Amazing Open Task!! 5.G.3 and 5G.4

Here is another good one I did with kiddos this morning!

Credit to: https://www.teacherspayteachers.com/Product/2D-Shapes-5th-Grade-1107908

I love this task!! It is open and there are so many possibilities for integration. This lesson integrates multiple mathematical practices! It also integrates 5.G.3-4 with 5.NBT.7! 🙂

Here are some pictures of kiddos work:

I love this question because it is so open and it provides natural differentiation! You can extend in multiple ways! For younger students you can make the cost lower. For older students higher. You can add a question about area. With lowers grades only use squares and rectangles with area and upper grades start adding triangles, trapezoids, parallelograms, circles, etc. 🙂 Great task!!

2D Shapes 5.G.3 & The Keeping Quilt

Loved this activity I did with my kiddos this week! I read the above book to my kids and had amazing discussions about generational differences, cultural differences, and so many other things! Then we moved into our math lesson. We have been studying 2D shapes for a week now and this is sort of the culmination of your studies this week. 🙂 I always try to tie in some type of picture book with each unit. I thought about tangrams and how they can be made into a perfect square. I thought!! Oh yeah! Quilt square time!!

I made up the following project along with my students. I first had my kids build their square puzzle from the eight tangrams. Many of them struggled to make a perfect square. They were able to make rectangles and composite figures but really struggled with the perfect square. We had many conversations about growth mindset during this activity. I then placed them with partners to try and build and perfect square. After about 10 minutes of good struggle I showed them pictures of square puzzles they could build. They built their squares, traced, and started designing their quilt pieces. Below you will find the project. They will complete the remainder of their project at home for homework next week.

It ties in social studies because I am asking them to tell a story about their culture and self using their pieces.

• Designs should tell a story about you
• Your culture
• Examples include: hobbies, family, religion, sports, etc.

It ties in math because they have to take their shapes and pick two options from the list below:

Keeping Quilt Project

• You must do two of the following activities:
• List attributes describing our shapes (ex: parallel sides)
• Brainstorm a list of classifications based on your shapes (ex: triangle)
• Venn Diagram comparing/contrasting shapes
• Chart which sorts your shapes
• Tables which sorts your shapes
• Hierarchal Tree Diagram
• Written description of shapes (3 or more sentences)

Feel free to use this with your class! Change the project to meet the needs of your standards! I think this is a great masterpiece built by me and my kiddos. Pictures to come next week of our projects! I can’t wait to share! 🙂

Been a while…..

I can finally breathe this week and share a few great things going on in my classroom this month! I have been working really hard on incorporating questioning, discourse, and accountable talk in my classroom! 🙂 Today I did a great activity!

** List as many 2D shapes as you can think of.

Create a large hierarchal diagram using your white sheet of paper. We will do a gallery walk. After gallery walks, we will add color and designs to our diagrams.

The kids did a gallery walk after and had students look for any misconceptions and provide feedback on their peers posters. Below you will find some pictures of their products:

My kids have been very successful with supporting each other through discussions this 9 weeks. I have combined my new questioning skills with accountable talk and they are really taking off with deep discussions about math. I think next time I do an activity like this one I will include question stems for their writing to make their feedback a little more focused on the math topic itself and not on how pretty their shapes are, etc.

We also completed a Read-A-Thon last week for Dr. Seuss week. I used a task from my Blanton Book for my Algebra Class.

Blanton, M. L. (2008). Algebra and the elementary classroom. Heinemann: Portsmouth, NH.

We read Spaghetti and Meatballs for All by Marilyn Burns as follow up to the activity and discussed the differences/similarities between this task and the books problem. Below you find some student samples:

My students really struggled with finding the pattern in order to predict 20 and 100. They were very successful with the carrying out the pattern for one digit numbers. Finding the rule was the difficult part for them. After much discussion we were able to come to understanding of the rule.

After completing our task and and reading our book I had my students read various math related picture books and Dynamath magazines. We completed the below brainstorming wheel when complete.

Students were required to write one thing they learned about math while reading. Then pass their wheel around the group. Each student has continued rotations until the wheel was filled with math knowledge.

I will try to get back to once a week! I have so many great things I need to share! Life has taken over!

Formative Data and Accountable Talk

Below is a task I gave my kids today:

How Many Cookies?

For one dozen cookies you need to use 1/2 of a cup of sugar. You
have 4 cups of sugar. You have plenty of all of the other
ingredients.

Part 1:

How many dozens of cookies can you make? Draw a visual
fraction model and write an equation that matches this task.

Part 2:

Write a similar problem that matches “3 divided by 1/3.”

Part 3:

Solve your new problem by drawing a visual fraction model and
writing an equation

*I got this from NCDPI under 5th Grade Math tasks for NF.7.

