Battleship 5.G.A.1

lundta Picture Problems , ,

Incorporating games into any lesson will make the learning process more engaging and hands-on. This will also be a fun activity for the students to do! The game Battleship is a great way to introduce and practice graphing points on a coordinate plane.

For this activity, students will have to understand the location of points on a coordinate plane in relation to the origin (0, 0). To understand this students will be playing on a modified version of the game board for Battleship to include all four quadrants. The game board could also be modified where the students only place their battleships in the first quadrant so it better represents real world problems. I would have developed these game boards prior to the lesson, which will be a laminated sheet of paper. Students will be placed into pairs and on their game board they will place their five battleships anywhere on the graph. Then they take turns calling out coordinate points to try and sink their opponents five battleships. For each miss they will mark those boxes on the graphs with an open circle to indicate that the shot was missed on that point. However, for each hit they will x that portion out and the opponent then receives another turn.

After the activity has completed, there will be a class discussion about how Battleship relates to graphing points on a coordinate plane. Additionally, the activity will acknowledge how the first number in the pair describes the location of the point from the origin on the x-axis and similarly for the y-axis.

Battleship can be integrated with history, geography, and science. For history, it can be related to when battleships were first invented and marketed, in 1943. Then connect the introduction of battleships to World War II and how it effected the war. Whereas for geography, the coordinate plane that is used to play the game on is similar to latitude and longitude lines on a map. This will lead to classroom discourse of how the crew needs to have a vast knowledge of the world map and where the latitude and longitude lines are in relation to other battleships. Additionally, this activity can be integrated within science by looking into buoyancy of the materials used in creating these massive ships. This game also could be used with the Periodic Table as the playing field for Battleship.

To teach culturally, as a class we can examine battleships for different countries. Then discuss the similarities and differences between them all. While looking at how the countries cultural influence plays a role in how their battleships appear and function.

CCSS.MATH.CONTENT.5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

CCSS.MATH.CONTENT.5.G.A.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

CCSS.MATH.Practice.MP6: Attend to precision by understanding the location of coordinate points in relation to the origin when taking hits at their opponents battleship.

CCSS.MATH.Practice.MP7: Look for and make use of structure by recognizing the pattern of coordinate points in each quadrant. For instance, that a coordinate pair in the first quadrant will result in (positive, positive), in the second quadrant (negative, positive), third quadrant will be (negative, negative), and the fourth quadrant is (positive, negative).  

 

Baseball Geometry 8.G.B.7

baileymartoncik Uncategorized ,

The shape of the baseball field is full of math and geometry! This is a wonderful way to connect ideas from math class to the real world and the everyday lives of your students. Whether or not your students participate in the game of baseball, baseball has been a very large part of American culture and history.

Some of your students may have never thought of the baseball diamond as a square. Post a picture in your classroom of the bases from a birds eye view. Point out that when you connect each base with a line you have a perfect square!

Questions to ask your students:

How far is it from home plate to first base? 1st to second? 2nd to third? 3rd to home?

How far does the catcher have to throw the ball to get it to 2nd base?

How can we figure this out?

What information do we need?

Possible way to implement this in your classroom:

Have pictures of baseball fields posted around the room or on each students desks. Have students partner up in pairs or groups of three.  Have these questions written on the board and release them to figure it out! Make sure you have previously taught the Pythagorean Theorem, but do not tell them this is the method they should be using. Let your students decide that this is a real life application of the Pythagorean Theorem. Once students have found their answers have them present their answers, process, and how they know they are right!

 

CCSS.MATH.CONTENT.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CCSS.ELA-LITERACY.WHST.6-8.7
Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration..

Changing Serving Sizes 5.NF.6

meganbutler2 Uncategorized

Dessert is always something that people crave to have. Why not incorporate favorite desserts into math class!

For this activity, students will have to change serving sizes of dessert recipes so that everyone in their class gets a piece. Show the pictures of delicious treats and discuss that the recipes for these sweets only have a serving size of 4 which is a bummer since there are 24 students in the class. Discuss with the class what they need to do in order to make sure there is enough of the treat for everyone in the class to eat or bring home.

