Lesson 1 - Quantity Each Product Concept



1) One item

Let's start with one example.

https://s9.postimg.cc/cwdrzocfz/20180403_100731-1.jpg\">

We shall view it as picture.

https://s9.postimg.cc/vopn3b6a7/20180403_101112-1.jpg\">

There are two totals here, Quantity Total and Product Total.

Quantity Total means total boxes, 12.

Product Total means total weight, 1200g.

This is the characteristic of this table. We are dealing in two measurements.

We shall now put the information into the table.

https://s9.postimg.cc/d9565ya67/20180403_100731-2.jpg\">

So the total weight is 1200 g or 1.2 kg.

Let's do some problem sums.

https://s9.postimg.cc/uay07hc0f/20180403_101724-1.jpg\">

https://s9.postimg.cc/s6dn6exj3/20180403_101733-1.jpg\">

https://s9.postimg.cc/svwfirqcv/20180403_101739-1.jpg\">

https://s9.postimg.cc/5ufud164v/20180403_101744-1.jpg\">




2) Two different items

In actual problem sums, we may deal with two different items.

Let's look at this example.

https://s9.postimg.cc/jo4724gqn/20180403_102304-1.jpg\">

Now we have Cups at $3 each and Teapots at $10 each.

We shall view this as picture.

https://s9.postimg.cc/q1ta5e8rz/20180403_102400-1.jpg\">

We shall put the information into the table.

https://s9.postimg.cc/rguuu6mqn/20180403_102304-2.jpg\">

The workings will be as follow.

https://s9.postimg.cc/at3crozov/20180403_102304-3.jpg\">


Let's do some problem sums.

https://s9.postimg.cc/uay07p1sf/20180403_102804-1.jpg\">

https://s9.postimg.cc/vd86q901b/20180403_102808-1.jpg\">

https://s9.postimg.cc/ywu4g1v1b/20180403_102814-1.jpg\">

https://s9.postimg.cc/jo472agsf/20180403_102818-1.jpg\">




3) To find the Quantity or Each.


As we have learnt, Product = Quantity × Each,
we shall find the reverse.

https://s9.postimg.cc/5hog73nxr/20180403_103110-1.jpg\">

Let's look at this example.

https://s9.postimg.cc/xhsjrfh4f/20180403_103231-1.jpg\">

First, we shall view it as picture.

https://s9.postimg.cc/4s5nurxov/20180403_103110-2.jpg\">

Next, we shall put the information into the table.

https://s9.postimg.cc/ilu0judfj/20180403_103231-2.jpg\">

Then we shall solve the unknowns.

https://s9.postimg.cc/n7q4s6jj3/20180403_103231-3.jpg\">


Easy? Let's practice on the following problem sums.

https://s9.postimg.cc/ozj3n7kxb/20180403_103626-1.jpg\">

https://s9.postimg.cc/wfid90gcf/20180403_103632-1.jpg\">

https://s9.postimg.cc/6wq0w0c7z/20180403_103637-1.jpg\">

https://s9.postimg.cc/a3kkfmoy7/20180403_103642-1.jpg\">



4) Three different items

Let's order some food.

https://s9.postimg.cc/5hog7bdpr/20180403_104002-1.jpg\">

In picture, it looks like this.

https://s9.postimg.cc/ywu4gbxov/20180403_103933-1.jpg\">

We shall now put the information into the table.

https://s9.postimg.cc/svwfj9qi7/20180403_104002-2.jpg\">

Let's do the following workings.

https://s9.postimg.cc/qekoc0ebj/20180403_104002-3.jpg\">

Let's start our last problem solving session.

https://s9.postimg.cc/ws9rfati7/20180403_104357-1.jpg\">

https://s9.postimg.cc/pp1vzp3i7/20180403_104406-1.jpg\">

https://s9.postimg.cc/jbcswfqwf/20180403_104412-1.jpg\">

https://s9.postimg.cc/9qt69kgzz/20180403_104419-1.jpg\">


We have come to the end of this lesson.
We shall learn how to solve QEP in Units and Numbers in the following lessons.

This is the Module 4 of Table Method.


Readers are advice to read the first 3 modules before reading this module.

Table Method - A logical way to do Primary School Maths.
Table Method 2 - Quantity Amount Table
Table Method 3 - Before After Table

In this module, we are dealing with two measurements, Quantity and Product.

Quantity means number of items or people.

Each means how much or how heavy of an item. It may means an average.

