Mathematics and gesture
33 pages
English

Mathematics and gesture

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33 pages
English
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Tout savoir sur nos offres

Description

  • expression écrite - matière potentielle : mathematicians
  • expression écrite
  • exposé - matière potentielle : the subject for the better part
Mathematics and Gesture SLSA Atlanta 2009 Mathematics and gesture. An odd couple: the supreme form of disembodied thinking and its crude corporeal antithesis. If mathematics engenders forms of thought which exceed that available to speech, gesture seems an atavistic return to simian calls and signals before speech. The antithesis is puzzling. Mathematics has many affiliations -- structural, aesthetic, experiential -- with music. Music is thoroughly gestural: literally in terms of its production through the playing of instruments, but also by the sonic gestures inherent in its composition and internal dynamics.
  • forms of thought
  • psychoanalytic understanding of unconscious interiority
  • language of sets
  • internal dynamics
  • arrows
  • gestures
  • mathematical entity
  • diagrams
  • sets
  • mathematics
  • 3 mathematics

Sujets

Informations

Publié par
Nombre de lectures 53
Langue English

Exrait

1 3. 5.2

Integrated Algebra Curriculum Map

Semester 1: Units 1, 2 and 3 Semester 2: Units 4, 5, 6, and 7
Essential Content/Skills
(with
suggested
days
Performance Indicators Common Core Resources Assessment Modifications
Question
instruction for each unit)
(Appendix B)
Standards
(Appendix A)
to instruction
(Appendix C) (*see footnote)
Unit 1: Relationships between Quantities and reasoning with Equations and Inequalities

1A: Number Theory and Operations (9 days instruction)
What makes Classifying Numbers/Comparing Numbers N.6 Evaluate expressions N.RN.3
something a
o

Classifying numbers according to which set involving factorials,
mathematical each number belongs absolute values, and
term?
o

Comparing and ordering real numbers exponential expressions
How do we Properties of Real Numbers N.1 Identify and apply the N.RN.3
translate
o

To understand and use the properties of properties of real numbers
written rational numbers. (closure, commutative,
information
o

To reason logically with given facts to a associative, distributive,
into conclusion identity, and inverse)
mathematical Distributive Property/ Combining Like Terms N.1 Identify and apply the
terms?
o

To understand and apply the distributive properties of real numbers
property. (closure, commutative,
associative, distributive,
identity, and inverse)
A.13 Add, subtract and
multiply monomials and
polynomials.
Adding and Subtracting Rational Expressions N.1 Identify and apply the
(Fractions) properties of real numbers
o

To evaluate expressions using the property (closure, commutative,
of numbers. associative, distributive,
o

To understand and apply addition and identity, and inverse)
subtraction of signed numbers
Multiplying and Dividing Rational Expressions N.1 Identify and apply the
o

To understand and apply the rules for properties of real numbers
multiplication and division of rational (closure, commutative,
numbers. associative, distributive,

4.2

2.1, 2.2

3.2

Diagnostic
Delayed
Test
Learners
Use algebra tiles
to simplify
expressions
Advanced
Learners
Have students
write complicated
expressions for
partners to solve
ELL’s
Should construct
math glossaries in
English and use
them during class
and on homework
assignments.

1

Essential
Question

2.1

2.1

Content/Skills
(with
suggested
days
Performance Indicators Common Core Resources Assessment Modifications
instruction for each unit)
(Appendix B)
Standards
(Appendix A)
to instruction
(Appendix C) (*see footnote)
identity, and inverse)

N.6 Evaluate expressions
involving factorials,
absolute values, and
exponential expressions
Evaluating Algebraic Expressions (PEMDAS) N.6 Evaluate expressions
o

Symbols in algebra involving factorials,
absolute values, and
o

Order of operations exponential expressions
o

Evaluating Algebraic Expressions
Evaluating Algebraic Expressions with A.5 Write algebraic
Parenthesis equations or inequalities
o

Order of operations with parentheses that represent a situation
(grouping symbols) N.6 Evaluate expressions
involving factorials,
absolute values, and
exponential expressions
Modeling verbal Relationships with Variables A.1 Translate a quantitative N.Q.2, A.SSE.1, 1.1
o

