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Homework Guidelines for Mathematics

Mathematics is a language, and as such it has standards of writing which should be observed. In a writing class, one must respect the rules of grammar and punctuation, one must write in organized paragraphs built with complete sentences, and the final draft must be a neat paper with a title. Similarly, there are certain standards for mathematics assignments.

How should I format my homework?

Write your name and class number clearly at the top of at least the first page, along with the assignment number, the section number(s), or the page number(s). If you are not stapling or paper-clipping the pages together, then put your name (or at least your initials) on all the pages.

Use standard-sized paper (8.5" × 11" for North Americans; A4 for others), with no "fringe" running down the side as a result of the paper’s having been torn out of a spiral notebook. Do not use sticky-notes, scented stationery, or other nonstandard types of paper.

Use standard-weight paper , not onion skin, construction paper, or otherwise abnormally thin or heavy paper.

Attach your pages with a paper clip or staple. Do not fold, tear, spit on, or otherwise "dog-ear" the pages. It is better that the pages be handed in loose (with your name on each sheet) than that the corners be folded or shredded.

Clearly indicate the number of the exercise you are doing. If you accidentally do a problem out of order, or separate one part of the problem from the rest, then include a note to the grader, directing the grader to the missed problem or work.

Write out the original exercise (except in the case of word problems, which are too long).

Do your work in pencil, with mistakes cleanly erased, not crossed or scratched out. If you work in ink, use "white-out" to correct mistakes.

Write legibly (that is, suitably large and suitably dark) ; if the grader can't read your answer, it's wrong.

Write neatly across the page , with each succeeding problem below the preceding one, not off to the right. Do not work in multiple columns down the page (like a newspaper); your page should contain only one column.

Keep work within the margins . If you run out of room at the end of a problem, continue onto the next page; do not try to squeeze lines together at the bottom of the sheet. Do not lap over the margins on the left or right; do not wrap writing around the notebook-paper holes.

Do not squeeze the problems together, with one problem running into the next. Use sufficient space for each problem, with at least one blank line between the end of one problem and the beginning of the next.

Do "scratch work," but do it on scratch paper ; hand in only the "final draft." Show your steps, but any work that is scribbled in the margins belongs on scratch paper, not on your hand-in homework.

Show your work . This means showing your steps, not just copying the question from the assignment, and then the answer from the back of the book. Show everything in between the question and the answer. Use complete English sentences if the meaning of the mathematical sentences is not otherwise clear. For your work to be complete, you need to explain your reasoning and make your computations clear.

For tables and graphs, use a ruler to draw the straight lines , and clearly label the axes, the scale, and the points of interest. Use a consistent scale on the axes, and do a T-chart, unless instructed otherwise. Also, make your table or graph large enough to be clear. If you can fit more than three or four graphs on one side of a sheet of paper, then you're drawing them too small.

Do not invent your own notation and abbreviations, and then expect the grader to figure out what you meant. For instance, do not use "#" in your sentence if you mean "pounds" or "numbers". Do not use the "equals" sign ("=") to mean "indicates", "stands for", "leads to", "is related to", or anything else in a sentence; use actual words. The equals sign should be used only in equations , and only to mean "is equal to".

Do not do magic. Plus/minus signs ("±"), "= 0", radicals, and denominators should not disappear in the middle of your calculations, only to mysteriously reappear at the end. Each step should be complete.

If the problem is of the "Explain" or "Write in your own words" type, then copying the answer from the back of the book, or the definition from the chapter, is unacceptable. Write the answer in your words, not the text's.

Remember to put your final answer at the end of your work, and mark it clearly by, for example, underlining it or drawing a box around it. Label your answer appropriately; if the question asks for measured units, make sure to put appropriate units on the answer. If the question is a word problem, the answer should be in words.

In general, write your homework as though you're trying to convince someone that you know what you're talking about.

You should use your instructor or grader as a study aid, in addition to the text, study guides, study groups, and tutoring services. Your work is much easier to grade when you have made your work and reasoning clear, and any difficulties you have in completing the assignment can be better explained by the grader. More importantly, however, completely worked and corrected homework exercises make excellent study guides for the Final. Also, if you develop good habits while working on the homework, you will generally perform better on the tests.

In summary, schools today have made the development of essential skills, the provision of significant and meaningful learning experiences, and the development of the workforce some of its primary goals for student success. As such, they want their instructors to guide the students toward a higher level of confidence and competence. In math, that translates into a greater need for clarity in mathematical writing. The intention on these "Homework Guidelines" is that you and your instructor communicate better, and that you succeed both in your present mathematics courses and in future mathematical communication with co-workers and clients.

For further information, review these examples of acceptable and unacceptable solutions, and this sheet showing neat and messy papers.

Instructors: These "Homework Guidelines" are copyrighted by Elizabeth Stapel.

You are welcome to use these "Homework Guidelines," in part or in whole, as an asset in teaching your own classes. The only conditions of use are that distribution, if any, of the Homework Guidelines be made at no cost to the recipient(s), that the original copyright notice be retained on copies of this page, and that the following notice be included on all derivative works:

Based on "Homework Guidelines" http://www.purplemath.com/guidline.htm Copyright Elizabeth Stapel Used By Permission

These "Guidelines" are also available as a printer-friendly PDF .

If you would like an example sheet for your students (displaying the differences between acceptable and unacceptable formatting), try this PDF .

URL: https://www.purplemath.com/guidline.htm

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10 Quick Tips for Building an Interactive Math Course in Canvas

• July 31, 2020

Fall semester is coming and you’re teaching online… let’s pause for a small scream here 😭

Next year we’ll all be experts and there will be no end of talks, papers, and blog posts that we can use to figure out what to do. But right now we need the quick and dirty. What can we do NOW, and fast, to make our online math course content more interactive and engaging?

If you’re getting ready to teach math online and your school’s LMS is Canvas , here are 10 quick tips to get you rolling.

#1: Include LaTeX in a Canvas Page

Canvas has built-in LaTeX functionality that you can access from any edit window that has a toolbar. Click on the little “square root” symbol and you’ll get a pop-up equation editor. You can ignore the equation editor part and just type LaTeX into the box. Make sure to switch view to “Advanced” and then insert what you created.

You can use this toolbar feature to include LaTeX in Pages, in Quiz questions, and even in Quiz answer options! Which leads us to…

#2: Include LaTeX in Canvas Quizzes

Same trick as above but there are some differences if you’re using the “New Quiz Engine” in Canvas instead of the old quizzes. The short answer is to ignore the MathQuill equation editor used in the new engine, and to write your LaTeX right in the edit window between the delimiters ““\(” and “\)“.