Product means the multiplication of Quantity and Each. It is also a measurement of Amount or Mass or Volume.

In the next few lessons, we shall learn how to use this table to solve problem sums.

Lesson 5 - Before After Ratio


In lesson 3, we have learnt about Equal After.
In lesson 4, we have learnt about Unequal After.

In this lesson, we shall learn about After in Ratio.

Let's look at one example.

https://s9.postimg.org/e7rewpxhb/20180402_093246-1.jpg\">

Alan has 5 times as many kites as Ben.
In order to balance up both side, we shall divide Alan's amount by 5, and divide Ben's amount by 1.

https://s9.postimg.org/e7rewrfhr/20180402_093246-2.jpg\">

1) Cross Multiplication Method

We shall first cross multiply 1 to the left side, and then cross multiply 5 to the right.

https://s9.postimg.org/7haxnfn7z/20180402_094234-1.jpg\">

Let's try some exercise.

https://s9.postimg.org/ky7w6dpun/20180402_094402-1.jpg\">

https://s9.postimg.org/gp3646zfz/20180402_094402-2.jpg\">

https://s9.postimg.org/v8ab5m0an/20180402_094402-3.jpg\">

https://s9.postimg.org/wakho53of/20180402_094402-4.jpg\">



2) Ratio Start

Let's review the first example.

https://s9.postimg.org/e7rewpxhb/20180402_093246-1.jpg\">

We shall view this in picture.

https://s9.postimg.org/74jjhczu7/20180402_094726-1.jpg\">

We shall now put it into the table.

https://s9.postimg.org/y2dgj3zwv/20180402_093246-3.jpg\">

Since the After are in Ratio, we shall write the After in fraction. Then we shall cross multiply the denominators.

https://s9.postimg.org/uiritcf7j/20180402_093246-4.jpg\">

Let's try some problem sums.

https://s9.postimg.org/rpyb8rwpb/20180402_095059-1.jpg\">

https://s9.postimg.org/4ohq30hm7/20180402_095105-1.jpg\">

https://s9.postimg.org/sfh3l4pj3/20180402_095110-1.jpg\">

https://s9.postimg.org/h34i3c1en/20180402_095115-1.jpg\">



3) The Comparison Start

Let's look at the following example.

https://s9.postimg.org/8xmg58xr3/20180402_095427-1.jpg\">

We shall start in Comparison Method. We shall first view it in picture.

https://s9.postimg.org/9n58hngb3/20180402_095436-1.jpg\">

We shall now put the information into the table.

https://s9.postimg.org/fo2xeqq2n/20180402_095427-2.jpg\">

We shall write the equation in fraction and do the cross multiplication.

https://s9.postimg.org/woltnfxz3/20180402_095427-3.jpg\">

Easy? Let's try some problem sums.

https://s9.postimg.org/kmqftd9bz/20180402_095911-1.jpg\">

https://s9.postimg.org/ii62san4v/20180402_095916-1.jpg\">

https://s9.postimg.org/3yyxqvma7/20180402_095921-1.jpg\">

https://s9.postimg.org/dw9yjxegf/20180402_095927-1.jpg\">



4) The Complement Start

Let's look at the following example.

https://s9.postimg.org/7vc9mwpa7/20180402_100242-1.jpg\">

In this example, the total Before is given. We shall start will 1u and 40 - 1u.

We first view it in picture.

https://s9.postimg.org/4ohq3bf4v/20180402_100333-1.jpg\">

Then we put the information into the table.

https://s9.postimg.org/6t234f3wv/20180402_100242-2.jpg\">

Finally, we write the After in fraction, cross multiply and find 1u.

https://s9.postimg.org/ch8dvbven/20180402_100242-3.jpg\">

Easy? Now we shall do some problem sums.

https://s9.postimg.org/ss8hrrxnj/20180402_100741-1.jpg\">

https://s9.postimg.org/rpyb98mjz/20180402_100746-1.jpg\">

https://s9.postimg.org/9zwmo4w3j/20180402_100757-1.jpg\">

https://s9.postimg.org/ldj5yzysv/20180402_100751-1.jpg\">


In conclusion, whenever a problem sums ends with ratio, we can write the equation in fraction and cross multiply it.

Lesson 4 - Before After Number


In the last lesson, we learned about how to form an equation when the problem sums stated that the After are equal.

In some problem sums, a Key Number may be given.
This number may be a part, a total, or a difference.

