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This is what the Google Keep app looks like on an iPad.

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Google Keep is a free productivity app that is part of the Google Suite. I found it via Common Sense Education's search tool, but I was already familiar with this application. This means that although it can be used on an iPad, it is also easily accessible via smartphone or any internet browser.
Teachers could use this app in a variety of ways, whether for themselves or for students. It allows the user to makes lists, save links, upload photos, and more; it also allows for voice dictation and drawing.This makes it an exceptionally useful tool in the classroom during any subject, since it could be used to hold notes, important links, to do lists, schedules, and important formulas, to name a few.
Teachers could include Google Keep in lesson plans by specifically noting it as technology to be used for differentiation or accommodation, or just in general. It is relatively easy to access, so it would be simple to send students a link. Teachers could also create notes or templates of notes for students and add them as collaborators.
For the students referenced in the case study, I would provide individualized collaborative notes pinned to the top of the Google Keep app. Since these students have been experiencing difficulty with memory, this would allow them to easily access notes on concepts they might otherwise have to memorize.

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This is what Noisil looks like on an iPad.

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Noisli is a background noise app I found via Common Sense Education's search tool. It costs $1.99, and it is intended to help its users focus and relax. You might notice the control bars in the photo; Noisli allows users to customize their background noise to suit their own needs. It has 16 options on two pages, each of which can be enabled or disabled and set at the desired volume level. It also allows users to set an optional timer, after which point the noise will stop.
Teachers could use this app in any of the content areas to help students focus on appropriate content/assignments and/or relax. This would be appropriate for students who have trouble "blocking out external stimuli," as in the case study, or perhaps even for students who have anxiety disorders. It would require that students have access to headphones.
Teachers can incude Noisli in lesson plans by listing them as accommodations for students at specific points during the lesson, like independent work time; teachers should also make note of the need for headphones. Specifically for the students in the case study, I would ensure that they had headphones prior to the lesson, and I would give them time at the beginning of the day to customize their sound in order to prevent them from spending work time on that. I would also let them know in advance that they would be using it during independent work time, and I would remind them with a sticky note on their desk at the beginning of that time.

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Notability is a productivity app I found via Common Sense Education's search tool. It is free for download but has an option paid premium version, the price of which depends on the user's location. Notability is a high-powered, multipurpose app designed for intensive note-taking and more. It allows for PDF annotation, note-taking via typing or handwriting (with stylus) on multiple types of digital paper, drawing, highlighting, and voice-to-text dictation, to name some of its most useful features. It also allows voice recording, which is linked to notes and annotations. Additionally, it allows users to organize and search their notes easily.
Teachers could use this app in any of the content areas for students to have an engaging means of taking notes or for students to have access to PDF notes to annotate. This could be used for all students during a lesson or as an accommodation for specific students, noted in a lesson plan. If all students use iPads or technology, it would be discreet enough to protect students socially.
To support the students from the case study, I would use Notability on my own iPad during direct instruction. I would cast my screen onto my SMARTboard for students to see my work and notes as they participate with their own iPads on Notability, and I would record my direct instruction using the recording feature. Afterward, I would share my notes and recording with the two students so they could listen again to any portions they may have missed if distracted. This could support them given their difficulties with memory as well as with blocking out distractions.

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Sticky Notes HD is a productivity app I found via appcrawlr.com. It costs $0.99 and allows users to make quick or more in-depth notes that are easily accessible via the app. It also has a widget function which allows the user to access notes quickly via the iPad's "today" screen if the feature is activated.
This could be useful for students who need quick, simple reminders during any subject. For the students in this case study, I would use the app to let them make a "cheat sheet" in order to quickly access important formulas or "rules" for the algebra lesson. This would reduce memory difficulty.
Teachers could note this as an accommodation on a lesson plan or could provide all students with the opportunity to create a "cheat sheet" for quick access, if appropriate.

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How to use Notability - everything you need to know - ft. Journey2Med

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Rain Rain Sleep Sounds, more commonly known as Rain Rain, is a free app for iOS devices. I found it via appcrawlr.com. The app is host to a variety of background sounds to help users focus and relax. Some of the sounds are free, while some require a paid subscription. The app allows users to choose a sound, the volume, and how long the sound should play.
Teachers could use this app during any lesson to help students for whom focusing on a task is challenging. It can help block distractions during assignments or when a student is stressed. I would provide this as an accommodation for the students referenced in the case study during independent work time to help them block out distractions. They would also need headphones.

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GoodNotes is a productivity app that I found via appcrawlr.com. The first 3 notebooks are free, but it costs $7.99 to unlock more notebooks and handwriting recognition. GoodNotes is primarily a note-taking app which allows users to create different notebooks and folders to store their notes. It allows annotation of PDFs, handwritten note-taking, typing, importing pictures, and more. It is also a popular tool for digital planning.
This app would be useful for any subject, since teachers could provide (or students could take) applicable notes. Its digital paper templates could be useful for math specifically, since they include a couple types of grid paper.
For the students from the case study, I would provide colorful, engaging, guided notes for the algebra lesson. If all students have access to iPads and this app, I would provide these for the whole class. If not, the two students would use the iPad to follow along with the guided notes and fill them in. This would help the two students stay engaged, and they could refer back to their notes whenever necessary to support memory. I could also share my own notes with them if necessary.