You can read more at our earlier article Using LaTeX with the New Canvas Quiz Engine .

#3: Add Checkboxes to Modules

Having organized, step-by-step content in Modules helps students know exactly what to do, and when to do it. You can help them keep track of what they’ve done by adding Requirements to elements of the Module; this will add little checkmarks to the right of each item based on whether the student has marked it as done, or submitted the assignment, or whatever condition you’ve set. It looks like this to the student:

You set this up by clicking the three vertical dots in the upper right corner of the module and choosing Edit. Then set up any requirements you want.

#4: Make Pretty Buttons

Students are more likely to do something when there is a nice big button to click. Something like this:

You can add a button like that from any edit window if you toggle to the “HTML Editor” mode and then insert the code below. Obviously replace the text with what you want the button to say, and replace the link with whereever you want the button to go to when pressed. You can put external links here or choose from one of the internal Link options (Quizzes, Announcements, Discussions, etc) that are available in the sidebar to the right of the Edit window.

Here’s a nice HEX color picker if you want to change the button background or text color: htmlcolorcodes.com .

#5: Embed YouTube videos

This is easy, just use the “video” button in the Editor toolbar and paste the video link into the General field. Note that you can change the size of the video. Works great; students will be able to watch the video right there on your page instead of bouncing out to another window.

For an interactive feeling to your online documents I would strongly recommend including as many videos as possible, whether you made them or not. Students will go search for videos anyway, and find terrible ones that don’t really apply to what you’re covering in class — so you might as well find the good ones and highlight them for your students.

#6: Remove Inline Previews for YouTube Links

If you use the “link” button in the Editor toolbar to create a hyperlink to a YouTube video in the middle of a paragraph, the default behavior is for Canvas to include a little inline preview of the video, like the tiny video in this screenshot:

Obviously you want to get rid of that. It’s easy but not obvious unless you already know how. Here’s how: click on the link in question and then on the “link” tool in the Editor toolbar. Check the box “Disable inline previews for this link” and then press “Update Link”:

#7: Embed Live Desmos Graphs

One way to fight “tool overload” for students is to embed your tools directly into whatever medium the students are already using. For example, you can embed live Desmos graphs and activities into Canvas Pages so that students can interact with the material right inside of your online content (the following is a screenshot, it’s not live *here*):

It’s so crazy easy to embed live Desmos: just put the following in the HTML code for your page, where you want the embed to appear (with your own Desmos link, of course):

Note you can change the size of the embed. This iframe trick doesn’t work for every website, but it does work for Desmos, and…

#8: Embed Live WolframAlpha

…it also works for WolframAlpha . Note that you can pre-populate the input field before capturing the link, so that your students don’t just start with a blank WolframAlpha page (again, this screenshot isn’t live *here*, but it’s interactive in Canvas):

The code for embedding WolframAlpha is exactly the same as for Desmos, but with a different link:

I’m sure there are lots of amazing, interactive things that would embed directly into Canvas with this type of iframe code… let me know if you discover anything especially cool!

#9: Sort of Integrate Calendly

A lot of external tools are integrated into Canvas, like WebEx , Zoom , Piazza , etc. What “integrated” means, and how useful it is, really depends on the tool. For example, WebEx has some scheduling features within Canvas and I think interacts with the Canvas Calendar, but Piazza basically seems to just have a menu item for the sidebar and then embeds its entire website into the body of the Canvas site if you click on that menu item.

That Piazza type of integration is pretty minimal, but here’s something even more minimal: you can create an External URL as an Item inside a Module, but set it to open within Canvas instead of in a new tab, like this:

Then when students click on the Item in the Module, the site will pop up inside a box in Canvas, like this:

In this case, the link I included was to the scheduling site Calendly , which I use to manage student appointments (and highly recommend). This means that students can be going through their Module in order and automatically encounter this scheduling opportunity, which I hope will encourage them to Acutally Use the scheduling opportunity.

This trick doesn’t work with all types of External URLs; for example if you just put a link to www.google.com in the URL field then you’ll get this warning:

So, YMMV, but try it out and see what works!

#10: Use Rubrics and Speed Grader

This last one is for YOU and your sanity. Using Canvas Rubrics with the Speed Grader can really cut down on your grading time, and make it easier for you to leave feedback for your students. It also makes your assignment expectations really clear to the students, and gives you more opportunities to quickly communicate back and forth with them.

Here’s how the Speed Grader looks for a simple Text Entry submission of a Reflections assignment (with some fake answers):

You can see the student’s work on the left, and then make comments and click on the Rubric boxes on the right. There’s lots of information online about how to make Canvas Rubrics, but you don’t have time for that. Here’s a crash course…

After you’ve created and saved an Assignment, a “+Rubric” button will appear at the bottom, as shown below left. After clicking on it you can make a Rubric, adding Criteria and additional Ratings levels as you wish, as shown below right. Make sure to click the button “Use this rubric for assignment grading” so that you can use it with the Speed Grader.

That’s pretty much it. You can save Rubrics if you have a lot of the same kind of assignment. Students can see this Rubric when they open the Assignment, so they know exactly how they will be graded.

You can allow students to resubmit and then the Speed Grader will show you any new things that need grading; once you update the rubric scores for the new assignment, Canvas will automatically change the grade in the gradebook. It’s also easy to leave comments for students and have them reply right in the assignment interface, which helps cut down on email overload. The time save from the Speed Grader is in the bookkeeping even more than the grading. If any of you suddenly have heavier teaching loads or larger classes due to university cutbacks (ahem) then keeping down the per-student bookkeeping work is really going to be invaluable this fall. Good luck!

I’ve lost track of all the sources that I learned these things from, so let me just say Thank You to the internet in general, and also to all of my wonderful colleagues at JMU who are also suddenly becoming Canvas experts (especially CW and CW!).

Bonus Tip #1: Link to an anchor within a page

Another suggestion from one of our infamous CWs is to use HTML to inert a link to an anchor elsewhere on the page, to help students navigate around a long Canvas Page with a lot of content. While in the HTML editor, insert the anchor tag in the place you want students to be able to jump to, like this:

Then you can link to the anchor from anywhere else in the page, in the same way you would include a regular link in HTML, like this:

You can also jump to that internal reference point from outside the Page, so that when someone follows your link it will jump to the correct section of the page. Just add the internal reference to the end of the link, like in this (fake) example: http://www.fakesite.com/pagename.html/#important_section.

Pretty much anything basic that you can do in HTML will work on your Canvas Page in the HTML editor. A good basic reference without a lot of CSS stuff in the way (that’s another blog post) is w3schools.com . Have fun :)

Related posts:

Thanks for sharing! One other fun hack that can be especially helpful for practice quizzes is using “pop-up dialog boxes”. Here’s a sample code:

In a particular page, you can add the following code: ———————————————- General in-line text (in html editor) – – – – – – – – – – – – – degree .