Let's look at them one by one.

1) Number as a Part

Let's look at this example.

https://s9.postimg.org/mpuudtv2n/20180326_123916-1.jpg\">

First we visualise it as a picture.

https://s9.postimg.org/igq4bpp9b/20180326_124011-1.jpg\">

We shall put the information into the Table.

Since the problem sum stated that Ben has 30 marbles, we shall put this Key Number 30 into the table.

https://s9.postimg.org/hsh9sal9b/20180326_123916-2-1.jpg\">

We shall form a Part equation and solve it.

https://s9.postimg.org/z5rk77tfz/20180326_123916-2-2.jpg\">

So we should take note of the Key Number given in the problem sums.

Let's try the following problem sums.

Ratio Start

https://s9.postimg.org/v9e8be0sf/20180326_124626-1.jpg\">

https://s9.postimg.org/gq739yzxr/20180326_124635-1.jpg\">

Comparison Start

https://s9.postimg.org/louloiqvz/20180326_124641-1.jpg\">

https://s9.postimg.org/3m1ixanbj/20180326_124650-1.jpg\">

Complement Start

https://s9.postimg.org/jx1mtn2e7/20180326_124657-1.jpg\">

https://s9.postimg.org/3ysx3hsqn/20180326_124702-1.jpg\">


2) Number as Total

In some problem sums, the Key Number may be Total. We shall add the Afters to get a Total.

Let's look at this example.

https://s9.postimg.org/ovp58avy7/20180326_125319-1.jpg\">

We may visualise it as a picture.

https://s9.postimg.org/5133m9grj/20180326_125221-1.jpg\">

We shall put the information into the Table.

https://s9.postimg.org/wboeu8ou7/20180326_125319-2.jpg\">

Since the Key Number given is a Total, we shall add the Afters.

We shall then form the Total equation and solve it.

https://s9.postimg.org/mseq08qvz/20180326_125319-3.jpg\">

Let's try some problem sums.

Ratio Start

https://s9.postimg.org/iw1e4gg8v/20180326_130236-1.jpg\">

https://s9.postimg.org/ezo28gftr/20180326_130241-1.jpg\">

Comparison Start

https://s9.postimg.org/tvmlg4yz3/20180326_130247-1.jpg\">

https://s9.postimg.org/ldd5bskqn/20180326_130253-1.jpg\">


3) Number as Difference

In some problem sums, one After may be more than the other. The Key Number given is the Difference between the 2 Afters.

Let's look at this example.

https://s9.postimg.org/4cu93c573/20180326_130902-1.jpg\">

We can visualise it as a picture.

https://s9.postimg.org/402ux6pi7/20180326_130856-1.jpg\">

Since Jerry is lesser than Tom, we shall put the Number at his row.

https://s9.postimg.org/dlwfczo8f/20180326_130902-2.jpg\">

We shall put the bigger After on the Left side of the equation, and the smaller After on the Right side on the equation plus the Key Number.

https://s9.postimg.org/twwj9eg6n/20180326_130902-3.jpg\">

Let's try the following problem sums.

Ratio Start


https://s9.postimg.org/q0j7dlaof/20180326_131453-1.jpg\">

https://s9.postimg.org/uz6ps46rj/20180326_131458-1.jpg\">

Complement Start

https://s9.postimg.org/pnrt7fn9r/20180326_131506-1.jpg\">

https://s9.postimg.org/41csqegzj/20180326_131514-1.jpg\">

In this lesson, we have learned how to solve problem sums with Key Number given.

In the next lesson, we shall learned how to solve problem sums with Ratio at the After.

Please send in your comment on any of the modules you have read.

Lesson 4 - Simple Interest


When we deposit our money in the bank, the bank will reward us with interest.

In general,
Deposit + Interest = Total

If the interest is 3% per annum (year), then after 4 years, the total interest will be 3u × 4 = 12u.

Let's look at the following example.

https://s9.postimg.org/dz9tq4phr/20180325_000958-1.jpg\">

In picture, it looks like this.

https://s9.postimg.org/uob9lhw7j/20180325_000949-1.jpg\">

Note the interest is 2.5u x 2 = 5u.

