Lesson Study Group B February 2012 FUN with Functions! Lesson Study Group B February 2012

Objectives I will be able to use a function table to write an equation. I will be able to use the equation to complete the missing values in the function table. Algebra and FUNCTIONS 1.5

Prior Knowledge 7 9 6 3 4 1 Finding Patterns Find a pattern between the yellow column and the blue column. It is not a pattern until you have checked 3 rows! 4 1 7 9 6 3 Teacher Modeling The pattern is subtract 3 The pattern is

Prior Knowledge 3 5 9 12 15 27 36 Finding Patterns Find a pattern between the yellow row and the blue row. The pattern is multiply by 3 The pattern is Ask: How do you prove it is a pattern? Choral: YOU HAVE TO CHECK THREE! Where do I start to find my pattern? TPS/WB Then find pattern: display on WB 3 5 9 12 15 27 36

Prior Knowledge 1 8 2 36 9 24 6 16 4 Finding Patterns Find a pattern between the yellow column and the blue column. 16 4 1 8 2 36 9 24 6 The pattern is divide by 4 The pattern is What do you compare? Blue to yellow or yellow to blue? Choral: Yellow to blue Find pattern: WB (TWPS to explain)

Prior Knowledge 3 5 7 1 9 2 Finding Patterns Find a pattern between the yellow row and the blue row. The pattern is add 2 The pattern is Find pattern: WB: Be ready to share: Random Select 3 5 7 1 9 2

What is a Function? x 8 y + 4 12 Teacher Talk A function is a rule, that for every value of x (input) gives exactly one value of y (output).

What is a Function? x 7 y + 4 11 Students read definition to their partners. Explain what it means to partners (call on student with correct answer after listening to their discourse). A function is a rule, that for every value of x (input) gives exactly one value of y (output).

x + 5 = y y = x + 5 Functions is the input (x) + 5 is the rule In the incomplete equation + 5 = ___ is the input (x) + 5 is the rule Teacher Talk x + 5 = y _____ is the output (y) y = x + 5

What is a Function Table? x y 4 1 8 2 36 9 24 6 A function table is a way of organizing values. Now you can find a pattern between an x value and a y value to write an equation. a a a a a a Ask: How many rows of x and y do we need to prove that our pattern is accurate? (Show me on fingers) a a

Connecting a Function to its Table Let’s imagine this equation + 5 = ___ The input is a number going in. + 5 is the rule x (input) y (output) The output is the result of applying the rule ( + 5) Write in some values for x and y to show students.

Steps for Writing an Equation Step 1: Find a pattern Step 2: Identify the rule Step 3: Write an equation by adding x and y to the rule.

Writing an equation 5 15 9 27 12 36 x y x y y = 3x The rule is… · 3 9 27 12 36 x y The rule is… · 3 = ___ Ask: Do we start with the x column or the y column? Students: Find pattern. Write rule. (WB) Teacher: Model writing equation 3x = y y = 3x

Writing an equation 7 4 9 6 3 x y x y The rule is… - 3 = ___ y = x - 3 x y The rule is… - 3 = ___ Students find rule. Think to yourself: What is going to be with the rule? Students self-check as teacher models writing equation y = x - 3

Writing an equation x 5 7 1 y 9 2 3 x y + 2 The rule is… = ___ 1 y 9 2 3 x y Students find rule. Think to yourself: What is going to be with the rule? Students self-check as teacher models writing equation + 2 The rule is… = ___ y = x + 2

Writing an equation x 25 35 10 5 y 7 2 1 x y ÷ 5 The rule is… = ___ Students find rule. Students: Write the equation using the rule: WB 1-16KIM ÷ 5 The rule is… = ___ y = x ÷ 5

Steps to Completing a Function Table Steps for Writing an Equation Steps to Completing a Function Table Step 1: Find a pattern Step 2: Identify the rule Step 3: Write an equation by adding x and y to the rule. Step 4: Use the x value to calculate the y value. DENISE and CRAIG Start Have students read steps 1-3 Then reveal step 4

