Linear Functions Sort

Grade Level(s):  8^th Grade

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

CCSS.MATH.CONTENT.8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.

·         CCSS.MATH.CONTENT.8.EE.C.8.A: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

·         CCSS.MATH.CONTENT.8.EE.C.8.B: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Targeted Needs of Student:

Practicing linear functions, understanding different functions and how to describe them, kinesthetically matching each function

Goal:

To provide students with examples and non-examples of many different linear functions

Materials Needed:

1.      Worksheet

2.      Scissors

3.      Glue

4.      Scratch Paper

Explanation/Summary:

Students will cut the sort apart and then match each line written in slope intercept form to the description that goes along with. The descriptions vary from an actual line that has been graphed to a description of what the line should look like. Then they can glue this in their notebook for reference.

Resource:

www.teacherspayteachers.com

Graphing Linear Functions

Grade Level(s):  8^th – 9^th Grade

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

CCSS.MATH.CONTENT.8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.

·         CCSS.MATH.CONTENT.8.EE.C.8.A: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

·         CCSS.MATH.CONTENT.8.EE.C.8.B: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Targeted Needs of Student:

Graphing equations, understanding the importance of neat work with equations, understanding slope and linear functions, self-checking answers

Goal:

To practice how to graph equations with lines

Materials Needed:

1.      Worksheets

2.      Rulers

3.      Pencils

4.      Scratch Paper

Explanation/Summary:

Students will graph each of the lines that are in slope intercept form on the coordinate plane with letters on it. As they graph, letters and numbers will be hit by the same line. Then they will write the corresponding letter with the letter on the bottom of the page to answer the question, “What’s green and fluffy and comes from outer space?”

Resource:

www.exponentialcurve.blogspot.com

Domino Match Up

Grade Level(s):  Various Grades

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

Various standards can be applied to this strategy.

Targeted Needs of Student:

Practicing various topics, self-checking answers, mastering a concept, alternative to worksheets

Goal:

Providing an alternative way to practice mathematical concepts

Materials Needed:

1. Domino set for each student
2. Scratch paper

Explanation/Summary:

Students will take the set of dominos and start at the domino that says “START.” Then they will complete the problem and find the answer to the problem on another domino. The next problem will be written on that domino as well and students will work to complete that problem next. This is basically a matching activity for students to get an answer, look for the answer, and then start to complete another problem. When they get the answer and that domino has “FINISH” on it – they are done.

Resource:

Shared by Brian Avolio at NEMS

Hands on Equations

Grade Level(s):  6^th – 8^th Grade

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

CCSS.MATH.CONTENT.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Targeted Needs of Student:

Using manipulatives to represent variables, introducing one step equations with variables, balancing equations, visual representation of balancing equations

Goal:

Providing students with a visual and kinesthetic way to balance equations with variables

Materials Needed:

1. Balance mat
2. Pawns
3. 0 – 5 Number dice
4. 6 – 10  Number dice

Explanation/Summary:

Students will use this mat to place pawns and numbers on it to represent an equations. The pawns will represent a variable (one color per variable – blue might mean x and red might mean y) and then the number dice represent a number (such as 5 being added to 2x or 5 + 2x). Then students will determine the number that the pawns represent using the strategy.

Resource:

Shared at the NCCTM Conference

True and False Number Strings

Grade Level(s):  Kindergarten – 8^th Grade

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

CCSS.MATH.CONTENT.1.OA.D.7: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Targeted Needs of Student:

Understanding the importance and meaning of the equal sign, understanding balancing equations, thinking critically about math

Goal:

Providing explanation of the equal sign and how to balance both sides of the equation.

Materials Needed:

1. Paper and pencil
2. Whiteboard and expo marker

Explanation/Summary:

To understand the sides of the decimal, the teacher will show the beginning statement of a number equaling itself (such as 6 = 6) and then they will decompose the number to show that the equation can be written a different way while still meaning the same thing. Each time that they write a new equation, the teacher will discuss with the students if that statement is true or false.

