33
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- expression écrite - matière potentielle : mathematicians
- expression écrite
- exposé - matière potentielle : the subject for the better part

- forms of thought
- psychoanalytic understanding of unconscious interiority
- language of sets
- internal dynamics
- arrows
- gestures
- mathematical entity
- diagrams
- sets
- mathematics
- 3 mathematics

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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, write their own

better spending solve similarity problems solution requires solving a

A.REI.1, A.REI.3

proportion

decisions? Indirect Measurement and Scale Drawing linear equation or linear N.Q.1, N.Q.2, 3.5 problems

o

To investigate scale factors and ratios of inequality in one variable N.Q.3, A.CED.4,

perimeters, areas, and volume A.25 Solve equations

A.REI.1, A.REI.3

ELL’s

o

To apply proportions using scale drawings involving fractional Should construct

expressions. math glossaries in

to find distances. A.26 Solve algebraic English and use

proportions in one variable them during class

which result in linear or and on homework

quadratic equations assignments.

Motion Problems/ Distance-Rate-Time A.5 Write algebraic N.Q.1, N.Q.2, 3.6

o

To define one variable in terms of another. equations or inequalities N.Q.3, A.CED.4,

o

To translate, set-up and solve distance-rate-that represent a situation

A.REI.1, A.REI.3,

time problems F.IF.6

4

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)

Geometric Figures G.1 Find the area and/or N.Q.1, N.Q.2, Activity Lab

o

Area and Perimeter of Composite Figures perimeter of figures N.Q.3, A.CED.4, (4.7, 10.9)

o

Surface Area and Volume of Rectangular composed of polygons and

A.REI.1, A.REI.3

Prisms and Cylinders circles or sectors of a circle

o

Circumference and Area of Circles G.2 Use formulas to

calculate volume and

surface area of rectangular

solids and cylinders

Review Percent/ Percent of Change N .5 Solve algebraic N.Q.1, N.Q.2, 3.7

o

To understand and apply the ratio of percent problems arising from N.Q.3, A.CED.4,

of change. situations that involve F.IF.6

o

To apply the percent proportion to solve fractions, decimals, percents

percent problems.

Percent Error / Relative Error M.3 Calculate the relative N.Q.1, N.Q.2, 3.7

o

To understand and apply the percent of error error in measuring square N.Q.3, A.CED.4,

in calculating area and volume. and cubic units, when there F.IF.6, G.GMD.3

is an error in the linear

measure

1D: Solving Inequalities (6 days instruction)

How do Simple Inequalities and Their Graphs A.4 Translate verbal A.CED.1, 4.1, 4.2, 4.3

inequalities

o

To find the solution to an inequality in one sentences into mathematical A.CED.3,

compare and variable. equations or inequalities

A.REI.1, A.REI.3

contrast to

o

To plot inequalities on a number line. A.6 Analyze and solve

equations?

o

Using the addition property to solve verbal problems whose

inequalities. solution requires solving a

Do we use linear equation or linear

different

o

Using the subtraction property to solve inequality in one variable

mathematical inequalities A.21 Determine whether a

procedures

o

Using multiplication and division to solve given value is a solution to a

when working inequalities.

given linear equation or

with linear inequality in one

inequalities? variable.

A.24 Solve linear

inequalities in one variable

G.6 Graph linear

inequalities

Multi-Step Inequalities A.5 Write algebraic A.CED.1, 4.4

o

Solving inequalities with one variable equations or inequalities A.CED.3,

that represent a situation

A.REI.1, A.REI.3

Delayed

Learners

Should be given

steps for solving

inequalities and

allowed to use

during class until

memorized

Advanced

Learners

Students should

discuss situations

that can be

represented by

inequalities and

determine

reasonable

solutions

5

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)

Multi-Step Inequalities A.6 Analyze and solve A.CED.1, 4.4

o

Solving inequalities with one variable verbal problems whose A.CED.3,

ELL’s

solution requires solving a

A.REI.1, A.REI.3

Have students

Inequalities with Variables on Both Sides linear equation or linear A.CED.1, 4.4

explain the word

inequality in one variable A .CED.3, problems to a

A.24 Solve linear

A.REI.1, A.REI.3

partner

Compound Inequalities (and/or) inequalities in one variable A.CED.1, 4.5

o

Solving and graphing compound A.CED.3,

inequalities.

