Final Padlet Portfolio - Madison Gjovik by Madison L Gjovik https://padlet.com/gjovikm/n2h1u6cnuw4cg323 6.EE (Expressions and Equations) 1, 2, 3, and 4 en-us 2023-07-16 20:16:15 UTC 2025-12-28 19:46:10 UTC hello@padlet.com CCSSM 6.EE (Expressions and Equations) 1-4 gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645845623 Apply and extend previous understandings of arithmetic to algebraic expressions.

1. Write and evaluate numerical expressions involving whole-number exponents

2. Write, read, and evaluate expressions in which letters stand for numbers

2a. Write expressions that record operations with numbers and with letters standing for numbers.

2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas uased in real-world problems. Perform arithmetic operations, including those involving whole-number exponsents, in the conventional order when there are no perentheses to specify a particular order (Order of Operations).

3. Apply the properties of operations to generate equivalent expressions. 

4. Identify when two expressions are equivalent (i.e. , when the two expressions name the same number regardless of which value is substituted into them)

]]> 2023-07-16 20:25:27 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645845623 Why choose this topic? gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645847838 During my time as a tutor, I have had many conversations with students from grades 6 to 12 about algebraic operations. I've discovered that students commonly struggle with the list of topics covered in 6.EE 1-4. When I saw this topic in the list, I was determined to explore this topic further by using my past experience to make sense of 6.EE 1-4 myself and solidify my teaching methods for my future students. 

I also remember learning this content myself and having trouble manipulating equations correctly. My first experiences learning algebra were difficult because it was so different from what we had been learning previously. I would like to use the experiences of me and my students to create a collection of resources to clearly and smoothly introduce algebraic expressions to sixth-grade students. ]]> 2023-07-16 20:41:50 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645847838 Summary of 6.EE 1-4 gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645847901 The first four topics of 6.EE tackle the introductory ideas of algebraic expressions and equivalence. Students must learn to view expressions as versatile statements and use the properties they know to manipulate them as needed. These few topics will heavily emphasize the commutative and distributive properties. Students must also be able to create algebraic expressions out of real-world situations or verbal statements. For example, if we were to ask students to take three away from two times x, they should recognize this is equivalent to saying 2x - 3. Expression equivalence is covered in this topic as well. Treating portions of the equation as whole units, using properties they've learned along the way, and manipulating equations as needed are crucial skills students will gain from learning the content covered in 6.EE. ]]> 2023-07-16 20:42:13 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645847901 Video: "Algebra Basics: What is Algebra - Math Antics" gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645860737 https://www.youtube.com/watch?v=NybHckSEQBI

This video introduces the overall concept of algebra and how we will use it when covering the topics in 6.EE. The video does a great job of comparing algebra to the notions of arithmetic, something students are already comfortable with. It also provides a look at what students will eventually be able to accomplish with what they've learned from algebra: creating linear functions to describe certain scenarios. What I particularly liked about what Math Antics did in this video is how they talked about variables. It's intimidating to switch from expressions containing only numbers to expressions that contain letters and numbers. However, Math Antics described the purpose of the variable as a placeholder, much like how in the expression 1 + 2= ? the ? is the placeholder for the answer, or 3. Overall, when introducing the use of variables in equations to students, this video could be a valuable teaching resource. ]]> 2023-07-16 22:12:16 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645860737 gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645860923 2023-07-16 22:13:28 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645860923 SolveMe Mobiles gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645863913 https://solveme.edc.org/mobiles/

This resource was introduced to me through another class at OSU. To summarize, it uses the balance mechanics of a mobile to visually represent equivalence between two sets of shapes. Some of the shapes have value or weight to them, others are unknown. Through this activity, students must solve for the unknown values of the shapes. There are pre-made puzzles already available on the website, or teachers and students have the option to create their own puzzles. The visual aspect of these puzzles makes solving for the weights or values of the shapes less like an algebraic equation and more like a fun puzzle for students to enjoy. Oftentimes, students see math problems and are instantly disinterested. This model of algebra provides a new and exciting way of viewing algebraic expressions without the daunting form of an equation. The added option for students to make their own puzzles also allows students to experiment with equivalence, thus practicing CCSSM 6.EE.3 and 6.EE.4. They can edit the weight and amount of shapes added as well as the number of mobiles on the screen. They can make problems as simple or complicated as they would like, which makes this website an enjoyable way for anyone at any level of understanding to explore algebraic expressions. ]]> 2023-07-16 22:31:24 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645863913 ThoughtCo: "Understanding Equivalent Equations" gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645867888 https://www.thoughtco.com/understanding-equivalent-equations-4157661

This page offers quite a few useful examples of when equations are equivalent to one another, a topic covered in 6.EE.3 and 6.EE.4. A strong understanding of equivalence among equations is something necessary for students to be successful in algebra. Because of this, students need plenty of examples and explanations behind the meaning of equivalence, especially when variables are involved. The examples and non-examples provided in this page are straightforward, practical, and increase in difficulty as the page continues. While I think asking a student to read this material on their own could lead to some confusion, it could be a great teaching aid. Using the examples available on the website and using the student-friendly vocabulary offered on the page would be great inspiration for a lesson plan. My biggest critique is that it's not the most student-friendly. If there were more images depicting the algebraic expressions and a greater use of student-friendly language, this resource would be great to offer to students to strengthen their understanding of equivalence.]]> 2023-07-16 22:54:10 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645867888 BYJU'S: "Variables and Constants in Algebraic Expressions" gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645870380 https://byjus.com/maths/variable/#:~:text=In%20Maths%2C%20a%20variable%20is,9%20and%204%20are%20constants.

