Showing posts with label reasoning and proof. Show all posts
Showing posts with label reasoning and proof. Show all posts

Monday, November 17, 2014

Shape Card Sort

Grade Level(s):  Kindergarten

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.K.G.A.1: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Targeted Needs of Student:
Recognizing and naming different shapes, sorting shapes by color and type, understanding different shapes, contrasting and comparing different shapes

Goal:
To challenge students to think about what makes a shape different and similar

Materials Needed:


1.      Sort for each student
2.      Paper
3.      Glue




Explanation/Summary:
Students will take all of their cards and organize them by shape and color. Then they will glue them on paper and use them for a reference as we start to discuss shapes and sorting objects.

Resource:                          


Number Concept Bag

Grade Level(s):  Kindergarten – 1st 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.K.OA.A.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Targeted Needs of Student:
Visual representation of decomposing numbers, understanding the value of a number, adding to make a number, kinesthetic activity to make 10

Goal:
To provide students with a visual and kinesthetic way to make ten

Materials Needed:


1.      Tokens
2.      Plastic bags
3.      Marker




Explanation/Summary:
Students will either be given a bag already made or will be able to make the bag themselves. The bag will be filled with a certain amount (5 or 10) of tokens and then on the outside a large line will be drawn. When the bag is sealed, students can manipulate the tokens inside to create number sentences that represent the number.
 


Resource:                          


Shape Search of 2D and 3D Shapes

Grade Level(s):  Kindergarten

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.K.G.A.3: Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").

Targeted Needs of Student:
Recognizing 2D and 3D shapes around the room, drawing 2D and 3D shapes, comparing and contrasting 2D and 3D shapes

Goal:
To provide students with examples of 2D and 3D shapes

Materials Needed:


1.      Worksheets
2.      Clipboards
3.      Writing utensils




Explanation/Summary:
Students will be given the worksheet and allowed to put the worksheet on a clipboard. They will go around the room and draw at least 2 examples of certain 2D and 3D shapes that they find.  Then they will discuss in a classroom discussion about the similarities and differences of 2D and 3D shapes.

Resource:                          



Equal Shmequal Book

Grade Level(s):  1st – 2nd 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 of the equal sign, visual representation of tug of war to show equal sign, balancing equations, integration of literature in math

Goal:
To provide students with representation of balancing both sides of the equal sign through literature  

Materials Needed:


1.      Equal Shmequal by Virginia Kroll




Explanation/Summary:
Teacher will read book and then facilitate a discussion about the importance of the equal sign. Then students can use the animals to represent different numerical values and balance those. The book describes a group of animals who are trying to balance a tug of war game.

Resource:       


Linear Functions Sort

Grade Level(s):  8th 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:



Spider Tally Data

Grade Level(s):  Kindergarten

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.K.MD.B.3: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Targeted Needs of Student:
Collecting data, asking for opinions, counting tallies, analyzing data, comparing data of two different survey answers

Goal:
To introduce data collection and data analysis

Materials Needed:


1.      Worksheet
2.      Writing utensils
3.      Clipboards




Explanation/Summary:
Students will each get a worksheet and a clipboard. Then they will go around the room and ask their classmates if they are afraid of spiders or not afraid of spiders. Then they will tally next to the appropriate response and count those answers. To write about the data, they will write the amount of people who said yes and no and last draw a spider. The teacher can then facilitate a discussion on analyzing the data.

Resource:



Math Bingo App

Grade Level(s):  1st – 2nd 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.C.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Targeted Needs of Student:
Fluently adding and subtracting, using technology to master mathematical concepts, fun way to practice adding and subtracting

Goal:
To provide students with practice adding and subtracting

Materials Needed:


1.      iPad or iPod




Explanation/Summary:
Students can use this app to practice addition and subtraction. The screen shows a bingo board and flashes up math problems for students to complete. If they get the correct answer to the problem, then they get a monster placed on a bingo square. The goal of the game is to get five questions correct that all are lined up on the board.

Resource:

Apple Store also shared with me by in SES 472


Pentominoes

Grade Level(s):  4th 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.3.MD.D.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Targeted Needs of Student:
Measuring perimeter, using unknown units to determine perimeter, counting units, using weird shapes to find the perimeter, understanding surrounding perimeter

Goal:
To provide students with manipulatives to introduce measuring perimeter

Materials Needed:


1.      Pentominoes Set
2.      Writing utensils
3.      Blank paper




Explanation/Summary:
After the teacher models, students will each use a Pentominoe to find the perimeter. They will trace the pentominoe and then count the amount of units to find the perimeter. These shapes are each very different and not symmetrical, so students will have to work individually on their shape.

Resource:




Quadratic Equation Booklet
Grade Level(s):  High School

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.HSA.REI.B.4: Solve quadratic equations in one variable.
·         CCSS.MATH.CONTENT.HSA.REI.B.4.A: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
·         CCSS.MATH.CONTENT.HSA.REI.B.4.B: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Targeted Needs of Student:
Solving quadratic equations, representing quadratic equations on a graph, using a hand-held booklet to reference y-intercepts, visually seeing and understanding slope and y-intercepts

Goal:
To provide students with a reference booklet to find the slope and y-intercepts of quadratic equations

Materials Needed:


1.      Bookets
2.      Cards with problems on them
3.      Glue
4.      Scissors
5.      Writing utensils



Explanation/Summary:
Students will first be given the template for the booklet. Then they will fold the book as directed on the website (with teacher guidance) and therefore create a booklet with blank coordinate planes. On each page of the book, there will be a blank plane and a corresponding blank page. The students will go from station to station where they will get a card to post on the blank pages. They will solve the card and then draw the graph that goes with the equation on the card glued. 
 


Resource: