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Goal: • V.5.3.1 Apply the formula V = l × w × h and V = b x h to find the volume of right rectangular prisms in real world problems (5.MD.C.5b) MA.5.M.5
• V.5.3.2 Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts in real world problems (5.MD.C.5c) MA.5.M.6

Grouping:  I will be grouping students based on their level of readiness. Finding Volume is a very difficult concept for 5th graders, and  the readiness can be developmental.  Some groups may have to see/make visual representations, while others may be able use the formula immediately.  Learning goal V.5.3.2 is even more challenging; I would work on this one with small groups of students who had already shown mastery of the other goal.

Types of Learning Activities: I will have different activities for students to work on while I will meet with groups and address the needs of their level. I would have games to play in Buzz, for example, this game from study ladder: https://www.studyladder.com/games/activity/calculating-the-volume-of-rectangular-prisms-26331, independent work on practice problems using worksheets or white boards, hands-on manipulatives, such as unifix cubes for students to use in creating rectangular prisms. Yet another group can be be watching videos on Khan Academy, etc. for review., and a group can be completing a journal writing explaining how they would solve a real world volume problem.

Technology: As you can see from above, technology can be integrated throughout my groups. I also like to use the Odyssey program for extra instruction with my students.

Lynn Carlson

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Differentiating Addition and Subtraction of Integers

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Differentiating Addition and Subtraction of Integers

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Activity:  Students will work both individually and collectively to explore addition and subtraction of integers using various techniques. They will also compare and contrast the uses of the operations and how they are useful in real-world applications. They will work on computation as well as problem solving skills.
Goal: AS.7.3.1 Apply properties of operations as strategies to add and subtract rational numbers MA.7.C.7 (7.NS.A.1d). AS.7.3.2 Solve real-world mathematical problems involving the addition and subtraction of rational numbers MA.7.C.8 (7.NS.A.3).
Grouping: Students will be grouped by readiness in order to better facilitate the small group time that I spend with students and making it easier to focus on students' common and possibly some individual needs at that time.
Learning Activity: As with most everyone else, it seems to me that the best way to repurpose our classtime would be to incorporate stations. However, the readiness groupings could be fluid in order to differentiate based on changing needs of the students during the unit.  As mentioned above, I would be working with small groups to focus on needs that could be identified using an assessment for learning that I could create on Buzz. We could explore their common errors or misunderstandings, look at more examples, and they could also work together to determine errors in examples that I provide in order to see if they can find the errors at this time or to ask more challenging questions of some groups. At another station, students would be watching videos from Math Antics and Khan Academy and completing practice assessments as learning, while getting immediate feedback. At another station, students would be attempting online games from mathgoodies.com and sheppardsoftware.com. After playing these games, students would complete a discussion board entry on Buzz where they will be able to work with their peers to further develop their understanding, no matter what their level of understanding was when they started. After completing the stations, students would be asked to create a Padlet entry where they journal their progress and struggles with the goals. These entries would continue to give me information about where the students' individual needs still exist and I would be able to provide the student with additional feedback and/or additional resources based on these needs.
Technology: My students will need their Chromebooks in order to access online resources including Padlet, Buzz, YouTube, Math Antics, Khan Academy, mathgoodies.com, and sheppardsoftware.com to complete the learning activities.

-Donna Nadolski

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Goal: 6.AF.4: Understand that solving an equation or inequality is the process of answering the following question: Which values from a specified set, if any, make the equation or inequality true?  Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.AF.5: Solve equations of the form x + p = q, x -p = q, px = q, and x/p=q fluently for cases in which p, q and x are all nonnegative rational numbers.   Represent real world problems using equations of these forms and solve such problems.

6.AF.6: Write an inequality of the form x>c, x≥ c, x<c, or x ≤ c, where c is a rational number, to represent a constraint or condition in a real-world or other mathematical problem.  Recognize inequalities have infinitely many solutions and represent solutions on a number line diagram.

Grouping: I will group students based on their performance and current levels of readiness.   This would be beneficial for both the students and myself.  Students that are able to grasp the concept can move forward and work on independent or assigned group tasks, while I can spend more time with struggling learners in a smaller group reviewing the information with them.
Type of Learning Activity:  I would have designated learning stations set up in the classroom.  Station 1: students would work collaboratively with their group members to solve various equations and inequalities.  Station 2 : Students would solve and analyze equations and inequalities solutions to check if the solutions are accurate and reasonable.  The will also be required to explain their reasoning and problem solving skills that they used to arrive at their conclusion.  Station 3: Students will watch assigned Khan Academy videos/tutorials on how to solve equations and inequalities. Station 4: students will use Padlet to create their own real-world equations and inequality problems.  In addition to creating their own problem, students will also be required to explain their problem solving reasoning.
Technology:  Students will use their Chromebooks to work on the assigned learning tasks using BUZZ, Padlet and Khan Academy videos on solving equations and inequalities.

-Tiffany Kranz

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Goal: 8.AF.2: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by transforming a given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Grouping: I will use readiness to determine how to group my students.
This is beneficial to me because I can work with select groups.
Learning Activity: I will use learning stations. Station 1, students will solve multi-step equations that may have one solution, infinitely many solutions, or no solution. They will discuss how and identify transforming equations into simpler equations will result with the same solution. Station 2, students will solve multi-step equations with rational numbers that may have one solution, infinitely many solutions, or no solution. Again they will discuss how transforming equations can result with the same answer. Station 3, students will analyze multi-step equations that have been solved for (error analysis). They will work together and discuss each equation to see if the answer is correct. They will also discuss their methods on how they came up with their resulting answer. Station 4, students will use Padlet to create their own equations. They will provide an equation for each situation, one solution, infinitely many solutions, and no solution. Students will describe what each of these situations mean.
Technology: Padlet and Khan Academy videos on solving multi-step equations.

Megan Kienzle

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For my learning activity, students will be examining graphs and situations and writing equations in slope-intercept form, and interpreting the slope and y-intercept in context.
Goal: 8.AF.6 -  Recognize in y = mx + b that m is the slope (rate of change) and b is the y-intercept of the graph, and describe the meaning of each in the context of a problem.
Grouping: I would use random grouping for this activity. I have grouping strip cards. I would give students each one card, and then group them based on one of the grouping symbols on the card.
Learning activity: I would use learning stations for this activity. Station 1: Students will review finding the slope, and y-intercept from a graph using laminated graph cards. Station 2: Students will use their chromebooks to practice this concept on Khan academy. Station 3: Students will write equations based on situation cards, in slope-intercept form. Station 4: Students will be given a graph. Using padlet, they must write the equation of the line and come up with a scenario that could be represented by the graph.
Technology: Students will be using the online tools at Khan academy and use Padlet to post their thoughts and ideas.

Michelle Magiera

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Kelly Shih - Differentiating Counting Money

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Kelly Shih - Differentiating Counting Money

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Learning Activity
For my lesson, students will learn to count dimes. Students already have knowledge of counting pennies and nickels.  They will practice counting coins individually and with a partner.

Learning Goal
MO.1.3.1 Find the value of a collection of pennies, nickels, and dimes MA.1.M.3

Type of Grouping
Students will be grouped based on their level or readiness.  Students will be at different levels of understanding when counting pennies and nickels. There will be students who need more assistance than others to be successful in counting dimes.

Type of Learning Activity to Best Fit Grouping
I would have students working at different stations.  Some students would watch a video  on counting money, play online money games, and practice by themselves while others can play money games with partner.  When I do stations, students work individually and with others of different ability levels, but when students meet with me, they are grouped by ability level.  With students grouped by ability, I am able to remediate or enrich students as needed.
What technology you would use to help provide this differentiation experience
Students will use BUZZ to find the videos, online games, and discussion board.

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For my learning activity, students are reviewing how to solve multi-step equations and inequalities with rational numbers and learning how to make connections with real-life examples.
Goal: 8.AF.1 Solve linear equations with rational number coefficients fluently, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems.
Grouping: I would group the students based on their level of readiness. I think that this would be beneficial because it would allow me to spend more time with those groups that are struggling and need extra practice.
Type of Learning Activity: I would have learning stations set up around the classroom. Station 1 would be practice problems that the groups can work on together and discuss any problems or questions that they might have. Stations 2 & 3 would involve the use of the students' Chrome books. At station 2, students would read articles and use the interactive tools assigned to them involving multi-step equations and inequalities on the website, Ck-12. At station 3, students would post their own real-life examples using Padlet. Station 4 would contain a board game that I've created which contains several multi-step equations and inequalities.
Technology: The students will be using Padlet to share their ideas and examples and they will also read articles and use interactive tools online to expand on their knowledge of this topic.

Leslie Curtis

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Goal: M.2.3.1 Estimate length using units of yards, feet, inches, centimeters, and meters (2.MD.A.3) MA.2.M.2
Grouping: I would group my students by level of readiness. I would do this so students that still need hands on practice estimating and measuring can do so while students whom have proven mastery at that activity can be given opportunity to extend and enrich their learning.
Learning Activities: After initial activities, I would break the class in to at least two groupings, perhaps even making small groups or partnerships within those groups. One group would be given hands-on activities to complete, such as working with a partner or in a group to estimate, then measure, given objects in the room. They would work together to decide which unit of measurement to use, then they would estimate the length of the object. Finally they would actually measure and record the results. For the other group, I would supply a shareable Google Doc with various opportunities to estimate a measurement. For example: How long is a school bus? How wide is a football field? Then, they would record their estimations on the Doc before researching on the internet to find out the actual measurement. They would the record their research results as well.
Technology: The first grouping would be using "old fashioned" technology - pencil, paper, and measuring tools :)
The second group would use their computers, Google Docs, and the Internet to complete their activity.

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For my learning activity, the students explore how businesses analyze data to help communicate with their customers. The students create graphs based on evidence they have gathered about popular parks. Then the students share the graphs, analyze the data, and form questions about their data as well as other students.

Goals:
3.DA.1: Create scaled picture graphs, scaled bar graphs, and frequency tables to represent a data set—including data collected through observations, surveys, and experiments—with several categories. Solve one- and two-step “how many more” and “how many less” problems regarding the data and make predictions based on the data.

Grouping Students:
I will group students based on interest and readiness levels. The students that want to collect data about Deep River Water Park will work together and the students that want to collect data on Six Flags will work together. Within those groups I will use pre-assesments to divide both groups into smaller groups of students with similar readiness levels. I can then use each learning style to create my learning activities.

Types of Learning Activities:
I will have a research station where the students will read either about other water park popularity data or amusement park popularity data. From this, students can create their survey questions which they will use for creating their graphs. Another station will be where students work with me on understanding how to create different types of graphs and decide which graph they will create  for their survey. I will also have a station where students will watch Khan Academy if they are struggling with this skill of analyzing data or creating different graphs based on their surveys. Another station will be where groups come together to answer each others surveys to gather their data. At this station they will use a google doc page to keep track of their information from their surveys. Finally, there will be a station where students blog about their findings and how analyzing their data helped them understand why the parks are so popular. This will also be where they can respond to each other and ask questions about their findings.

Technology:

The students will use technology to research about different water park popularity data and other amusement park popularity data. Google Docs will be used to keep track of information collected from surveys. Khan Academy will be used as a resource for my lower level readiness groups as additional review they may need to better understand the skill we are working on. Finally students will use Buzz to blog about their findings and how analyzing their data helped them understand why the parks are so popular. This will also be where they can respond to each other and ask questions about their findings.

-Katie McMahon

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Differentiating Adding and Subtracting in the Real World

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Differentiating Adding and Subtracting in the Real World

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Students will be working both individually and together to solve real world addition and subtraction problems.  Opportunities will be provided to both strengthen computation skills as well as problem solving skills.

Goals:
AS.K.3.1 Solve real-world problems that involve addition and
subtraction within 10, by using objects or drawings to represent the problem (K.OA.A.2) MA.K.CA.2
AS.K.3.2 Fluently add and subtract within five (K.OA.A.5) MA.K.CA.2

Grouping Students:
Students will be grouped based on their readiness level. Using previous performance on classroom activities and assessments, students will be placed/assigned tasks based on need to allow for more individualized instruction.  Groups will be kept flexible and fluid as activities in the unit progress.

Types of Learning Activities:
Different math stations will be set up in the classroom.  The first one will be myself working with small groups solving problems at the level of their instruction.  This will allow me to take out the reading factor when solving math problems if necessary.  It will also allow time to model strategies and discuss important vocabulary.  Another area would have students working on their computation in RenPlace's Math Facts in a Flash.  A third area would provide hands-on activities with students working together to solve problems.  The last area would have students working together to create their own math problem for the rest of the class to solve.  These problems could be displayed in a class Google Doc or Discussion Board for future use.

Technology:
Students would be working with the program Math Facts in a Flash found in Renaissance Place.  https://hosted119.renlearn.com/118336/default.aspx This program allows students to work at their own level and pace, deciding how much practice they may need and when to self assess.  Also, after coming to consensus on their group problem, students will publish that problem on a Google Doc or Discussion Board to share with classmates, who will have the opportunity to solve at a later date.  (possibly as an individual assignment the following day)  The provided activities seem to fit the Augmentation level of SAMR, since students are both working at their own level and pace on Math Facts and sharing ideas on a Google Doc.

-Dawn Daley

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Learning Activity:
Students will formulate a research question about their favorite meals in order to make a recommendation.  These questions should require the use of data to make an informed recommendation.  The data collected should be in categorical and numerical form.  Line plots, bar graphs, line graphs, and tables should be used to make predictions and collect data.

Learning Goal:
RID.5.3.1 Students will be able to formulate a question(s) that can be addressed with data and make predictions about the data, use observations, surveys, and experiments to collect, represent, and interpret the data used in tables, line plots, bar graphs, and line graphs.  They can recognize differences in representing categorical and numerical data.

Types of Grouping:
Students will be assigned a small group at the same level of readiness.  However, I could see this activity being more personalized and learner driven to suit each individual child. Conferencing with each student would allow the teacher to make this activity more learner driven than placing students in small groups.

Type of Learning Activities That Would Best Fit Your Grouping:
Students who are more ready would need less support in this activity.  Learning stations walking them through this process would be set up.  One learning station would focus on picking a restaurant with a particular meal to collect data on.  Another station would focus on formulating a research question that would lead to data to analyze.  A third station would be research based.  For example, if students were struggling with finding data, a list of helpful websites with data would be given or developed by students who are not struggling.  A fourth station would be developing their projects on how to showcase their data.  (advertisement, poster, Slides, etc...)

Technology:
Technology is a necessity in this activity. Students will be using google docs to create and complete an outline to keep their project focused. This shared doc will be shared with the teacher and other students.  This will allow me to provide feedback.  Students will also use a variety of websites to   collect their data.  I would also pull some videos to help students who are struggling with how to read graphs to gather data. At times, it may also be appropriate to use a discussion board to pose purposeful questions. Technology would also be used to create the final project.  Students will be given choice in the final representation of their research question.  They may choose google Slides, Publisher, or even create a unique video.

-Amy Helmuth

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Goal: •F.3.3.1 Generate simple equivalent fractions (for example, 1/2 = 2/4; 4/6 = 2/3) and explain why they are equivalent (3.NF.A.3b) MA.3.NS.7
Grouping:  I will be grouping students based on their level of readiness. Fractions are a very difficult concept for children, and  the readiness can be developmental.  Some groups may have to see/make visual representations, while others may be able to */ numerators/denominators.
Types of Learning Activities: I will have learning stations set up. I will meet with groups and address the needs of their level, including independent work, etc. Another station, will contain hands-on manipulatives, such as plastic shapes, to create and note visual examples of equivalent fractions.  A station could have students playing:  http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm as reinforcement.
Yet another group can be be watching videos on Khan Academy, etc. for review., and lastly, a group can be filling a diagram on a shared Google Doc sorting fractions into greater than half, equal to half and less than half.
Technology: As you can see from above, technology can be integrated throughout my groups. I like to use DreamBox and Odyssey to differentiate my students.
Robin Pulido

