Problem Solving,Mathematical Investigation & Modeling

I. Learning Outcomes:

At the end of this topic, students should be able to;

1. Know when to use “look for a pattern” in solving problems.

2. Solve problems by identifying a pattern.
3. Perform look for a pattern strategy using Polya’s Four Basic Principles of
Problem Solving.

II. Subject Matter

Topic: Strategy: Look for a Pattern

Duration: 30 minutes
Reference: Badger Maths Problem Solving Book 1 For Years 4 - 5
Materials: Laptop
Powerpoint Presentation

III. Learning Activities

Teacher’s Activity Students’ Activity

A. Activity
Share your experience in everyday life.
How do you describe it? Do you
find any repetitions on what you’re Students’ answer may vary.
doing? ( The presenter randomly selects
1-2 student to share their thoughts).

Present a problem using powerpoint

presentation. The students are given 5
minutes to solve the problem and are
given the freedom on how they are going
to come up an answer.

A marine biologist is researching the

structure of a nautilus. The shell’s pattern 21, 34, 55. Each number in the sequence
follows a sequence discovered by the is the sum of the two numbers that have
mathematician Fibonacci. Insert the next come before it.
three numbers. 0 , 1, 1, 2, 3, 5, 8, 13, _, _,
_.

B. Analysis
1. Process the activity. 1. Students will solve the problem in their
2. Ask further questions. own way.
a) How did you solve the 2. Students answer may varied depending
problem. in their way of solving.
b) Ways in solving the problem.
 ⚫ The presenter present the topic. (
Strategy: Look for a Pattern)

The presenter will discuss the

following;
A problem can be solved by looking
1. How to solve problems using looking into the relationship and the elements of a
for a pattern strategy? list and identifying the pattern.

2. What is a pattern? A pattern by definition is a regular,

systematic repetition and maybe
numerical,visual or behavioral.

3. When does look for a pattern is 1. A list of data is given.

appropriate to use? 2. A sequence of numbers is involved.
3. You are asked to make a prediction or
generalization.
4. Information can be expressed and
viewed in an organize manner, such a
table.

4. Use Polya’s Four Basic Principles of 1. Understand: The numbers are

Problem Solving in performing look increasing.We are looking for a number
for a pattern. ( Demonstrate an example) greater than 32.
2. Plan: The strategy is to identify the
What is the next number in the list? 1, pattern.
2, 4, 8, 16, 32, _. 3. Do: Convert the problem into
expression.
An = 2(n-1) ; where An is the nth term and n
is the number of terms.

4. Check: Substitute the givens in the

formula.
C. Application

Activity: Solving

Direction: Solve the following problem

using Polya’s Four Basic Principles of
Problem Solving in performing look for a
pattern.

1) The Ross family are working on a 1. Understand: The number of circuits of

fitness program. On the first day, they the oval increases each day. How many
cycle around the oval three times; on the days must they exercise before they reach
second day, seven times; and on the third their goal? Is there a pattern?
day, eleven times, and so on. How many
days must they exercise before they reach 2. Plan: The strategy is to identify the
their goal of cycling around the oval 31 pattern.
times?

3. Do: Create a table.

Days Circuits
1 3
2 7
3 11
4 15
5 19
6 23
7 27
8 31

The numbers are increasing by four

circuits a day.Therefore, it will take 8
days for the Ross family to reach their
goal of 31 circuits of the oval

4. Check: Check using the formula n+4,

where n is the number of circuits. The 7th
day is equal to 27, 27+4= 31; therefore in
day 8 they have 31 circuits.
D. Abstraction
The students will count 1-3 to know their
The presenter will group the students into group. Then they should actively
three. participate in the said activity.

Direction: The members will be shuffled The group will help with each other to
in each group and solve the following solve the given problem involving pattern.
problem involving look for a pattern. The team that got the correct answer will
have the authority to give
Activity: punishments( sing, dance, act, etc) to the
losing teams.

Each hexagon below is surrounded by 12 SOLUTION:

dots.
a) Find the number of dots for a pattern
with 6 hexagons in the first column.
b) Find the pattern of hexagons with 229
dots.
 1st Total
Pattern
column dots

1 12 12

2 12 + 16 28

12 + 16 + 21 49
3

12 + 16 + 21
4 75
+ 26

12 + 16 + 21
5 106
+ 26 + 31

12 + 16 + 21
6 + 26 + 31 + 142
36

12 + 16 + 21
7 + 26 + 31 + 183
a) The 36 + 41

12 + 16 + 21
8 + 26 + 31 + 229
36 + 41 + 46

number of dots for a pattern with 6

hexagons in the first column is 142.

b) If there are 229 dots then the pattern

has 8 hexagons in the first column.

IV. Evaluation

Direction: Solve the following problem using Polya’s Four Basic Principles of
Problem Solving in performing look for a pattern.

1. What are the next seven numbers in the sequence 1,3 ,6 ,10 ,15, _, _, _, _ ,_ , _, _ ?
2. Miriam plants three seeds for every eight seeds that her mother plants. How many
seeds has Miriam planted when her mother has planted 64 seeds?

V. Assignment

What is the sum of numbers in 12th row of the following pattern?

 1
3 5
7 9 11
13 15 17 19
21 23 25 27 29