math book report example

Mathematics Project Competition and Mathematics Book Report Competition for Secondary Schools

Aims: The Mathematics Project Competition and Mathematics Book Report Competition for Secondary Schools are organised by the Education Bureau since 2001 and 2007 respectively. They aim at promoting students' interest in learning Mathematics and developing students' generic skills through project learning and reading.

• Relevant Circulars  PDF  
• Application Form of Mathematics Project Competition for Secondary Schools   DOCX  
• Application Form  of Mathematics Book Report Competition for Secondary Schools   DOC  
• Poster of Mathematics Project Competition and Mathematics Project Competition for Secondary Schools  PDF  

Mathematics Project Competition for Secondary Schools

• Online nomination form  Online Form  
• Information sheet   DOCX  

Mathematics Book Report Competition for Secondary Schools

• Cover sheet  DOCX  
• Junior Secondary Category Suggested Book List  PDF  
• Senior Secondary Category Suggested Book List  PDF  
• Results of Mathematics Project Competition for Secondary Schools  PDF  
• Results of Mathematics Book Report Competition for Secondary Schools  PDF  

2021/22  

• Results of Mathematics Project Competition for Secondary Schools   PDF  

  2020/21

How to Write a Book Report

Use the links below to jump directly to any section of this guide:

Book Report Fundamentals

Preparing to write, an overview of the book report format, how to write the main body of a book report, how to write a conclusion to a book report, reading comprehension and book reports, book report resources for teachers .

Book reports remain a key educational assessment tool from elementary school through college. Sitting down to close read and critique texts for their content and form is a lifelong skill, one that benefits all of us well beyond our school years. With the help of this guide, you’ll develop your reading comprehension and note-taking skills. You’ll also find resources to guide you through the process of writing a book report, step-by-step, from choosing a book and reading actively to revising your work. Resources for teachers are also included, from creative assignment ideas to sample rubrics.

Book reports follow general rules for composition, yet are distinct from other types of writing assignments. Central to book reports are plot summaries, analyses of characters and themes, and concluding opinions. This format differs from an argumentative essay or critical research paper, in which impartiality and objectivity is encouraged. Differences also exist between book reports and book reviews, who do not share the same intent and audience. Here, you’ll learn the basics of what a book report is and is not.

What Is a Book Report?

"Book Report" ( ThoughtCo )

This article, written by a professor emeritus of rhetoric and English, describes the defining characteristics of book reports and offers observations on how they are composed.

"Writing a Book Report" (Purdue OWL)

Purdue’s Online Writing Lab outlines the steps in writing a book report, from keeping track of major characters as you read to providing adequate summary material.

"How to Write a Book Report" ( Your Dictionary )

This article provides another helpful guide to writing a book report, offering suggestions on taking notes and writing an outline before drafting. 

"How to Write a Successful Book Report" ( ThoughtCo )

Another post from ThoughtCo., this article highlights the ten steps for book report success. It was written by an academic advisor and college enrollment counselor.

What’s the Difference Between a Book Report and an Essay?

"Differences Between a Book Report & Essay Writing" ( Classroom)

In this article from the education resource Classroom,  you'll learn the differences and similarities between book reports and essay writing.

"Differences Between a Book Report and Essay Writing" (SeattlePi.com)

In this post from a Seattle newspaper's website, memoirist Christopher Cascio highlights how book report and essay writing differ.

"The Difference Between Essays and Reports" (Solent Online Learning)

This PDF from Southampton Solent University includes a chart demonstrating the differences between essays and reports. Though it is geared toward university students, it will help students of all levels understand the differing purposes of reports and analytical essays.

What’s the Difference Between a Book Report and a Book Review?

"How to Write a Book Review and a Book Report" (Concordia Univ.)

The library at Concordia University offers this helpful guide to writing book report and book reviews. It defines differences between the two, then presents components that both forms share.