Translating English phrases to algebraic verbal phrase into an
expressions and equations algebraic expression
A.2 Write verbal

expressions that match
given
mathematical expressions
A.3 Distinguish the
difference between an
algebraic expression and an
algebraic equation
A.4 Translate verbal
sentences into mathematical
equations or inequalities
A.5 Write algebraic
equations or inequalities
that represent a situation
1B: Solving Equations (8 days instruction)
One-Step Equations A.5 Write algebraic A.CED.1, 3
equations or inequalities A.CED.3
that represent a situation
A.REI.1, A.REI.3
A.6 Analyze and solve
verbal problems whose

Delayed
Learners
Should be given
steps for solving
equations and
2

Essential Content/Skills
(with
suggested
days
Performance Indicators Common Core Resources Assessment Modifications
Question
instruction for each unit)
(Appendix B)
Standards
(Appendix A)
to instruction
(Appendix C) (*see footnote)
One-Step Equations solution requires solving a A.CED.1, 3

allowed to use
linear equation or linear A.CED.3 during class until
What does it inequality in one variable.
A.REI.1, A.REI.3
memorized.

mean to A.25 Solve equations Use simple
balance an involving fractional examples initially,
equation? expressions. building to more
Two-Step Equations A.CED.1, 3.1

complicated ones.

o

To understand and solve 2-step equations. A.CED.3


o

Using deductive reasoning to justify steps in
A.REI.1, A.REI.3
What does it solving equations
Advanced
mean to solve
o

To write and solve equations that model real
Learners
an equation? world situations Have students
Solving Equations with Combining Like Terms N.1 Identify and apply the A.CED.1, 3.2

look for multiple
and Distributive Property properties of real numbers A.CED.3 ways of solving
o

To understand and apply the distributive (closure, commutative,
A.REI.1, A.REI.3
the equations.
property to solve equations. associative, distributive, Have them try and
o

To write and solve equations that model identity, and inverse) construct an
real world situations A.5 Write algebraic equation with no
equations or inequalities solution
that represent a situation

A.22 Solve all types of
linear equations in one
variable.
Solving Equations with Variables on Both A.5 Write algebraic A.CED.1, 3.3

Sides/ Identities and No Solution equations or inequalities A.CED.3
o

To understand how to solve equations with that represent a situation
A.REI.1, A.REI.3
variables on both sides. A.6 Analyze and solve
o

To write and solve equations that model verbal problems whose
real world situations solution requires solving a
linear equation or linear
inequality in one variable.
A.22 Solve all types of
linear equations in one
variable.
Solving Equations with Fractions A.25 Solve equations A.CED.1, Extra

ELL’s
involving fractional A.CED.3 Should construct
expressions.
A.REI.1, A.REI.3
math glossaries in
English and use
3

Essential Content/Skills
(with
suggested
days
Performance Indicators Common Core Resources Assessment Modifications
Question
instruction for each unit)
(Appendix B)
Standards
(Appendix A)
to instruction
(Appendix C) (*see footnote)

Transforming formula and solving literal A23 Solve literal equations A.CED.2, 3.4

them during class
equations for a given variable A.CED.3, and on homework
o

To transform formulas for particular A.CED.4, assignments.
variables
A.REI.1, A.REI.3


Consecutive Integer Problems A.6 Analyze and solve
A.REI.1
Extra

o

To write and solve equations that model verbal problems whose

real world situations involving consecutive solution requires solving a
integers, odd and even inclusive linear equation or linear

inequality in one variable.
Test 1

1C: Proportional Reasoning (8 days instruction)
What are Ratio and Rates, Unit Rates, Transforming A.26 Solve algebraic N.Q.1, N.Q.2, 3.4
Delayed
proportions Formulas proportions in one variable N.Q.3, A.CED.4,
Learners
and how are
o

To understand and apply ratio in solving Which result in linear or
A.REI.1, A.REI.3
Use a table to
they related to problems. quadratic equations. organize
rates, ratios,
o

To find unit rates and to convert rates. M.1 Calculate rates using information
scales and Solving Proportions appropriate units. N.Q.1, N.Q.2, 3.4

fractions?
o

To understand and solve algebraic M.2 Solve problems N.Q.3, A.CED.4,

involving conversions

How does an proportions within systems, given the
A.REI.1, A.REI.3


understanding relationship between the
Advanced
of percents and units.
Learners
proportions Similar Figures A.6 Analyze and solve N.Q.1, N.Q.2, 3.5 Have students
help us make
o

To understand and apply proportions to verbal problems whose N.Q.3, A.CED.4,

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