How To: Create Your Own (Digital) Foldables

Want to create digital versions of your own Foldables for use in your classroom or during professional development sessions? The process is so easy! Read on for an illustrated step-by-step tutorial. With a little bit of practice, you can whip up a professional, custom Foldable in less than 5 minutes!

If you want to learn about Foldables, definitely start with the master, Dinah Zike herself! Check out her website and her amazing resourcesguaranteed to spark your creative juices about how you can use 3D graphic organizers to help students organize their learning!

My professional journey with Foldables began several years ago when I had the incredible opportunity to attend a Dinah Zike Academy in Comfort, Texas. I cannot recommend this professional development experience enough. In just a few short days I went from knowing next-to-nothing about Foldables and journaling to feeling like an Interactive Notebook pro—fully prepared to take my Foldable learning and apply it in my high school math and science classes that fall. I owe so much of my Foldable work to Dinah and her wonderful team!

The first step to creating a digital Foldable is to sketch it out on paper. Might seem counterintuitive, but this sketch will give you a “feel” for how the Foldable will look, info on how many columns/rows you will need later, and will also help with correctly “double-siding” your Foldable if you choose to tackle that (see my upcoming post on creating double-sided Foldables). Your sketch doesn’t have to be fancy or to-scalejust include your tabs, your labels for those tabs, and at least one anchor tab (for gluing your Foldable down into its final homea journal, composition book, bound book, etc.).

Here’s a quick sketch of a Foldable we’ll create throughout this posta Solving Quadratic Equations Foldable for use in Algebra I:

This is a 4-tab Shutterfold Foldable that opens like a pair of shutters on a window.

Not sure where to start with your Foldable design? Check out the samples here to get started!

With your paper sketch complete, you’re ready to create your digital version. I create my Foldables in Microsoft Word. I like the robust suite of editing options provided in Word, as well as the precise design tools that aren’t yet available in GoogleDocs.

Here we go with some step-by-steps…

Open Microsoft Word and create a new, blank document. Click on the Insert ribbon, then select Table. Highlight the size of your desired table. Based on my sketch, I’m going to need a 2 row by 4 column table, so I’ll select that.

Here’s the inserted table, which will act as the “frame” for our Foldable.

This “frame” needs a bit of work to make it into our finished Foldable. We’ll start by selecting the whole table in order to make changes to it. Hover over the upper left corner of your table, making the four-way icon appear.

Left-click on this four-way icon to select the entire table.

Next, hover over and then right-click on the four-way icon to display a context menu. Select Table Properties from near the bottom of this menu.

This will open up the Table Properties menu. On the Table tab, click on Borders and Shading at the bottom.

From here, you can change the border width. A thicker border makes your Foldable much easier to cut out! Click the drop-down menu under Width to change the width from ½ pt to 6 pt. Now your Foldable will have thick borders for easier folding and cutting.

Next, you can resize the widths and heights of your rows and columns to match your needs. Hover over the column/row dividing line, then click and drag to resize the columns and/or rows. Here’s a short GIF overviewing this process:

Creating Foldable 1.gif

Worried that your rows aren’t exactly the same size? Highlight both rows, then right click to bring up the context menu. Use the Distribute Rows Evenly option to make your rows the exact same width.

Creating Foldable 2.gif

Confession here: I hardly ever resize my columns/rows “by hand” like this… Instead, I enter exact row and column values in the Row and Column tabs in the Table Properties menu. More on this in a follow-up post…!

To create cohesive anchor tabs, we need to merge the two cells in the first column and then merge the two cells in the last column. Start by highlighting the two cells you want to merge. Then, right click on one of the highlighted cells to display the context menu. Click on Merge Cells.

Now, our Foldable looks like thisit has the right shape, thick borders, and two anchor tabs for gluing!

Now we’re ready to enter our content.

The standard for solving quadratic equations in Algebra I (in Texas) states:

A.8A: The student is expected to solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.

So, we’ll title the four tabs using the wording from this standard.

