7_Solving Word Problems Using The Bar Model Method copy.ppt

DEPARTMENT OF EDUCATION
Solving Word
Problems with
the Bar Model
Method
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What are the twin goals of Mathematics in the
K to 12 curriculum?
CRITICAL THINKING
and
PROBLEM SOLVING

Objectives
At the end of this session, you should be
able to:
 describe and elaborate the features
of the bar model method;
 explain the two main types of bar
models and their usage;

Objectives
At the end of this session, you should be
able to:
 draw part-whole and comparison
models to represent quantities and
relationships given in word problems;
 apply bar modeling to solve word
problems involving whole numbers,
fractions, ratios and percent ;

Activity 1: Let’s Try
Task :
•For 5 – 10 minutes, read and analyze each
problem assigned to your group. Solve each
one using bar models. Show your complete
and neat solution (manila paper).
•Present your output (maximum of 5 minutes
only).

Assigned Word Problems
• Group 1 – No. 1 and No.2
• Group 2 – No. 2 and No. 3

1. At a mall, Laura spent ₱988. This is 4
times as much money Michelle spent at
the same mall. How much did they spend
altogether?

# 1
Laura
Michelle
988
?
Laura and Michelle spent ₱1,235 altogether.
4 units ₱988
1 unit ₱988 ÷ 4 = ₱247
5 units 5 x ₱247 = ₱1,235

2. Ian started saving some money on
Monday. Each day he saved ₱20 more
than the day before. By Friday of the same
week Ian had saved ₱350. Find the
amount Ian saved on Wednesday.

# 2
Monday
₱350
Tuesday
Wednesday
Thursday
Friday
Php
20
Ian saved ₱70 on Wednesday.
Php
20
Php
20
Php
20
Php
20
Php
20
Php
20
Php
20
Php
20
Php
20
10 x ₱20 = ₱200
₱350 – ₱200 = ₱150
5 units ₱150
1 unit ₱150 ÷ 5 = ₱30
Wednesday:
₱30 + ₱20 + ₱20 = ₱70

3. Three-fifths of a group of children
were girls. If there were 24 girls, how
many children were there in the
group?

?
24 girls
There were 40 children in the group.
3 units 24
1 unit 24 ÷ 3 = 8
5 units 5 x 8 = 40

total no. of pencils
no. of pencils sold
in the morning
no. of pencils sold
in the evening

200
no. of pencils sold
in the morning
no. of pencils sold
in the evening
Jayson has 400 pencils
in the beginning.
5 units 200
1 unit 200 ÷ 5 = 40
10 units 10 x 40 = 400

5. On Monday, the ratio of the number
of beads Anna had to the number of
beads Wilma had was 4:7. On
Tuesday, after Wilma gave 36 beads to
Anna, they both had the same
number of beads. How many beads
did Anna have on Monday?

# 5
Monday
Anna
Wilma

# 5
Tuesday
Anna
Wilma

# 5
Anna
Wilma
36
Anna has 96 beads
on Monday.
Monday
3 units 36
1 unit 36 ÷ 3 = 12
Anna: 4 units 8 x 12 = 96

6. A profit of ₱4 500 is to be divided
among three friends, A, B and C, in
the ratio of 3:4:5. Find the share of
each friend.

# 6
A
C
B ₱4500
12 units ₱4 500
1 unit ₱4 500 ÷ 12 = ₱375
A: 3 units 3 x ₱375 = ₱1 125
B: 4 units 4 x ₱375 = ₱1 500
C: 5 units 5 x ₱375 = ₱1 875
A will receive ₱1 125, B will receive ₱1 500 and C will
receive ₱1 875.

7.Mr. Palattao bought a guitar for
₱6,400. After using it several
months, he sold it for 25% less than
the amount he paid for it. How
much did Mr. Palattao receive for his
guitar?

# 7 ₱6 400 (100%)
? 25%
(less than the original
price of the guitar)
4 units ₱6,400
1 unit ₱6,400 ÷ 4 = ₱1,600
3 units 3 x Php 1 600 = ₱4,800
Mr. Palattao received ₱4,800 for selling his guitar.

8. Michelle had 65 more yellow ribbons
than red ribbons. After giving away 30
ribbons of each color, the number of
red ribbons became 50% of the
number of yellow ribbons. Find the
total number of ribbons Michelle had
left.

Yellow
Red
30
65
Even after giving away 30 ribbons of each color, there are
still 65 more yellow ribbons than red ribbons. So:
1 unit 65
3 units 3 x 65 = 195
30
65
?
Michelle had a total of
195 ribbons left.

1. Who among you are already familiar with bar
models prior to this session? Any first-timers?
2. What were your thoughts while doing the
activity?
3. Did you attempt to use other strategies to solve
the problems? Why?
4. Which of the questions did you find easy to
answer? Which ones were not? Why?
5. Did you notice any similarities and/or differences
in your solutions?

Bar Model Method
A problem-solving heuristic
that enables pupils to
understand, visualize and
represent mathematical word
problems and their solution
The Model Method
Part-Whole Model
Comparison Model
Examples

Bar Model Method
•was introduced in Singapore
in the 1980’s
•to address low achievement
in basic numeracy skills and
difficulties in solving word
problems
The Model Method
Part-Whole Model
Comparison Model
Examples

Learners use rectangular bars
to illustrate how the known
and unknown quantities in a
word problem are related.
The Model Method
Part-Whole Model
Comparison Model
Examples
Bar Model Method

Bar Model Method
Rectangles are easy to draw,
divide, represent larger
numbers and display
proportional relationships.
The Model Method
Part-Whole Model
Comparison Model
Examples

Bar Model Method
 CPA teaching approach
Concrete – Pictorial – Abstract
The Model Method
Part-Whole Model
Comparison Model
Examples
 Aligned with Bruner’s enactive,
iconic and symbolic modes of
representing ideas

Part – Whole Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Shows a quantitative relationship
between a whole and the other
parts

Part - Whole Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Addition or Subtraction
part part
whole
whole = part + part
part = whole - part

Part - Whole Model
The Model Method
Part-Whole Model
Comparison Model
Examples
?
given
Multiplication

Part - Whole Model
The Model Method
Part-Whole Model
Comparison Model
Examples
whole (given)
part (?)
Division

Part - Whole Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Three-fifths of a group of children
were girls. If there were 24 girls,
how many children were there in
the group?

Part - Whole Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Mr. Palattao bought a guitar for
₱6400. After using it several
months, he sold it for 25% less than
the amount he paid for it. How
much did Mr. Palattao receive for
his guitar?

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
• Shows how the larger quantity
and smaller quantities are
related in addition and / or
subtraction
• Also used to show multiplicative
relationship between quantities

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
larger quantity
smaller quantity
difference
larger quantity – smaller quantity = difference
smaller quantity + difference = larger quantity
larger quantity – difference = smaller quantity
Addition or Subtraction

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
larger quantity ÷ smaller quantity = multiple
smaller quantity × multiple = larger quantity
larger quantity ÷ multiple = smaller quantity
Larger quantity
Smaller quantity
Multiplication or Division

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
At a mall, Mrs. Gonzaga spent
₱988. This is 4 times as much
money Mrs. De Silva spent at
the same mall. How much did
they spend altogether?

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Ian started saving some money on
Monday. Each day he saved ₱20
more than the day before. By Friday
of the same week Ian had saved
₱350. Find the amount Chris saved
on Wednesday.

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Jayson is selling pencils. He sold of
them in the morning and of the
remainder in the afternoon. If
Jayson sold 200 more pencils in the
morning than in the afternoon, how
many pencils did Jayson have in the
beginning?

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
A profit of ₱4,500 is to be divided
among 3 persons, A, B, and C in the
ratio of 3:4:5. Find the share of each
person.

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
On Monday, the ratio of the
number of beads Anna had to the
number of beads Wilma had was
4:7. On Tuesday, after Wilma gave
36 beads to Anna, they both had
the same number of beads. How
many beads did Anna have on
Monday?

