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Big Idea Algebra provides language through
which we communicate the patterns in mathematics. |
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4.3 A.
Patterns |
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Descriptive Statement: Algebra provides the language
through which we communicate the patterns in mathematics. From the
earliest age, students should be encouraged to investigate the
patterns that they find in numbers, shapes, and expressions, and by
doing so, to make mathematical discoveries. They should have
opportunities to analyze, extend, and create a variety of patterns
and to use pattern-based thinking to understand and represent
mathematical and other real-world phenomena. |
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Essential Questions |
Enduring Understandings |
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- How can change be best represented
mathematically? (4.5C1; 4.5F1; 4.5F2; 4.5F3; 4.5F4)
- How can patterns, relations, and functions be used as tools to
best describe and help explain real-life situations? (4.5C1) |
- The symbolic language of algebra is used to
communicate and generalize the patterns in mathematics.
- Algebraic representation can be used to generalize patterns and
relationships. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1. Recognize,
describe, extend, and create patterns.
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Using concrete
materials (manipulatives), pictures, rhythms, & whole numbers
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Descriptions using
words and symbols (e.g., “add two” or “+ 2”)
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Repeating patterns
·
Whole number
patterns that grow or shrink as a result of repeatedly adding or subtracting a
fixed number (e.g., skip counting forward or backward)
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4.3 B. Functions and Relationships |
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Descriptive Statement: The function concept is one of the
most fundamental unifying ideas of modern mathematics. Student begin
their study of functions in the primary grades, as they observe and
study patterns. As students grow and their ability to abstract
matures, students form rules, display information in a table or
chart, and write equations which express the relationships they have
observed. In high school, they use the more formal language of
algebra to describe these relationships. |
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Essential Questions |
Enduring Understandings |
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- How are patterns of change related to the
behavior of functions? (4.5F1; 4.5F2; 4.5F3; 4.5F4) |
- Patterns and relationships can be represented
graphically, numerically, symbolically, or verbally. (4.5E1) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1. Use
concrete and pictorial models of function machines to explore the basic concept
of a function. |
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4.3 C. Modeling |
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Descriptive Statement: The function concept is one of the
most fundamental unifying ideas of modern mathematics. Student begin
their study of functions in the primary grades, as they observe and
study patterns. As students grow and their ability to abstract
matures, students form rules, display information in a table or
chart, and write equations which express the relationships they have
observed. In high school, they use the more formal language of
algebra to describe these relationships. |
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Essential Questions |
Enduring Understandings |
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- How are mathematical models used to describe
physical relationships? (4.5E2)
- How are physical models used to clarify mathematical
relationships? (4.5E3) |
- Mathematical models can be used to describe and
quantify physical relationships. (4.5E2)
- Physical models can be used to clarify mathematical relationships.
(4.5E3) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1. Recognize
and describe changes over time (e.g., temperature, height) |
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2. Construct
and solve simple open sentences involving addition or subtraction.
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Result unknown
(e.g., 6 – 2 = __ or n = 3 + 5)
·
Part unknown
(e.g., 3 + ˙ = 8) |
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4.3 D. Procedures |
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Descriptive Statement: Techniques for manipulating
algebraic expressions - procedures - remain important, especially
for students who may continue their study of mathematics in a
calculus program. Utilization of algebraic procedures includes
understanding and applying properties of numbers and operations,
using symbols and variables appropriately, working with expressions,
equations, and inequalities, and solving equations and inequalities. |
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Essential Questions |
Enduring Understandings |
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- What makes an algebraic algorithm both
effective and efficient? (4.5D1) |
- Algebraic and numeric procedures are
interconnected and build on one another to produce a coherent whole.
- Reasoning and/or proof can be used to verify or refute conjectures
or theorems in algebra. (4.5D1; 4.5D3; 4.5D4; 4.5D5) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1. Understand
and apply (but don’t name) the following properties of addition:
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Commutative (e.g.,
5 + 3 = 3 + 5)
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Zero as the
identity element (e.g., 7 + 0 = 7)
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Associative (e.g.,
7 + 3 + 2 can be found by first adding either 7 + 3 or 3 + 2)
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