Mathematics 5 - Quarter 3 - Week 6

Mathematics 5 - Quarter 3 - Week 6

​Lesson 1

Formulating the Rule in Finding the Next Term in a Sequence

​Lesson 2

Simple Equations Involving One or More Operations

Answer each question as fast as you can.

5 seconds lang per question.

Fill in the Blank

What comes next?

{1, 2, 3, 4, 5, 6, _, ...}

Fill in the Blank

What is missing in the set of letters below?

{A, B, C, D, E, F, G, H, I, _, K, L, M, N,...}

Multiple Choice

What should be next after bananas?

Multiple Choice

What should be the 3rd coin?

Multiple Choice

Formulating the Rule in Finding the Next Term in a Sequence

Lesson 1​

What is a SEQUENCE?

A sequence is a set of things (usually numbers) that are in a special order.

Each number in the sequence is called a term (or sometimes "element" or "member").

​Each number in the sequence is called a term (or sometimes "element" or "member").

What is a PATTERN?

​A pattern is a repetitive sequence and can be found in nature, shapes, events, sets of numbers and almost everywhere you care to look.

What is a RULE?

A rule is a pattern or a way to find the value of each term.

When the set has non-repeating (hindi umuulit) terms or elements, check first if it is increasing or decreasing, then use rule.

Example:

{1, 2, 3, 4, 5, 6,...} - The rule is +1.

{11, 9, 7, 5, 3, 1,...} - The rule is -2.​

RULE

When the set has repeating (umuulit) terms or elements, use pattern.

Example:​

{​3, 11, 16, 27, 3, 11, 16, 27, ...}

-The pattern is ​3, 11, 16, 27.

{95, 96, 97, 95, 96, 97,...}​

- The pattern is ​95, 96, 97.

PATTERN

When to Use Patterns and Rules

Let's have some examples.

The highlighted numbers from the number sequence are:

1, 4, 8, 13, 19, 26, 34, 49.

To find the

2nd term add 3,

for the 3rd term add 4, for the 4th term add 5, for the 5th term add 6, for the 6th term add 7, for the 7th term add 8, for the 9th term add 9.

Therefore, the rule in the sequence is

(+3, +4, +5, +6, +7, +8, +9).

​The numbers inside the heart are multiplied by consecutive odd numbers 3, 5, 7. Starting with 3 x 3 = 9, then 9 x 5 = 45, then 45 x 7 = 315, so the missing number in the last heart is 2,835, because 315 x 9 = 2,835.

The series of number inside the circle uses even numbers as factors: 2 x 2 = 4; 4 x 4 = 16; 16 x 6 = 96

So, the missing number inside the last circle is 768 (96 x 8 = 768).​

​Eighteen days before Sofia Amanda’s debut, her parents planned to give her gifts. On the first day, they gave one gift, on the second day, three. On the third day, five and on the fourth day, they gave seven gifts. How many gifts did they parents give on the eighteenth day?

​As the sequence continues:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35

​3, _ ,15, 31, _, _, 255

​The rule for this one is 2x + 1, wherein 2 is the constant value (it cannot be changed) as well as the +1. The x is the variable (can be changed according to the computation).​

Multiply the variable by two, then add 1 to it to get the answer. In this case, the sequence started at 3, so the number to be used as the first variable is between 1 or 2 only. 1 is the variable since it gives an answer of 3 if it is multiplied by two and added with 1.

So, the sequence is 3, 7, 15, 31, 63, 127, 255.

Multiple Choice

What's next?

{12, 34, 56, 78, 12, 34, 56, 78, _, ...}

• 12

• 34

• 56

• 78

Multiple Choice

Complete the sequence.

star, circle, star, circle, _____, _____

• star

• circle

• circle, star

• star, circle

Multiple Choice

What comes next?

{2, 4, 6, 8, 10, _, ...)

• 8

• 10

• 12

• 14

Multiple Choice

What rule applies to the sequence below?

3, 6, 9, 12, 15, 18

• +2

• +3

• +4

• +5

Multiple Choice

What rule applies to the sequence below?

8, 15, 29, 57, 113

• Multiply by 2 and add 2

  2x + 2

• Add 8 then subtract 1

  (x+8) - 1

• Multiply by 2 then subtract 1

  2x - 1

• Subtract 3 then multiply by 3

  (x-3) x 3

Simple Equations Involving One or More Operations

Lesson 2

​An equation is a sentence in Mathematics that contains an equal sign (=). The equal sign tells you that the expression on the left is equivalent to the expression on the right.

​2 x 3 = 3 x 2

3 + 5 = (3 x 3) - 1

Multiple Choice

Is this an equation?

1 + 3 = 4

Multiple Choice

Is this an equation?

x + y = z

Multiple Choice

Is this an equation?

2x + 1

Multiple Choice

Is this an equation?

2x = 4

Multiple Choice

Is this an equation?

3 + 11 + 16 + 27

PROPERTIES OF EQUALITY

1.     Addition Property of Equality

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.

For all real numbers a, b, and c:

If a = b, then a + c = b + c.

PROPERTIES OF EQUALITY

2.     Multiplication Property of Equality

If two expressions are equal and you multiply both sides by the same number, the resulting expressions will also be equivalent.

For all real numbers a, b, and c:

If a = b, then a • c = b • c (or ab = ac).

Let's have some examples.

​Let us solve the examples on the board.