"Book Reviews" (Univ. of North Carolina)

The University of North Carolina at Chapel Hill’s writing guide shows the step-by-step process of writing book reviews, offering a contrast to the composition of book reports.

Active reading and thoughtful preparation before you begin your book report are necessary components of crafting a successful piece of writing. Here, you’ll find tips and resources to help you learn how to select the right book, decide which format is best for your report, and outline your main points.

Selecting and Finding a Book

"30 Best Books for Elementary Readers" (Education.com)

This article from Education.com lists 30 engaging books for students from kindergarten through fifth grade. It was written by Esme Raji Codell, a teacher, author, and children's literature specialist.

"How to Choose a Good Book for a Report (Middle School)" (WikiHow)

This WikiHow article offers suggestions for middle schoolers on how to choose the right book for a report, from getting started early on the search process to making sure you understand the assignment's requirements.

"Best Book-Report Books for Middle Schoolers" (Common Sense Media)

Common Sense Media has compiled this list of 25 of the best books for middle school book reports. For younger students, the article suggests you check out the site's "50 Books All Kids Should Read Before They're 12."

"50 Books to Read in High School" (Lexington Public Library)

The Lexington, Kentucky Public Library has prepared this list to inspire high school students to choose the right book. It includes both classics and more modern favorites.

The Online Computer Library Center's catalogue helps you locate books in libraries near you, having itemized the collections of 72,000 libraries in 170 countries.

Formats of Book Reports

"Format for Writing a Book Report" ( Your Dictionary )

Here, Your Dictionary supplies guidelines for the basic book report format. It describes what you'll want to include in the heading, and what information to include in the introductory paragraph. Be sure to check these guidelines against your teacher's requirements.

"The Good Old Book Report" (Scholastic)

Nancy Barile’s blog post for Scholastic lists the questions students from middle through high school should address in their book reports.

How to Write an Outline

"Writer’s Web: Creating Outlines" (Univ. of Richmond)

The University of Richmond’s Writing Center shows how you can make use of micro and macro outlines to organize your argument.

"Why and How to Create a Useful Outline" (Purdue OWL)

Purdue’s Online Writing Lab demonstrates how outlines can help you organize your report, then teaches you how to create outlines.

"Creating an Outline" (EasyBib)

EasyBib, a website that generates bibliographies, offers sample outlines and tips for creating your own. The article encourages you to think about transitions and grouping your notes.

"How to Write an Outline: 4 Ways to Organize Your Thoughts" (Grammarly)

This blog post from a professional writer explains the advantages of using an outline, and presents different ways to gather your thoughts before writing.

In this section, you’ll find resources that offer an overview of how to write a book report, including first steps in preparing the introduction. A good book report's introduction hooks the reader with strong opening sentences and provides a preview of where the report is going.

"Step-by-Step Outline for a Book Report" ( Classroom )

This article from Classroom furnishes students with a guide to the stages of writing a book report, from writing the rough draft to revising.

"Your Roadmap to a Better Book Report" ( Time4Writing )

Time4Writing offers tips for outlining your book report, and describes all of the information that the introduction, body, and conclusion should include.

"How to Start a Book Report" ( ThoughtCo)

This ThoughtCo. post, another by academic advisor and college enrollment counselor Grace Fleming, demonstrates how to write a pithy introduction to your book report.

"How to Write an Introduction for a Book Report" ( Classroom )

This brief but helpful post from Classroom  details what makes a good book report introduction, down to the level of individual sentences.

The body paragraphs of your book report accomplish several goals: they describe the plot, delve more deeply into the characters and themes that make the book unique, and include quotations and examples from the book. Below are some resources to help you succeed in summarizing and analyzing your chosen text.

Plot Summary and Description

"How Do You Write a Plot Summary?" ( Reference )

This short article presents the goals of writing a plot summary, and suggests a word limit. It emphasizes that you should stick to the main points and avoid including too many specific details, such as what a particular character wears.

"How to Write a Plot for a Book Report" ( The Pen & The Pad )

In this article from a resource website for writers, Patricia Harrelson outlines what information to include in a plot summary for a book report. 

