Q&A - P4 Math

[MathIzzzFun]

kyy:

Hi,


I can understand where the 2+3=5 comes from now but I still can't grasp why
2 (left over) + 3 (short) = 5 --> so there are 5 friends.

Hi

You may want to try using physical buttons or beads to \"role-play\".

eg 1. I am in a room with some children, I have 2 sweets. If I want to give every child 1 sweet, I will need 3 more. How many children are in the room?

To find out how may children there are, we first find out how many sweets are needed. In this case, we have 2 and we need 3 more, so we need 5 in total. Since I need to give 1 sweet to each child, then there are 5 children ( 5 sweets total / 1 sweet per child).

eg 2. I am in a room with some children, I have 2 sweets. If I want to give every child 2 sweets, I will need 8 more. How many children are in the room?

Again, we need to find out how many sweets are needed so that every child gets 2 sweets. In this case, the total number of sweets needed is 2 (already have) + 8 (short) = 10. Since now each child gets 2 sweets, number of children = 10 sweets / 2 sweets per child = 5 children.

cheers.

[MathIzzzFun]

PiggyLalala:

MathIzzzFun:

Karen had some sweets to give to her friends. If she gave her friends 3 sweets each, she would have 2 sweets left over. But if she gave each friend 4 sweets, she would need another 3 sweets. How many sweets did Karen have?


My child got this sum wrong and she wrote her corrections as such:
No of Friends ---2+3=5
No. of Sweets 3x5+2 = 17

Neither she nor I can understand the logic behind the above number statements. Can someone help explain please?

Thanks

hi,

\"If she gave her friends 3 sweets each, she would have 2 sweets left over.\"
- imagine now each friend has 3 sweets and Karen has 2 sweets left.

To give each friend 4 sweets - ie to give 1 more to each friend, she needs 3 more sweets. This means she needs a total of 2 + 3= 5sweets so that she could give 1 more to each friend.

Total number of friends is therefore = 5

Total number of sweets = 5 (number of friends) x 3 (if she gives 3 sweets to each) + 2 (she has 2 sweets left) = 17

cheers.

Thank you MathsIzzzFun. Have come across this type of sums. Your solution provides another way of doing the question. Will explain using this method to my ds again. Hope he can grasp the concept better with this new method. Previously we have solved the question using model but ds cant grasp the concept fully. :thankyou: for your alternative method

u r welcome

cheers.

[MathIzzzFun]

MathIzzzFun:

kyy:

Hi,


I can understand where the 2+3=5 comes from now but I still can't grasp why
2 (left over) + 3 (short) = 5 --> so there are 5 friends.

Hi

You may want to try using physical buttons or beads to \"role-play\".

eg 1. I am in a room with some children, I have 2 sweets. If I want to give every child 1 sweet, I will need 3 more. How many children are in the room?

To find out how may children there are, we first find out how many sweets are needed. In this case, we have 2 and we need 3 more, so we need 5 in total. Since I need to give 1 sweet to each child, then there are 5 children ( 5 sweets total / 1 sweet per child).

eg 2. I am in a room with some children, I have 2 sweets. If I want to give every child 2 sweets, I will need 8 more. How many children are in the room?

Again, we need to find out how many sweets are needed so that every child gets 2 sweets. In this case, the total number of sweets needed is 2 (already have) + 8 (short) = 10. Since now each child gets 2 sweets, number of children = 10 sweets / 2 sweets per child = 5 children.

Another way to solve this problem is by listing:

http://i56.tinypic.com/e04sp2.jpg\">

cheers.

[kyy]

Hi MathIzzfun,


Thank you for your patience in trying to explain and your effort to illustrate in many ways.

I can understand the logic using the guess and check listing method. I can understand the logic of your explanation in your eg 1 and eg 2 based on those scenarios.

In the case of eg 2.
I am in a room with some children, I have 2 sweets. If I want to give every child 2 sweets, I will need 8 more. How many children are in the room?

