Upload
yazid
View
61
Download
0
Embed Size (px)
DESCRIPTION
Sequences and Equations. Common Core State Standards. MACC.7.EE.1.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - PowerPoint PPT Presentation
Citation preview
Sequences and Equations
Common Core State Standards
MACC.7.EE.1.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
MACC.7.EE.1.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Highlights Mathematical Practice #8Look for and make use of repeated reasoning.
Sequences and EquationsThese dot diagrams show the beginning of a sequence of patterns:
What would the fifth pattern in the sequence look like?
Sequences and EquationsThese dot diagrams show the beginning of a sequence of patterns:
Something look like this?
Sequences and Equations
If we were to continue the pattern, how many dots of each color will there be in the 10th pattern?
Sequences and Equations
How can we write an algebraic expression for the number of white dots?
term 1 2 3 4 5 nwhite dots 1 3 5 7 9 ???
Sequences and Equations
How can we write an algebraic expression for the number of white dots?
term 1 2 3 4 5 nwhite dots 1 3 5 7 9 2n –
1
Sequences and Equations
How can we write an algebraic expression for the number of black dots?
term 1 2 3 4 5 nblack dots 2 3 4 5 6 ???
Sequences and Equations
How can we write an algebraic expression for the number of black dots?
term 1 2 3 4 5 nblack dots 2 3 4 5 6 n +
1
Sequences and Equations
How can we write an algebraic expression to find the total number of dots?
One way to do this is by looking at the patterns again.
Sequences and Equations
How can we write an algebraic expression to find the total number of dots?
term 1 2 3 4 5 ntotal dots 3 6 9 12 15 ???
Sequences and Equations
How can we write an algebraic expression to find the total number of dots?
term 1 2 3 4 5 ntotal dots 3 6 9 12 15 3n
Sequences and Equations
How can we write an algebraic expression to find the total number of dots?
Another way to do this is by looking at the algebraic expressions we found.
Sequences and Equations
Number of white dots +
Number of black
dots =Total
number of dots
2n – 1 n + 1 3n
Sequences and EquationsThese dot diagrams show the beginning of a sequence of patterns:
What would the fifth pattern in the sequence look like?
Let’s look at another pattern:
Write an algebraic expression to find the number of white dots.
term 1 2 3 4 nwhite dots 2 3 4 5 ???
Let’s look at another pattern:
Write an algebraic expression to find the number of white dots.
term 1 2 3 4 nwhite dots 2 3 4 5 n + 1
Let’s look at another pattern:
Write an algebraic expression to find the number of black dots.
Let’s look at another pattern:
Write an algebraic expression to find the number of black dots.
term 1 2 3 4 nblack dots 3 4 5 6 n + 2
Let’s look at another pattern:
Write an algebraic expression to find the total number of dots.
Algebraically,
term 1 2 3 4 ntotal dots 5 7 9 11 2n +
3
Using a table,