"How to Write a Book Summary" (WikiHow)

Using Harry Potter and the Sorcerer’s Stone as an example, this WikiHow article demonstrates how to write a plot summary one step at a time.

Analyzing Characters and Themes

"How to Write a Character Analysis Book Report" ( The Pen & The Pad )

Kristine Tucker shows how to write a book report focusing on character. You can take her suggestions as they are, or consider  incorporating them into the more traditional book report format.

"How to Write a Character Analysis" (YouTube)

The SixMinuteScholar Channel utilizes analysis of the film  Finding Nemo to show you how to delve deeply into character, prioritizing inference over judgment.

"How to Define Theme" ( The Editor's Blog )

Fiction editor Beth Hill contributes an extended definition of theme. She also provides examples of common themes, such as "life is fragile."

"How to Find the Theme of a Book or Short Story" ( ThoughtCo )

This blog post from ThoughtCo. clarifies the definition of theme in relation to symbolism, plot, and moral. It also offers examples of themes in literature, such as love, death, and good vs. evil.

Selecting and Integrating Quotations

"How to Choose and Use Quotations" (Santa Barbara City College)

This guide from a college writing center will help you choose which quotations to use in your book report, and how to blend quotations with your own words.

"Guidelines for Incorporating Quotes" (Ashford Univ.)

This PDF from Ashford University's Writing Center introduces the ICE method for incorporating quotations: introduce, cite, explain.

"Quote Integration" (YouTube)

This video from The Write Way YouTube channel illustrates how to integrate quotations into writing, and also explains how to cite those quotations.

"Using Literary Quotations" (Univ. of Wisconsin-Madison)

This guide from the University of Wisconsin-Madison’s Writing Center helps you emphasize your analysis of a quotation, and explains how to incorporate quotations into your text.

Conclusions to any type of paper are notoriously tricky to write. Here, you’ll learn some creative ways to tie up loose ends in your report and express your own opinion of the book you read. This open space for sharing opinions that are not grounded in critical research is an element that often distinguishes book reports from other types of writing.

"How to Write a Conclusion for a Book Report" ( Classroom )

This brief article from the education resource  Classroom illustrates the essential points you should make in a book report conclusion.

"Conclusions" (Univ. of North Carolina)

The University of North Carolina at Chapel Hill’s Writing Center lays out strategies for writing effective conclusions. Though the article is geared toward analytical essay conclusions, the tips offered here will also help you write a strong book report.

"Ending the Essay: Conclusions" (Harvard College Writing Center)

Pat Bellanca’s article for Harvard University’s Writing Center presents ways to conclude essays, along with tips. Again, these are suggestions for concluding analytical essays that can also be used to tie up a book report's loose ends.

Reading closely and in an engaged manner is the strong foundation upon which all good book reports are built. The resources below will give you a picture of what active reading looks like, and offer strategies to assess and improve your reading comprehension. Further, you’ll learn how to take notes—or “annotate” your text—making it easier to find important information as you write.

How to Be an Active Reader

"Active Reading Strategies: Remember and Analyze What You Read" (Princeton Univ.)

Princeton University’s McGraw Center for Teaching and Learning recommends ten strategies for active reading, and includes sample diagrams.

"Active Reading" (Open Univ.)

The Open University offers these techniques for reading actively alongside video examples. The author emphasizes that you should read for comprehension—not simply to finish the book as quickly as possible.

"7 Active Reading Strategies for Students" ( ThoughtCo )

In this post, Grace Fleming outlines seven methods for active reading. Her suggestions include identifying unfamiliar words and finding the main idea. 

"5 Active Reading Strategies for Textbook Assignments" (YouTube)

Thomas Frank’s seven-minute video demonstrates how you can retain the most important information from long and dense reading material.

Assessing Your Reading Comprehension

"Macmillan Readers Level Test" (MacMillan)

Take this online, interactive test from a publishing company to find out your reading level. You'll be asked a number of questions related to grammar and vocabulary.

