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