———————————————- Later in the html editor – – – – – – – – – – – – –

The degree of a vertex is …

When the page is rendered, you can click on the word and the definition will pop up. This can be REALLY great on practice quizzes where you can remind students of definitions.

******************** FYI: this functionality may disappear at some point and may be replaced. It’s based on the old Canvas style guide before they moved over to React.

Sample screen shot from canvas page attached.

Hi Katie, Thanks for this tip! I am unable to see your screen shot but if you email it to me (laurataalman at gmail) then I will post it here as an update so people can use this tip. Thank you for sharing it! Laura

Well, it didn’t let me put the code in there. Sorry about that.

When trying to do this, my stuents keep getting an error message from the embedded desmos that says,

“Sorry! Something went wrong. Please try again later.”

this error occurs when the students try to login with Google (from the embedded desmos page on canvas)

It happens for me as well when I try to login. I have triple checked the code plenty of times, so it’s not a problem with something being misspelled.

Any suggestions?? Please!

Hi Miguel, I’m sorry, I’m not sure how to fix that. In my experience this works fine from Chrome when embedded into Canvas. I wonder if maybe Desmos was down that day? Also I’m sorry to have responded over a month after your question — I’m sure my answer is of no use now even if I knew what the problem was! -Laura

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Latex template for math assignment.

whats your favorite template for math assignments? im currently looking for some right now.

Eberly Center

Teaching excellence & educational innovation, creating assignments.

Here are some general suggestions and questions to consider when creating assignments. There are also many other resources in print and on the web that provide examples of interesting, discipline-specific assignment ideas.

Consider your learning objectives.

What do you want students to learn in your course? What could they do that would show you that they have learned it? To determine assignments that truly serve your course objectives, it is useful to write out your objectives in this form: I want my students to be able to ____. Use active, measurable verbs as you complete that sentence (e.g., compare theories, discuss ramifications, recommend strategies), and your learning objectives will point you towards suitable assignments.

Design assignments that are interesting and challenging.

This is the fun side of assignment design. Consider how to focus students’ thinking in ways that are creative, challenging, and motivating. Think beyond the conventional assignment type! For example, one American historian requires students to write diary entries for a hypothetical Nebraska farmwoman in the 1890s. By specifying that students’ diary entries must demonstrate the breadth of their historical knowledge (e.g., gender, economics, technology, diet, family structure), the instructor gets students to exercise their imaginations while also accomplishing the learning objectives of the course (Walvoord & Anderson, 1989, p. 25).

Double-check alignment.

After creating your assignments, go back to your learning objectives and make sure there is still a good match between what you want students to learn and what you are asking them to do. If you find a mismatch, you will need to adjust either the assignments or the learning objectives. For instance, if your goal is for students to be able to analyze and evaluate texts, but your assignments only ask them to summarize texts, you would need to add an analytical and evaluative dimension to some assignments or rethink your learning objectives.

Name assignments accurately.

Students can be misled by assignments that are named inappropriately. For example, if you want students to analyze a product’s strengths and weaknesses but you call the assignment a “product description,” students may focus all their energies on the descriptive, not the critical, elements of the task. Thus, it is important to ensure that the titles of your assignments communicate their intention accurately to students.

Consider sequencing.

Think about how to order your assignments so that they build skills in a logical sequence. Ideally, assignments that require the most synthesis of skills and knowledge should come later in the semester, preceded by smaller assignments that build these skills incrementally. For example, if an instructor’s final assignment is a research project that requires students to evaluate a technological solution to an environmental problem, earlier assignments should reinforce component skills, including the ability to identify and discuss key environmental issues, apply evaluative criteria, and find appropriate research sources.

Think about scheduling.

Consider your intended assignments in relation to the academic calendar and decide how they can be reasonably spaced throughout the semester, taking into account holidays and key campus events. Consider how long it will take students to complete all parts of the assignment (e.g., planning, library research, reading, coordinating groups, writing, integrating the contributions of team members, developing a presentation), and be sure to allow sufficient time between assignments.

Check feasibility.

Is the workload you have in mind reasonable for your students? Is the grading burden manageable for you? Sometimes there are ways to reduce workload (whether for you or for students) without compromising learning objectives. For example, if a primary objective in assigning a project is for students to identify an interesting engineering problem and do some preliminary research on it, it might be reasonable to require students to submit a project proposal and annotated bibliography rather than a fully developed report. If your learning objectives are clear, you will see where corners can be cut without sacrificing educational quality.

Articulate the task description clearly.

If an assignment is vague, students may interpret it any number of ways – and not necessarily how you intended. Thus, it is critical to clearly and unambiguously identify the task students are to do (e.g., design a website to help high school students locate environmental resources, create an annotated bibliography of readings on apartheid). It can be helpful to differentiate the central task (what students are supposed to produce) from other advice and information you provide in your assignment description.

Establish clear performance criteria.

Different instructors apply different criteria when grading student work, so it’s important that you clearly articulate to students what your criteria are. To do so, think about the best student work you have seen on similar tasks and try to identify the specific characteristics that made it excellent, such as clarity of thought, originality, logical organization, or use of a wide range of sources. Then identify the characteristics of the worst student work you have seen, such as shaky evidence, weak organizational structure, or lack of focus. Identifying these characteristics can help you consciously articulate the criteria you already apply. It is important to communicate these criteria to students, whether in your assignment description or as a separate rubric or scoring guide . Clearly articulated performance criteria can prevent unnecessary confusion about your expectations while also setting a high standard for students to meet.

Specify the intended audience.

Students make assumptions about the audience they are addressing in papers and presentations, which influences how they pitch their message. For example, students may assume that, since the instructor is their primary audience, they do not need to define discipline-specific terms or concepts. These assumptions may not match the instructor’s expectations. Thus, it is important on assignments to specify the intended audience http://wac.colostate.edu/intro/pop10e.cfm (e.g., undergraduates with no biology background, a potential funder who does not know engineering).

Specify the purpose of the assignment.

If students are unclear about the goals or purpose of the assignment, they may make unnecessary mistakes. For example, if students believe an assignment is focused on summarizing research as opposed to evaluating it, they may seriously miscalculate the task and put their energies in the wrong place. The same is true they think the goal of an economics problem set is to find the correct answer, rather than demonstrate a clear chain of economic reasoning. Consequently, it is important to make your objectives for the assignment clear to students.

Specify the parameters.