"Reading Comprehension Practice Test" (ACCUPLACER)

ACCUPLACER is a placement test from The College Board. This 20-question practice test will help you see what information you retain after reading short passages.

"Reading Comprehension" ( English Maven )

The English Maven site has aggregated exercises and tests at various reading levels so you can quiz your reading comprehension skills.

How to Improve Your Reading Comprehension

"5 Tips for Improving Reading Comprehension" ( ThoughtCo )

ThoughtCo. recommends five tips to increase your reading comprehension ability, including reading with tools such as highlighters, and developing new vocabulary.

"How to Improve Reading Comprehension: 8 Expert Tips" (PrepScholar)

This blog post from PrepScholar provides ideas for improving your reading comprehension, from expanding your vocabulary to discussing texts with friends.

CrashCourse video: "Reading Assignments" (YouTube)

This CrashCourse video equips you with tools to read more effectively. It will help you determine how much material you need to read, and what strategies you can use to absorb what you read.

"Improving Reading Comprehension" ( Education Corner )

From a pre-reading survey through post-reading review, Education Corner  walks you through steps to improve reading comprehension.

Methods of In-text Annotation

"The Writing Process: Annotating a Text" (Hunter College)

This article from Hunter College’s Rockowitz Writing Center outlines how to take notes on a text and provides samples of annotation.

"How To Annotate Text While Reading" (YouTube)

This video from the SchoolHabits YouTube channel presents eleven annotation techniques you can use for better reading comprehension.

"5 Ways To Annotate Your Books" ( Book Riot )

This article from the Book Riot  blog highlights five efficient annotation methods that will save you time and protect your books from becoming cluttered with unnecessary markings.

"How Do You Annotate Your Books?" ( Epic Reads )

This post from Epic Reads highlights how different annotation methods work for different people, and showcases classic methods from sticky notes to keeping a reading notebook.

Students at every grade level can benefit from writing book reports, which sharpen critical reading skills. Here, we've aggregated sources to help you plan book report assignments and develop rubrics for written and oral book reports. You’ll also find alternative book report assessment ideas that move beyond the traditional formats.

Teaching Elementary School Students How to Write Book Reports

"Book Reports" ( Unique Teaching Resources )

These reading templates courtesy of Unique Teaching Resources make great visual aids for elementary school students writing their first book reports.

"Elementary Level Book Report Template" ( Teach Beside Me )

This   printable book report template from a teacher-turned-homeschooler is simple, classic, and effective. It asks basic questions, such as "who are the main characters?" and "how did you feel about the main characters?"

"Book Reports" ( ABC Teach )

ABC Teach ’s resource directory includes printables for book reports on various subjects at different grade levels, such as a middle school biography book report form and a "retelling a story" elementary book report template.

"Reading Worksheets" ( Busy Teacher's Cafe )

This page from Busy Teachers’ Cafe contains book report templates alongside reading comprehension and other language arts worksheets.

Teaching Middle School and High School Students How to Write Book Reports

"How to Write a Book Report: Middle and High School Level" ( Fact Monster)

Fact Monster ’s Homework Center discusses each section of a book report, and explains how to evaluate and analyze books based on genre for students in middle and high school.

"Middle School Outline Template for Book Report" (Trinity Catholic School)

This PDF outline template breaks the book report down into manageable sections for seventh and eighth graders by asking for specific information in each paragraph.

"Forms for Writing a Book Report for High School" ( Classroom )

In this article for Classroom,  Elizabeth Thomas describes what content high schoolers should focus on when writing their book reports.

"Forms for Writing a Book Report for High School" ( The Pen & The Pad )

Kori Morgan outlines techniques for adapting the book report assignment to the high school level in this post for The Pen & The Pad .

"High School Book Lists and Report Guidelines" (Highland Hall Waldorf School)

These sample report formats, grading paradigms, and tips are collected by Highland Hall Waldorf School. Attached are book lists by high school grade level.

