MATH 4 PPT Q3 - Patterns And Algebra.pptx

National Training of Trainers on
Critical Content of K to 10 Program
April 23 to May 4, 2018
Makati City

DEPARTMENT OF EDUCATION
BUREAU OF CURRICULUM DEVELOPMENT
How many
faces can you
see?

This session aims to develop and deepen the participants’
understanding on the critical content and competencies in
Mathematics Grade 4. More specifically, they should be able to:
 determine the missing term/s in a sequence of numbers (e.g.
odd numbers, even numbers, multiple of a number, factors of a
number, etc.)
 construct assessment items on determining the missing terms
in a sequence.
Session 1 Objectives

SEQUENCE
-an ordered set of numbers, letters, shapes or symbols
-each number, letter, shape or symbol in the sequence is
called a term
PATTERNS
- can be recognized, named, extended, and created using
shapes, numbers, and symbols with their attributes.

Determine the pattern of the sequence.
SEQUENCE OF NUMBERS & LETTERS
1) x, y, z, x, y, z, ...
2) 2, 5, 8, 11, …
3) 2, 4, 8, 16, …
4) 6, 13, 27, 55, ...
5) 15, 12, 9, …
6) 48, 24, 12, …

Determine the next three terms.
SEQUENCE OF NUMBERS & LETTERS
1) x, y, z, x, y, z, ...
2) 2, 5, 8, 11, …
3) 2, 4, 8, 16, …
4) 6, 13, 27, 55, ...
5) 15, 12, 9, …
6) 48, 24, 12, …
Answer: x, y, z
Answer: 14, 17, 20
Answer: 32, 64, 128
Answer: 111, 223, 447
Answer: 6, 3, 0
Answer: 6, 3, 1 ½

SEQUENCE OF SHAPES & SYMBOLS
Look for the pattern in each sequence then determine
next three terms.
, ,
,
, ____
1.

next three terms.
____
, , , ,
2.

next three terms.
, , , ____
3.

next three terms.
4. A, C, E, G, I, ____
5. AZ , BY, CX, ____

THINK-PAIR-SHARE

1. Given the table below, find the missing terms and
state the rule.
A pattern is to add 13 to each term to get the next term.
48 + 13 = 61 61 + 13 = 74
So 61 and 74 will be the next terms in the arithmetic
sequence.
Position 1 2 3 4 5 6
Value of Term 9 22 35 48
+13 +13 +13 +13
+13

2. Extending Arithmetic Sequences
Identify a pattern in each sequence and then
find the missing terms.
48, 42, , , , 18, 12, . . .
Look for a pattern. A pattern is to subtract 6
from each term to get the next term.
42 – 6 = 36 36 – 6 = 30 30 – 6 = 24
So 36, 30, and 24 are the missing terms.
–6 –6 –6 –6 –6 –6

3. Each month, Eva chooses 3 new DVDs from her DVD
club. How many DVD’s will she have on the 4th month?
Eva’s DVDs
Month DVDs
1 3
2
3
4
Value
Position
The number of DVDs Eva has after each month
shows a pattern: Add 3. This pattern can be written
as a sequence. 3, 6, 9, 12, 15, 18, 21 … Therefore,
by the 4th month, Eva will have 12 CD’s.
+ 3
+ 3
12
9
+ 3
6

4. Identify the pattern in the sequence and
name the next three terms.
, , ,24, 19, 14 , 9
Look for a pattern. As the missing terms are at the
beginning of the pattern. Working backwards,
pattern is to add 5 to get the next term.
24 + 5 = 29 29 + 5 = 34 34 + 5 = 39
So 29, 34, and 39 will be the next three terms.
+5 +5 +5 +5 +5 +5

5. What do you have to do to each number in
Column A to get the number next to it in Column B?
10 ÷ 2 =
The numbers in Column A are divided by 5 to
get the numbers in Column B.
5
5
5
15 ÷ 3 =
25 ÷ 5 =
50 ÷ 10 = 5

6. Identify a pattern in the sequence. Name
the missing terms.
24, 34, 31, 41, 38, 48, , , ,…
A pattern is to add 10 to one term and
subtract 3 from the next.
48 – 3 = 45 45 + 10 = 55 55 – 3 = 52
So 45, 55, and 52 are the missing terms.
+10 –3 +10 –3 +10 –3 +10 –3

7. Here is a number pattern. What three numbers should go in
the boxes?
The first pattern is to subtract 1 from the previous number.
100 - 1 = 99, 99 - 1 = 98, 98 - 1 = 97
So, the numbers that should go in the boxes are 3, 97 and 4.
- 1 - 1 - 1
+1 +1 +1
1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4
The second pattern is to add 1 to the previous number.