I asked my students to first split their CRA Journal Entry into three sections for Concrete, Representational, and Abstract.

Students were asked to complete this task using all three strategies. As they completed the task I walked around interviewing them, probing, and scaffolding as needed. Using this Open Strategy Sharing Template from Kazemi and Hintz I completed by formative data collection.

As I walked around I asked the students their first way of solving, to get an idea of their favored and most efficient strategy. Below is a great example of a concrete model:

Notice this student efficiently showed how many times 1/3 fit into 3 wholes and how many times 1/2 fits into 4 wholes.

I then grouped the students into small groups of 3 and had them discuss the following questions:

What was the known information?

What was the unknown information?

How much is a dozen worth?

Did you have to use the dozen?

How many halves make a whole?

How can a visual fraction model help you with this task?

What do you need to know to write the equation?

What is different about dividing a fraction versus dividing by a whole?

How can you help yourself understand dividing by fractions, by simply changing your language?

How many times does a half fit into four wholes?

If I asked you to divide 1/3 by 3, how does that change?

Lets talk about Part 3, what was easy, and what was hard?

How do we connect multiplication to division?

I worked with a group who need extra probing and questioning skills during this time as a part of interventions. I did periodic checks throughout the discussion to make sure students were on task. Each group had a leader in charge of asking questions and maintaining the discussion.

After discussing the questions we came back as group discussed as whole quickly highlighting AHA moments.

This is a great structured system for immediately responding to formative data. Your students learn so much from each other. Questioning and discourse become extremely important during small group discussions. Rigorous classroom instruction such as this provide life-long learners and flexible thinkers.

Equality

Equality Task

I absolutely loved this task and so did my kiddos. I would have never believed that I would be reading full chapters, watching videos, and completing activities with my students totally wrapped around understanding what an equal sign represented. I am so amazed out how much information I got from this short task and how much rich discussion I was able to have with my students around an equal sign. It was so amazing!

I used my questioning and discourse sheet with this task. I thought it was a great task to push me towards algebraic questioning. I have found myself writing questions in my plans and formative data collection sheets. I am obsessed with asking the right questions now, not only for my students, but for myself. Grad school has opened my eyes to whole new level of rigor. In fact, my ASIS  team came to observe for essential questions and rigor in our school on Tuesday and I quote: “I was a rockstar!” oh yeah, they were very impressed with my questioning skills, the students’ accountable talk, and the level of rigor going on in my room. I owe all my new skills in questioning and discourse to this class and all my classes so far.

I started by presenting the problem with the question: What does an equal sign mean to you? I asked them to solve the problem. I anticipated the answers they would give by using my Open Sharing Strategy form: 12, 8, 16 and walked around collecting data. In both of my classes that I completed this task the results were varying:

 

Class	12	16	8	Other
5B	5 students	No students added across the numbers in this class.	11 students	One student chose 7. I am assuming they made a calculation error, since they were so close. Another student chose 10.
5C	5 students	2 students	8 students	No students in this class gave alternate answers.

 

After the students solved this task, I placed them with partners strategically. I put students who answered 8, with students who answered 16, 12, or other. I put the following questions on the board for them discuss:

 

What does the blank represent?

How can you use manipulatives to help you solve?

How can you use a balance to help you solve?

What is the known information?

What is the unknown information?

Can you represent the square in a different way?

How could you read this question in a different way?

 

As they discussed I walked around and interviewed them. I asked each student in my class was an equal sign meant to them. I was only able to collect data with one class in this area. My first class was the first one I completed this with, so I learned from that class and decided to collect with this one.

 

Students who understood an equal sign as a relationship	Students who did not understand an equal sign as a relationship
9 students They stated that an equal sign meant: the same as blank=blank equivalent the same same both ways different ways, but the same	8 students They stated that an equal sign meant: the answer sum operation you need to add, subtract, multiply, divide total

 

Students who seemed to border: 2 students The students stated that an equal sign meant: different things depending on the situation depends on the situation like if you only have 3+4= __ then it is the answer If you have two sides that it means the same and you have to make them the same

 

The first class I completed this activity with I kind of just jotted notes randomly. I became more efficient with my data collecting the second go-round. Students in this class that did not understand the meaning of an equal sign said:

• put an answer
• an answer after an equation
• “I think the equal sign means the total”
• answer right next to it
• same as the answer
• put altogether

In this class I didn’t collect any data from the students that seemed to understand. I learned from this and interviewed everyone the second time.

 

After I had the kids had their discussion I brought them together and we discussed the following questions:

 

What others signs do you use in math to show a relationship?

What do they show?

How does 9+3 relate to blank + 4?

What do you think the blank represents?

How can you make both sides the same?

How can drawing help you if you are struggling?