If you have specific parameters in mind for the assignment (e.g., length, size, formatting, citation conventions) you should be sure to specify them in your assignment description. Otherwise, students may misapply conventions and formats they learned in other courses that are not appropriate for yours.

A Checklist for Designing Assignments

Here is a set of questions you can ask yourself when creating an assignment.

• Provided a written description of the assignment (in the syllabus or in a separate document)?
• Specified the purpose of the assignment?
• Indicated the intended audience?
• Articulated the instructions in precise and unambiguous language?
• Provided information about the appropriate format and presentation (e.g., page length, typed, cover sheet, bibliography)?  
• Indicated special instructions, such as a particular citation style or headings?  
• Specified the due date and the consequences for missing it?
• Articulated performance criteria clearly?
• Indicated the assignment’s point value or percentage of the course grade?
• Provided students (where appropriate) with models or samples?

Adapted from the WAC Clearinghouse at http://wac.colostate.edu/intro/pop10e.cfm .

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Assignments on writing

Examples of short assignments, term papers, designing assignments that enable students to write well.

Writing well requires mastery of writing principles at a variety of different scales, from the sentence and paragraph scale (e.g., ordering information within sentences so content flows logically ) to the section and paper scale (e.g., larger-scale structure ). To simplify teaching, you can begin the term with shorter assignments to address the smaller-scale issues so you can more easily focus on the larger-scale issues when you assign longer assignments later in the term. At all scales, students best learn to communicate as mathematicians if the assignments are as authentic as possible: if the genre and rhetorical context are as similar as possible to those encountered by mathematicians.

Many of the following ideas are currently implemented in M.I.T.’s communication-intensive offerings of Real Analysis and Principles of Applied Mathematics .

• Require that at least one question on each problem set be typed up and written in the style of an expository paper (rather than the usually terse and sometimes scattered style of a homework solution).
• Assign short exposition tasks such as summarizing the proof of a theorem done in class or filling in the gaps in an explanation given briefly in class.
• To help students learn LaTeX or how to use equation editors, have an assignment requiring at least basic math formatting due early in the semester so students aren’t required to learn it as they’re researching and writing their term papers. Begin with simple math formatting exercises, building to more complex: e.g., see the assignments for M.I.T.’s Real Analysis recitations 1 (text with math) , 2 (table and figure) and 13 (slides containing a figure with LaTeXed labels) .
• Begin with communicating simple arguments, building to more complex (e.g., having students explain the heapsort algorithm and then revise the explanation based on feedback provides a rich opportunity for teaching about writing clear definitions, giving conceptual explanations as well as rigorous details, and presenting information in an order that is helpful to readers.) See the sequence of assignments from M.I.T.’s Principles of Applied Mathematics .
• Have students revise part of a concise textbook such as Rudin’s, Principles of Mathematical Analysis in the style of a more-thorough lecture note.
• Before an exam, have students formulate and submit to you a list of 2+ questions they have about the material. Students have a hard time formulating precise questions, yet this is an important communication and learning skill. Some students may feel they understand the course material, so permit questions that go beyond the scope of the course. You can use the questions to focus a review session. More detail about this assignment is given in this lesson plan from M.I.T.’s communication-intensive offering of Real Analysis.

The following books, articles, and websites contain short writing assignments.

• Stephen Maurer’s Undergraduate Guide to Writing Mathematics has an extensive appendix of writing exercises designed to target various aspects of writing mathematics.
• Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go , by A Crannell et al . [link goes to MAA review] This 119 page book from the MAA contains “writing projects suitable for use in a wide range of undergraduate mathematics courses, from a survey of mathematics to differential equations.” Each prompt is written in the form of an (often amusing) letter from someone who needs help with a “real-world” problem that requires math expertise. Students must solve the problem and write a letter of response. On his website, Tommy Ratliff (one of the co-authors) gives a brief account of using such projects in his calculus course.
• Annalisa Crannell’s Writing in Mathematics website has writing assignment for Calculus I, II, and III as well as links to colleagues’ websites that have further writing assignments.
• Quantitative Writing from Pedagogy in Action, the SERC Portal for Educators, has many examples of short and long writing assignments based on “ill-structured problems,” which are “open-ended, ambiguous, data-rich problems requiring the thinker to understand principles and concepts rather than simply applying formulae. Assignments ask students to produce a claim with supporting reasons and evidence rather than ‘the answer.'”
• The Nuts and Bolts of Proofs by Antonella Cupillari includes exercises for an introductory proof-writing course. Proof topics include calculus and linear algebra.
• Platt, M. L.. (1993). Short essay topics for calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 03.1 , 42-46.

Additional information about journal-writing assignments and other writing-to-learn assignments can be found on the page about using writing to help students learn math .

For each assignment, indicate your expectations about audience and length, so students know how much explanation to include. An appropriate audience is often other students in the class who are unfamiliar with the specific topic of the assignment, or other math majors not in the class.

Term papers enable students to pursue areas of their own interest and so can be among the most rewarding assignments for students. To help students succeed, give students guidance for choosing a sufficiently focused topic, for finding helpful sources, and for using sources appropriately. See this assignment for proposing a term paper topic , from M.I.T.’s Principles of Applied Mathematics –it includes guidance for how to choose a good paper topic.

One of the (interesting) challenges of assigning a term paper is generating a list of possible paper topics. Ideally, each topic should have well-defined scope and have at least two or three available resources accessible to students in the course. You may want to emphasize to the students that they are not expected to do original mathematics research. However, the paper must be their own — they cannot paraphrase and closely follow a published survey paper.

One of your institution’s librarians may be happy to collaborate with you to show students how to find useful sources.

To provide students with an authentic rhetorical context for their term papers, consider showing them samples of expository papers and suggesting that they write for a journal that publishes expository papers (e.g., The American Mathematical Monthly , Math Horizons , Mathematics Magazine , and The College Mathematics Journal .

Don’t assign a term paper unless a variety of topics exist at an appropriate level. For example, a term paper may not be appropriate for an introductory class in analysis.

Be aware that plagiarism may be an issue particularly in large classes on subjects for which a wealth of material is available online. In such classes, you may find it to be helpful to tightly specify the paper topics or to supply a specific slant to the papers (e.g., apply such-and-such method to an application of your choice). Vary the assignments from year to year. These precautions may be less important in small classes.

In some classes (e.g., applied mathematics classes), it may be necessary to carefully guide students to choose topics that contain sufficient mathematical content. For that reason, using caution when approving unfamiliar topics.

