TheMathBooklets

Thursday, 30 May 2019

N10 Numbers : Simple Word Problems

Word Problems can be confusing for learners because they need to

(1) understand the words,

(2) translate words into the required mathematics relationship

(3) form the equation to solve the problem

The usual format of the Word Problems:

(a) The price of a book is $5. The price of a pen is $3 less than the book. How much does the book cost?

(b) Albert has 147 marbles. Tom has 98 marbles. How many more marbles does Albert have than Tom?

Words such as 'more than' and 'less than' are commonly used in word problems.

Solving Simple Word Problems

Method: Who -> What -> How [Storytelling (More Less)]

Step 1: Who and their Number(Underline)

Step 2: What is the story? (Draw andlink)

Step 3: How to Solve (Answer/Conclusion)

Example:
A lemon weighs 250g. An apple weighs 120g more than lemon. What is the weight of the apple?

Step 1: Who and their Number(Underline)

Understand the terms/words -> Read each sentence and Underline Keywords => Name the Story WHO and Numbers->

Step 2: What is the story? (Draw and link)

-> (Translate words into mathematics relationship)

Step 3: How to Solve (Answer/Conclusion)

-> Complete Model and Solve

-> (form the equation to solve the problem)

Apple weighs 250g + 120g = 370g.

Example:

Albert has 560 marbles. Tom has 259 marbles. How many more marbles does Albert have than Tom?

Step 1: Who and their Number(Underline)

-> 'spotting' and underline keywords (Who and numbers)

Who Number

Albert 560

Tom 259

Step 2: What is the story? (Draw and link)

~ how many more marbles does Albert has;

~ number of marbles that Tom needs to equal number as Albert.

--> Draw Diagram

Step 3: How to Solve (Answer/Conclusion)

⁴5 ⁵6¹0

- 2 5 9

2 0 1

Albert has 201 more marbles than Tom.

~~~~ END ~~~~ :)

Tuesday, 21 May 2019

N11 Numbers: Word Problems using Models

COMMON TERMS in WORD PROBLEM / PROBLEM SUM

Using Model for WORD PROBLEM

Example:

There are 3 times more apples than oranges. There are 8 apples. How many oranges are there?

Understanding the sentence:

The word ‘3 times’ is used to describe apples.

The term ‘more’ can be expressed as:

4u = 8

u=8/4 = 2. There are 2 oranges.

Model Method(Storytelling - Who What How)

(1) Read the sentence carefully and spot the word patterns.

(2) Note (a) Who are there and the number/fractions in the sentence.

(3) Note what happened, link to model form, and answer the question.

Method:

Step 1: Who and their Number(Underline)

Step 2: What is the story? (Draw and link)

Step 3: How to Solve (Answer/Conclusion)

Example 1 (More Less)

There are thrice as many apples as banana. There are 12 fruits. How many apples are there?

Step 1: Who + Number (Underline)

Who number

Apple (3/1)

Banana

Total 12

Step 2: What is the story? Draw and link.

Step 3: How to Solve (Answer/Conclusion)

There are 12 fruits

3u + u = 12

4u = 12

u = 3.

There are 3x3 = 9 apples

Example 2 (Come and Go)

John had 12 more pies than Clive at first. After John had eaten 4 pies, he had twice as many pies as Clive in the end. How many pies did Clive have?
Method

Example 3 (Come and Go)

Janice had 32 more sweets than Rebecca as first. After Rebecca had eaten 14 of his sweets, Janice had thrice as many sweets as Rebecca. How many sweets did Janice have at first?

Example 4 (Come and Go, changed multiples)

There were twice as many men as women at a party. After 15 women had left the party, the number of men in the party was thrice the number of the remaining women. How many adults attended this party?

Method (Come and Go)

Example 5 (Growing Up)

Kevin is 8 years old. His father is 34 years old. In how many years' time will his father's age three times of Kevin's age?

Method

In 5 year times, father's age will be three times of Kevin's age.

Example
Dennis had 120 marbles more than Jean at first. After Dennis had given away 150 of his marbles to Calvin, Jean had thrice as many marbles as Dennis. Find the number of marbles Dennis had at first.

(Using Model)

Step1: Circle/Underline Keywords. Actors? Dennis, Jean

Step2: Numbers? Draw and Link

Step3: Solve:

J D

u = 3(u – 30)

u = 3u - 90

2u = 90, u = 45

Dennis has 45 + 120 = 165 marbles at first

Example

Tammy had $800 more than Kris at first. After Kris had spent $340, Tammy had 5 times as much money as Kris. Find the amount of money Tammy had at first.

(Using Model)

Step1: Circle/Underline Keywords. Actors? Tammy, Kris

Step2: Numbers? Draw and Link

Step3: Solve:

T K

u + 800 = 5(u-340)

u + 800 = 5u - 1700

4u = 2500

u = 625

Tammy has $625 + $800 = $1425

Example3

(Using Model)

Joshua had 45 more stickers than Melvin at first. After Melvin used 15 of his stickers, Joshua had thrice as many stickers as Melvin in the end. Find number of stickers Joshua had at first.

Step1: Circle/Underline Keywords. Actors? Joshua, Melvin

Step2: Numbers? Draw and Link