We shall put it into the Table.

https://s9.postimg.org/agxtt81b3/20180325_000958-2.jpg\">

We shall now solve it.

https://s9.postimg.org/56sv20h33/20180325_002401-1.jpg\">

Let's try some problem sums.

https://s9.postimg.org/80w0fo1bj/20180325_002609-1.jpg\">

https://s9.postimg.org/v2cllf8ov/20180325_002614-1.jpg\">

https://s9.postimg.org/p1ewoctsf/20180325_002621-1.jpg\">

https://s9.postimg.org/sxs8kbc73/20180325_002626-1.jpg\">

Lesson 3 - Goods and Services Tax


A tax is what the government received from the people.

In Singapore, we have to pay Goods and Services Tax (GST) when we buy in some companies. The present GST is 7%.

The general rule for tax is
Sales + GST = Paid

Let's look at this example.

https://s9.postimg.org/461cley1r/20180324_170039-1.jpg\">

In picture, it looks like this.

https://s9.postimg.org/jg17s1vyn/20180324_170032-1.jpg\">

In Table Method, it looks like this.

https://s9.postimg.org/axrrnq4vj/20180324_170039-2.jpg\">

Easy? We shall solve it.

https://s9.postimg.org/8gg0ghnjz/20180324_170039-3.jpg\">

There are problem sums with discount and GST.

From the original amount, we find the payment amoount after discount. Then we add the 7% GST to find the total amount .

In reverse, from the Amount with GST, we shall find the payment amount. Then we can add the discount to get the original amount.

Let's do some problem sums.

https://s9.postimg.org/7ffrrdlzz/20180324_170525-1.jpg\">

https://s9.postimg.org/fxp7vpksv/20180324_170543-1.jpg\">

https://s9.postimg.org/xaziak8e7/20180324_170555-1.jpg\">

https://s9.postimg.org/lymwsrk9r/20180324_170604-1.jpg\">

Lesson 2 - Discount


The general rule for discount is
Selling Price - Discount = Paid

We will pay less than the original Selling Price.

In a sales, a Discount is given total attract more people to buy.

Let's look at this example.

https://s9.postimg.org/nk26kr29b/20180324_164623-1.jpg\">

In picture, we can see it like this.

https://s9.postimg.org/a3581ycj3/20180324_164702-1.jpg\">

In Table method, we shall write like this.

https://s9.postimg.org/afwm83s7z/20180324_164623-2.jpg\">

Take note that Paid is Sales minus Discount.

Let's solve it.

https://s9.postimg.org/kr8z0sesf/20180324_164623-3.jpg\">

Let's try some problem sums.

https://s9.postimg.org/xwoh6mt5r/20180324_165231-1.jpg\">

https://s9.postimg.org/nmm27eazz/20180324_165238-1.jpg\">

https://s9.postimg.org/6m35ypatb/20180324_165243-1.jpg\">

https://s9.postimg.org/oow8pwr8f/20180324_165249-1.jpg\">

Lesson 1 - Part Whole Concept


Each part of a problem sum may be in percentage.
We shall write the percentage as units.
We shall also convert all fractions and decimals into percentage.

Let's look at this example.

https://s9.postimg.org/g093ix6kf/20180324_162328-1.jpg\">

We shall look at in picture.

https://s9.postimg.org/gprvvehfj/20180324_162453-1.jpg\">

So 100u - 20u - 15u = 65u. This is what he has left.

In Table Method, it looks like this.

https://s9.postimg.org/adcql3933/20180324_162328-2.jpg\">

Now we shall form an equation and solve it.

https://s9.postimg.org/gr1tod8u7/20180324_162328-3.jpg\">

Easy right? Now let's try these problem sums.

https://s9.postimg.org/5ep86rfmn/20180324_162922-1.jpg\">

https://s9.postimg.org/6480j5b1b/20180324_162928-1.jpg\">

https://s9.postimg.org/gr1tokbgv/20180324_162934-1.jpg\">

https://s9.postimg.org/wpajeoxz3/20180324_162940-1.jpg\">

In conclusion, percentage is similar to other Quantity Amount problem sums.

In the next lesson, we shall see more on the applications of percentage in problem sums.

There is a corruption in this post. The images will not been be shown.


We have informed the website, and are awaiting for their maintenance.

14/4/2018




This is an add one to Table Method 1, and is suitable for Primary 6 pupils.

We shall discuss the use of Percentage problem sums in Part Whole concept.

In percentage problems, we shall write 1u as 1%, or 100u for 100%.

If there are fractions or decimals, we shall convert them into percentage.