A poorly focused assignment will leave students confused about what is expected of them and is likely to result in poor writing. Students are likely to write their best if the assignment is interesting and if students are told (or are able to confidently identify for themselves) the following:

• educational objectives of the assignment
• audience knowledge and interest, and author’s relationship to the audience
• purpose of the text to be written (e.g., to convince, to entertain mathematically, to teach, to spark interest)
• content to be addressed
• details of the genre ( proof ? research paper? funding proposal?)
• how the writing will be graded
• an effective writing process (you can provide support by assigning intermediate due dates or revision )

The following resources explain these points and give further guidance for designing effective assignments:

• Bahls, P., Student Writing in the Quantitative Disciplines: A Guide for College Faculty , Jossy-Bass 2012, pp. 36-46, contains sections on structuring writing assignments (includes sample prompts), sequencing assignments throughout a course, and sequencing writing from course to course.

General resources (not specific to mathematics)

• How can I avoid getting lousy student writing?
• What makes a good writing assignment?
• The webpage Integrating Writing and Speaking Into Your Subject , provided by MIT’s Writing Across the Curriculum, has several subpages about writing assignments.
• Creating Writing Assignments , MIT’s Writing Center

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Math Assignment

 What is an annotated bibliography?

Assignments in math courses are usually a list of problems to be solved. Each question may be of various difficulties and types, which are marked and returned to the student to be used as a source of feedback. Math assignments are designed to provide opportunities for 'doing math' and to consolidate students’ understanding of the content. The questions often come from the most recent week of learned material, but some questions may require students to synthesize concepts from further back. This is because learning math is cumulative by nature; you continuously build upon what you've learned before. Because math assignments are typically used as a checkpoint for understanding, they tend to weigh less than other assessments in terms of grade, therefore, it's important to treat them as learning opportunities instead of a tool for maximizing course grades.

Click on the Timeline for a visual representation of the timeline. Click on the Checklist for a document containing the checklist items for a math assignment.

According to your start and end dates ( 2024-06-18 to 2024-06-24 ), you have 6 days to finish your assignment.

Step 1: Understand the questions Complete by Tue Jun 18, 2024

Read through the assignment once it’s released and understand the questions. Read the questions early to prime your brain; too many students start too late.

• For some courses, assignments come out before or as content is covered, so having the questions in your mind as you see the content can help prime you to actively learn the content and will also help you know where to look for relevant material in the lecture notes and/or videos. Active learning of content means you are asking yourself questions as you are learning, actively monitoring your understanding of the topic, and anticipating next steps.
• Read all the questions to estimate the range of tested material, make note of anything you don’t understand. Understanding the question correctly reduces the chance of getting stuck.

The hardest thing being with a mathematician is that they always have problems.

– Tendai Chitewere

Step 2: Gather materials and review Complete by Wed Jun 19, 2024

• Gather required materials (lecture notes and/or videos, textbook sections).
• Study the material (definitions, concepts, solved problems, etc.) until you are familiar with it. Identify connections across concepts/topics and practice additional problems. Regularly reviewing your material will also help you to find relevant information quickly if you get stuck on a question.

Step3: Solve questions and get help Complete by Sun Jun 23, 2024

Part a: attempt to solve each question.

• Rule of thumb for time allocation: one hard question may take significantly longer than all easy questions combined. Consider how long you’ve taken to solve all the easy questions. It may take at least twice as long to solve one hard question. Try all easy questions as soon as possible to gauge how long the rest could take.
• Try giving yourself a break for a day before attempting them again to allow time for your mind to continue working subconsciously.
• Still stuck? Check out Math problems: What to do when you're stuck for more strategies and tips.
• Keep track of unsolved questions and what stages you were stuck at. Don’t throw away any work in progress.Your instructor or TA can provide better help if you can narrow down on the issue.

The only way to learn mathematics is to do mathematics.

– Paul Halmos

Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

– Paul Halmos  

Part B: Get help on unsolved questions

• The sooner you ask for support, the more time you and the instructor/TA will have for follow-up conversations.
• Focus on asking questions to help you close the gap between your understanding, and the understanding you need to complete the question.  Questions such as “Can I get a hint on #4?” or “What is the answer?” are not typically helpful in increasing your problem-solving abilities.
• For questions you were challenged by, but were able to solve after receiving help from the instructor or TA, make sure that you fully understand how to come up with the solution in case a similar question is asked on a test.
• Many students find it helpful to study together. Make sure you understand what your instructor’s expectations are around group work (if you’re not sure, ask!). Be mindful about how much you post about an assignment solution on the course’s discussion board and if you’re in doubt, consider posting privately. Familiarize yourself with the academic integrity standards expected in your courses.

The goal of seeking help is to try to find out how to approach questions that you are stuck on. From this extra help you still may not see the complete picture of how to solve the problem. To see this may require that you go back to Part A , now with the instructor/TA’s suggestions in mind.

I have not failed. I've just found 10,000 ways that won't work.

– Thomas Alva Edison

Step 4: Check your solutions Complete by Mon Jun 24, 2024

• It’s important that you spend some time away from your solutions before you check them. For problems you did solve, try to figure out if you can check your own answer like you would have to on a test (i.e. don’t look up answers in a book or online).
• You could ask the instructor/TA for guidance, but avoid questions such as “Did I do this right?” Instead, ask yourself whether you are asking the right questions about your solution. 
• Remember not to focus only on the final answer, but also on how you communicated your answer. Ask yourself if a typical student in the class could follow along with what you’ve written. 
• Remember to cite any external sources that you used in your work, including work completed with others (if this was permitted).

Step 5: Review Marked Assignments Complete by Mon Jun 24, 2024

After receiving your marked assignment check over incorrect questions as well as those you got right. Review posted solutions and read them critically. Often, there are different approaches to a problem and you may learn about some of these new approaches through this review.

MS Word Cover Page Templates

Download, personalize & print, mathematics assignment cover pages.

Posted By: admin 14/11/2018

Cover pages of assignment play a vital role in attaining high grades in studies. Therefore, the students are advised to design a cover page with the assignment. It is important for the cover page to be relevant to the assignment it covers.

A student has to put a lot of efforts in making math assignment. This assignment requires the student to stay to the point and accurate. The cover page of the mathematics assignment plays an important role in impressing the teacher.

Tips to create the cover page:

Here are a few tips that can help a student design a cover page for the assignment

• The student making the cover page should follow the format which is being followed by the entire institutes. The subject area should be indicated on the cover page clearly so that the teacher can readily know about the basic details of the assignment and the student submitting the assignment.
• The cover page should be signed by the student. The student should make sure that he signs the cover page at the right bottom corner of the cover page.
• The cover page should be in A4 size and it should be well attached to the assignment. It should be kept in mind that the cover sheet should be the first page to be seen by the recipient of the assignment.
• The cover sheet should include the details such as student’s name, the subject of the assignment, roll number, class and section name, the topic of the assignment, name of the instructor of math subject.
• The student can add a decent colored background on the cover page and some borders to enhance the beauty and elegance of the cover page.

Many students believe that the most important part of the assignment is its content. They put a lot of emphasis on assignment and don’t pay much attention to the cover page. Such students often fail to get good marks because their representation of assignment does not impress the teacher.

Your teacher may not have asked you to prepare the cover page with the assignment but when there are few students who create the cover page and make their assignment stand out. Such student’s assignments compel the teacher to give them high grades than those students who don’t create the cover page.

Some students often forget to mention their name or roll number in the assignment. It creates a problem for the teacher during grading. The students are asked to create a separate to give the information about the author of the assignment, the subject details to make it convenient for the teacher to grade the student.

Importance of creating cover page:

Creating the mathematics assignment cover page makes the student well-versed with the format and techniques with which, a cover page is made attractive and professional looking.

The students of mathematics find it easier to make the cover page of the engineering or architectural projects when they enter their professional life.

The first cover page shown here is simple and easy to comprehend. The color combination is nice and trendy. The top image has some formulas written over that shows it is a mathematics assignment. The center white portion has enough space to give headline of the assignment with its little introduction underneath, while the rest of the space can further be utilized for details about the student or the teacher. There is a professional hint provided in this cover page.

Cover page format: MS Word 2007 | 2010 | 2013 File Size: 827 KB License: [Only for personal use] Download

This cover page is stylish and modern having an interesting appeal to it. The shades of blue and a lighter background give the cover page an elegant look. The heading of the assignment can be followed by the name of the student presenting it, while the right margin can be utilized to state the important facts about the assignment topic. Overall this cover page gives a comprehensive look of both being smart and descriptive.

Cover page format: MS Word 2007 | 2010 | 2013 File Size: 2 MB License: [Only for personal use] Download

The third cover page shown here is a unique combination of aqua green, white and black. The look of the cover page is impressive and pleasant with a nice choice of colors. The background image shows that the assignment belongs to mathematics. The heading of the assignment and title can be easily placed at the top, while the rest of the space is utilized with the name of the writer, date of submission, and a brief abstract of the assignment at the bottom. This is a must go to cover page.

Cover page format: MS Word 2007 | 2010 | 2013 File Size: 848 KB License: [Only for personal use] Download

Another well-designed cover page. It has a distinct look, dividing the cover page into two halves. The upper white portion for mentioning the title heading of the assignment, while the lower blue portion for giving a brief abstract regarding the work. The center design is enhancing the impression of the assignment, making it look warmer and more elegant.

This last cover page is smart, attractive having vibrant colors, and thus eye-catching. The design of the cover page pushes the text toward the right, bringing the focus of the reader towards the text. The heading of the assignment is highlighted on the dark pink background that enhances the font. Further important definitions or details can also be mentioned in the space below. This cover page can be the first choice of students liking trendy colors and styles.

Cover page format: MS Word 2007 | 2010 | 2013 File Size: 806 KB License: [Only for personal use] Download

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How to Structure Your PSMT Report for QCAA Mathematical Methods

Feeling a little overwhelmed and aren’t sure how you’re meant to approach your problem-solving and modelling task (PSMT) for QCAA Maths Methods ?

It may seem a little out of left field that you need to write a report instead of complete an exam that covers different mathematical topics, but don’t worry — we’ll guide you through how to structure it!

What are you waiting for? Let’s get started on familiarising ourselves with the QCAA Methods PSMT.

What is a Problem-Solving and Modelling Task (PSMT)? Structure of a PSMT for Maths Methods Tips for Writing a PSMT Breaking Down the Instrument-Specific Marking Guide (ISMG)

What is a Problem-Solving and Modelling Task (PSMT)?

A PSMT is an assessment task designed to evaluate your ability to respond to an investigative mathematical scenario or stimulus . The specific task provided will be related to the mathematical concepts and techniques you have been learning in class.

You will be required to create a written report, no longer than 10 pages and 2000 words , to address the following assessment objectives:

• Selecting, recalling and using facts, rules, definitions and procedures 
• Comprehending mathematical concepts and techniques 
• Communicating using mathematical, statistical and everyday language and conventions 
• Evaluating the reasonableness of solutions 
• Justifying procedures and decisions by explaining mathematical reasoning 
• Solving problems by applying mathematical concepts and techniques 

The other key features of this report include providing a response that addresses the real-life application of mathematics, using technology, using tables/graphs/diagrams, and following the structure of a report (past tense and third person) . Now that you know what a PSMT is all about, let’s find out how to set it out and what each section needs!

Struggling your way through the PSMT? Here’s how to decide whether to drop down to General Maths for your QCE or not!

Structure of a PSMT for Maths Methods

#1: title page.

Should include: the title of the report, your name, the year, and a relevant image.

#2: Contents Page

A clear table of contents that correlates with the different sections of the report is required. Learn how to create a table of contents page on Microsoft Word here.  

#3: Introduction (100 words)

Explain the purpose of your QCAA Methods PSMT  (what is the scenario/context) and list the contents of the report (each step that was taken to develop and evaluate your solution).

Example: This report consists of the formulation, evaluation and justification of a pendant design. Factors, such as, target consumer, size, weight, hole for stringing, materials and aesthetic, will be utilised to guide the decision choices made. The pendant will consist of a variety of types of functions, including logarithmic, parabolic, cubic and circular. The mathematical feasibility and practicality of the pendant will also be considered by utilizing both technological and mathematical methods and procedures, including transformations and graphing of functions, simultaneous equations and Desmos. Strengths, limitations and recommendations will also be given about the pendant.

#4: Background (50-150 words)

Discuss any considerations or research you had to do in order to address the task

Example: Research was conducted on currently existing pendants, which were used to support the design of the new pendant. Both fashion jewellery and fine jewellery were investigated in order to determine appropriate materials, dimensions and designs.

#5: Observations and Assumptions (200-350 words)

Observations .

These are the things you may have come across while researching (so you’ll have a few in-text references here). It can be effective to use diagrams and statistics . Aim for at least four. 

Examples: The density of the materials used can heavily impact the weight and durability of the pendant Pendants sizes average between 9.5-25.4mm  Fashion pendants on average cost between $10-$99 (Lovisa, 2020) All measurements must be positive values, so when graphing, pendant must entirely be in the first quadrant to avoid negative values 

Assumptions 

As the task can be somewhat vague, some assumptions will have to be made in order to make it more specific . Aim for at least four.

Ensure you justify the reasons for/implications of each assumption. 

