Patterns and Algebraic rules

Slides:



Advertisements
Similar presentations
Patterns and Algebraic rules
Advertisements

Chapter 3 Math Vocabulary
If: What will the following be: And what about: Multiplying Terms or ?
SequencesEquations Algebra. Sequences Help Pattern no. n Number of sticks How many sticks are there in each pattern?
Algebra n th Term. Algebra When we are working to find the n th term we are looking to find patterns in number sequences.
Addition Multiplication Subtraction Division. 1.If the signs are the same, add the numbers and keep the same sign = = If the.
Goal: I will solve linear equations in one variable. ❖ Linear equations in one variable with one solution, infinitely many solutions, or no solutions.
Patterns and Expressions Lesson 1-1
Year 9 Mathematics Algebra and Sequences
Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.
Objectives The student will be able to:
Objectives The student will be able to:
6-3: Solving Equations with variables on both sides of the equal sign
Objectives The student will be able to:
Lessons 2.2 and 2.3 Adding and Subtracting Real Numbers
Algebra 1 Notes: Lesson 2-2 Rational Numbers
Objectives The student will be able to:
LESSON 1.11 SOLVING EQUATIONS
Where letters are numbers and numbers are letters!
Key Stage 3 Mathematics Key Facts Level 6
Exponent Rules.
Bell Ringer (NWEA) RIT band
Warm-up September 14, 2017 Change to a decimal: 87% 7%
Warm-Up 13 x 3 14 x 4 12 x 11 9 x 13.
Exponents & Powers.
Expressions and Formulas
Math Objective: Solve Two-Step Equations
Sequences Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 7, 11, 15, 19, … 7, 11, 15, 19, … Answer:
Patterns and Algebraic rules
Algebraic Equations Solving One Step Equations with Whole Numbers
Solving Equations with the Variable on Both Sides
Objectives The student will be able to:
Objectives The student will be able to:
Nth term maths 06/12/2018.
vms x Year 8 Mathematics Equations
One step equation with Multiplication and Division
Two Step Equation.
Equation with variables on both sides
One step equation with Addition and Subtraction
Objectives The student will be able to:
Objectives The student will be able to:
Two step equation Operations
Multiplying and Dividing Integers
Objectives The student will be able to:
Objectives The student will be able to:
Two step equation Brackets
Objectives The student will be able to:
Objectives The student will be able to:
2.2 Solving Equations with Variables on Both Sides
Objective The student will be able to:
Objectives The student will be able to:
Objectives The student will be able to:
Objective The student will be able to:
Objectives The student will be able to:
Warm-Up 2x + 3 = x + 4.
Do Now Simplify. 1. 5(7) – (18 – 11)  (40 – 35) (12 – 4)
Objectives The student will be able to:
8 + (-6) = 2 ______ Different Signs Subtract.
Bell Ringer Solve the following: 1. ) 7(4 – t) = -84 2
Objectives The student will be able to:
Objectives The student will be able to:
Objectives The student will be able to:
Objectives The student will be able to:
Objective The student will be able to:
Homework Review.
Objectives The student will be able to:
Multiplying more than two integers
Subtracting integers without number line 3 digit.
Recognize the Operation
Adding integers without number line 2 digit.
Presentation transcript:

Patterns and Algebraic rules

Rule recap Remember: We look for a number pattern in a sequence: The rule is add 2 to the previous term. , , , The rule is add 4 to the previous term. , , , Hand out worksheet 1

Using rules in shape patterns. Remember, when we have a shape pattern it helps if we draw a table: Term 1 2 3 4 5 No of sides 8 12 16 20

Writing our rule as a formula The rule is add 4 to the previous term. Is there another way to get from the term number to the number of sides? What other mathematical sequence matches 4,8,12,16,20? The multiples of 4!! If we multiply the term number by 4 we get the number of sides!!

The number of sides = 4 × the term number. The formula The number of sides = 4 × the term number.

Using algebra in our formula To use algebra we must follow some rules: Always put what you are trying to find first. Put the number you multiply by before a letter.

The change to algebra. Lets look at our formula again: The number of tiles = 4 × the term number. It would be useful to simplify the formula: Letters (for our variables) and numbers. The number of tiles can be "t" The term number can be "n"

There is one more thing we need to do: The algebraic formula There is one more thing we need to do: We never use a multiplication sign in algebraic formulas. Worksheet 1 ends

Two stage formulas Some rules are not as straight forward and you may have to use two stages. This means that after multiplying your term number, you may need to add or subtract a number to reach your answer. Hand out worksheet 2

The pattern

Pattern table Term 1 2 3 4 5 No of Tiles 7 9 11

The rule Remember we noticed that the sequence pattern matched the multiples of a number? We can use that every time. Our sequence matches the multiples of 2 so lets see how that works:

The first stage Term 1 2 3 4 5 No of Tiles 7 9 11 × 2 6 8 10 We are not quite there, what do we need to do to reach the number of tiles?

The second stage Term 1 2 3 4 5 No of Tiles 7 9 11 ×2 6 8 10 Add 1 We need to add one after we have multiplied.

The formula The formula is: the number of tiles = 2 × the term number + 1 Remember to change to algebra we use letters: the number of tiles can be "t" the term number is always "n"

t = 2n + 1 The algebraic formula Remember: no multiplication sign. Worksheet 2 ends

Other two stage formulas Find a formula for these in the same way: 1 2 3

Solution Term 1 2 3 4 5 No of tiles 5 9 13 17 21 Term ×4 4 8 12 16 20 Add 1 5 9 13 17 21 Formula is: number of tiles = 4 × term number + 1 Algebraic formula is: t = 4n + 1