Provide multiple recipes with a serving size of 4 so that students have the options of choosing (recipes in link below). Once students get into groups they must use multiplication of fractions to figure out how much of each ingredient is needed to make a serving size of 24 for their recipe. Once the new recipes with the proper serving size is created, the students will create a poster with how they solved the problem and the amounts of each ingredient that is needed. Students will present their recipes to the class. Once the class has agreed that all calculations are correct and the ingredient amounts will create the proper serving size, the class can make these desserts (must be no bake recipes).

Since students can still complete the task without converting into different units, I will not give the conversion chart to all students, to reduce confusion since we have not gone over it before. If students ask about converting, I will provide it to those students who ask for it to add a challenge.

This activity could be used culturally by using recipes from different cultures. Students from the class could bring in family recipes that are from a different culture. This opens up conversation about different cultures and allows students to share their backgrounds.

CCSS.MATH.CONTENT.5.NF6- Solve real world problems involving multiplication of fractions and mixed fractions, by using visual fraction models or equations to represent the problem.

CCSS.Math.Practice.MP6- Attend to precision by having students calculate multiplication problems using fractions accurately and effectively expressing numerical answers with a degree of precision appropriate for each problem in context to the real-world problem.

CCSS.Math.Practice.MP1- Make sense of problems and persevere in solving them by checking their answers to problems using different methods and asking themselves “does this make sense?”

Recipe Options-2o1lm1c

 

How to Introduce Complex Numbers N.CN.A

jessicacole CCSS-Math Learning Progressions, HS Algebra, HS Number and Quantity

High School:  Algebra 2

 

Complex Numbers

 

This learning progression will be taught to a class that consists of sophomores and juniors in high school who are currently taking Algebra 2.  The Common Core State Standards that will be addressed come from two different domains.  The first domain is from High School:  Algebra-Arithmetic with Polynomials and Rational Expressions.  The CCSS Math cluster that will be addressed is “Understand the relationship between zeros and factors of polynomials.”  The second domain is High School: Number and Quantity-The Complex Number System.  The CCSS Math clusters that will be addressed are “Perform arithmetic operations with complex numbers,” “Represent complex numbers and their operations on the complex plane,” and “Use complex numbers in polynomial identities and equations.”  The third domain is from High School: Number and Quantity-The Real Number System.  The cluster that will be addressed is “Extend the properties of exponents to rational exponents.”  Students will also meet Mathematical Practices 1, 2, 3, 7, and 8.

 

The textbook that I will use as a resource is Glencoe’s Algebra 2:  Integration, Applications, and Connections.  The lesson will be taught from sections eight through ten of chapter five of this book.  These sections transition students from simplifying expressions including radicals and rational exponents to simplifying expressions containing numbers that are a part of the complex plane.

 

The central focus of this learning progression is an introduction to complex numbers and the complex plane.    The progression begins with the strategies that are used in simplifying expressions involving radicals.  These strategies will help student s understand how to use complex numbers and how to simplify expressions that contain complex numbers.   Students will be first introduced to what a complex number is and will then learn how to graph them in the complex plane.  The purpose of this learning progression is for students to gain a better conceptual understanding of the complex plane and will lead into solving quadratic equations that do not have real solutions.  This progression is set up so that the entry tasks from each section review a concept or ask students to think critically about a problem that will help them understand the new information that will be taught during the lesson.  How students do on this introductory information will influence where each lesson begins.  This will then influence how far we get in the planned lesson and so the next day’s lesson will also be affected.  Each lesson has been set up to be flexible and to run off of the previous lesson.  Beginning the class with questions that lead students to recall information that they have previously learned and to explore a new way of thinking will help students be more successful during the remainder of the class period and will help students become more interested in what they are learning.  Kubiszyn and Borich state in the book Educational Testing and Measurement that by imbedding a formative assessment into each lesson, “well-constructed performance test can serve as a reaching activity as well as an assessment.  This type of assessment provides immediate feedback on how learners are performing, reinforces hands-on teaching and learning…it moves the instruction toward higher order behavior.”

 

 

Common Core State Standards

 

Extend the properties of exponents to rational exponents.

CCSS.MATH.CONTENT.HSN.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

 

Perform arithmetic operations with complex numbers.