Examples: The pendant is for the average adult consumer, and will be considered ‘fine jewellery’ and so will have dimensions, weight and cost as such  The entire area of the pendant will have the same depth (meaning that the pendant will be flat), as creating variety in depth will make the volume of the pendant difficult to calculate  The domains and ranges of the functions will correlate to the dimensions of the pendant (i.e. 1 unit = 1cm) The cost calculated is the estimated cost for the materials of the pendant, not including the construction cost

#6: Developing a Solution (300-400 words)

Design/model considerations and decisions .

Discuss the design choices you made using mathematical concepts and techniques to justify . Reference other designs/models and how they have impacted your design choices.

Refer to your observations and assumptions and how they have influenced your design choices.   

Example: As circles are a common shape of pendant, it was decided that this pendant should have a similar shape. Along with the observations taken about pendant size, it was decided that this pendant should have both a length and width of 2cm. Instead of using just a circle function, however, in order to make it more unique, the pendant’s shape was made of two logarithmic functions and a parabola. When the first logarithmic function was created, the second one was the same but translated vertically (across the y-axis). This meant that they intersected perfectly at (1,2) – the top middle of the pendant. The logarithmic functions ranged from 0.5 to 2. As both functions would continue straight down as the range decreased, a parabola was required to create the ‘bottom half’ of the ‘circle’. To make sure it was equal, the parabola had a minimum at (2,0)…

Calculations (few words, insert screenshots of calculations instead)

This section can have multiple subdivisions within and differ widely depending on what exactly the task is. Generally, however, the use of technology must be demonstrated, the mathematical concepts used should be explained and appropriate and accurate mathematical concepts and techniques should be applied .

Note that in the main body of the report, you should include only one of each type of calculation; include the rest in the appendix.

For the pendant-designing task used in the examples, the subdivision consisted of Determining Functions, Determining Points of Intersection, Determining Area, Determining Volume, and Calculating the Weight and Cost of Materials.  

Completed Design/Model 

Include the completed design/model here and make sure that it is appropriately labelled (points of intersection could also be labelled on example below).

#7: Evaluation of Results (500-600 words)

Reasonableness .

Discuss which aspects of your design/model are reasonable and which aspects are unreasonable and provide justification. Explain how the unreasonable aspects could be improved.

Include aspects that were not taken into account and may have an effect on the design/model. Also, revisit the assumptions and consider any revisions that could be made to improve your design/model. 

Example: The dimensions, materials and the domains and ranges of the functions that make up the pendant are reasonable as they are based on current pendant designs. The reasonableness of the results has been assessed by both plotting the functions on Desmos and simultaneous equations. Although Desmos was generally informative, it was not quite accurate, as some functions did not appear to intersect… It is important to note that the construction cost of the pendant was not taken into account, and therefore the overall cost of designing and creating the pendant is likely to be much higher. 

Discuss the strengths of your design/model, such as the design choices, development process, calculations and practicality in terms of the real world.  

Example: The main strength of the pendant is that all the functions intersect perfectly, as all the points of intersection were successfully solved for. In terms of the real world, this means that the pendant can be built accurately according to these calculations with no gaps between portions of the pendant. This also meant that the area and volume of the pendant could be calculated accurately using integration. Another strength of the pendant is that there is a loop that is big enough for a chain of 5mm width to go through. These factors, along with the estimated cost and weight being $628.35 and 16.5g respectively, mean that this pendant is suitable for the average adult consumer. 

Limitations 

Discuss the limitations of the design/model of your QCAA Methods PSMT, such as the design choices, development process, calculations and practicality in terms of the real world. Explain how you would address these limitations (further calculations, more research, other considerations etc.)

Example: A limitation of this report is that the physical construction of the pendant was not considered. If and how the materials can be cut/shaped into the designed format is unknown. Although the materials were chosen according to existing pendants, the weight and costs of the materials are only estimations and based on little research. More research needs to be conducted about the density, weight and construction costs of the materials. Another restriction is that the surface of the pendant is flat, as although practical, it gives a 2D element to the pendant, thus reducing its appeal. Therefore, it is recommended that further research is conducted into the physical construction of the pendant to make sure it is practical.  

#8: Conclusion (50 words)

Sum up the report by producing a final response to the task. Discuss the k ey findings of the process and evaluation, as well as how it could be improved at the end of your QCAA Methods PSMT.

Example: Through the evaluation of other pendants, consideration of all observations and assumptions and accurate application of mathematical processes, a pendant was successfully designed. Although there are some areas of improvement and further investigation into the physical construction of the pendant is recommended, overall, the pendant is unique, practical and visually appealing.

#9: Bibliography

List all of your references here. Check which style of referencing your teacher wants.

#10: Appendix

All your tables, graphs, diagrams and calculations that weren’t in the main body of the report should be here . This section is not marked and does not count towards the word or page count.  

Still stuck? Check out our local team of Brisbane Maths Methods tutors !

Tips for Writing a PSMT for QCAA Maths Methods + A Breakdown of the ISMG 

Not sure what mark you should be aiming for in the PSMT? Here’s what mark you need to be on track for an ATAR above 90 !

#1: Experiment with different designs/models before choosing one — and it’s okay if your design/model is not perfect, you can talk about its limitations in the evaluation section. #2: The graphing calculator on Desmos is a great way to graph functions and test the reasonableness of your design. #3: The WolframAlpha calculator is a great tool to help solve or double check any complex calculations. #4: Ensure all tables, graphs, images and diagrams are appropriately labelled. #5: Aim for at least four observations and four assumptions. #6: Ensure that your report can be understood independently of the task sheet and that it is presented as a real report and not a school assignment. #7: See the table below for what is and isn’t included in the page and word count for this assessment.

Breaking Down the Instrument-Specific Marking Guide ( ISMG ) 

The ISMG is split into four distinct criteria: Formulate, Solve, Evaluate and Verify, and Communicate . Let’s explore what each of them is about!

This criterion is all about your ability to effectively plan. This includes: 

• Considering all the different aspects of the task and addressing them in your observations and assumptions 
• Your observations and assumptions being accurate and relevant to the task 
• Not only stating, but documenting (supporting with evidence) your observations and assumptions 
• Effectively translating the task from a real-world problem to a mathematical scenario by identifying the mathematical concepts, processes and techniques required to develop your design/model 

This criterion is all about how effectively you apply mathematical concepts and techniques to develop your design/model. This includes: 

• Utilising technology 
• Using complex, not basic, mathematical concepts and techniques that are relevant to the task 

Evaluate and Verify

This criterion is all about your ability to apply mathematical concepts and techniques to develop your design/model. This includes: 

• Utilising the results, assumptions and observations to justify your evaluation 
• Discussing how limitations can be improved 

Communicate

This criterion is all about the flow and presentation of your report. This includes: 

• Correct spelling, grammar and referencing 
• Appropriate and accurate use of mathematical language 
• Coherent structure 

If you’re studying General Maths, check out our guide to writing a PSMT here!