I can understand the above but what I can’t grasp is how do I translate that to solving my problem when the total no of sweets is not known and we are dealing with the gaps and differences between two sets of 3s and 4s.

[usaik]

Hi,


I need help on the following?

Q. There are a total of 28 chickens and cows in a farm. If the total number of cows’ legs is 40 more than the total number of chickens’ legs. Find the number of chickens and cows in the farm.

If guess and check method is forbidden, what is the next easiest method this problem can be solved by a P4?

Appreciate advice very much. Thank you.

[MathIzzzFun]

usaik:

Hi,


I need help on the following?

Q. There are a total of 28 chickens and cows in a farm. If the total number of cows' legs is 40 more than the total number of chickens' legs. Find the number of chickens and cows in the farm.

If guess and check method is forbidden, what is the next easiest method this problem can be solved by a P4?

Appreciate advice very much. Thank you.

Hi

Assume all are cows.
Cow legs = 28 x 4 = 112
Chicken legs = 0
Difference = 112

If there is 1 chicken, then
Cow legs = 27 x 4 = 108
Chicken legs = 2
Difference = 108 - 2 = 106

112-106 = 6
So, for every 1 additional chicken, the difference reduce by 6.
112 - 40 = 72 --> need to reduce the difference by 72
72/6 = 12, so increase the number of chickens by 12.

So, we have 28-12 =16 cows, 12 chickens.

cheers.

[MathIzzzFun]

kyy:

Hi MathIzzfun,


Thank you for your patience in trying to explain and your effort to illustrate in many ways.

I can understand the logic using the guess and check listing method. I can understand the logic of your explanation in your eg 1 and eg 2 based on those scenarios.

In the case of eg 2.
I am in a room with some children, I have 2 sweets. If I want to give every child 2 sweets, I will need 8 more. How many children are in the room?

I can understand the above but what I can't grasp is how do I translate that to solving my problem when the total no of sweets is not known and we are dealing with the gaps and differences between two sets of 3s and 4s.

Hi

Let's look at the these questions:

1) I am in a room with some children, I have 2 sweets. If I want to give every child 1 sweet, I will need 3 more. How many children are in the room?

2) Karen had some sweets to give to her friends. If she gave her friends 3 sweets each, she would have 2 sweets left over. But if she gave each friend 4 sweets, she would need another 3 sweets. How many sweets did Karen have?

The two questions are actually the same, with different start point.

In question 1, all the children do not have any sweet.

In question 2, all the children do not have any sweets. But we can assume that the first statement was carried out - \"If she gave her friends 3 sweets each, she would have 2 sweets left over.\", and each friend has 3 sweets, and Karen has 2 sweets left. Now, compare this with question 1-

- Karen has 2 sweets, each friend has 3 sweets.
- I have 2 sweets, each child has no sweet.

The starting point is different - 3 sweets and 0 sweet.

Next, in question 1, it says \" if I give each child 1 sweet, I need 3 more\".

Karen's question says \"if she gave each friend 4 sweets, she would need another 3 sweets.\" ... since we already assume each friend has 3 sweets, we are now starting with each friend already having 3 sweets each. Now, to give each friend 4 sweets, means to give 1 sweet to each friend so that each friend will have a total of 4 sweets ie to give 1 sweet to each friend, Karen needs 3 more - this is the same as question 1.

So, Karen's question becomes the same as question 1 with a new starting point - so we can \"reduce\" Karen's question to question 1, and after solving, add 3 sweets to each friend/child and you will arrive the total number of 17 sweets.

cheers.

[usaik]

Hi MathIzzzFun,


Thank you for the working!

Regards

[MathIzzzFun]

usaik:

Hi MathIzzzFun,


Thank you for the working!

Regards

avec plaisir

cheers.

[kyy]

Hi,


I realised the thing that made me and many others confused was that we kept forgetting the actual number of children does not change and we do not know how many there are.

For visual/kinetic learners like us, using manipulatives really help one to see it clearly.

Thanks again