CCSS.MATH.CONTENT.HSN.CN.A.1
Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.

CCSS.MATH.CONTENT.HSN.CN.A.2
Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

CCSS.MATH.CONTENT.HSN.CN.A.3
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

 

Mathematical Practices

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8  Look for and express regularity in repeated reasoning.

Learning Progression

Learning Progression-Complex Numbers-164vuer

 

Build a playground 7.G.B.6 and MP4

kimberlyyounger Geometry Curriculum Aligned with CCSS-Math, ML Modeling, Technology Teaching Issues , , ,

By: Kimberly Younger, Rachel Van Kopp, Lizzie Englehart and Naomi Johnson

This lesson is focused on a 7th grade standard CCSS.Math.Content.7.G.B.6 but could be used for 6th through 8th grade depending on the application. This lesson focuses on the use of formulas to find area and problem solving of a real-world problem with the use of technology.

The prompt is “The school district is building a new playground for the new elementary school down the road. They have hired Playgrounds R’ Us to build it, but the supervisor wants to know what students would want on a playground. Create a playground with the following requirements.”

The students are building on their knowledge of area and perimeter formulas and applying it to a problem. The students are given a square footage for the playground, they must use three or more different shapes to represent their equipment, and the total square footage of the equipment must cover 30% of the playground’s area or more.

The students are given a packet which includes direction, a rough draft grid paper, final draft grid paper (submitted for approval), a screen shot of their Geogebra playground and a write up about their playground.

Below is an example of the packet students received. (link to the packet)

Below is a student’s sample playground

Rough Draft Blueprint                                Final Draft Blueprint                               Geogebra Blueprint

Table for Blueprint

Extension for “Build a Playground”:

As an extension to this lesson, students will later be able to work with 3 dimensional figures and nets to build the playground they have constructed in our lesson. This lesson emphasized finding and working with area of various geometrical figures and special reasoning. Using the knowledge, they have gained through our lesson, the students will be able to create the net that would best fit the equipment shape that they have presented to us on their “blue prints”.

In order to create the appropriate net, students will need to understand that the 3-dimensional shapes base will be the shape they have placed on their map in the lesson “Build a Playground”. This extension will cover CCSS.math.content.7.g.b.6 which states “Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.” This extension will help students make connections to the relationships between 2-dimensional figures and 3-dimensional figures, and connect the concepts of surface area and volume to real-world scenarios.

Disneyland Drive! – 8.F.B.4, 8.F.B.5

hendrixky ML Functions, ML Modeling ,

Students are put to the test in this fun and highly interpretive summative review of the previous unit: linear functions!

You and your family are going on a trip to Disneyland, but you must drive there! Your parents have decided that they don’t want the wear-and-tear of such a trip on their own vehicle, so they have narrowed it down to two (2) rental vehicles. However, they are having a hard time figuring out which one would be the most efficient/economical choice. Your job is to gather all the information you can, and construct a minimum of five (5) equations, graph them on GeoGebra, and lastly must decide which car your parents should choose for your vacation!

In order to complete this lesson, students will be split into groups of 3-5 members. The class as a whole will have a set gas price, but each group will have different vehicles as well as a monetary cap that they must remain under.

ModelingLessonPlan

Rocket Math: 8.F.A.3, 8.F.B.5, MP4

natashasmith2 ML Functions, ML Modeling , , ,

 

 

Rocket Math

By: Natasha Smith, Mariana Rosas, Paloma Vergara, & Melisa Sanchez-Leyva

 

 

 

 

This modeling lesson is for an 8th-grade classroom and is focused on the standards CCSS.MATH.CONTENT.8.F.A.3 and CCSS.MATH.CONTENT.8.F.B.5. This lesson introduces students to the concept of nonlinear functions. In the lesson, students will be able to explore the concept of a nonlinear function and expand their knowledge of what a function can look like.

This lesson follows a similar format to Dan Meyers’ 3 Acts. Students will start by watching a video of a model rocket launch. Individually, they will quickly draw a graph of what they think the relationship between the height of the rocket and time is. Next, they will work in groups to plot the points estimating the relationship of the height of the rocket at each second. Lastly, the teacher will take them outside and launch a model rocket to prove or disprove students’ theories. The model rocket will have a Pocketlab attached to it which will provide an exact graph of the height of the rocket at each time point. Students will compare their graphs to the Pocketlab graph. We decided to launch the rocket again instead of providing students with a graph from the original launch in the final act as it adds an element of excitement to the activity and the students will enjoy going outside to watch the rocket launch.

