ozora:

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

http://i40.tinypic.com/i42046.png\">

this problem is made up of a number of equations, similar to this type of problem sums:
Three boys, Alan, Bernard and Calvin sat for a test. The average score of Alan and Bernard was 78 marks, the average score of Bernard and Calvin was 74 marks and the average score of Alan and Calvin was 80 marks. Find the marks scored by each of them.

The key is to figure out how to combine specific equations together to eliminate some variables. Since this problem is about angles, we need to do some inference on angles before we begin to combine equations together.
In any angle problems, we always look for same angle properties. The key is to look for parallel sides or sides with same lengths (isosceles triangles). However, none of that exists in this diagram. However we do note that n = m.
The other property that we need to take note of, is that the interior angles of a triangle adds up to 180 or the interior angle of a quadrilateral adds up to 360. This property gives us another inference (on equation) that is not normally stated in the figure diagrams.
In this case, we don't have a quadrilateral shape, but we do have triangle shapes.
There are 3 triangles:
a + f + n = 180
p + e + d = 180
m + b + c = 180

so, with the 2 inferences that we have made (m=n, and the equations that gives 180), we can move on to the next step.

amongst all the 4 equations given in the problem sum, a + m = 135 is the most useful to start of with because it can be translated to a + n = 135, since m = n. (a + n) is useful because it gives us part of the equation that will lead us to 180. All we need now, is to link it to f.

We find that equation 4, will give us that variable, f. So, we will start off with adding equation 1 and equation 4, which will utilize our inference that
a + f + n = 180

http://i44.tinypic.com/33mr12o.png\">

there are other combinations to solve this, but the main idea is to make the necessary inferences on angles and interior angles of a triangle, and then look for equations with variables that will utilize the inferences.

Sun_2010:

cimman:

[quote=\"Sun_2010\"]Thanks tanker... Waiting to get one 4 DD and one 4 me ... :boogie: :boogie:

I am converting from iPhone to Samsung - my eyes have decided that size matters

another convert to the android camp. Good for you.

Thanks
can rely on you to help if I hit problems?
DD staunchly refuses to be associated with Apple

By the way I preordered yesterday.
Limited options - no choosing colour, and 16GB only


Ps - sorry tankee, iphone decided that your nick should be tanker :rotflmao:[/quote]No problem. Drop me a note anytime.

Sun_2010:

Thanks tanker... Waiting to get one 4 DD and one 4 me ... :boogie: :boogie:

I am converting from iPhone to Samsung - my eyes have decided that size matters

another convert to the android camp. Good for you.

CloudeeDaz:

dolphinsiah:

[quote=\"cimman\"]well, my way of seeking a Balance Life is to login to Kiasuparents forum in the wee hours of the morning. Works very well for me and I'll balance it off with 2 jugs of coffee in the morning.

Just Curious ...you are a Night Owl or a Early Riser?

Me ...I am a Early Riser...my day start before 4am....
Like a farmer.....

Have a great Weekend.... :xedfingers:

hihi
Just curious....what time do you go to bed? [/quote]some people just needs 5 hours of sleep. I can do that for a few days, but not on a long term basis. Maybe dolphin is like that.

dolphinsiah:

cimman:

well, my way of seeking a Balance Life is to login to Kiasuparents forum in the wee hours of the morning. Works very well for me and I'll balance it off with 2 jugs of coffee in the morning.

Just Curious ...you are a Night Owl or a Early Riser?

Me ...I am a Early Riser...my day start before 4am....
Like a farmer.....

Have a great Weekend.... :xedfingers:

I'm a late person. Just so happens I'm currently in a different timezone.

well, my way of seeking a Balance Life is to login to Kiasuparents forum in the wee hours of the morning. Works very well for me and I’ll balance it off with 2 jugs of coffee in the morning.

bookwormkids:

tianzhu:

[quote=\"bookwormkids\"]
2)
Catherine has a box containing some black and white counters. When she adds in 15 white counters, 65% of the counters in the box are black. If she adds in another 40 black counters, 75% of the counters in the box are black. How many white counters are there in the box at first?

Hi Tianzhu, my son would like to know:

When 40 black counters are added, the number of white counters remain unchanged. So when 15 white counters are added,did the number of black counters remain the same?

Thanks for your time.

[/quote]this is a query on problem interpretation. In the context of Singapore Maths Problem sums (regardless of Maths topic), whenever something is not mentioned, it has a value of 0. eg. Tom and Mary each brought $10 to school. During recess time, Tom spent $5 on food and $2 on stationary. How much did Mary have in the end ?

Notice that the problem sum gave information on how much Tom spent but no information on how Mary spent her money. If nothing was mentioned about Mary, we must assume Mary spent nothing.
Of course, in the real world, if you boss never mentioned anything about your bonus for the year, we just say the bonus is unknown and not assume there's no bonus. The language of Maths problem sum does not reflect how we normally express ourselves. Because of this, we must learn how Maths problem sums are typically structured (from a language viewpoint) and what needs to be inferred.

This problem belongs to a category of problems I call \"Double If\" problems. The word \"when\" can be substituted for \"if\".
In most Double If questions, the 2 If scenarios are not linked, except at the initial conditions (Before values). ie. if something happened to the white counters in the first scenario, then in the second scenario, we start off with a clean slate, ie. assume nothing happened to the white counters. Nothing is carried over from the 1st If scenario to the 2nd If scenario.

This is an unusual question because it carried information from the 1st If scenario to the 2nd If scenario. The clue to this lies in the keyword \"another\", \"...adds in another 40 black counters\". If the word \"another\" is used, it means there is a precedent, or a prior condition. The next question to ask is, what does the precedent refers to ? It refers to conditions in the 1st If scenario.