Sample Rubrics

"Book Review Rubric Editable" (Teachers Pay Teachers)

This free resource from Teachers Pay Teachers allows you to edit your book report rubric to the specifications of your assignment and the grade level you teach.

"Book Review Rubric" (Winton Woods)

This PDF rubric from a city school district includes directions to take the assignment long-term, with follow-up exercises through school quarters.

"Multimedia Book Report Rubric" ( Midlink Magazine )

Perfect for oral book reports, this PDF rubric from North Carolina State University's Midlink Magazine  will help you evaluate your students’ spoken presentations.

Creative Book Report Assignments

"25 Book Report Alternatives" (Scholastic)

This article from the Scholastic website lists creative alternatives to the standard book report for pre-kindergarteners through high schoolers.

"Fresh Ideas for Creative Book Reports" ( Education World )

Education World offers nearly 50 alternative book report ideas in this article, from a book report sandwich to a character trait diagram.

"A Dozen Ways to Make Amazingly Creative Book Reports" ( We Are Teachers )

This post from We Are Teachers puts the spotlight on integrating visual arts into literary study through multimedia book report ideas.

"More Ideas Than You’ll Ever Use for Book Reports" (Teachnet.com)

This list from Teachnet.com includes over 300 ideas for book report assignments, from "interviewing" a character to preparing a travel brochure to the location in which the book is set.

"Fifty Alternatives to the Book Report" (National Council of Teachers of English)

In this PDF resource from the NCTE's  English Journal,  Diana Mitchell offers assignment ideas ranging from character astrology signs to a character alphabet.

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A Beginner's Guide to Writing a Book Report (with Examples)

Last Updated: March 13, 2024 Fact Checked

• Researching
• Drafting the Report
• Reviewing & Revising

Sample Book Reports & Summaries

Expert q&a.

This article was co-authored by Jake Adams and by wikiHow staff writer, Raven Minyard, BA . Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,410,052 times.

A book report is a short essay that summarizes and analyzes a work of fiction or nonfiction. Writing a book report may not seem fun at first, but it gives you a great chance to fully understand a work and its author. In this article, we’ll teach you everything you need to know about how to write a book report, from choosing a book and outlining to drafting and editing your final paper.

Things You Should Know

• Read the entire book and take notes on important themes, characters, and events. Use your notes to create an outline with evidence that supports your analysis.
• Include the title and author in your intro, then summarize the plot, main characters, and setting of the book.
• Analyze the author’s writing style, as well as the main themes and arguments of the book. Include quotes and examples to support your statements.

Researching Your Book Report

• For example, find out if your teacher wants you to include citations, such as page numbers from the book, in your report.
• Ask your teacher how much of your paper to devote to summary versus analysis. Most book reports are direct summaries with objective analysis rather than your personal opinions. In contrast, a book review or commentary is more opinion-driven.

• Some popular books for book reports include To Kill a Mockingbird by Harper Lee, Animal Farm by George Orwell, and The Hunger Games by Suzanne Collins. Choose a book at your grade level.

• Author: Who wrote the book? Do you know any other works by this author?
• Genre: Is the book fiction or nonfiction? If it’s fiction, is it historical, fantasy, horror, etc.? If it’s nonfiction, is it a biography, memoir, science, etc.?
• Audience: Who would find this book appealing? Is it intended for a specific age range or gender? Do you typically enjoy books like this?
• Title: Does the title catch your interest? Does it fit well with the book’s content?
• Book Cover/Illustrations: What does the book cover convey and does it accurately represent the book? How do you feel when you look at it? If the book has illustrations, what are they and do they hold your interest?

• Take breaks while reading to keep your attention sharp. Try to find a pace that is comfortable for you. If you get distracted after 15 minutes, read in 15-minute intervals. If you can go an hour, read for an hour at a time.
• Give yourself enough time to read the entire book. It’s very difficult to write a book report if you’ve just skimmed over everything. Don’t procrastinate!
• Don’t trust online book summaries. You can’t guarantee that they are accurate or true to the text.

• For example, look for a sentence that clearly describes a main setting in the book, such as “The castle was gloomy and made out of large black stones.”

Outlining Your Book Report

• Introduction: Introduce the title, author, and publication information. Include a brief overview of the book’s genre and main theme, and state your purpose for writing the report.
• Summary: Concisely summarize the plot or central idea, highlighting main events, characters, and conflicts. Focus on important aspects while avoiding spoilers.
• Analysis and Evaluation: Evaluate the author’s writing style and use of literary devices, like foreshadowing, metaphors, imagery, etc. Discuss the strengths and weaknesses of the book and use quotes and examples from the text.
• Themes and Messages: Identify the book’s main themes or messages and how they develop through the course of the book. Provide specific quotes and examples.
• Character Analysis: Analyze the main characters in the book, their development, and their relationships. Explain their motivations, personalities, and significance to the story. Provide examples and quotes to support your analysis.
• Personal Reflection: Depending on your teacher’s instructions, you might share your personal opinions and discuss what you liked and disliked about the book. Reflect on how the book relates to broader themes or issues.
• Conclusion: Summarize your main points and conclude with your final thoughts or reflections on the book.
• Bibliography: If required, include a works cited page or bibliography listing all the sources you used to write your book report.
• Outlining takes time, but it saves you more time once you reach the editing stage.
• Some people prefer to outline with pen and paper, while others just type up a list on the computer. Choose the method that works best for you.

• Be careful not to overuse quotes. If it seems like every other line is a quote, try to dial back. Aim to include a maximum of one quotation per paragraph. Quotes and examples should still take a backseat to your summary.

• For example, you’ll likely need to focus primarily on discussing the most important characters or the characters that appear most frequently in the text.
• When you are finished with your outline, go back through it to see if it makes sense. If the paragraphs don’t flow into one another, move them around or add/delete new ones until they do.
• Also, check to see if your outline covers all of the major elements of the book, such as the plot, characters, and setting.

Writing Your Book Report

• For example, a sentence summary might state, “This book is about the main character’s journey to Africa and what she learns on her travels.”
• Don’t take up too much space with your introduction. In general, an introduction should be 3-6 sentences long, though in rare cases, they may be longer or shorter.

• Use vivid language when you can and include plenty of details. For example, you might write, “The farm was surrounded by rolling hills.”

• For instance, if the main character moves to Africa, you might describe what happens before the move, how the move goes, and how they settle in once they arrive.

• For example, you might write that the main character is “a middle-aged woman who enjoys the finer things in life, such as designer clothes.” Then, connect this description to the plot summary by describing how her views change after her travels, if they do.
• Expect to introduce the characters in the same sentences and paragraphs as the plot introduction.

• You might write, “The author argues that travel gives you a new perspective. That is why her main characters all seem happier and more grounded after visiting new places.”
• For fiction, determine if the author is using the story to pass along a certain moral or lesson. For example, a book about an underdog athlete could encourage readers to take chances to pursue their dreams.

• For example, an author who uses lots of slang terms is probably going for a hip, approachable style.

• Some teachers require, or strongly suggest, that you include the author’s name and the book title in your concluding paragraph.
• When writing a conclusion , don’t introduce any new thoughts. Any important points should be made in your body paragraphs. Save the space for your recap.

Reviewing and Revising Your Book Report

• Before you submit your paper, make sure that you’ve spelled the author’s name and any character names correctly.
• Don’t trust your computer’s spell check to catch all the errors for you. Spell check can be helpful, but it isn’t perfect and can make mistakes.

• If you’re nervous about asking, try saying something like “It would be great if you could go over my book report and make sure that it reads smoothly.”
• Remember, no one’s first draft is perfect, so don’t get upset if someone suggests you do something differently. They want to help make your report the best it can be, so don’t take constructive criticism personally.

