Transcript Florida Sunshine State Standards in Mathematics (2007)

Teaching to the
Next Generation SSS
(2007)
Elementary Pre-School Inservice
August 17, 2010
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 Level
Old GLE’s
New Benchmarks
K
1st
2nd
3rd
4th
5th
6th
7th
8th
67
78
84
88
89
77
78
89
93
11
14
21
17
21
23
19
22
19
Implementation
Schedule
for
NGSSS
2008 - 2009 2009 - 2010 2010 - 2011
Original FCAT Original FCAT
(FT Items)
SF (2004)
SF (2004)
New FCAT
New Adoption
K - 2nd
2007 Standards 2007 Standards 2007 Standards
3rd
2007 Standards 2007 Standards 2007 Standards
w/ transitions w/ transitions
4th
1996 Standards 2007 Standards 2007 Standards
w/ transitions
5th
1996 Standards 1996 Standards 2007 Standards
Coding Scheme for SSS
K-8
MA.
3.
A.
2.
1
Subject
Grade
Level
Body of
Knowledge
Big Idea/
Supporting
Idea
Benchmark
MA.3.A.2.1
Topics not Chapters
Resources with enVisionMATH
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
Four-Part Lesson
1.
Daily Spiral Review: Problem of Day
2.
Interactive Learning: Purpose, Prior Knowledge
3.
Visual Learning: Vocabulary, Instruction, Practice
4.
Close, Assess, Differentiate: Centers, HW
Conceptual Understanding
Conceptual Understanding
Conceptual Understanding
Old Instruction vs New Instruction
Old Instruction vs New Instruction
NGSSS
Algebraic Thinking
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.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)
Arithmetic
7 + 3 = _____
Algebra
vs.
_____ = 7 + 3
The language of arithmetic focuses on
ANSWERS
The language of algebra focuses on
RELATIONSHIPS
How Does Algebraic Thinking Start?
Students begin describing
mathematics in pictures, words,
variables, equations, charts, and
graphs.
Repeating Patterns
A
B

Begins in Kindergarten

Creating and Extending
Patterns

Naming the Pattern
C…
...
Repeating Patterns
...
1
2
3
4
5
6
7
8
9

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, ….
Repeating Patterns
...
1






2
3
4
5
6
7
8
9
What is the next figure? How do you know?
What is the 32nd figure? How do you know?
What is the 58th figure? How do you know?
Write how you know what numbers are hexagons.
Write how you know what numbers are squares.
Write how you know what numbers are triangles.
PATTERNPATTERNPAT…
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

What’s the core?

What’s the 70th letter? How do you know?

What’s the 75th letter? The 76th? The 77th?

Write how you can determine the letter in
position n, where n can be any whole
number?
Growing Patterns
…

Describe in words, mathematically

Why is it difficult to describe the nth
term?
Dragon Math
Make a series of pattern block dragons
that look like this:
…
Year 1
Year 2
Year 3
In words, how do you describe the pattern?
Finding the Rule
Age
1
2
3
4
Total
Finding the Rule
Age
Total
1
1
2
1
3
1
4
1
1
3
5
Finding the Rule
Age
Total
1
1
1
2
1
2
3
1
3
4
1
4
3
5
Finding the Rule
Age
Total
1
1
1
3
2
1
2
5
3
1
3
7
4
1
4
9
5
Finding the Rule
Age
Total
1
1
1
3
5
2
1
2
5
8
3
1
3
7
11
4
1
4
9
14
n
Let n stand for age, finish the chart.
Finding the Rule
Age
Total
1
1
1
3
5
2
1
2
5
8
3
1
3
7
11
4
1
4
9
14
n
1
n
2n+1
3n+2
Can you explain each rule above, from the
the dragons? Can you visualize the rule?
What Did We Do?





Took an “interesting to kids” situation
Made a chart to organize the data
Described the data and made a
generalization in words
Described the data and generalization
with a variable
Tied in a visual aspect—justify the rule
Letter Patterns
Objectives
Describe the growth pattern
 Record data on T-chart
 Describe the rule for growth in words
 Represent the rule with an expression
 Graph the function table

Growing the Letter “T”

Create the letter “T” using 5 color tiles.
Year 0
Year 1
Year 2
Growing the Letter “T”
# of Years
T - Chart
0
1
2
# of Tiles
5
6
7
●
●
●
10
n
15
___
n___
+5
Growing the Letter “I”

Create the letter “I” using 7 color tiles.
Year 0
Year 1
Year 2
Growing the Letter “I”
# of Years
T - Chart
0
1
2
# of Tiles
7
8
9
●
●
●
10
n
___
17
n___
+7
Making a Chart

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
T - Chart
# of Tiles
1
2
3
4
7
12
17
22
●
●
●
●
●
●
n
5n
___
+2
1st
2nd
3rd

How many tiles are needed to make the nth
term?
(5n + 2)

Can you explain why the nth term has that
rule?

What would this look like if you graphed it?
Graphing a Function
.
.
.
y
x
What Have We Done?
Considered a sample of the types of
patterns that students will encounter
 Described the patterns in words
 Used charts to see the patterns
 Generalized to a rule with a variable in
order to predict

Equality Principles

If you have an equation, you can +, -,
×, or ÷ both sides by the same
number
(except dividing by zero), and keep
things “balanced.”
45
Equality Principles


If you have an equation, you can +, -,
×, or ÷ both sides by the same
number
(except dividing by zero), and keep
things “balanced.”
If two things are equal, one can be
substituted for the other.
46
Equality Principles
=

Does not mean “find the answer”

Represents a balanced situation
47
Grade 3
48
Grade 3
Verbal & Algebraic Equations




Three times a number , increased by 1 is 25.
If 3 is added to twice a number, the result is
17
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.
FIND THE NUMBER!
Grade 4
Grade 4
Grade 4
Grade 4
Sunshine Superstars Math
Grade 5
y
Grade 5
Z
Groundworks, Grade 3
+
=
+
+
What is the value of
What is the value of the
12
=
17
7
?
?
5
Groundworks, Grade 3
+
=
−
+
20
Square + Square = 20
=
5
Square − Square + Triangle =
5
What number is the square? The triangle?
How did you know?
Groundworks, Grade 3
Square + Square + Square = 21
Square – Triangle – Triangle = 1
What is the square?
7
_______
3
What is the triangle? _______
Groundworks, Grade 4
A.
=
B. Cylinder + Square = 3 Cylinders
C. ______ = 6 Spheres
Groundworks, Grade 4
Balance Challenge (B)
Balance Challenge (C)
Groundworks, Grade 5
Shape
Grids (D)
13
12
A 13
15 12 11
Building a Strong Algebra
Foundation
With the algebra strand in 3-5,
we’re teaching kids HOW to think,
not WHAT to think.
(Marilyn Vos Savant)
Teaching the Content
 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?
 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?