Math Online

Lesson Plans, Interactive Activities,

Worksheets, and Links for Grades K - 12

 

Algebraic Thinking

 

Key:  I = Introduced, D = Developing, A = State Assessed, M = Mastered

First Grade

D

Sort objects by two of the following attributes: color, size, shape, and kind.

www.harcourtachieve.com

I

Describe how objects in a group are alike and how they are different.

http://www.sanrio.co.jp/english/multimedia/s_gallery/kt_demo.html

http://www.funbrain.com/cgi-bin/ob.cgi

D

Identify and describe growing patterns found in literature, in the environment, in physical arrangements, and in pictures.

www.harcourtachieve.com

http://www.sesameworkshop.org/sesamestreet/games/flash.php?contentid=110880&

D

Translate a repeating pattern from one format to another (e.g., red-blue-blue to snap-clap-clap).

www.harcourtachieve.com

D

Create, describe, and extend concrete, visual, auditory, or number patterns.

www.harcourtachieve.com

I

Identify the unit of a two-part repeating pattern.

www.harcourtachieve.com

D

Show or represent number sentences, involving addition and subtraction and numbers 0-20, with concrete objects.

D

Use mathematical terms and symbols appropriately.

I

Interpret and solve simple open addition sentences, including finding the missing addend.

www.harcourtachieve.com

http://www.bbc.co.uk/schools/numbertime/games/test.shtml

I

Apply the commutative property of addition.

 

Second Grade

D

Sort objects by two or more attributes.

D

Identify the rules by which objects or numbers have been sorted.

D

Extend a growing pattern, involving objects, shapes, or numbers.

http://math.rice.edu/~lanius/counting/patan4.html

D

Identify the unit of a three-part repeating pattern.

http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/5_Patterns/index.html

D

Translate a repeating pattern from one format to another (e.g., red-blue-blue to snap-clap-clap).

I

Determine the output number for a particular input number given a one-operation rule involving addition or subtraction.

D

Interpret and solve open sentences that involve addition or subtraction.

D

Communicate and use mathematical terms and symbols appropriately.

D

Show or represent number sentences, involving addition and subtraction and numbers 0-20, with concrete objects.

D

Demonstrate knowledge of and use the commutative property of addition.

I

Show that subtraction is not commutative.

D

Apply the addition and subtraction properties of 0 (adding or subtracting 0 doesn’t change a given number).

I

Describe qualitative change (e.g., a student growing taller).

I

Describe quantitative change (e.g., a student growing 2 inches in 1 year).

Third Grade

A

Sort objects by two attributes.

D

Sort objects by two or more attributes.

M

Devise, carry out, and explain how a group of objects has been sorted.

A

Identify the rules by which objects or numbers have been sorted.

D

Recognize, describe, complete, translate, or create patterns of figures or numbers.

A

Extend repeating and growing numerical or geometric patterns.

http://www.funbrain.com/cracker/index.html

http://teams.lacoe.edu/documentation/classrooms/linda/algebra/activities/pattern_grow/pattern_farm.html http://pbskids.org/cyberchase/parentsteachers/lessonplans/lesson4.html

A

Represent repeating geometric patterns as repeating numerical patterns.

http://teams.lacoe.edu/documentation/classrooms/linda/algebra/activities/patterns/growpattern.html

D

Describe a growing pattern, involving objects, shapes, or numbers.

A

Determine the output number for a particular input number given a one-operation function rule involving addition or subtraction.

D

Demonstrate knowledge (with words or symbols) of the commutative properties of addition and multiplication.

D

Show or represent and solve open sentences, involving addition, subtraction, and multiplication, with concrete objects or pictures.

A

Solve open sentences that involve addition and subtraction of whole numbers zero to twenty.

A

Connect open sentences to real-world situations.

D

Demonstrate knowledge and understanding of grade level mathematical terms.

I

Demonstrate understanding that an equation is a number sentence stating two quantities are equal.

D

Use the commutative property of addition and multiplication.

D

Show that subtraction is not commutative.

M

Apply the addition and subtraction properties of 0 (adding or subtracting 0 doesn’t change a number).

I

Apply the zero and identity properties of multiplication (adding 0 or multiplying by 1 doesn’t change a number).

I

Use arrays to represent the commutative property of multiplication.

D

Describe qualitative change (e.g., a student growing taller).

D

Describe quantitative change (e.g., a student growing two inches in one year).

Fourth Grade

D

Generalize and extend or complete patterns involving geometric figures or numbers.

A

Extend numerical and geometric patterns.

http://www.mathsyear2000.org/magnet/minus2/craterpairs/index2.html

http://www.hbschool.com/activity/buzz/buzz.html

http://www.primarygames.co.uk/pg2/splat/splatsq100.html

D

Represent and analyze patterns and relationships using words, tables, and graphs.

A

Determine the function rule for data in a function table.

A

Apply basic function rules.

A

Solve open sentences involving addition and subtraction.

A

Solve open sentences involving multiplication and division.

A

Connect open sentences to real-world situations.

I

Represent the idea of a variable as an unknown quantity by using a letter or a symbol.

D

Demonstrate understanding that an equation is a number sentence stating that two quantities are equal.

D

Use the commutative, associative, zero, and identity properties for addition and multiplication.

I

Investigate how a change in one variable relates to a change in a second variable.

D

Divide efficiently and accurately with single-digit whole numbers.