This lesson incorporates multiple types of technology. For the video used in the lesson, teachers would achieve best results by filming their own rocket launch as they will want to use the exact same type of model rocket in both the video and the in-class launch. The video representation should be similar to this video. Students will also be using the website Desmos to graph points. Lastly, the teacher will be using a Pocketlab. The Pocketlab is a wireless sensor that can be attached to different objects and will record different types of data and output graphs. For this lesson, the Pocketlab can be attached to the model rocket and will record the height (altitude) of the rocket as time passes.

Lesson Plan and Worksheet.

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How to Prove Two Triangles are Similar G.CO

jessicacole CCSS-Math Learning Progressions, Geometry Curriculum Aligned with CCSS-Math, HS Geometry

 

High School: Geometry I


Proving Geometric Theorems

By Emily Ivie

This learning progression was designed primarily for students who are in a traditional classroom
setting and have similar mathematical abilities. This class consists of 28 students, mainly
sophomores, who are studying geometry as part of their graduation requirement. The geometry
class has been designed to cover topics at a pace that meets the state requirements of content
topics in high school geometry. Since the class is set up on a semester system, the majority of the
students in this class have been a part of this class since the start of the school year and have had
the same exposure and background knowledge about geometry. Many students enjoy talking and
taking part in discussions during class, that is why I am going to teach this learning progression
in a student-lead conversation.

Standards:
The Common Core State Standards that will be satisfied are from the High School Geometry:
Congruence: Prove Geometric Theorems cluster. In the Congruence domain we will cover
CCSS.MATH.CONTENT.HSG.CO.C.9. Prove theorems about lines and angles and we will also
prove theorems about triangles and parallelograms with standards
CCSS.MATH.CONTENT.HSG.CO.C.10 and CCSS.MATH.CONTENT.HSG.CO.C.11. In this
course, students focus on mastering basic geometry knowledge that is required by the state, while
integrating in common core standards and mathematical practices. In this learning progression
the students will use four mathematical practices including: MP4, MP5, and MP7.
The curriculum these students are learning is based off the McDougal Littell: Geometry by
Larson, Boswell, and Stiff. This textbook is a resource used to design lectures, find worksheets,
and create practice problems through. The start to each class day will begin with a warm up
problem, followed with an introduction to a new topic with notes, classroom activity, and then
discussion. The notes are put up on the projector at the beginning of class so that students who
finish their warm up activity early can start writing the notes.

Accommodations:
Throughout the learning progression accommodations are made for students with IEPs and ELL
students. For the students who need a longer amount of time to write down their notes, they are
able to get the notes from me a day early so that they do not fall behind during lecture and are
able to participate in the discussion during note. Another accommodation made is that I let my 2
ELL students sit next to each other because they feel most comfortable working in partners this
way. In addition to these accommodations, the learning progression designed has activities that
are accessible to all learners. They do not require internet or any other tools beside from the
classroom whiteboards, pen, and paper.

Central Focus:
The central focus of this learning progression is for students to understand how specific theorems
about lines, triangles, and parallelograms were proved and how you can apply them. Students
will also have an understanding as to why it is important to know these theorems when applying
them to everyday life situations.