 

Then I had them do a few more from our book to see how the results would differ. Minus one of my EC students who has trouble with even basic addition, every student was able to successfully complete a task similar from our books by the third try. Many got it the second try. I also gave them this list of equations and we discussed the differences, properties, forms, etc.

 

3+5=___  or   3+___=8

8=3+___  or   __=3+5

8=__

3+5=__+5

3+5=__+4

 

After my this task many of students came up to me and were continuing to discuss as we cleaned up for class change. They were so proud of themselves for truly understanding what an equal sign meant. They seemed to be fascinated by the discussions we had taken part in. It was an amazing feeling.

 

My students have benefited greatly from tasks we have completed for grad class and conceptual understanding I have gained. I actually received an email from a student today and it said:

 

Thank you so much for being my teacher I used to hate math even though I was good at it the reason I hated it is because I did not understand it but u helped me understand it and now I love math

 

The above statement is my reason for loving grad school. It has made me a better teacher. This student had an amazing teacher before me, but she is very traditional and gives a lot of “tricks’ in her teaching. I think the above sums up the why behind conceptual teaching! I am truly blessed to be a part of this program. It was totally meant to be!

100th Day Activities

Spinner

It has been a little while since I posted! Here is a great activity my co-worker shared with me. I took it and put my spin on it! 🙂 Using football lingo, a hundreds board, and Valentine’s candy hearts we raced to 100 on the 100th day of school. The kids really enjoyed it!

NS.5 Integers

I have been incorporating Concrete, Representational, and Abstract methods into my problem solving daily with students. In 6th Grade it can rather difficult at times to find concrete methods, but I am digging and finding new and innovative ways to concretely represent different problems. Below you will find a manipulative that my students created using a sentence strip, slider ziploc bag, stapler, and markers. I cut and stapled the ziploc bag on myself to save class time.

My students have used this several times this week to complete problems dealing integers from -10 to 10. I keep them in my manipulative mailbox in the back of my room. We used it to introduce opposites this week as well.

Later in the week I also used red/yellow counters to explore positive and negative charges. Problems such as the one below work really well with red/yellow counters.

Eight positively charged atoms are combined with seven negatively charged atoms. Which integer represents the resulting charge?

In addition to counters visual representations work really nicely with charges. Same concept but drawing such as this using elimination help as well.

I have my students cross one negative for every positive and the use what’s left to figure out the resulting charge. I have also had students explore abstract methods with problems such as these as well. They seem very comfortable with writing equations to represent these situations.

Last but not least, we have explored a problems that might not necessarily lend themselves well to concrete, so I ask them to find at least two ways to solve the problem. Below is an example:

Denver, Colorado is called “The Mile High City” because its elevation is 5280 feet above sea level. Someone tells you that the elevation of Death Valley, California is −282 feet.

1. Is Death Valley located above or below sea level? Explain.
2. How many feet higher is Denver than Death Valley?
3. What would your elevation be if you were standing near the ocean?

With this problem I asked my students to come up with their own method of solving. I walked around and observed and analyzed their methods of solving. Using the below open sharing template I grouped my students. This template comes from Kazemi and Hintz book called Intentional Talk How to Structure and Lead Productive Mathematical Discussions. 

Open Strategy Sharing Template

I then, grouped my students with a students who had different ways of solving the above problem. I asked them to figure why I placed them with their partner. I had a large group of abstract thinkers, so I placed them in what I called a “representational battle” group. Their job was to pair up and battle to see who could come up with the best representation of the above problem. Here are the results. Who do you think had the best representation? I think they were all amazing, considering these students often rebel against concrete/representational methods!

I tried these “representational battles” with my abstract thinkers twice this week and they went great! A little friendly competition never hurt anyone! 😉

Odds and Evens Task

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I completed the above task from (Blanton, M. L. (2008). Algebra and the elementary classroom. Heinemann: Portsmouth, NH.) with my students this week. I have only had a chance to try it with one group so far, next week I am going to try it with my other two groups to see what happens. I was very intrigued by this task of generalizing arithmetic in my readings with Dr. Richardson this week. Dr. Richardson’s task to use was similar:

What happens when you add an odd number and an even number? Is the result even or odd? Make a conjecture that shows what you found. How do you know your conjecture is true? Will it always work?

After completing the task I watched the following video and was amazed how a student, not much different than my students was able to make a better conjecture than my own, because my brain is so procedurally set up. I have had to train my brain over the past couple of semesters in grad school, to become more conceptual, not only for my students, but also for teaching purposes. I continue to grow as a teacher for my students every day that I work towards becoming a more conceptual thinker. This in turn helps me lead them with tasks that build algebra foundation and flexible problem solvers.

Below you will find the various pictures of journal entries from some of my students during this task. I think you will find them rather amazing.

