Teaching to the Next Generation SSS (2007) Elementary Pre-School Inservice August 17, 2010

Next Generation Sunshine State Standards Next Generation Sunshine State Standards Eliminates:  Mile wide, inch deep curriculum  Constant repetition Emphasizes:  Automatic Recall of basic facts  Computational fluency  Knowledge and skills with understanding

Comparison of Standards Grade LevelOld GLE’sNew Benchmarks K st nd rd th th th th th 9319

ImplementationScheduleforNGSSS Original FCAT (FT Items) New FCAT SF (2004) New Adoption K - 2nd 2007 Standards 3rd w/ transitions 2007 Standards w/ transitions 2007 Standards 4th 1996 Standards 2007 Standards w/ transitions 2007 Standards 5th 1996 Standards 2007 Standards

MA.3.A.2.1 SubjectGradeLevel Body of Knowledge Big Idea/ Supporting Idea Benchmark Coding Scheme for SSS K - 8 MA.3.A.2.1

Topics not Chapters

Daily Review WB Problem of the Day Interactive Learning Quick Check WB Center Activities Reteaching WB Practice WB Enrichment Interactive Stories (K-2) Letters Home Interactive Recording Sheets Vocabulary Cards Assessments Resources with enVisionMATH

Four-Part Lesson Daily Spiral Review: Problem of Day Interactive Learning: Purpose, Prior Knowledge Visual Learning: Vocabulary, Instruction, Practice Close, Assess, Differentiate: Centers, HW

Conceptual Understanding

Old Instruction vs New Instruction

Algebraic Thinking NGSSS Grades 3 - 5

: Participants will explore: Students’ progression from arithmetic to algebraic thinking Algebraic thinking “thread” in Grades 3 through 5. Introducing algebraic thinking through patterns

Algebra Thread MA.3.A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables and graphs. (Moderate Complexity) MA.3.A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables and graphs. (Moderate Complexity) MA.4.A.4.1 Generate algebraic rules and use all four operations to describe patterns, including non-numeric growing or repeating patterns. ( High Complexity) MA.4.A.4.1 Generate algebraic rules and use all four operations to describe patterns, including non-numeric growing or repeating patterns. ( High Complexity) MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations. (Moderate Complexity) MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations. (Moderate Complexity)

Arithmetic Algebra Arithmetic Algebra = _____ vs. _____ = The language of arithmetic focuses on ANSWERS The language of algebra focuses on RELATIONSHIPS

Students begin describing mathematics in pictures, words, variables, equations, charts, and graphs. How Does Algebraic Thinking Start?

Repeating Patterns... Begins in Kindergarten Begins in Kindergarten Creating and Extending Patterns Creating and Extending Patterns Naming the Pattern Naming the Pattern A B C …

Repeating Patterns... What is the core of the pattern? What is the core of the pattern? To get at the predictive nature, you need to have terms specified: 1, 2, 3, 4, 5, 6, 7, …. To get at the predictive nature, you need to have terms specified: 1, 2, 3, 4, 5, 6, 7, …

Repeating Patterns... What is the next figure? How do you know? What is the next figure? How do you know? What is the 32 nd figure? How do you know? What is the 32 nd figure? How do you know? What is the 58 th figure? How do you know? What is the 58 th figure? How do you know? Write how you know what numbers are hexagons. Write how you know what numbers are hexagons. Write how you know what numbers are squares. Write how you know what numbers are squares. Write how you know what numbers are triangles. Write how you know what numbers are triangles

PATTERNPATTERNPAT… What’s the core? What’s the core? What’s the 70 th letter? How do you know? What’s the 70 th letter? How do you know? What’s the 75 th letter? The 76 th ? The 77 th ? What’s the 75 th letter? The 76 th ? The 77 th ? Write how you can determine the letter in position n, where n can be any whole number? Write how you can determine the letter in position n, where n can be any whole number?

Growing Patterns Describe in words, mathematically Describe in words, mathematically Why is it difficult to describe the nth term? Why is it difficult to describe the nth term? …

Dragon Math Make a series of pattern block dragons that look like this: … In words, how do you describe the pattern? Year 1Year 2Year 3

Finding the Rule AgeTotal

AgeTotal

AgeTotal

AgeTotal

AgeTotal n Let n stand for age, finish the chart.

