By: Erlyn M. Geronimo

WARM UP EXERCISEExpress the following in symbols:Y is 2 greater than xMarias age 3 years ago if she is m years old nowThe sum of two consecutive odd numbers if the smaller number is kThe length L is twice the width WThe value of a two digit number if the tens digit is x and the units digit is yThe number c is two less than the product of a & b

USING PICTORIAL MODELS TO SOLVE WORD PROBLEMSTranslating word problems into algebraic equations is a skill not easily acquired by students in the higher elementary and lower secondary school. Formulating and manipulating algebraic expressions require a level of abstraction which is not easily attained by students.The use of pictorial representations connects better with the intuitive perception of students, helping them understand relationships between the quantities involved in the problem and leading them to a strategy in solving it.

Using Venn DiagramsOne of the pictorial models that are useful in finding relationships between sets is the Venn Diagram. Having a visual model of the sets in consideration provide an efficient way of determining cardinalities of said sets.

Example 1A grade six teacher asked her class of 42 students when they studied for her class the previous weekend. Their responses were as follows:9 said they studied on Friday18 said they studied on Saturday30said they studied on Sunday3said they studied on both Friday and Saturday10said they studied on both Saturday and Sunday6said they studied on both Friday and Sunday2said they studied on Friday, Saturday, and Sunday

Example 1Assuming that all 42 students responded and answered honestly, answer the following questions:How many students studied on Sunday but not on either Friday or Saturday?How many students did all their studying on one day?How many students did not study at all for this class last weekend?

Example 1FridaySaturdaySunday248127162

Example 1Assuming that all 42 students responded and answered honestly, answer the following questions:How many students studied on Sunday but not on either Friday or Saturday?How many students did all their studying on one day?How many students did not study at all for this class last weekend? 16252

Example 2Every GOOP is a GORP.Half of all GORGS are GORPS.Half of all GORPS are GOOPS. There are 40 GORGS and 30 GOOPS. No GORG is a GOOP.How many GORPS are neither GOOPS nor GORGS?

Example 2Every GOOP is a GORP.Half of all GORGS are GORPS.Half of all GORPS are GOOPS. There are 40 GORGS and 30 GOOPS. No GORG is a GOOP.How many GORPS are neither GOOPS nor GORGS?GOOPSGORPSGORGS2030102010

Example 3?

Example 3

Example 4On a balance scale, two spools and one thimble balance 8 buttons. Also, one spool balances one thimble and one button. How many buttons will balance one spool?

On a balance scale, two spools and one thimble balance 8 buttons. Also, one spool balances one thimble and one button. How many buttons will balance one spool?

Singapore Model Method or Block Model MethodThe Model building approach to solving word problems was developed locally years ago by Hector Chee, a very experienced Mathematics teacher, and has been widely used in the teaching of math in primary schools in Singapore. Kids in Singapore are introduced to the method from as young as Primary One (the equivalent of Grade One).

Part-Whole ModelIn this model, a whole is divided into two or more parts.When the parts are known, we can find the whole by addition. When the whole and one part are known, we can find the unknown part by subtraction.

Example 5Donna spent PhP240 on a photo album. When she spent 3/8 of her remaining money on a novel; after which half of her money was left.How much did Donna spend on the novel?What fraction of her money did Donna spend on her photo album?

Example 5Donna spent PhP240 on a photo album. When she spent 3/8 of her remaining money on a novel; after which half of her money was left.

NovelMoney LeftPhoto Album24022401120

Example 5How much did Donna spend on the novel?What fraction of her money did Donna spend on her photo album?

NovelMoney LeftPhoto Album24022401120P3602/10 or 1/5

Example 6There are 240 cows and goats on a farm.Three-fifths of the goats is equal to 3/7 of the cows.Find the difference in the number of cows and goats in a farm.

GOATS:COWS:240difference

Example 6Find the difference in the number of cows and goats in a farm.

GOATS:COWS:240difference1224012024040

Comparison ModelIn this model, two or more quantities are compared. If the two quantities are given, we can find their difference or ratio.If one quantity and either the difference or ratio is given, we can find the other quantity.

Example 7JB, James and Joseph collected 242 soda cans for the school recycling campaign. James collected twice as many soda cans as JB.Joseph collected four times as many soda cans as James. How many more cans did Joseph collect than JB?

Example 7JB, James and Joseph collected 242 soda cans for the school recycling campaign. James collected twice as many soda cans as JB.Joseph collected four times as many soda cans as James. How many more cans did Joseph collect than JB?

JB:James:Joseph:242

Example 7How many more cans did Joseph collect than JB?JB:James:Joseph:242112421227154154

Example 8Claire, Pam and Tanya have 500 stickers among themselves. Pam has 5 more stickers than Claire. Tanya has thrice as many stickers as Pam. How many stickers has Tanya?

Example 8C:P:5T:500Claire, Pam and Tanya have 500 stickers among themselves. Pam has 5 more stickers than Claire. Tanya has thrice as many stickers as Pam. How many stickers has Tanya?555

Example 8C:P:5T:500How many stickers has Tanya?555520500+54801963033+15

Before-After ModelWhen a quantity or quantities change, a comparison is made between the new value(s) and the original value(s). This is sometimes combined with the comparison method in the more complicated word problems.

Example 9Mike and Sarah had a total of PhP540.Mike spent PhP240. He now has three times as much money as Sarah. How much more money had Mike than Sarah at first?

Example 9Mike and Sarah had a total of PhP540.Mike spent PhP240. He now has three times as much money as Sarah. How much more money had Mike than Sarah at first?Sarah:Mike:BeforeAfter240540300

Example 9How much more money had Mike than Sarah at first?Sarah:Mike:BeforeAfter2405403004300175390

Example 10The number of pupils who passed a mathematics test is 108 more than the number of pupils who failed.If 36 more pupils pass the test, the number of passers will be 10 times the number of failures. Find the number of pupils who took the test.

Example 10Passed:Failed:ActualIfThe number of pupils who passed a mathematics test is 108 more than the number of pupils who failed.If 36 more pupils pass the test, the number of passers will be 10 times the number of failures. Find the number of pupils who took the test.3636 108

Example 10Passed:Failed:ActualIfFind the number of pupils who took the test.108363636+ 1082+ 111802+ 99180220120561642

Example 11One third of a number is 13 less than one-half of that number. What is the number?

Let x be the number+ 13 =62x + 78 = 3xx = 78

Example 11One third of a number is 13 less than one-half of that number. What is the number?

13617878

AcknowledgmentSpecial thanks to A/P Flordeliza Francisco of Ateneo de Manila University for most of the examples used in this presentation.

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