A.REI.1, A.REI.3

Test 2

Unit 2: Linear Relationships

2A: Relations and Functions (5 days instruction)

What makes a Writing a Function Rule A.5 Write algebraic A.CED.1, 1.4

relation a

o

Recognizing equations that describe a equations or inequalities A.CED.2, F.IF.1,

function? functional relationship. that represent a situation F.IF.2, F.IF.5,

o

Using tables to write function rules G.3 Determine when a F.BF.1a, b

Domain and Range of a Function relation is a function, by F.IF.1, F.IF.2, 1.4

How do we

o

Identifying independent (domain) and examining ordered pairs and F.IF.5, F.BF.1a, b

write and use dependent (range) variables. inspecting graphs of

function relations

notation? Relations and Functions G.3 Determine when a F.IF.1, F.IF.2, 5.2

o

To represent relations and functions using relation is a function, by F.IF.5, F.BF.1a, b

mapping diagrams, tables, and function examining ordered pairs and

rules inspecting graphs of

o

To determine when a relation is a function. relations

Function Notation/ Evaluating Functions/ A.5 Write algebraic A.CED.1, 5.3, 5.4

Function Rule equations or inequalities A.CED.2, F.IF.1,

o

Identifying and graphing functions, using a that represent a situation F.IF.2, F.IF.5,

table G.4 Identify and graph F.BF.1a, b

o

To understand and write function rules. linear quadratic (parabolic),

o

To determine the range of a function given absolute value, and

the domain and function rule exponential functions

o

Modeling real world situations using

function rules

Delayed

Learners

Have students

substitute

solutions into the

function rule to

check their

answers.

Advanced

Learners

Discuss why

specific variables

are graphed on the

x-axis and others

on the y-axis. Use

terms independent

& dependent

variable

ELL’s

Have students

explain the

terminology to a

partner

6

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)

2B: Linear Relationships (9 days instruction)

What kinds of Direct Variation N.5 Solve algebraic A.CED.2, 5.5

Delayed

relationships

o

To model and solve equations of direct problems arising from A.CED.3,

Learners

are expressed variation, using the equation

y=kx

situations that involve A.CED.4, Have students use

by linear

o

To find the constant of variation given a fractions, decimals,

A.REI.10

, F.IF.4, each ordered pair

equations? table of values. percents, and F.IF.6, F.IF.7a, in a table to write

o

To determine whether or not a relationship proportionality/direct F.LE.5 equations rather

varies directly variation. than just one

How can A.5 Write algebraic

different equations or inequalities

graphing that represent a situation

choices affect Graphing a Line (Using a Table) A.CED.2, Extra

interpretation

o

Identifying and graphing functions, using a A.CED.3,

of the data? table A.CED.4,

Advanced

A.REI.10

, F.IF.4,

Learners

F.IF.6, F.IF.7a Arrange a

Finding the slope of a line/ Rate of Change A.32 Explain slope as a rate A.CED.2, 6.1

selection of

o

To understand slope as a rate of change of change between A.CED.3, equations in order

o

To find the slope of a line given two points dependent and independent A.CED.4, from steepest to

on the line variables.

A.REI.10,

F.IF.4, least steep

o

To determine the slope of a line based on A. 33. Determine the slope F.IF.6, F.IF.7a,

the graph of the line of a line, given the F.BF.3, F.LE.5

o

To identify the slopes of horizontal and coordinates of two points on

vertical lines the line.

Graphing a line using Slope, y-intercept Form A.34 Write the equation of a A.CED.2, 6.2, 6.3

ELL’s

o

To write the equation of a line given a point line, given it s slope and the A.CED.3,

on the line and its slope coordinates of a point on the A.CED.4,

o

To identify and graph linear functions. line

A.REI.10

, F.IF.4,

o

To investigate how changing the A.35 Write the equation of a F.IF.6, F.IF.7a,

coefficients of a function will affect its line, given the coordinates F.BF.3

graph. of 2 points on the line

A.37 Determine the slope of

o

To model real world problems involving a line, given its equation in

linear relationships any form.

7

Writing Equations of a Line

o

Given any point and a slope

o

Given any two points

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)

G.5 Identify and generalize

how changing the

coefficients of a function

affects its graph

A. 34 Write the equation of A.CED.2, 6.4, 6.5

a line given its slope and the A.CED.3,

coordinates of a point on the A.CED.4,

line.

A.REI.10,

F.IF.4,

A.35 Write the equation of a F.IF.6, F.IF.7a,

line, given the coordinates F.BF.3

of 2 points on the line

A.A.39 Determine whether

a given point is on a line,

given the equation of the

line

Parallel Lines A.36 Write the equation of a A.CED.2, 6.6

o

To discover that parallel lines have equal line parallel to the

x-

or

y

- A.CED.3,

slopes axis. A.CED.4,

o

To determine if lines are parallel

based on

A.REI.10

, F.IF.4,

their graphs or equations F.IF.6, F.IF.7a,

o

To write equations of lines parallel to each F.BF.3, F.LE.5

other

2C: Systems of Equations (7 days instruction)

