patterns and functions looking for and analyzing patterns functions geometric growing patterns 1
TRANSCRIPT
1
Patterns and Functions
• Looking for and Analyzing Patterns• Functions
Geometric Growing Patterns
2
Geometric Growing Patterns
Step1 Step 2 Step 3
3
Geometric Growing Patterns
Step1 Step 2 Step 3
How many squares would there be in step 12? In step 20? Can you write an equation to represent the growing pattern?
Step # squares
1
2
3
4
5
Turn over your
paper and
Graph it!
4
Growing Patterns
Step1 Step 2 Step 3
How many squares would there be in step 10? In step 20? Can you write an equation to represent the growing pattern?
Step # squares
1
2
3
4
5
Turn over your
paper and
Graph it!
5
Patterns and Functions
• Looking for and Analyzing Patterns• Functions
Geometric Growing PatternsContexts with Growing PatternsInput-Output FunctionsRead pp. 244-245
6
Border TilesIn light of what we learned yesterday about
variables and our learning so far today, let’s revisit the Border Tiles problem.
Choose a variable and write an expression to represent the number of tiles needed for any size square pool. (I used p = length of the side of a square pool)
• (p+2) + (p+2) + p + p• 2 (p + 2) + (2p)• 4(p + 1)• (p +2)2 – p2
7
Patterns and Functions
• Looking for and Analyzing Patterns• Functions
Geometric Growing PatternsContexts with Growing PatternsInput-Output FunctionsRecursive Patterns and FormulasExplicit FormulasRead page 246
8
Dot Pattern Problem
9
Strings of Pattern Blocks
10
Linear Functions
and Reflect!
At this point, we have considered many functions: border tiles, dot pattern, and strings of pattern blocks, geometric growing patterns, just to mention a few.
• Which are linear functions?• Which are not linear? • Are they still functions?
11
Linear Functions
• Rate of Change and Slope• Zero Slope and No Slope• Proportional and Non-proportional
Situations• Read pages 248-249
Identify at least one proportional situation and at least one non-proportional situation we have graphed today.
12
Linear Functions
• Rate of Change and Slope• Zero Slope and No Slope• Proportional and Non-proportional
Situations• Parallel, Same, and Perpendicular Lines• Graphs• Read page 250
13
Graphs and Context-Match the Graphs
14
Connecting Representations
The Hot Dog Problem:
Brian is trying to make money by selling hot dogs from a cart at the stadium during music performances and ball games. He pays $35 per night for the use of the cart. He sells hot dogs for $1.25 each. His costs for the hotdogs, condiments, napkins, and other paper products are on average $ 0.60 per hot dog. The profit from a single hot dog is, therefore, $ 0.65.
15
Connecting Representations
• Context• Table• Verbal Description• Symbols• Graph
16
Function Language(page 255)
• Independent and Dependent Variables
• Discrete and Continuous Functions
• Domain and Range