8. The daily start times for showing a movie are
listed below. If this pattern continues, what is the start
time for the 4th show?
A pattern is to add an hour and a half ( 1 hr and 30 mins).
2:00 + 1 hr 30 mins = 3:30 3:30 + 1 hr 30 mins = 5:00
5:00 + 1 hr 30 mins = 6:30
So, the fourth show will start in 6:30 p.m.

9. A sequence of four figures is shown below. If
the figures were continued, how many circles would
there be in Figure 10?
For each figure, two circles, that is, one circle on each
edge is added.
Thus, figure 5 will have 9 circles; Figure 6, 11 circles;
figure 7, 13; figure 8, 15; figure 9, 17; and figure 10,
19 circles.
1 + 2 =3 3 + 2 =5 5 + 2 =7

10. Jean is arranging squares in the following way.
For each figure, 2 squares are added at the right.
Figure 4 will be
Draw figure 5.
While Figure 5 will be

ENRICHMENT

X = 24
2 + 4 = 6; 4 + 6 = 10; 6 + 8 = 14
6 + 10 = 16; 10 + 14 = 24
16 + 24 = 40
1. Find the value of x in the pattern illustrated below.
Show your solution.

X = 64
2. Here is part of a wall chart that lists numbers from 1
to 100.
43
53
?

3. Here is the beginning of a pattern of tiles..
If the pattern continues, how many tiles will be in Figure 6?
Answer:

4. Carlo has to form figures 1 to 4 with matchsticks.
Figures 1, 2, and 3 are shown below. He needs four
matchsticks to form figure 1, seven matchsticks to form
figure 2, and ten matchsticks to form figure 3. He uses the
same rule each time to make the next figure in the pattern.
How many matchsticks will he need to form figure 4?
Answer: 13 matchsticks; 3 matchsticks are added for each succeeding figure.

CREATE YOUR OWN SEQUENCE

CREATE YOUR OWN SEQUENCE
1.Individually, construct a sequence of numbers,
shapes or symbols. Include the rule on how to
find the missing term.
2.Choose the best 2 sequences within the group.
3.Present the sequence to the class. Challenge
another group to answer the sequences within 1
minute*.

This session aims to develop and deepen the participants’
understanding on the critical content and competencies in
Mathematics Grade 4. More specifically, they should be able to:
Finds the missing number in an equation involving properties
of operations.
Construct an assessment items on finding the missing
number in an equation involving properties of operations.
Session 2 Objectives

18 × 5 = ?
Solve mentally.

a. (40 + 5) + (n + 15) = ( n + 15) + (40 + ___)
b. ( 8 + 3 ) +( 4 + 7) = ( ____ + 4 ) + ( 3 + ___ )
COMMUTATIVE PROPERTY OF ADDITION
COMMUTATIVE PROPERTY OF MULTIPLICATION
a. 6 × 5 × 7 = ___ × 5 × 6
b. ___ × 5 × 6 =6 × ___ × 10
Properties of Addition/Multiplication

a. ( 3 + 8 ) + 9 = 3 + ( ___ + 9 )
b. 6 + ( ___ + 5) =(6 + 2) + ___
ASSOCIATIVE PROPERTY OF ADDITION
ASSOCIATIVE PROPERTY OF MULTIPLICATION
a. (5 × 10) × 9 = 5 × (10 × ___)
b. 9 × (8 × ___) =(___ × 8) × 6

a. 9 + _____ = 9
b. 5 + (6 + 0) = 5 + _____
IDENTITY PROPERTY OF ADDITION
IDENTITY PROPERTY OF MULTIPLICATION
a. 1 × 6 = ___
b. ___ × 25 = 25

a. 12 × _____ = 0
b. 0 × 33 = ____
DISTRIBUTIVE PROPERTY OF MULTIPLICATION
OVER ADDITION
a. ( 10 x 2) + (10 x 5) = ___ ( 2 + 5)
b. 4 × (5 + 6) = (4 × ____) + (____× 6)
c. 6 x (5 + 10) =( ____ x 5) + (6 x ___ )
ZERO PROPERTY OF MULTIPLICATION

Reference: https://learnzillion.com/lesson_plans/3624-4-understand-the-commutative-property-when-using-3-addends-c/?card=50237
Property Used:
Commutative Property of
Addition
Why?
They have the same score
as they landed on the same
numbers only in a different
order.

Property used:
Associative Property of
Addition
Why?
It is better to group
together 5 + 5 first as they
sum up to 10, then add 9 to
get 19.

“HELP ME FIND MY MISSING PART”

CREATE YOUR OWN PROBLEM

CREATE YOUR OWN PROBLEM
1.By group, construct an assessment
about the properties of
addition/multiplication (5 items; 1
should be a word problem)
2.Present the sequence to the class.

With a for teaching,
LEARNING IS POSSIBLE.

Angel Rocena
lmrocena@up.edu.ph
angelrocena@gmail.com

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