Once you’ve received your marks from this PSMT, you should see how you’re tracking for your goal ATAR with our QCE Cohort Comparison Tool !

Completing this assessment at the start of Year 11? Here’s why you might be struggling in Year 11 !

On the hunt for other QCAA Maths Methods resources?

We’ve created a bunch of helpful articles and practice questions for studying QCAA Maths Methods. Check them out!

• Unit 3 IA2 Short Answer Practice Questions
• Unit 4 IA3 Short Answer Practice Questions
• Download QCAA Maths Methods Practice Exam for External Assessment Revision
• QCAA Practice Questions for Unit 3 & 4 Maths Methods External Assessment
• The Ultimate Guide to QCAA Maths Methods Unit 3: Further Calculus
• The Ultimate Guide to QCAA Maths Methods Unit 4: Further Functions and Statistics

Stuck completing this PSMT at the end of Year 11 because you’re school’s trying to get ahead? Don’t fall behind with these tips !

Are you looking for some extra guidance with the QCAA Maths Methods PSMT?

We have an incredible team of qld tutors and mentors.

We can help you master the QCAA Maths Methods syllabus and ace your upcoming Maths Methods assessments with personalised lessons conducted one-on-one in your home or online!

We’ve supported over  8,000 students over the last 11 years , and on average our students score mark improvements of over 20%!

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WWDC24 Highlights

Apple Reveals Apple Intelligence

iOS 18 Makes iPhone More Personal and Intelligent Than Ever

iPadOS 18 Takes iPad to the Next Level

macOS Sequoia Brings New Ways of Working and Transformative Intelligence to Mac

watchOS 11 Offers Powerful Health and Fitness Insights, and More Personalization

visionOS 2 Brings New Spatial Computing Experiences to Apple Vision Pro

Home and Audio Updates Elevate Entertainment and Bring More Convenience

Text of this article

June 10, 2024

Relive the biggest moments from WWDC24

Today Apple kicked off its 2024 Worldwide Developers Conference, revealing groundbreaking new technologies and features during a keynote that was live-streamed from Apple Park to millions around the world. During the weeklong event, developers and students will have unique access to Apple experts, as well as insight into new tools, frameworks, and features to help elevate their apps and games.

This year’s keynote revealed Apple Intelligence , the personal intelligence system that combines the power of generative models with users’ personal context — at the core of iPhone, iPad, and Mac to deliver intelligence that’s incredibly useful and relevant. Major updates also come to iOS 18 , iPadOS 18 , macOS Sequoia , and watchOS 11 , including the biggest-ever redesign of the Photos app, game-changing productivity tools, and new ways for users to express themselves and customize their devices. visionOS 2 brings powerful new ways to interact with Apple Vision Pro and exciting updates to spatial photos and Mac Virtual Display, and tvOS 18 infuses useful information in Apple TV+ films and shows on users’ biggest screen in the home.

Beginning this month, Apple Vision Pro is also coming to more countries and regions, including China mainland, Hong Kong, Japan, Singapore, and next month will come to Australia, Canada, France, Germany, and the U.K.

Apple Intelligence harnesses the power of Apple silicon to understand and create language and images, take action across apps, and draw from users’ personal context to simplify and accelerate everyday tasks. A cornerstone of Apple Intelligence is on-device processing, which delivers personal intelligence without collecting users’ data. Private Cloud Compute sets a new standard for privacy in AI, with the ability to flex and scale computational capacity between on-device processing, and larger, server-based models that run on dedicated Apple silicon servers.

With iOS 18 , users will now be able to arrange apps and widgets in any open space on the Home Screen, customize the buttons at the bottom of the Lock Screen, and quickly access more controls in Control Center. With the biggest redesign ever of the Photos app, photo libraries are automatically organized in a new single view in Photos, and helpful new collections keep favorites easily accessible. All-new text effects come to iMessage, amplifying any letter, word, phrase, or emoji with dynamic, animated appearances to bring conversations to life. Users can also now communicate over satellite in the Messages app, even when a cellular or Wi-Fi connection isn’t available.

With iPadOS 18 , the iPad experience is more versatile and intelligent than ever with new features and apps designed for Apple Pencil. The Calculator app comes to iPad with Math Notes, which allows users to type or write out mathematical expressions and see them instantly solved in their own handwriting. New handwriting tools in Notes including Smart Script make handwritten notes more fluid, flexible, and easier to read.

With macOS Sequoia , Continuity between iPhone and Mac gets better than ever with iPhone Mirroring, enabling full access to and control of iPhone directly from Mac. Safari gets another big update with the new Highlights feature for effortless information discovery on webpages while browsing. Gaming is even more immersive with Personalized Spatial Audio that puts players in the middle of the action like never before. And Apple Intelligence unlocks new ways for Mac users to enhance their writing and communicate more effectively, create playful images in seconds, and more. Apple Intelligence takes full advantage of the power of Apple silicon and its Neural Engine, and will be supported by every Mac with an M-series chip.

watchOS 11 offers breakthrough insights into users’ health and fitness, and more personalization than ever. The new Vitals app surfaces key health metrics and context, the ability to measure training load offers a game-changing new experience when working out, and the popular Activity rings are even more customizable. The Smart Stack and Photos face use intelligence to feature more individualization, and Apple Watch and the Health app on iPhone and iPad offer additional support for users who are pregnant. Check In, the Translate app, and new capabilities for the double tap gesture come to Apple Watch for added connectivity and convenience.

Just months after its initial release, visionOS 2 brings powerful spatial computing experiences to Apple Vision Pro, including new ways for users to create spatial photos with the images already in their library, intuitive hand gestures to easily access important information at a glance, and new features for Mac Virtual Display, Travel Mode, and Guest User. visionOS 2 also introduces exciting new capabilities like Follow Your Breathing in the Mindfulness app, SharePlay for Photos, and multiview in the TV app.

With tvOS 18 , intelligent new features like InSight — and updates to Enhance Dialogue and subtitles — level up cinematic experiences, while new Apple Fitness+, Apple Music, and FaceTime capabilities get even better on users’ biggest screen. The Home app gains new features with iOS 18, like guest access and hands-free unlock with home keys, delivering effortless and secure access to the home. AirPods software updates will transform the way users respond to Siri with new gestures, take calls with friends and loved ones, and immerse themselves in their favorite games.

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