Comparison Model
The Model Method
Part-Whole Model
Comparison Model
Examples
Michelle had 65 more yellow
ribbons than red ribbons. After
giving away 30 ribbons of each
color, the number of red ribbons
became 50% of the number of
yellow ribbons. Find the total
number of ribbons Michelle had
left.

Examples
The Model Method
Part-Whole Model
Comparison Model
Examples
Sam and Jane have stamps in the
ratio of 7: 8. Jane gives Sam 200 of
his stamps, so that the new ratio of
Sam to Jane is now 11: 4. How many
stamps are there together?

Examples
The Model Method
Part-Whole Model
Comparison Model
Examples
A, B, C and D earned the same
amount of money every month. A
spent three times as much as B. D
spent twice as much as C. B saved
twice as much as A. C saved three
times as much as D. Find the ratio of
B's savings to D's savings.

Activity 2: Let’s Apply
Task :
• For 10 - 15 minutes, read and analyze each
problem assigned to your group. Solve
each one using bar models. Show your
complete and neat solution (manila
paper).
• Present your output (maximum of 5
minutes only).

Whole numbers - #1 and #3
Fractions - #1 and #5
Ratio and Proportion - #2 and #4
Percents - #2 and #4

1. Two numbers have a sum of
64. One of the numbers is 12
less than the other number.
Find the two numbers.

# 1
First Number
Second Number
64 + 12 = 76
2 units 76
1 units 76 ÷ 2 = 38
First number: 38
Second number: 38 – 12 = 26
64
12
The first number
is 38, while the
second is 26.

# 1
First Number
Second Number
64 - 12 = 52
2 units 52
1 units 52 ÷ 2 = 26
First number: 26 + 12 = 38
Second number: 26
64
12
The first number
is 38, while the
second is 26.

2. The total of five consecutive
odd numbers is 795. What
becomes of the middle number
if it is decreased by 25?

# 2
1st Odd Number
Php 795
2
When decreased by
25, the middle
number will be 134.
10 x 2 = 20
795 – 20 = 775
5 units 775
1 unit 775 ÷ 5 = 155
3rd Number / Middle Number:
155 + 4 = 159
When decreased by 25:
159 – 25 = 134
2nd Odd Number
3rd Odd Number
4th Odd Number
5th Odd Number
2 2
2 2 2
2 2 2 2

Activity 2: Let’s apply

60 pupils
boys
There were 24 boys.
5 units 60
1 unit 60 ÷ 5 = 12
2 units 2 x 12 = 24

Sports Plus Target ₱400
4 units ₱400
1 unit ₱400 ÷ 4 = ₱100
9 units 9 x ₱100 = ₱900
David had ₱900 at first.

2. Two numbers are in the
ratio 3:5. If the difference
between the numbers is 36,
find the two numbers.

First Number
Second Number
36 (difference)
2 units 36
1 unit 36 ÷ 2 = 18
First number: 3 units 3 x 18 = 54
Second number:5 units 5 x 18 = 90
The first
number is 54,
while the
second
number is 90.

4. In a swimming club, the ratio of
the number of boys to the
number of girls is 5:9. If there
are 104 more girls than boys in
the club, how many children
are there altogether?

Boys
Girls
104
There are 364
children altogether.
?
4 units 104
1 unit 104 ÷ 4 = 26
14 units 14 x 26 = 364

2. Of the Grade Six pupils in a school,
27 usually walk to school. This
represents 30% of the total
number of Grade Six pupils in the
school. How many Grade Six pupils
are there?

?
27 children walk
to school
There are 90
Grade Six pupils in
the school.
3 units 27
1 unit 27 ÷ 3 = 9
10 units 10 x 9 = 90
10% 10% 10%

4. Separate 360 into 2
numbers such that one is
125% of the other. What
are the numbers?

Smaller number
The two
numbers are
160 and 200.
360
9 units 360
1 unit 360 ÷ 9 = 40
Smaller number: 4 × 40 = 160
Larger Number: 5 × 40 = 200
25%
Larger number 25%
100%

7_Solving Word Problems Using The Bar Model Method copy.ppt

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