 

My students continue to impress me with their willingness to try new things. They humor me always, no matter how crazy my questions might be. It has been a fun run with these 5th grade kiddos, this year. Can’t wait to see the ultimate results of all my new research and applications I have taken from my grad classes with this students. My 6th graders are little tougher to crack, but you will find in a later post, how I am working towards fostering a love for flexible thinking in my group of 6th graders.

Overcoming Obstacles

As I sat this morning killing time during my two hour delay I read an article called Overcoming to Leadership by Susan Moore Johnson and Morgaen L. Donaldson. This article really hit close to home for me. I am what you could call a “second stage” teacher. I am currently in my tenth year of teaching. I crave a collegial environment and love working in teams. I also love sharing what I learn in my graduate classes with other teachers.

It is often hard and very intimidating getting in front of my peers and sharing what I learn, in fear that people will see me as a suck up or person who is not worth listening to. The question remains, how do set up a school free of these feelings of fear and norms of isolation within our four classroom walls?

I often feel great success in my room, but wish to share what is working and not working with my peers. When I share in small groups of willing teachers I feel great success and excitement, but when I share in bigger groups I feel teacher’s scrutiny and unwillingness learn new things. Structure of schools has come up over and over in my readings about leadership this semester, but proven frameworks have not been widely revealed. How do we structure our schools so that observation of peers, collegiate conversations, and freedom of fear to lead is a norm?

I know not everyone is like me. I know we all come from different generations and not everyone wishes to lead PD and other teachers, but everyone has a skill to be shared for the good of our students and teachers across schools. I have newfound goal for teacher leadership.

My new goal as a teacher leader is research frameworks that do work and share them with administrators and district leaders alike. Get the word out, that if we foster leaders in our teachers than we will make great strides in student achievement and retain excellent teachers at the same time! My hope is that one day I will be a leader of change. I have found a new desire to learn more about adult education. My passion as a teacher leader lies in professional development and curriculum writing, but in order to succeed in sharing with others, I need to build relationships, learn how to approach different generations, and styles of teachers. Reading these articles is a start, but where can we find good professional development for teachers willing to work with other teachers? Obviously, one day I aspire to go back to school for my doctorate and hopefully one day teach at the college level, but one step at a time. Experience is key! 🙂

Opening Minds

I am loving the new book I am reading for my Leadership/Research course in grad school! It is amazing the difference that language can make in our students and children’s lives as parents and teachers. Simple changes can make the world of difference!

Opening Minds Using Language to Change Lives by Peter H. Johnston has open my eyes even more to practical ways we can instill a growth mindset in our children and students. This book is not only good for teachers, but also parents to read.

Many of you have heard of growth mindset versus fixed mindset if you have heard of this research previous to this book. In this book they call them dynamic learning frames versus fixed-performance frames. The idea is that some children are instilled with ideas that they were born intelligent or not so intelligent and there is nothing they can do to change that. This is obviously a fixed mindset. As parents and teachers it is out job, especially in the early years, to show our children that they can train their brains and grow their brains to do whatever they want to do if they work hard! I love this!

I remember hearing about this last year in an opening workshop in my district and being fascinated. I then went on to attend a math leadership conference for NCCTM and heard Jo Boaler author of 

and What’s Math got to do With It. She also has a great website with research articles and tasks called youcubed.org. This was when I realized how life-changing language and tasks we give our children can really make a difference! I haven’t yet read the mathematical mindsets book above, due to my many readings in grad school, but I certainly had it on hold when I heard she was coming out with a new book! I can’t wait to read this one! Currently, however I am reading Opening Minds and it has really captured my interest again! I am almost already half way done with this one, and I only have to read half of it by February for my book study group. 🙂

This book offers practical changes in language you can make in your classroom. He offers two types of feedback that can lend themselves to fixed versus dynamic frames, they are called person-oriented and process-oriented. As math teachers it is well known that we have to be specific in our feedback to students when they are completing performance tasks and higher-orders tasks in our rooms. Without this specific process oriented feedback, our students will not properly be probed and scaffolded towards deep, flexible thinking where they are required to justify their strategies. I myself still have a hard time with this type of thinking, so I have to really check myself in the classroom as a present challenges to my students.

This book is amazing! I can’t wait to share more. The biggest take away I can share right now is no more saying:

“Great job” or “Good girl”

Now we want to be specific! “You really worked hard on your picture of that multiplication problem!” “Explain to me how you did that!” Simple changes like this in your classroom will make the world of difference.

Parents this is also for you too! This can be used in our wording in the household too! Think about ways you can change the way you give negative or positive feedback to your children!

Instead of saying: “I am really disappointed in you.” (person-oriented) you might say I really liked the how hard you worked on cleaning your bedroom last week!” “What was different this week?” “Tell me about that”. This is a silly example, but you can see the difference.

I hope this gets you excited about using language to change your children’s lives!