• For example, double-check that you are using the correct font, font size, and margins.
• Once you've finished proofreading, revising, and checking that you've addressed all the requirements, you're ready to submit your book report!

• Even though your book report is your own work, avoid using “I” too much. It can make your writing feel choppy. Thanks Helpful 0 Not Helpful 0
• It might be tempting to watch the movie or read the online notes instead of reading the book. Resist this urge! Your teacher will be able to tell the difference. Thanks Helpful 0 Not Helpful 0

Tips from our Readers

• Calm down and walk around if you get too frustrated while writing. If you write a book report while angry, you're more likely to misspell things!
• Choose a unique book. Harry Potter or Percy Jackson is an absolute no. Everyone chooses those. Try something different!
• Write when anything comes to mind! You don't want to lose your ideas!

• Give yourself plenty of time to write your report. Don’t wait until the last minute or you may feel rushed. Thanks Helpful 1 Not Helpful 0
• Stealing or using another person’s work is considered plagiarism and academic dishonesty. Make sure that the work you submit is all your own. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ https://www.aresearchguide.com/write-book-report.html
• ↑ Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 24 July 2020.
• ↑ https://grammark.org/how-to-write-a-book-report/
• ↑ https://library.valleycollege.edu/elements_of_book_report.pdf
• ↑ https://takelessons.com/blog/steps-to-writing-a-book-report
• ↑ https://www.infoplease.com/homework-help/homework-center-writing-book-report
• ↑ https://liberalarts.oregonstate.edu/wlf/what-setting
• ↑ https://www.tcc.edu/wp-content/uploads/archive/writing-center-handouts/essay-types-plot-summary.pdf
• ↑ https://www.cornerstone.edu/blog-post/six-steps-to-really-edit-your-paper/

About This Article

To write a book report, start by introducing the author and the name of the book and then briefly summarizing the story. Next, discuss the main themes and point out what you think the author is trying to suggest to the reader. Finally, write about the author’s style of writing, paying particular attention to word choice and the overall tone of the book. For tips on editing and polishing your paper before turning it in, keep reading! Did this summary help you? Yes No

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10 Steps to Writing a Successful Book Report

• Writing Essays
• Writing Research Papers
• English Grammar
• M.Ed., Education Administration, University of Georgia
• B.A., History, Armstrong State University

A book report should contain the basic elements, but a good book report will address a specific question or point of view and back up this topic with specific examples, in the form of symbols and themes. These steps will help you identify and incorporate those important elements in a process that takes three to four days.

How To Write a Book Report

• Have an objective in mind, if possible. Your objective is the main point you want to argue or the question you plan to answer. Sometimes your teacher will offer a question for you to answer as part of your assignment, which makes this step easy. If you have to come up with your own focal point for your paper, you may have to wait and develop the objective while reading and reflecting on the book.
• Keep supplies on hand when you read. This is very important. Keep sticky-note flags, pen, and paper nearby as you read. Don't try to take "mental notes." It just doesn't work.
• Read the book. As you read, keep an eye out for clues that the author has provided in the form of symbolism. These will indicate some important point that supports the overall theme. For instance, a spot of blood on the floor, a quick glance, a nervous habit, an impulsive action--these are worth noting.
• Use your sticky flags to mark pages. When you run into any clues, mark the page by placing the sticky note at the beginning of the relevant line. Mark everything that piques your interest, even if you don't understand their relevance.
• Note possible themes or patterns that emerge. As you read and record emotional flags or signs, you will begin to see a point or a pattern. On a notepad, write down possible themes or issues. If your assignment is to answer a question, you will record how symbols address that question.
• Label your sticky flags. If you see a symbol repeated several times, you should indicate this somehow on the sticky flags, for easy reference later. For instance, if blood shows up in several scenes, write a "b" on the relevant flags for blood. This may become your major book theme, so you'll want to navigate between the relevant pages easily.
• Develop a rough outline. By the time you finish reading the book , you will have recorded several possible themes or approaches to your objective. Review your notes and try to determine which view or claim you can back up with good examples (symbols). You may need to play with a few sample outlines to pick the best approach.
• Develop paragraph ideas. Each paragraph should have a topic sentence and a sentence that transitions to the next paragraph. Try writing these first, then filling out the paragraphs with your examples (symbols). Don't forget to include the basics for every book report in your first paragraph or two.
• Review, re-arrange, repeat. At first, your paragraphs are going to look like ugly ducklings. They will be clunky, awkward, and unattractive in their early stages. Read them over, re-arrange and replace sentences that don't quite fit. Then review and repeat until the paragraphs flow.
• Re-visit your introductory paragraph. The introductory paragraph will make the critical first impression of your paper. It should be great. Be sure it is well-written, interesting, and it contains a strong thesis sentence .