Lesson 1: Lines
We will start with an introduction to lines: parallel, transversal, and perpendicular. Since many of
the students have already had an introduction to this topic, it will be much easier to engage in a
class in student lead discussion when I ask them, “What does it mean for two lines to be parallel/
transversal/perpendicular?” This discussion of defining certain types of lines will begin to build
their mathematical thinking and conceptual understanding that they will use again during their
partner tasks. During the entry task students will demonstrate MP 7 looking for a way to identify
structure. After reviewing the entry task and understanding these definitions, I will give students
different geometric pictures and we will play a game of “I Spy”, students will be given colored
pencils and required to make a key. We will go around the class and identify specific types of
lines and angles. Once each student has identified and color marked one type of each line and
angle, I will show the students how to prove theorems about line angles. My example I will show
in class will be proving how vertical angle are congruent. I will ask students specific questions to
guide their learning such as: “What do we know about the lines and angles in this diagram? Are
their any linear pairs? What about supplementary?” These questions will formatively assess my
students knowledge about how well they conceptually understand how to identify lines and
angles. When students answer these questions, I will be looking for them to make the connection
between the next steps such as, “since we have angles that are linear pairs, we can use the linear
pair postulate.” This assessment will show students understanding of
CCSS.MATH.CONTENT.HSG.CO.C.9. proving theorems about lines and angles. After students
have worked through the vertical angle theorem, I will ask them to prove that alternate interior
angles are congruent. They will turn in their proof as part of their summative assessment. Once
looking at their proof, I will give feedback based on their reasoning and mathematical thinking.

Lesson 2: Triangles
My next activity will start with reminding my students about the properties of triangle. We will
be expanding our proof knowledge of triangles building off of the prior lesson where students
learned about proving lines and angles and we will try to prove properties about triangles. I will
work through one property about triangles and hold a discussion. After this, we will break up into
groups and I will give each group one theorem about triangles to solve. Then once enough time
has passed, each group will go up to the front board and give a presentation about the theorem
they proved. This lesson aligns with the following standard
CCSS.MATH.CONTENT.HSG.CO.C.10 proving theorems about triangles. Finally once groups
have put their proof up on the whiteboard, I will ask questions to assess their understanding such
as “What does this theorem tell us?”, “How can we apply this postulate to our problem?”, and
“Where do you start when proving this theorem?” These questions are important to ask students
to make sure that they are using tools (such as theorems) appropriately MP5. These
presentations will be a formative and summative assessment to make sure that students can
properly use the new information we just learned as well as explain their answers using old
vocabulary.

Lesson 3: Parallelograms
We will be expanding students understanding of proving line angles and triangles by introducing
parallelogram theorems. Ideally this lesson should be a fun activity that helps students with their
understanding of parallelogram proofs. Students will begin the lesson with a warm up in which
we will cover material learned in the previous day. Students will find a partner and share their
proof completed from the homework the night before. After we finish the entry task I plan to go
over the learning outcomes for the day, which is, students will be able to use their learned
understanding of parallelogram proofs. Shortly after that we will have a class discussion about
what a parallelogram is and I will encourage the use of specific vocabulary words like length,
adjacent, and angle. During our discussion I will hand out 4 parallelogram figures made from
construction paper to each student. We will go through each theorem about parallelograms:
labeling, folding, and drawing on each figure to show understanding for each theorem. Then I
will have the students take the time to try about write up their proofs of these theorems. While
the students working on folding there diagrams I will be walking around the classroom asking
questions about the theorems and how they proved the theorem. During this activity students will
achieve their learning target of CCSS.MATH.CONTENT.HSG.CO.C.11 and MP 4: “Model with
Mathematics” because students will use their parallelogram cuts outs to model their proofs.

Fence Fractions – 4.NF.B.3

kyleealmy ML Modeling, ML Number Systems, Technology Teaching Issues ,

 

Students are engaged in real world application of mathematical modeling when creating a fence using fractions that have unlike common denominators to add to make a whole. Tommy is building a fence and has one side length finished (1 whole) and needs help finding the other sides to his fence. The students will be given different fractions to analyze on geogebra–an online tool for students to use to help conceptualize fractions with unlike denominators. This lesson is designed for a 4th grade class modeling addition of fractions.  Students will be working individually to help Tommy create his fence.

Fence Lesson Plan-25objui

http://www.geogebra.org/m/ZrHpgCQv

Fun with Multiplying Binomials CCSS.MATH.CONTENT.HSA.SSE.A.1

isabelramos Assessment of CCSS-Math, CCSS-Math Learning Progressions, HS Algebra

This learning progression is made to take place in a high school Algebra classroom of 25 students. This class consists of freshman and sophomores. The desks in the classroom are arranged in groups of four. The lesson is based off the Algebra I textbook. The students have prior knowledge of binomials and what they look like and prior knowledge on the GCF.
learning progression-tt6ir7