I think Foldables are much more powerful when they have a relevant image, graphic, or mathematical notation on the corresponding tabs. Here I’ll include a sample quadratic equation that we can use to illustrate each solution method. I used Word’s built-in Equation Editor to enter these equations. Here’s a quick GIF showing how to insert an equation:

Creating Foldable 3.gif

And the Foldable now has a relevant equation on each tab:

You could also include images, tables, graphs, geometric figures, etc. on your tabssomething that helps illustrate the big idea for that tab/topic.

One last finishing touch: I like to include the title of my Foldable written along the anchor tabs. Type the title into the anchor tab cell and then select the Text Direction options under the Layout tab in the Table ribbon.

Creating Foldable 4.gif

Repeat on the other anchor tab and voila…!

A customized, professional, digital Foldable for use with your learnersdesigned exactly the way you like it!

What kinds of Foldables will you create using these tips?
What other tips do you have for creating digital Foldables?

Math Talk: ¼ of a Square (Part 2)

How might we use a Math Talk to help students connect fractions and a host of two-dimensional geometry concepts? How might this same Math Talk take learners into “a broad mathematical terrain of interconnected concepts, procedures, representations, and explanations”? (Kazemi & Hintz, 2014) How might a Why? Let’s Justify discussion routine overlaid on an extension Math Talk help deepen our understanding of why a particular geometric sketch is accurate? Let’s explore these ideas further…!

[Part 1 of this blog post discussed the original Math Talk and an Open Strategy Share discussion structure.]

Here is a “spin-off” Math Talk that emerged from the Open Strategy Share discussed in Part 1.

The group was presented with this sketch from one of their peers and asked to consider whether this image represented ¼ shaded. Note that the learner used a dot to mark the intended midpoint of the bottom of the square.

Triangle 1

Does the image above represent ¼ of the square shaded? How do you know?

We discussed this representation in pairs and small groups, then we shared some of our thinking whole group. For this particular Math Talk, we were using a Why? Let’s Justify discussion structure. Instead of trying to generate multiple solution pathways, we were considering one particular (potential) solution and working on justifying why this was or was not a solution.

Kazemi & Hintz (2014) summarize the goal of this structure as “to generate justifications for why a particular mathematical strategy works” (p. 3). Kazemi & Hintz continue: “During a Why? Let’s Justify discussion, the talk narrows upon a general claim in order to closely examine the mathematics and generate a discussion for it.” (p. 74).

The following justifications emerged from the group:

B suggested that the shaded triangle did represent ¼ of the square, since the base was half of the square’s side length and the height of the triangle was equal to the side of the square.

This verbal description resonated with some learners in the group, but others were unconvinced.

S suggested that so long as the bottom vertices of the triangle remain unchanged the top vertex of the triangle could actually lie anywhere along the top side of the square — and the triangle would always have ¼ of the area of the square. We sketched out some examples of S’s idea:

Triangle 2

S contended that all three of the triangles shown above represent ¼ of the square shaded in. The group agreed that the yellow triangle (a right triangle with its top vertex at the midpoint of the upper side of the square) definitely represented ¼ of the square, but some learners remained unconvinced about the other two examples.

A suggested that we draw in an altitude for each of the triangles we had sketched as a group. Our diagrams now looked like this:

Triangle 3

Adding in this additional structure (the altitudes) revealed something that wasn’t yet visible for all learners — namely, S’s contention that all three triangles had the same base and height, so must have the same area.

[Side note: This is a great example of what Jill Gough and Jennifer Wilson describe as “adding in an auxiliary line…to make what isn’t pictured visible” from their learning progression for SMP 7: I can look for and make use of structure. Check out their fabulous and thoughtful work on their blogs linked above.]

Consider how this Math Talk feels different than the Open Strategy Share version shared in Part 1 of this post. The Why? Let’s Justify discussion structure took us into another part of the mathematics — not merely considering a wealth of different approaches, but deeply considering one approach and focusing on creating convincing explanations to justify the mathematics used in that strategy.

In discussing the Why? Let’s Justify structure, Kazemi & Hintz (2014) contend: “Certain types of mathematical ideas lend themselves to a discussion that generates a justification for that idea” (p. 74). Not every problem or prompt is innately geared towards this particular discussion structure.

So what made this particular mathematical idea (specifically that the green triangle shown above does or does not represent ¼ of the square) a good fit for a Why? Let’s Justify discussion structure?