In this Module, we shall learn

1) Part Whole Concept
2) Sales and Discount
3) Goods and Service Tax
4) Simple Interest

Lesson 3 - Equal Concept


In every problem, we shall form an equation and solve 1u.

Then we shall find what is required by the question.

To form an equation, we shall use the Equal concept.

There are 5 ways we can start to set up a table, Number, Equal, Ratio, Comparison and Complement

1) Number

Let's look at this example.

https://s10.postimg.org/xvh0218ux/20180319_110116-1.jpg\">

This is a typical inter transfer question. As picture it looks like this.

https://s10.postimg.org/au0ewc6nd/20180319_110249-1.jpg\">

We shall put these information into the table.

https://s10.postimg.org/5vcwhv809/20180319_110116-2.jpg\">

Applying the Equal concept, we shall equate the 2 Afters.

https://s10.postimg.org/ltlm814t5/20180319_110116-3.jpg\">

Easy? Let's try some problem sums.

https://s10.postimg.org/6yx0tdxnt/20180319_110636-1.jpg\">

https://s10.postimg.org/v2nsho8ex/20180319_110642-1.jpg\">

https://s10.postimg.org/luvk0ytmx/20180319_110648-1.jpg\">

https://s10.postimg.org/cabxe2wl5/20180319_110655-1.jpg\">


2) The Equal or Ratio Start

When the two items are equal at first, we shall start as 1u for both items.

When the two items are in Ratio at first, we shall start the two items as Ratio units.

Let's first look at this example.

https://s10.postimg.org/ernolhlo9/20180319_111104-1.jpg\">

In picture, it looks like this.

https://s10.postimg.org/u0dlzaa7t/20180319_111158-1.jpg\">

Now we shall put them into the table.

https://s10.postimg.org/kftzcf0bd/20180319_111104-2.jpg\">

Since the Afters are equal, we shall form an equation and solve for 1u.

https://s10.postimg.org/7boezrik9/20180319_111104-3.jpg\">

Easy. Let's try some problem sums.

https://s10.postimg.org/ib9mbg909/20180319_111515-1.jpg\">

https://s10.postimg.org/pehhr26q1/20180319_111523-1.jpg\">

https://s10.postimg.org/cn3bkjp89/20180319_111529-1.jpg\">

https://s10.postimg.org/zbsik3yw9/20180319_111641-1.jpg\">


3) The Comparison Start

When an item is in comaprison with another, we shall start in comparison.

This is different from the school comparison method as described in lesson 2.

We have enough information to fill the table.

Let's see this example.

https://s10.postimg.org/qtj2fvfjt/20180319_112018-1.jpg\">

In picture, it looks like this.

https://s10.postimg.org/oc7b8mqih/20180319_112102-1.jpg\">

Let's put the information into the table, and solve it.

https://s10.postimg.org/3s2ha65mh/20180319_112018-2.jpg\">

Ready for some problem sums?

https://s10.postimg.org/706ymprqx/20180319_112357-1.jpg\">

https://s10.postimg.org/706ympk15/20180319_112403-1.jpg\">

https://s10.postimg.org/ajswcif15/20180319_112409-1.jpg\">

https://s10.postimg.org/hn0rs4cqx/20180319_112415-1.jpg\">


4) The Complement Start

When the Total of both items is given, we shall start with Complement method.

What is Complement?

There 10 apples on the table, Adam took 3 apples.
How many apples are left on the table?

7 apples, because 10 - 3 = 7.

So if Adam took 1u, 10 - 1u will be left.

Let's look at this example.

https://s10.postimg.org/s9ukxqft5/20180319_113001-1.jpg\">

In picture, it looks like this.

https://s10.postimg.org/j22ch2bbt/20180319_112942-1.jpg\">

When Tom has 1u, Henry will have the remaining 50 - 1u.

Let's put it in the table and solve it.

https://s10.postimg.org/eg688rfix/20180319_113001-2.jpg\">

Let's do some problem sums.

https://s10.postimg.org/706yn27a1/20180319_113353-1.jpg\">

https://s10.postimg.org/g7z73r6mh/20180319_113359-1.jpg\">

https://s10.postimg.org/x8i3cfby1/20180319_113404-1.jpg\">

https://s10.postimg.org/mloa6zw2x/20180319_113409-1.jpg\">


In conclusion, we have learnt how to start a problem sum in 1 of the 5 ways.

We have learnt how to use the Equal Concept to form an Equation.

In the next lesson, we shall look at problems with unequal Afters.