Which leads to the next question: What are the conditions for the 1st If scenario ? - no information was given about any activities on the black counters, and 15 white counters were added. This means that we must assume that 0 Black counters were added or removed, and 15 white counters were added.

In the 2nd If scenario, because of the word \"another\", we must provide the initial condition of 0 change in Black counters and 15 white counters added. On top of this, we have to add in 40 black counters.
http://i49.tinypic.com/iwjdjo.png\">

Contrast this to how the problem is normally worded:
Catherine has a box containing some black and white counters. When she adds in 15 white counters, 65% of the counters in the box are black. If she adds in 40 black counters, 75% of the counters in the box are black. How many white counters are there in the box at first?

in this case, because there is no keyword \"another\", the 2nd scenario is decoupled from the 1st scenario. We start off the 2nd IF scenario with a clean slate. 40 Black counters are added, and no White counters are added or removed. Notice the zero values in the boxes. There is no prior condition.
http://i47.tinypic.com/jqtijt.png\">

I call this concept, the \"Zero Assumption\" concept - if nothing is mentioned, assume 0 Change value. Problem interpretation concepts are an important component in my workshops.

elisammom:

Hi another question pls help


There are 4 times as many red pens as blue pens. 415 red pens and 46 blue pens were removed. As a result, the number of blue pens is 3 times as many as red pens. How many blue pens were there at first?
Tia

here's an alternative solution, if you're comfortable with simultaneous equations:
http://i49.tinypic.com/fjn81x.png\">

if not, you can try this variation:
http://i50.tinypic.com/e9giva.png\">

as you can see, it is just a variation of the same basic equations. When the values are tabulated, it is much easier to see all the possible relationships in the problem. If the total values for Pens are given, then that adds another dimension to the relationship. The table enables one to see 2 dimensional relationships ie. relationships concerning total Pens, and relationships concerning individual Red and Blue Pens.

In more complex problem sums, you will have 3 dimensional relationships:
There were 1000 students at the parade ground and indoor sports hall. 40% of the 600 students at the parade ground were girls. 60% of the students at the indoor sports hall were girls. After some students in both venues moved from one venue to the other, 30% of the students in the parade ground and 70% of the students at the indoor sports hall were girls. How many students were there in the indoor sports hall after the movement had taken place ? Ans: 450
when relationships are structured that you have the diagram below, and you have values linking the different layers, then it is a 3 dimensional problem.
http://i47.tinypic.com/n3126t.png\">
The table concept can be extended easily to support multi dimensional problems. If you're interested in finding out more about Table Heuristics, check out the workshops here: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=43&t=32278&start=190 , and drop me a PM.

Jamesbond:

http://i46.tinypic.com/161ant.jpg\">

Pl help....

the key thing to note in such problems is to figure out how to fit one shape onto another shape. That's easier said than done for some children who don't have the gift of spatial visualization. However, there are some general rules one can follow in the case of isosceles triangles and square.
http://i48.tinypic.com/1z4fnvb.png\">
Step 1: convert the triangles to a square. ie. a square is made up of 2 isosceles
triangles. The concept of tessellation is important here. Tessellate the triangle till you get a square.
http://i49.tinypic.com/dnha40.png\">

Step 2: draw lines to connect the vertices of the square together.
http://i46.tinypic.com/iqkgie.png\">

Step 3: from here, you should be able to pick out a unit shape (typically the smallest shape) that can be tessellated to fill the larger shape.
http://i47.tinypic.com/mvn347.jpg\">

The key point here is to tessellate the smaller regular shape to get the larger regular shape. You can view tessellation as a mirror reflection. Reflect the isosceles triangle till you get a square.
http://i47.tinypic.com/witu94.png\">

if you're ever stuck, start drawing lines to connect vertices of the regular shape, and then see if the smaller shapes that came out of that drawing can be tessellated to fill the larger shape.
I call this heuristic: Vertex Connection.

altp10:

Hi. I need help with the following Speed question.


Joel & Cliff ran a 100m race in which Joel crossed the finishing line just as Cliff reached the 90m mark.
a) Since Joel won the first race by 10m, he decided to start the second race 10m behind the starting line. Both boys ran at the same speed as in the first race. Who won the second race?
b) In the third race, Cliff started 10m ahead of the starting line. Again assuming that both boys ran at the same speed as in the first race, who was the winner of this race?

Thank you in advance.

in all speed problems, it is important to note that only 1 clock is used to measure time. As such, the key issue in speed problems is to know when to start and stop time measurement. Time is related to distance. For a given time, the distance traveled must be known. In more difficult speed problems, the start time and end times are vague and must be inferred based on logical reasoning and general knowledge. Luckily, there are only a few scenarios, so they can easily memorized.
In this case, general knowledge is called on to infer that both boys started the race at the same time. This is a simple inference, but nonetheless, it has to be noted it is an inference as it is not explicitly stated.

Speed problems are very similar to Rates problems as both deals with time. The difference between Rates and Speed is that Rates can be added (ie. Tap A and Tap B are turned on at the same time. John and Peter worked on the same Job at the same time), while Speed cannot.

In most Speed/Rates problems, there is a setup statement which tells us what is the rate or speed of the relevant objects. Thereafter, the rates or speed value do not change, unless it is explicitly stated. Learn to recognize the setup statements in each problem.
The first race is the setup statement, giving us information on the speed of Joel and Cliff. Thereafter, we copy the speed values to the 2nd and 3rd race.

http://i45.tinypic.com/au8576.png\"> http://i49.tinypic.com/2pz020k.png\">
http://i49.tinypic.com/14azjf9.png\">