First, this particular representation did not look like ¼ of the square at first glance. A deeper analysis of the shape was required in order to determine whether or not it represented ¼ of the square–and deeper still to justify why.

Second, during the Open Strategy Share for the preceding Math Talk, most of the group’s sketches of ¼-shaded involved only congruent shapes. The approach used in this Why? Let’s Justify discussion did not subdivide the square into congruent shapes/pieces. Learners would have to rely on different reasoning (beyond subdividing a shape into congruent pieces and shading ¼ of the congruent pieces) to justify whether or not this specific triangle represented ¼ of the square.

Third, this particular triangle exposed that we (as learners) lose some of our intuition about triangles when they are obtuse triangles. We don’t often “see” the altitude of an obtuse triangle in the way that we see (and reason with) the heights of acute and right triangles. This drawing exposed some of that loss of intuition and made us dig deeper into why something was true.

For these three reasons (and perhaps others?), this prompt providing a meaningful task for learners to engage in a Why? Let’s Justify discussion routine.

Side Note: Kazemi & Hintz (2014) challenge that “During the discussion, we need to listen for procedural descriptions that students might give and be sure not to have the conversation stop there. When we press beyond procedural explanations into explanations that include reasoning, we are supporting students in justifying their ideas” (p. 56).

This paragraph still convicts me. Did I press far enough in the justification discussion outlined above? Why does any triangle with a base half the width of the square and a height of the square have an area of ¼ of the square? Maybe I should have pushed our thinking a little bit further here…

How does the Why? Let’s Justify discussion structure compare to the Open Strategy Share structure? In what ways does it open up a different part of the mathematics? What additional considerations might a teacher attend to when planning a Math Talk like this?

(See Elham Kazemi & Allison Hintz’s book Intentional Talk: How to Structure and Lead Productive Mathematical Discussions for more information on the Open Strategy Share and Why? Let’s Justify discussion structures.)

Math Talk | ¼ of a Square (Part 1)

How might we use a Math Talk to help students connect fractions and a host of two-dimensional geometry concepts? How might this same Math Talk take learners into “a broad mathematical terrain of interconnected concepts, procedures, representations, and explanations”? (Kazemi & Hintz, 2014) How might an Open Strategy Share discussion structure overlaid on this Math Talk help students see a range of possibilities within this interconnected landscape? Let’s explore these ideas further…!

Consider the following Math Talk:

Take a few minutes (say, time yourself for 3 minutes) and sketch squares where ¼ of each square is shaded in a different way. One ground rule first… Let’s say that the following two depictions represent the same “way” to shade ¼ of a square. Instead of sketching different iterations of the same “type” of ¼…can you shade ¼ in a different way? How many different ways? Set your timer and see where your brain takes you…!

Where did your brain take you? How many different ways of shading ¼ of a square did you generate?

After working on this task individually for 2-3 minutes, learners share their thinking with their tablemates. In so doing, they consider and discuss Did we all approach this task the same way? and What additional approaches did my peers use? and What additional ideas do we now have as a group because of discussing each other’s work?

We have led this Math Talk with multiple groups of adult learners. Here is a sample of the collective work that has come out of this individual think time followed by small group discussion time:

What would you do with this work? What is the benefit of orchestrating an Open Strategy Share Math Talk over some of these examples?

Kazemi & Hintz (2014) suggest:

“Open strategy sharing is typically the first way to get mathematical discussions going in classrooms. It’s like having a good, basic recipe for a soup from which you can make all kinds of variations. Open strategy sharing allows you to nurture the norms needed for a productive math-talk community. And you can use this discussion structure to model how students should talk with one another.” (p. 17)

I particularly like how the Open Strategy Share discussion structure provides an initial access point for teachers looking to introduce or enhance math talk in their classrooms. Also, as Kazemi & Hintz discuss, these structures provide wonderful opportunities for students to learn how to talk about mathematics.

But, if this is the “basic recipe for soup,” what would your variation be? What would you choose to highlight or spin off from for a follow-up Math Talk at some later time? Where else instructionally might this Math Talk go?

Check out Part 2 of this blog post to see a sample follow-up Math Talk that utilizes the Why? Let’s Justify discussion structure.

