone would help we with the following question:

Count backwards in step of 5, starting at 31. What is the first negative number you come to? Try again, starting at 32. Use your answers to predict the first negative number if you started at 33 or 34. What happens if you start at 35 or 36. Try out different starting numbers until you can come up with a rule that works for any starting number. How would the rule change if you were counting backwards in steps of 10? Or steps of 2?

My son is in year 5 in the UK. They have learned about counting backwards and he can do that but neither him nor can we know how to solve this particular question, highlighted in bold (rule part). My wife said that the teacher told that this is just given as a challenging question and it's not in their syllabus (only counting backwards). Out of interest, I really want to know the answer.
We did the following:
31-5= 26, 26-5=21, 21-5=16, 16-5=11, 11-5=6, 6-5=1, 1-5=-4
32-5=27, 27-5=22, 22-5=17, 17-5=12, 12-5=7,7-5=2, 2-5= - 3
following the same pattern we got:
For 33 we get -2
34 we get -1
35 we get -5
36 we get -4
37 we get -3
38 we get -2
39 we get -1
40 we get -5
Thank you in advance
 
Jignesh77 said:
Good evening,

I hope someone would help we with the following question:

Count backwards in step of 5, starting at 31. What is the first negative number you come to? Try again, starting at 32. Use your answers to predict the first negative number if you started at 33 or 34. What happens if you start at 35 or 36. Try out different starting numbers until you can come up with a rule that works for any starting number. How would the rule change if you were counting backwards in steps of 10? Or steps of 2?

My son is in year 5 in the UK. They have learned about counting backwards and he can do that but neither him nor can we know how to solve this particular question, highlighted in bold (rule part). My wife said that the teacher told that this is just given as a challenging question and it's not in their syllabus (only counting backwards). Out of interest, I really want to know the answer.
We did the following:
31-5= 26, 26-5=21, 21-5=16, 16-5=11, 11-5=6, 6-5=1, 1-5=-4
32-5=27, 27-5=22, 22-5=17, 17-5=12, 12-5=7,7-5=2, 2-5= - 3
following the same pattern we got:
For 33 we get -2
34 we get -1
35 we get -5
36 we get -4
37 we get -3
38 we get -2
39 we get -1
40 we get -5
Thank you in advance
Click to expand...
Essentially what you did is find the remainder when performing a long division between the starting number and 5 and subtracting 5 from the remainder.

[imath] 33 = 6(5) + 3 \text{ and } 3 -5 = -2\\ \dots\\ 40 = 8(5) + 0 \text{ and } 0 -5 = -5 [/imath]
 
Thank you. English is not our first language. What does rule mean in the given context?
 
Jignesh77 said:
What does rule mean in the given context?
Click to expand...
In this context, "rule" refers to a pattern or formula that allows us to predict the first negative number we will come to when counting backward in any integer size steps (5,2,10, etc...), starting from any given number. It is a way to generalize the pattern we observed from counting backward in integer steps size starting from different numbers so that we can apply it to any starting number.

Perhaps filling in the blank for your son would be a good exercise.

To predict the first negative number encountered when counting backward in steps of a given size, we _____ the starting number by the step size using _____ _____ to obtain the _________. We then ________ the _________ from the step size. The resulting number is the first negative number encountered when counting backward in steps of the given size starting from the original number.
 
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