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Activity:  Students will with partners solve real world problems involving multiplying and dividing fractions based off of the work of Empson and Levi in  Extending Children's Mathematics: Fractions and Decimals.  Students may use drawings, equations, ratio tables, or any other method that demonstrates their conceptual understanding to solve the problem.
Goal: Based off of how students answer the questions depends on the specific score they are working towards• MDF.5.3.1Solve real-world problems involving multiplication of fractions and mixed numbers using equations (5.NF.B.6) MA.5.AT.3 • MDF.5.3.2 Solve real-world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions using equations (5.NF.B.7c) MA.5.AT.4 •MFD.5.2.5 Using a visual model Divide unit fractions by whole numbers and whole numbers by unit fractions (5.NF.B.7a; 5.NF.B.7b) MA.5.C.7 •MDF.5.2.3 Using a visual model, Multiply a fraction by a whole number or a fraction (5.NF.B.4)MA.5.C.5
Grouping:  Based off of students performance in the past (As Learning) will determine how they will be grouped. This meets the mathematical Teaching Practice of establish mathematics goals to focus learning. Students who demonstrated they can use equations will need to prove why equations work and are paired together.  Students who demonstrated they can solve will be working towards equations, and students who need a starting point will be paired together.  My main focus would be in small group towards the students who have difficulty getting started.
Learning Activity: Students will all be given the same problems just with a different set of goals at hand, as they move along in their progress. Students who can successfully solve a problem will need the least amount of my attention and would only need to be visited seldom to be given thought provoking questions. Students who are proficient may need to be reminded how they can "attack the problem" through a picture first to help them make sense of the problem.  I would focus the majority of the time with the students who cannot yet perform at a level 2.  Here we will have in depth discussions as a whole of what we could do.  As they draw pictures with misconceptions, students can point out to one another the faulty logics in their thinking and help make sense of the problem.
Technology:  In this case I really like the idea of using Google Docs to solve the problems.  This is because students can share their work with other groups and comment on each others' efficiency or inefficiency of a problem.   By doing so the students will meet most if not all of the eight mathematics teaching practices found in Principles to Action.

Joe Bysiek

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For my learning activity, students will be using ratios and rates to calculate simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions within and across measurement systems, percent increase and decrease, and percent error.
Goal: MA.7.C.6 Use proportional relationships to solve multi-step ratio and percent problems
Grouping: I will group my students based on same level of readiness.  I like grouping my students this way because I can provide each group with questions that meet their needs and skill level.

Type of Learning Activity: I will also use learning stations. My stations would include teacher instruction, technology, games, and review.  When they are with me, we will go over prior knowledge, misconceptions, and examples.  Students will also get an opportunity to work independently.  At the technology station, students will be prompted to look at additional resources, such as Khan Academy and Study Island where they look at videos for further understanding and can work on additional problems and get immediate feedback.  Students will also be given assessments on buzz to track student learning and growth. I plan on having students use Padlet and discussion boards. At the games station, I will have many math games that involve old and current lessons.  The review station will give students the opportunity to master previous lessons that they struggled with.  Students might use quizlet to review vocabulary or use Study Island or Khan Academy to go over a past lesson or two.
Technology: As you can see, technology will play a huge role in this lesson. In addition to using Buzz, quizlet, Padlet, Khan Academy, and Study Island, I plan on using Moby Max to provide a unique differentiation experience.

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For my learning activity, students will be exploring multiplication and division problems and trying to find the connection between the two operations. In my unit this is titled "What Do You Know About Multiplication and Division."
Goal: MD.3.3.3 Solve division problems as unknown-factor problems using the inverse relationship (for example, finding 32 ÷ 8 by finding the number that makes 32 when multiplied by 8) Grouping: I will group my students based on their learning style. I like to do this because I feel the students have an easier time discussing and explaining their thinking.
Type of Learning Activity: I will use learning stations. At each station students will find different problems and different types of tools: unifix cubes, cards, graph paper, paper and pencils, dice, etc. Some may be of use and some may not be. They will explore these tools and the problems with their groups. I will not tell them they are trying to find a connection between the problems. I'm hoping someone will "discover" it.
Technology: At one station I will have students use this online whiteboard on their chromebooks, https://awwapp.com/draw.html. Students love having any reason to use their chromebooks and this saves time of not having to get whiteboards and markers, fights over who has what color marker, plus the school won't have to purchase those markers that somehow always lose their caps. As most of you probably know by this point, I'm a huge Khan Academy supporting so I will have another station where students will watch multiplication and division videos on Khan academy for review of concepts. If a student feels that they do not need these videos because they already have a full understanding, I will have them reflect on why they feel they don't need them and explain their reasoning. I will read these reflections and if I feel they have any misconceptions, I will have them watch the Khan Videos another time.