6 = 6

6 = 4 + 2

4 + 2 = 4 + 2

4 + 2 = 1 + 5

Resource:

Shared at the NCCTM Conference 

EquaBeam Number Balance

Grade Level(s):  Various Grades

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

Various standards can be applied when using this balance.

Targeted Needs of Student:

Adding numbers, representing and understanding equal signs, balancing equations, showing multiplication and division in a representational way

Goal:

Providing students with visual balance of equations

Materials Needed:

1. EquaBeam
2. EquaBeam Weights
3. Scratch Paper
4. Writ

Explanation/Summary:

Students will be shown the balance along with equations to show the importance of balancing both sides of the equation. First the teacher will have a card of equations and then they will ask students to show this on the balance. For instance, the card might say 2 + 5 = ___ + 3. Students would use the middle of the balance to symbolize the equal sign and then place a weight on 2 and then on 5 on the left side of the balance and a 3 on the right side. They will find the number that goes in the box. This is a good strategy to use in small groups but not in whole group because students need to be able to explore.

Resource:

Shared at the NCCTM Conference

Versitiles

Grade Level(s): Various Grades

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

These can be used for generally any common core standard. The Versitiles worksheet that accompanies is on one topic that is CCSS aligned.

Targeted Needs of Student:

Matching answers to patterns, recognizing errors using patterns, practicing various mathematical topics.

Goal:

Providing students with a quick and easy way to self-check their answers.

Materials Needed:

1. Versitiles
2. Versitiles Worksheets
3. Projector

Explanation/Summary:

Students will be given a worksheet and then given the Versitiles. They will work the problems on the worksheet and then when they find the answer, they will look at the bottom of the page to see what way their tile needs to be to represent the answer. Each answer will have a different tile that will be placed in the Versitiles plastic container and when finished, the tiles together make a pattern. This is an easy way for the teacher to monitor practice and see which students understand the topic and which do not.

Resource:

Current OSTE – Brian Avolio at Northeast Middle School

Rules of Divisibility Charts

Grade Level(s): 5^th – 6^th Grade

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

CCSS.MATH.CONTENT.6.NS.B.2: Fluently divide multi-digit numbers using the standard algorithm.

Targeted Needs of Student:

Understanding divisibility rules, visually representing divisibility patterns, providing examples of divisibility rules, practicing recognizing patterns in numbers

Goal:

Providing students with proof that divisibility rules work using patterns.

Materials Needed:

1. Foldable with number charts on it
2. Scissors
3. Writing utensils
4. Coloring utensils

Explanation/Summary:

Students will be given number charts and shown how to represent the divisibility rules by shading in the multiples of every number from 2 – 10 (excluding 7). Then they will cut the foldable open to make flaps where they can write the divisibility rule with examples. This would be great to do as an activity after learning the rules and also teachers can have students fill out the divisibility rule foldable as she teaches each rule.

 

Resource:

www.teacherspayteachers.com

The Question Could Be Activity

Grade Level(s): Kindergarten – 12^th Grade

Content Area:                                                                        Process Area:

Numbers and Operations                                           Problem-Solving

Algebra                                                           Reasoning and Proof

Geometry                                                                    Communication

Measurement                                                             Representation

Data Analysis, Statistics, and Probability                    Connections

Common Core Standards:

• Any standard can be used for this strategy

Targeted Needs of Student:

Developing test taking abilities, reasoning skills, forming question and relating answers

Goal:

Providing students with ways to represent questions when given an answer.

Materials Needed:

1. Notecards with answers on them
2. Label cards “The answer is” and “The question could be.”
3. Blank notecards

Explanation/Summary:

Students will be given an answer such as “1/2 pizza” and then are asked to think of a question to go with it. The teacher can allow for students to use different concepts in math to form questions or they can have them create a question using a specific concept, such as multiplication or addition. This is great for test taking abilities and can be used as morning work, independent work, early bird work, or a math center.

Resource:

www.theteacherstudio.com