Finding the Rule Can you explain each rule above, from the the dragons? Can you visualize the rule? AgeTotal n1n2n+13n+2

What Did We Do? Took an “interesting to kids” situation Took an “interesting to kids” situation Made a chart to organize the data Made a chart to organize the data Described the data and made a generalization in words Described the data and made a generalization in words Described the data and generalization with a variable Described the data and generalization with a variable Tied in a visual aspect—justify the rule Tied in a visual aspect—justify the rule

Letter Patterns Objectives Describe the growth pattern Describe the growth pattern Record data on T-chart Record data on T-chart Describe the rule for growth in words Describe the rule for growth in words Represent the rule with an expression Represent the rule with an expression Graph the function table Graph the function table

Growing the Letter “T” Create the letter “T” using 5 color tiles. Create the letter “T” using 5 color tiles. Year 0Year 1Year 2

Growing the Letter “T” # of Years # of Tiles ___ n ___ ● ● ● 15 n + 5 T - Chart

Growing the Letter “I” Create the letter “I” using 7 color tiles. Create the letter “I” using 7 color tiles. Year 0Year 1Year 2

Growing the Letter “I” # of Years # of Tiles ___ n ___ ● ● ● 17 n + 7 T - Chart

Making a Chart Make the H’s below on your graph paper. Make the H’s below on your graph paper.  Make a chart of the term numbers and number of tiles.  Predict, before drawing, how many tiles for the next H. Draw it to check.

Growing the Letter “H” # of Years # of Tiles n ___ ● 5n + 2 T - Chart ● ● ● ● ●

How many tiles are needed to make the n th term? How many tiles are needed to make the n th term? Can you explain why the nth term has that rule? Can you explain why the nth term has that rule? What would this look like if you graphed it? What would this look like if you graphed it? 1st2nd3rd (5n + 2)

Graphing a Function x y...

What Have We Done? Considered a sample of the types of patterns that students will encounter Considered a sample of the types of patterns that students will encounter Described the patterns in words Described the patterns in words Used charts to see the patterns Used charts to see the patterns Generalized to a rule with a variable in order to predict Generalized to a rule with a variable in order to predict

If you have an equation, you can +, -, If you have an equation, you can +, -, ×, or ÷ both sides by the same number ×, or ÷ both sides by the same number (except dividing by zero), and keep (except dividing by zero), and keep things “balanced.” things “balanced.” 45 Equality Principles

If you have an equation, you can +, -, If you have an equation, you can +, -, ×, or ÷ both sides by the same number ×, or ÷ both sides by the same number (except dividing by zero), and keep (except dividing by zero), and keep things “balanced.” things “balanced.” If two things are equal, one can be If two things are equal, one can be substituted for the other. substituted for the other. 46 Equality Principles

= Does not mean “find the answer” Does not mean “find the answer” Represents a balanced situation Represents a balanced situation 47 Equality Principles

48 Grade 3

Verbal & Algebraic Equations Three times a number, increased by 1 is 25. Three times a number, increased by 1 is 25. If 3 is added to twice a number, the result is 17 If 3 is added to twice a number, the result is 17 When a number is increased by 8, the result is 13. When a number is increased by 8, the result is 13. Three times a number, increased by 7, gives the same result as four times the number increased by 5. Three times a number, increased by 7, gives the same result as four times the number increased by 5. FIND THE NUMBER!

Grade 4

Sunshine Superstars Math

y Grade 5

Z

Groundworks, Grade 3 What is the value of ? What is the value of the ? + ++ = 12 =

Groundworks, Grade 3 + − + = = 20 5 Square + Square = 20 Square − Square + Triangle = 5 What number is the square? The triangle? How did you know?

Square + Square + Square = 21 Square – Triangle – Triangle = 1 What is the square? _______ What is the triangle? _______ Groundworks, Grade 3 7 3

Groundworks, Grade 4 = A. B. Cylinder + Square = 3 Cylinders C. ______ = 6 Spheres

Balance Challenge (B) Balance Challenge (C) Balance Challenge (C) Groundworks, Grade 4

Groundworks, Grade 5 Shape Grids (D) Grids (D) A

With the algebra strand in 3-5, we’re teaching kids HOW to think, not WHAT to think. (Marilyn Vos Savant) Building a Strong Algebra Foundation Building a Strong Algebra Foundation

How might you use your curricular materials to help your students develop algebraic thinking in your classroom? How might you use your curricular materials to help your students develop algebraic thinking in your classroom? What do you expect your students to find challenging about algebraic thinking? What do you expect your students to find challenging about algebraic thinking? How will you help them overcome these challenges? How will you help them overcome these challenges? What misconceptions might students hold about algebra and/or algebraic terms that you will need to address? How will you address these? What misconceptions might students hold about algebra and/or algebraic terms that you will need to address? How will you address these? Teaching the Content