It occurred to me that many teachers simply didn’t know how to use the manipulatives themselves to scaffold learning and so they simply taught the way they knew how. Another reason was that they felt it took too long to get out the manipulatives and put them away so they opted for less mess and management. Both of these were understandable reasons and as an educator, I knew that I had to provide experiences for teachers to see the value in these powerful tools. I was on a mission to model how to use manipulatives when I went into rooms for coaching, but knew I wanted to provide them a resource to refer back to in the end. I created several tools such as resource sheets for tools for mathematics and scaffolding documents for addition and subtraction and multiplication and division, but these tools never got to the heart of what I wanted to provide for teachers.

It wasn’t until I met with Jennifer Ritter at Republic Public Schools that I realized how I would begin organizing these resources for teachers. Jennifer shared a trouble-shooting document that some of her teachers and specialists had begun for a third grade standard organized with the CRA method of number acquisition; Concrete ->Representational ->Abstract. I loved the idea of organizing standards this way and have been pondering for months how to best organize the examples into a resource for teachers.

See below for a modified version of what Jennifer and her team started. I hope to continue to collaborate with them to finish this project, but would love to open this project up to all interested in contributing.

This project is going to take time and lots of it. The videos will be linked over time, but I plan to start by creating ideas for each area at each grade level.

The process will look something like this:

- Create a Google Slideshow for each grade level that includes each standard.
- The standard will have the unwrapped expectations for the Missouri Learning Standard as well as a table with Concrete, Representational, Abstract columns.
- Under each column will be ideas for scaffolding students using manipulatives and diagrams. For now I will be simply putting the unwrapped standard under the abstract column, but I will eventually replace this with stems for the grade-levels that do not have those provided in our Item Specifications for Missouri.

Please feel free to offer suggestions and revisions if you use these documents by emailing me or replying below so that we can make these valuable resources for teachers.

Here is an example of the first grade resource I have started for our teachers:

The great thing about Google Slides is that there is an option to export individual slides as .png images or a .pdf so I can link them directly to our other standards documents.

Please realize that this is a work in progress and will be refined over time. I wanted to get this out there though in case anyone was looking to create a similar resource.

Feel free to contact me via email at mscastillosmath@gmail.com or on twitter to @MsCastillosMath.

]]>How do we practice Information Age skills? Which of the C’s do we actively engage with, share in the-struggle-to-learn with others, and intentionally insert into daily practice? Creativity and innovation, Communication, Critical thinking and problem solving, Collaboration, … At Trinity, a small cohort of faculty meet at either 7:15 a.m. or 3:30…]]>

This is so awesome!

Experiments in Learning by Doing

How do we practice Information Age skills? Which of the C’s do we actively engage with, share in the-struggle-to-learn with others, and intentionally insert into daily practice?

Creativity and innovation,Communication,Critical thinking and problem solving,Collaboration, …

At Trinity, a small cohort of faculty meet at either 7:15 a.m. or 3:30 p.m. to learn more about sketch noting. We call it #doodling #TedTalkTuesday (or #TEDTalkThursday). We meet, watch a TED talk, and doodle. We share our work and offer each other feedback.

But, how do we differentiate for faculty unavailable at these times? In other words, how can we leverage technology to learn and share together?

Challenged by members of the Trinity Faculty to exercise creativity and critical problem solving, I have started developing the following prototype to attempt to offer a solution to this identified need.

At the end of these eight 75-minute sessions, participants should…

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As Dan Meyer put it, “math class needs a makeover.” It breaks my heart to hear students say things like, “I’m not good at math” or “I hate math!” In my opinion, one of the first things that needs to change is the focus on correct answers and the need for…]]>

As Dan Meyer put it, “math class needs a makeover.” It breaks my heart to hear students say things like, “I’m not good at math” or “I hate math!”

In my opinion, one of the first things that needs to change is the focus on correct answers and the need for speed. This leads students to believe that the only way to be good at math is to be right (quickly). The other practice that needs to be eliminated is the language we use as teachers such as “that’s right” or “you’re so smart.”

You’re so smart is one of the most damaging things you can say to a child. What is smart? What do we value and what are we showing them that we value? Being smart needs to mean learning as a means in itself. Or rather, the journey of learning. This is not…

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So why do we wait until the last minute to teach geometry?

I would like to propose that we teach geometry throughout the year by incorporating geometric ideas into instruction of other standards. I would argue that too often we teach skills in isolation and don’t connect the mathematical ideas.

In Kindergarten, instead of giving students random objects, have them count shapes such as triangles, squares, rectangles, circles and as they develop the idea of cardinality have them confirm their count by labeling the objects. For instance, if they count nine triangles, they would say “there are 9 triangles.”

Provide multiple types of triangles so that they can develop the idea that triangles come in all sizes and orientations and that counting does not have to be an object of a particular size or congruency.

Put out squares and ask students to get 18 squares or lay out circles and say how many circles are there?

Give students a geoboard and ask them to make a shape with 6 sides. This is a great conversation starter and gives another context for counting while offering the opportunity to discuss shape names and properties.

When asking students to compare objects, ask them to compare a group of circles and a group of squares and ask which one has more?

Or provide a low floor, high ceiling task like this:

Build arrays of multiple shapes and then ask how many sides are in the array? How many corners (or vertices). Or build an array out of 3-D objects and ask how many faces are in the array.

Use the geometric subitizing cards by Graham Fletcher to have number talks about attributes.

Have students engage in conversation to solidify understanding and practice vocabulary with WODB sets like this one:

Look at your grade level standards for geometry. Are there opportunities to teach geometric concepts through operations and algebraic reasoning? Data? Fractions?

Leave comments here or on twitter to share your ideas!

]]>This task best supports CCSS 3.MD.D.8.

What do you notice? What do you wonder?

How much tape will it take to go around the entire board?

Give an estimate that is too low and one that is too high.

Extension:

This extension can incorporate conversion and address CCSS: 5.MD.A.1.

How much of Lego tape was left? How much of each color?

2 inches green, 13 inches blue, 13 inches grey, 36 inches red.

]]>This task may need a little set up by asking students about going to the arcade and telling them that this game gives you tokens and cards instead of tickets. Then you can trade them in for tickets. Each item is worth a different amount of tickets.

This task could support 5.OA.A.2 for order of operations or 5.NBT.B.5 or even 6.EE.B.6.

What do you notice? What do you wonder?

How many tickets is this worth? Give an estimate that is too high and one that is too low.

There were already 355 tickets on the card.

So a total of 1035 tickets + 355 tickets = 1,390 tickets!

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So you figured out how many tickets they got…what did they buy? The only setup you need is that **there were two boys and they split the tickets equally among them.**

If you want to dial this activity in a bit, you could add that they bought six items between them. You could further narrow the focus by saying they both bought the same items…but what’s the fun in that???

There are three different reveals here. Choose the first to perform another calculation and answer the additional questions. The second and third image show the total cost of the items they purchased.

Did they buy what you thought they would?

How much did they spend? Did they have any tickets left? How many?

Were you correct? Was your answer possible? Are there other combinations they could have bought?

(You couldn’t see the ball on the left so I had to add one in using Google Drawings – that’s the reason it looks out of place!)

]]>When we go to the arcade, my son doesn’t like to wait to turn in his tickets so we always end up with several separate sheets of ticket totals by the end of our visit.

The task below could be used for CCSS 4.NBT.B.4 and MLS 4.NBT.A.5.

I love this problem because act 3 allows the student to engage in MP3 “construct viable arguments and critique the reasoning of others” as well as MP6 “attend to precision.”

What do you notice? What do you wonder?

How many tickets does he have? Write a too high estimate, write a too low estimate.

The attendant came up with this total. Is he correct or incorrect?

Would you be happy or unhappy with this total? Why?

(Side note, when I asked him if I could take a picture of it for a math lesson he said “I rounded up for you.” I think there might be some great talk around this too:)

For example:

What does he mean he rounded up? What was he rounding to? The nearest 10, the nearest 100 or something else?

Here is the actual total with calculator strokes. I think this is important for students to see once they finish their calculations and discuss.

]]>Well, that got my brain going when I looked at that perfect little array on the sticker sheet and I jumped up to film:)

Best Fit CCSS Standard(s) 4.OA.A.2, 5.NBT.B.6

What do you notice? What do you wonder?

How many heart stickers will there be on each Valentine?

Estimate. Give a too high and a too low answer.

What information do you need to solve the problem?

Choose the image you prefer for this part of the task.

Were you correct?

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I first learned of this website from a Twitter chat that I regularly participate in and couldn’t wait to try it out with my students. I decided to try it out in our small groups and simply ask students the following questions:

- What do you notice?
- What do you wonder?
- What do you think will come next in the pattern? Can you draw it?
- Explain your thinking.

It didn’t take long for the room to be full of chatter around the task. The website quickly became a favorite and students would ask me throughout the day if we would be using it in small group.

In my opinion, the greatest challenge in teaching today is student motivation…and if you can find that magical tool that combines deep conversation, connections to mathematical concepts AND your students are excited about participating…you run with it for as far and long as you can!

One thing that I have noticed about students over the years is when they understand, when they TRULY understand a mathematical concept, they are eager to share their learning with others if given the chance to do so in a creative way.

The interesting part is that many times my students who are reluctant to share at first aren’t students who struggle with a math concept, they are students who understand the concept, but don’t want to be singled out by a teacher who always calls on them. They have come from classrooms that value answers and they have already lost their excitement for learning.

However, if we stop making mathematics about answers and start making it about problems that can have creative solutions, those students are just as excited to share as others because they get to show what they really care about…who they are and what they have to offer the group; Not a one word answer to someone else’s problem.

One of the many great things about Fawn’s website is that the tasks are low floor, high ceiling. Every student in the classroom can enter the task and begin talking about the mathematics they see. Look at this example. Each student in my classroom could count the number of objects, tell me what shapes they were, notice that there were more each time, etc. and the students who needed a challenge could easily set to work figuring out what the 7th image would look like while the rest of the students continued their conversations. It really is beautiful to see. Everyone working on the same task and every conversation a little different.

During this particular task I heard:

*“No the fourth shape would have four on the bottom row because each time they added a row to the bottom with one more”*

* “They just added one more to each row.”*

*“There is 1 triangle in the first one and 3 in the second one…”*

And students couldn’t wait to get up and explain their thinking to their peers. They even established ways to label their thinking to make it more clear to each other.

The amazing thing about these tasks is that they are giving students the opportunity to see patterns and relationships between numbers in a visual way so that they can create connections between concepts.

Math classrooms should be creative spaces for students to explore, connect, argue and explain. Places where students can be engaged in problems that are exciting and stimulating. When I find a resource that can support that goal, it’s a win!

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