Function Tables 5 10 7 12 15 13 18 15 20 17 22 The rule is: = = ___ = ___ + 5 x y x y 5 10 7 12 15 Students on WB: Find pattern and write rule on WB (show me) Turn into equation on WB (show me) I Do… Choral response starting w/#13 With #20 teacher model how to work backwards INVERSE OPERATION 13 18 15 20 17 22

Function Tables 6 18 12 5 15 4 7 21 3 9 10 30 The rule is: = ___ = · 3 = ___ = · 3 x y x y 6 18 12 5 15 4 Students on WB: Find pattern and write rule on WB (show me) Turn into equation on WB (show me) Students: Think Pair Share on #12 #30 on WB 7 21 3 9 10 30

Function Tables y = x - 6 18 12 10 4 20 14 9 3 16 10 6 Equation x – 6 = y y = x - 6 Equation x y 18 12 10 4 20 14 We Do – White Boards Write equation (show me) Fill in empty spaces on table TWPS (show me) 9 3 16 10 6

Function Tables y = x - 4 Equation x – 4 = y x 6 9 11 15 40 y 2 7 16 20 5 36 We Do – White Boards Write equation (show me) Fill in empty spaces on table TWPS (show me)

Function Tables y = x ÷ 4 20 5 8 2 4 1 24 6 12 3 28 7 Equation x ÷ 4 = y y = x ÷ 4 Equation x y 20 5 8 2 4 1 We Do – White Boards Write equation (show me) Fill in empty spaces on table TWPS (show me) 24 6 12 3 28 7

Function Tables y = x · 6 3 18 5 30 9 54 6 36 7 42 Equation x ·6 = y x We Do – White Boards Write equation (show me) Fill in empty spaces on table TWPS (show me) 9 54 6 36 7 42

Function Tables y = x +9 Equation x + 9 = y x 2 22 13 8 y 11 17 16 9 7 y 11 17 16 9 7 31 22 We Do – White Boards Write equation (show me) Fill in empty spaces on table (show me) We Do – White Boards Which to remove and which to keep?

Function Tables y = x ÷ 8 32 4 24 3 16 2 88 56 7 48 6 Equation x ÷8 = y y = x ÷ 8 Equation x y 32 4 24 3 16 2 11 We Do – White Boards Write equation (show me) Fill in empty spaces on table (show me) We Do – White Boards Which to remove and which to keep? 11 48 7 88 56 7 48 6

CST Released Question y = x + 9 y = x – 9 y = 9x y = Which equation could have been used to create this function table? y = x + 9 y = x – 9 y = 9x y = x y 9 81 2 18 4 36 11 99 Think write pair share (WB) Random select for justifying Justify your answer

Number of Family Members Word Problem Choose the number to complete the function table to find how much 9 tickets will cost. $8 $102 $136 $153 Number of Family Members Total Cost for Tickets 1 $17 2 $34 5 $85 9 Think write pair share (WB) Random select for justifying Justify your answer

Which table represents values of x and y such that y = x + 7? 1 8 4 10 x y 2 9 3 11 C. x Y 9 2 6 1 x y 4 11 2 9 Think write pair share (WB) Random select for justifying B. D. Justify your answer

Objectives I will be able to use a function table to write an equation. I will be able to use the equation to complete the missing values in the function table.

Ticket Out the Door! QUIZ You Rule! Complete quiz from today’s lesson with the following information: Rule Equation Explanation Complete function table Create your own function table with the following information: Rule Equation Completed Table: must have an x and a y include at least 4 rows of numbers Write a real life situation to go with your table 15-28 DENISE/CRAIG

Guess My Rule! Input Partner A Output Partner B Input Partner A Output Partner B pulls a card Partner A pulls a card Input Partner A Output Partner B Input Partner A Output Partner B