Understanding the function of variables in an algebraic expression is exactly what CCSSM 6.EE.2a covers. Introducing letters into mathematics is intimidating and may be extremely confusing for students. This resource not only tackles any confusion students may have about variables, but it also covers definitions of mathematical terminology, such as operation, coefficient, constants, and many others. In order to set students up for success in algebra, they must have strong foundational knowledge to work with. This foundational knowledge includes vocabulary. Allowing students to reference this resource for reminders or additional help would be a great way to ensure students are set up for success before handing them algebraic problems to solve.]]> 2023-07-16 23:06:09 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645870380 Video: "Combining like terms introduction" Khan Academy gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645887721 https://www.youtube.com/watch?v=CLWpkv6ccpA

Khan Academy is a great resource for just about any topic in math, but I found this video great because of the way it introduces variables and the act of combining like terms. The video introduces combining like terms by example first instead of using variables right off the bat. Using Chuck Norris and plums instead of x and y shows students the meaning of the process of combining like terms before telling them to simply add their coefficients together. The content covered in this video tackles the topics shared in 6.EE.4 quite nicely and would be a great resource to offer students who are struggling to understand how to combine like terms. ]]> 2023-07-16 23:54:14 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645887721 Resources to support teaching CCSSM 6.EE 1-4 gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645888451 2023-07-16 23:56:15 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645888451 gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645890007 Posted are resources to support any teacher trying to teach content listed in 6.EE topics 1-4. These resources range from games students can play to readings teachers can take advice from in their lessons. References are listed at the bottom of this page for each resource. ]]> 2023-07-16 23:58:54 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2645890007 Activity 1: Variables and Equivalence Problem Set gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2646663119 https://docs.google.com/document/d/1Dj5rObH28D79sYG-Z4GoVIyb9hUO6dXpLzfidxluuNs/edit?usp=sharing

After viewing the content covered in 6.EE 1-4, I noticed most of the content requires a great understanding of equivalence and the function of variables. Because of this, I decided to focus one of my self-made activities on practice with these concepts. In order for students to succeed in algebra, they must be confident in their own definitions of equivalence. I ensured this confidence would begin early on by offering early practice with algebra and equivalence before introducing the notions of solving for variables. This ties into the idea of showing the reasoning behind the procedures before introducing the procedure itself. If students have a strong understanding of equivalence, they will be able to understand why it's important to keep equations "balanced" and how to simplify expressions. In summary, this problem set is provided to give students ample opportunities to practice problems with equivalence to set students up for success in future algebra lessons. ]]> 2023-07-18 00:18:47 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2646663119 Activity 2: Experimenting with Variables gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2646726549 https://docs.google.com/document/d/1FPrQUkHzd0ZVtPoCU7sP-FmgZkh9NO2VZ_GvHN7-u0E/edit?usp=sharing

In this second activity, I wanted to allow students to think about algebra in a context other than a worksheet. The "mystery" behind what object creates motivation to create expressions with variables and solve for the variables. To mainly address the first four topics in 6.EE, this activity would focus more on creating equations than solving for the values. Ideally, this activity would have more objects, more difficult and intricate clues, and more varying units from object to object. This activity could also be altered by giving students the object and verbal statements about the length and weight, then having them find the weight and mass on their own using the appropriate tools. This alternative method of incorporating this activity would be more hands-on if students are looking for a more interactive lab. I have included some more side notes on how this activity would be ideally done on the second page of the document. ]]> 2023-07-18 01:20:04 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2646726549 Self-Made Activities gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2646731811 Below is a collection of activities designed by the creator of this portfolio. Activity 1 is a practice worksheet to strengthen understanding of equivalence and variables. Activity 2 is an activity to strengthen student understanding of converting English sentences into equations. Neither requires a strong understanding of how to solve for variables, but Activity 2 might be more challenging for students who struggle to solve for variables in equations. ]]> 2023-07-18 01:24:36 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2646731811 Final Reflection gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2647395722 2023-07-18 21:45:37 UTC https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2647395722 gjovikm https://padlet.com/gjovikm/n2h1u6cnuw4cg323/wish/2647395850 On an instructional level, I learned that the best way to introduce 6.EE 1-4 to sixth grade students is by introducing the purpose and function of variables before teaching them how to solve for variables. Furthermore, a lot of the content covered in 6.EE is reliant on a strong understanding of equivalence and simplification. Beginning with a thorough review of the definition of equivalence and giving students situations where variables would be useful will set students up for success in later algebra lessons. Using counting materials, real-world applications, and connections to past material will help students understand why solidifying understanding of equivalence is important and will help them better understand variables. The materials provided in this portfolio do just that to prepare students for more challenging algebra lessons. 

Beginning this portfolio, I thought it would be much easier to assemble a diverse collection of resources to help teachers who are planning on teaching the content covered in 6.EE topics 1-4. However, I was surprised to see the lack of resources online to support this content. Most resources online were resources to support students learning how to find the values of variables, not students who are learning what variables are and how to work with them in the first place. Most online materials were assembled to teach a class of eighth graders as a review, not for sixth graders with little to no algebra experience. However, if you search the internet thoroughly enough, you will be able to find resources that teach the first four topics of 6.EE even if they are few and far between. 

Algebra has a very negative connotation around it as a subject. Teachers can easily prepare students for future algebra lessons with the right preparation and engagement. Part of this preparation comes from lessons surrounding 6.EE 1-4. Because these first few topics are so important to student success in algebra, it was disappointing to see the lack of resources online to support this learning. When teaching this topic, creating your own materials to support student learning may be more necessary than other topics. I advise any middle school teacher to take their time with these topics because they are the backbone of most algebra lessons. Introducing new content to students is always the hardest part of learning, but if done correctly and thoroughly, providing a strong foundation of conceptual understanding before introducing new content will help students accept the new content easier. 
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