A

Add and subtract decimals (includes monetary units).

http://www.funbrain.com/football/index.html

http://www.funbrain.com/cashreg/index.html

I

Multiply decimals (includes monetary units).

 

Fifth Grade

D

Generalize and extend or complete patterns involving geometric figures or numbers.

A

Extend numerical patterns.

A

Extend geometric patterns.

A

Generalize numerical patterns using a variable.

D

Represent and analyze patterns and functions using words, tables, and graphs.

D

Determine or apply a function rule involving data in a function table.

A

Apply basic function rules.

M

Demonstrate understanding that an equation is a number sentence stating two quantities are equal.

A

Solve open sentences involving addition, subtraction, multiplication, and division.

A

Connect open sentences to real-world situations.

D

Represent the idea of a variable as an unknown quantity using a letter or a symbol.

A

Select an equation that represents a given mathematical relationship.

M

Apply commutative, associative, zero, distributive, and identity properties.

M

Show that division is not commutative.

D

Investigate how a change in one variable relates to a change in a second variable.

D

Use methods to compare and describe situations involving constant and/or varying rates of change and to solve real-world problems (e.g., extending rate charts).

A

Extend rate charts to solve real-world problems.

www.infoplease.com/ipa/A0110458.html

 

Seventh Grade

D

Represent, analyze, and extend geometric and numerical patterns.

A

Extend geometric and numerical patterns.

I

Develop understanding for arithmetic sequences.

A

Generalize patterns in data represented in tables and graphs.

A

Extend rate charts to solve real-world problems.

A

Apply function rules.

D

Create function rules.

D

Demonstrate understanding of different uses of variables.

A

Represent mathematical statements and real-world situations using symbols.

I

Translate one-variable verbal and written expressions into algebraic expressions.

A

Evaluate algebraic expressions given the value of two or more variables.

http://www.mathgoodies.com/puzzles2004/

A

Solve one-step linear equations.

A

Identify whole numbers that satisfy a given one-variable inequality.

D

Model algebraic equations with manipulatives, technology, and paper and pencil.

A

Solve real-world problems involving one-step linear equations.

http://www.gamequarium.com/prealgebra.html

I

Explore relationships between symbolic expressions and graphs of lines.

A

Select a scatterplot to represent data presented in tabular form.

D

Create a scatterplot to represent data presented in a tabular form.

D

Describe the relationship between two quantities represented in a scatterplot.

D

Describe how changes in one quantity or variable result in changes in another.

A

Interpret graphs which represent rates of change.

D

Use unit rates to solve problems (e.g., miles per hour, and words per minutes).

 

Eighth Grade

D

Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and (when possible) symbolic rules.

A

Generalize a variety of patterns with symbolic rules.

http://www.mathgoodies.com/puzzles2004/default.html

D

Develop understanding for arithmetic and geometric sequences.

D

Relate and compare different forms of representation for a relationship.

A

Represent situations and solve real-world problems using symbolic algebra.

D

Identify functions as linear or nonlinear.

I

Compare and contrast properties of functions from tables, graphs, or equations.

A

Formulate multi-step equations that represent relationships and real-world situations.

I

Develop meaning for intercept and slope.

I

Use a variety of forms to represent linear relationships.

A

Generate equivalent forms for simple algebraic expressions.

D

Recognize and generate equivalent forms for simple algebraic expressions.

A

Evaluate a first-degree algebraic expression given values for two or more variables.

http://mathematics.hellam.net/

A

Solve one- and two-step linear equations involving integers.

D

Use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, and paper and pencil).

A

Apply given formulas to solve real-world problems.

A

Solve one-step linear inequalities.

A

Connect the appropriate graph to a linear equation.

http://www.shodor.org/interactivate/activities/slopeslider/index.html

I

Identify the graphical representation of the solution to a one-variable linear inequality.

I

Develop understanding for particular values of patterns, relationships, and functions (e.g., x- and y- intercepts, slope, and maximum and minimum values).

D

Use a variety of representations to solve real-world problems (e.g., graphs, tables, and equations).

I

Compare linear relationships to non-linear relationships.

A

Connect symbolic expressions and graphs of lines.

A

Interpret graphs which represent rates of change.

D

Develop meaning for rate of change in real-world situations.

Algebra I

2.2.1

Recognize, analyze, extend, and create a variety of patterns

2.2.2

Use algebraic thinking to generalize a pattern by expressing the pattern in functional notation

2.2.3

Solve linear systems using a variety of techniques

2.2.4

Communicate the meaning of variables in algebraic expressions, equations, and inequalities

2.2.5

Identify and represent a variety of functions

2.2.6

Apply and interpret rates of change from graphical and numerical data

2.2.7

Analyze graphs to describe the behavior of functions

2.2.8

Interpret results of algebraic procedures

2.2.9

Apply the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities

2.2.10

Interpret graphs that depict real-world phenomena

2.2.11

Model real-world phenomena using functions and graphs

2.2.12

Articulate and apply algebraic properties in symbolic manipulation

2.2.13

Analyze relationships which can and which cannot be represented by a function

2.2.14

Graph inequalities and interpret graphs of inequalities

2.2.15

Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the real-life situations which the functions represent

2.2.16

Describe the transformation of the graph that occurs when coefficients and/or constants of the corresponding linear equations are changed

Amie Lambert               Jefferson County Schools