What does the Solving systems of equations graphically A.7 Analyze and solve A.CED.2, 7.1

intersection

o

To understand how to solve systems of verbal problems whose A.CED.3,

points of a equations graphically. solution requires solving A.CED.4, A.REI.6,

system of

o

To analyze special types of systems systems of linear equations

A.REI.10,

graphs tell us?

o

To understand how to solve a system using of 2 variables

A.REI.11

G.7 Graph and solve

a graphing calculator systems of linear equations

What and inequalities with

information rational coefficients in 2

does the variables

solution set of Solving systems of equations algebraically A.7 Analyze and solve A.CED.2, 7.2

a system of (substitution) verbal problems whose A.CED.3,

equations give

o

To understand how to solve a system by solution requires solving A.CED.4,

A.REI.6

us? using substitution systems of linear equations

of 2 variables

Test 3

Delayed

Learners

When solving

word problems

have students list

all the information

and what they

need to find

Advanced

Learners

Have students

8

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)

Solving systems of equations algebraically A.10 Solve systems of 2 A.CED.2, 7.2

write a system of

(substitution) linear equations in 2 A.CED.3, three equations

o

To understand how to solve a system by variables algebraically A.CED.4,

A.REI.6

that form a

using substitution G.7 Graph and solve triangle

systems of linear equations

Solving systems of equations algebraically and inequalities with A.CED.2, 7.3

(elimination) rational coefficients in 2 A.CED.3,

ELL’s

o

To understand how to use addition or variables A.CED.4, Have students

subtraction to solve a system

A.REI.5, A.REI.6

explain the

o

To understand how to use multiplication to difference

solve a system. between intercept

Applications of linear systems A.7 Analyze and solve A.CED.2, 7.4

and intersect

o

To model real world applications that lead verbal problems whose A.CED.3,

to writing and solving systems of equations solution requires solving A.CED.4,

systems of linear equations

A.REI.5, A.REI.6,

of 2 variables

A.REI.10,

G.7 Graph and solve

A.REI.11

systems of linear equations

and inequalities with

rational coefficients in 2

variables

2D: Graphing Inequalities (4 days instruction)

Why does the Graphing and modeling linear inequalities A.6 Analyze and solve A.CED.3,

solution set for

o

To understand how to graph linear verbal problems whose

A.REI.10,

a system of inequalities. solution requires solving a

A.REI.12

inequalities

o

To determine where the solution set lies on linear equation or linear

differ from the the coordinate plane (above or below the inequality in one variable

solution set of line) A.21 Determine whether a

a system of given value is a solution to a

equations? given linear equation or

linear inequality in one

variable.

G.6 Graph linear

inequalities

Graphing systems of linear inequalities A.40 Determine whether a A.CED.3,

o

To understand and graph systems of linear given point is in the solution A

.REI.10,

inequalities ser of a system of

A.REI.12

o

To identify the solution set on the inequalities.

5.7

6.7

Delayed

Learners

Make sure that

students are using

a number of

points to verify a

solution

Advanced

Learners

Write their own

inequalities and

solve them

graphically

9

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)

coordinate plane G.7 Graph and solve

ELL’s

o

To model real world problems that involve systems of linear equations

Emphasize the

writing and solving a system of linear and inequalities with difference

inequalities rational coefficients in 2

between the

variables

inequality

Test 4

symbols and what

they mean on a

graph

Unit 3: Descriptive Statistics and Data Analysis (9 days instruction)

Measures of Central Tendency S.4 Compare and contrast S.1D.2, S.ID.3 1.6

Delayed

How can we

o

To find mean, median, mode, and range the appropriateness of

Learners

use statistical

o

To represent data using a stem and leaf plot different measure of central Create their own

data to make

o

To interpret the data in a stem and leaf plot tendency for a given data list of numbers

informed set. where the median

decisions? S.16 Recognize how linear and mean are the

transformations of one-same

How can we variable data affect the

collect and data’s mean, median, mode,

present data in and range.

a way that Box and Whisker Plot S.5 Construct a histogram, N.Q.1, S.ID.1, NY2

Advanced

makes it

o

To understand the applications of box-and cumulative frequency S.1D.2, S.ID.3

Learners

accessible and whisker plots histogram, and a box-and-Describe a

useful?

o

To understand how the minimum, whisker plot, given a set of situation where

data the mean or the

maximum, and the 3 quartiles are used to S.6 Understand how the five median or the

construct a box-and-whisker plot. statistical summary mode would be

(minimum, maximum, and the best measure

the three quartiles) is used of central

to construct a box-and-tendency

whisker plot

S.9 Analyze and interpret

a

frequency distribution table

ELL’s

or histogram, a cumulative

frequency distribution table

or histogram, or a box-and-

whisker plot

S.11 Find the percentile

rank of an item in a data set

01