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

         

Step3: Solve: 

   Link - Joshua has thrice as many sweets as Melvin

                                          J             M

           ->      u + 45 = 3(u-15)

                                  u + 45 = 3u - 45

                                  2u = 90

                                    u = 45

Joshua has 45 + 45 = 90 stickers at first

Practice – Solve using Algebra method

 ~~~~ END ~~~~ :)

Mathematics Proficiency Assessment

PROFICIENCY ASSESSMENT

 Numbers (Level1-2)   

 Numbers (Level 3) 
 Fractions (Level 2) 
 Measurement (Level 1)  

Answer Key

 Number (Level 1-3) Answer keys 
 Fractions (Level 2) Answer Keys 

Assessment Matrix

 Proficiency Assessment Table  

TG1: Teaching Guide - Tutor's Roles during the Practice

Tutor Guide for Student’s Practice:

Before the Practice

Go through the content and practice questions before class.

During the tuition session

(1)  Select the Revision Topic 

A.  Go to https://themathbooklets.blogspot.com/p/primary-maths-practices.html

B.  Select the assigned practice. Example: N1-L1: Number Notation. Click on the link or use the book.

(2)  Revision 

A. Do topic revision 

B. Do Practice Revision

(a) Prepare the student: 

   (I) check his/her pencil case for necessary Stationery (pencil, ruler, erase, etc.) or calculator. 

   (II) Remind the estimated timing:       

Multiple choice question: ~ 1 minute

Short question: ~ 2 minutes

Problem sum: ~ 3 minutes

    (III) Remind the method:       

       a.  Read the question carefully and Circle/Underline key information 

       b.  Do by Drawing models and show working(writing the steps clearly)

       c.  Solve/Complete the question and place the answer on the answer_line.

(b) Write the Start Time and student to start doing the practice.

(c) During the Practice

Observe the student’s familiarity with and pace in doing the question. 

C. After the Practice

Mark the questions. Each question is 1 mark. Write the total mark on both the practice page and the student revision timeline page.

D. Coaching the student (after marking the question)

Correct Answer:

When the student does the question by following the steps: Praise the student and point out his/her good practice (to prevent careless mistake) and fluency (he/she has been practicing similar questions)

Wrong/No Answer (Careless or Don’t Know):

The student can either be making careless mistake(C) or does not know(DK) to do it.

                           Careless or Don’t Know?

Let’s determine:

1. Ask the student if there is any other keyword to circle/underline.

2. Highlight that the word ‘AVERAGE’ is also a keyword.

3. Ask student for Average definition/formula

    Don’t Know: If student cannot answer the meaning of Average

    Careless: If student can answer.

4. Ask student should the question be label as ‘Careless’ or ‘Don’t Know’ (to make sure that the student understands the ‘Careless’ / Don’t Know’ terms)

If Careless:

1.  Reiterate the practice of CIRCLE/DRAW/SOLVE (CDS)

2.  If the student loses focus/lack of attention, request him/her to draw STARTING/ENDING line.

and to complete question before taking a break à To start and end a question before any other distraction.

3.  RE-DO the question or another similar question until the student has the correct answer.

If Don’t Know:

1. The Student should still CIRCLE the keywords and DRAW and show the working of the portion that he/she understand.

     -> Praise the student as he/she has circled and did the necessary portion

2. REVISE the topic's portion again

3. Student RE-DO the same question again after the revision. The tutor can set additional 1-2 similar questions for the student to do as well.