(See Elham Kazemi & Allison Hintz’s book Intentional Talk: How to Structure and Lead Productive Mathematical Discussions for more information on the Open Strategy Share discussion structure.)

Math Talk: Solving Equations Visually

How might we use a Math Talk to help students sense-make about solving equations? How might this same Math Talk help students work on showing what they know and making their thinking visible? How might a Compare & Connect discussion routine overlaid on this Math Talk help deepen our understanding of strategies for solving equations? Let’s explore these ideas further…!

Here is one of my favourite Math Talks:

(Note: The idea for this particular Math Talk came from a session I attended at NCSM 2016 led by Crystal Lancour & Jennifer Trievel of Delaware. Thanks, y’all!)

Take a minute and think about how you would respond to this prompt. Can you solve this problem without first “translating” it into algebraic notation and solving via algebraic manipulation? Rather, can you solve this problem visually?

Also, can you (as Jill Gough and Jennifer Wilson encourage us to do) “show your work so that a reader understands without having to ask [you] a question”? (See more on Jill & Jennifer’s #ShowYourWork progressions here.)

How might we make our thinking visible for how we solved this problem?

Here is how S, a recent conference session participant, made her thinking visible:

Elephants 1 Final

She explained her thinking aloud as:

I removed 4 horses from each side. Then I was left with the fact that 2 elephants were as strong as 8 horses. I divided these 8 horses into two equal groups showing me that each elephant is as strong as 4 horses.

When asked “Did anyone else solve the problem this way?” the majority of the participants indicated that they solved this problem the same way as S had.

L, however, had a different approach. Here is how she made her thinking visible:

Elephants 2 Final.png

Can you understand what L did without asking her any questions? How is her approach similar to and different from S’s approach?

L explained her thinking to the group in this way:

I started by dividing the problem in half. I knew that if 2 elephants and 4 horses were as strong as 12 horses, then 1 elephant and 2 horses must be as strong as 6 horses. Knowing that 1 elephant and 2 horses were as strong as 6 horses, I removed 2 horses from both sides of this situation, leaving me with the fact that 1 elephant is as strong as 4 horses.

How did L look for and make use of structure? And, does her method work all the time?

We quickly considered what the corresponding algebraic manipulation might have looked like for S and L’s approaches. We decided to represent the strength of an elephant with the variable e and the strength of a horse with the numerical value of 1. Here is what we came up with for the corresponding algebraic methods for these two visual solution pathways:

S’s Method

Elephants 1 with Algebra Final.png

L’s Method

Elephants 2 with Algebra Final.png

Do both of these methods work every time? When might S’s method be advantageous? When might L’s method be advantageous?

Why might it be important for students to Compare & Connect these two methods in a Math Talk? (See Elham Kazemi & Allison Hintz’s book Intentional Talk: How to Structure and Lead Productive Mathematical Discussions for more information on the Compare & Connect discussion structure.)

Also consider:

How does L’s method push back on well-intentioned but over-structured “procedures” we might teach our students for solving equations?

More on this idea in an upcoming blog post on Sense-Making for Solving Equations.

Resources | Math Talks: Adapting the Number Talks Structure for Secondary Mathematics Classrooms

Recently I led a conference session at the TRC Annual Meeting exploring how the Number Talks structure can be adapted for secondary mathematics classrooms.

Here’s the description for this session:

How can effective Number Talk routines be adapted to meet the needs of secondary classrooms? Explore strategies and resources for implementing Math Talks in Gr. 6-Algebra. See how Math Talks can provide opportunities for students to communicate and justify mathematical ideas, reasoning, and arguments within a concise, organized classroom structure.

Here are the mathematical goals for this particular session:

Look familiar? These are excerpts from two of our Mathematical Process Standards here in Texas (the Texas equivalent of the CCSS’ Standards for Mathematical Practice (SMPs)).

Our pedagogical and instructional objectives for this session included:

Here is the participant handout from this session and here is the card sort with samples of secondary Math Talks.

I’ll unpack this conference session further in future blog posts. Just sharing the resources to start the conversation…!

Update:

Interested in joining this conversation live? Come join in this session live at CAMT 2017 in Fort Worth, TX or NCTM Regionals 2017 in Orlando, FL!