The objective: Sometimes it is possible to have a clear objective in mind before you start . Sometimes, it is not. If you have to come up with your own thesis, don't stress about a clear objective in the beginning. It will come later.

Recording emotional flags: Emotional flags are merely points in the book that bring about emotion. Sometimes, the smaller the better. For example, for an assignment for The Red Badge of Courage , the teacher might ask students to address whether they believe Henry, the main character, is a hero. In this book, Henry sees lots of blood (emotional symbol) and death (emotional symbol) and this causes him to run away from the battle at first (emotional response). He is ashamed (emotion).

Book report basics: In your first paragraph or two, you should include the book setting, time period, characters, and your thesis statement (objective).

Re-visiting the introductory paragraph: The introductory paragraph should be the last paragraph you complete. It should be mistake-free and interesting. It should also contain a clear thesis. Don't write a thesis early on in the process and forget about it. Your point of view or argument may change completely as you re-arrange your paragraph sentences. Always check your thesis sentence last.

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FREE Board Game Templates for Book Report and Math Activities

This post may contain affiliate links, view our disclosure policy for details.

This post is brought to you in partnership with Advancement Courses.

Spring break and summer are quickly approaching, and that means you might be running out of ideas to keep your students engaged.

Below, I’ve created several free board game book report templates that you can turn into math activities, plus a bonus free printable book report overview template!

Blank templates are a great starting point and give students an advantage while allowing them to be creative in their own designs. I have seven single-page board game templates plus one giant board (four pages put together) that you can print as needed. Some are colorful, some are black and white, but all are blank and ready for your creative design!

I recommend printing your game board(s) on card stock and laminating them to make sure they last as long as possible. Read a book as a class, have each student or group of students create a game board that pairs with locations and characters in the book, then let the games begin!

How Do I Use the Free Blank Game Board Templates?

Simply print one or all the game board templates for your students’ book reports, and let the students choose which game board they want to design on! Make sure they include in their game board design:

•  Locations
• Transportation
• Monetary Amounts or Relevant Numbers
• Students’ Names

PRINT HERE –> Game Board Templates PDF

Or via google drive here: blank game board templates pdf.

NOTE – I have found that many school districts black external Google Drive files.

Types of Math Games to Use with Game Board Templates:

Strategy games, adding / subtracting games, multiplication games, money games, fraction / decimal games, ideas on how to create math activities from children’s books:.

There are many ways to create math games from children’s books. Students can choose to utilize one portion of the book and turn it into a game. For example, if the main character goes to the grocery store for his mother, students can choose to create a grocery-themed game.

Or they can turn the entire plot into a creative game. If the book follows an adventurous journey, the creative game can feature locations on the journey with the goal of reaching the final destination from the book.

Free BONUS Printable Book Report:

If you need a shorter “book report” worksheet-style template, then this “My Favorite Book” worksheet is just what you need! It’s perfect for any age from kindergarten through 5th grade. Students fill in each of the blanks on one side, and then draw and color a scene from the book on the blank side of the “book”!

These make great classroom assignments to line on your door, art wall or school hallway!

PRINT HERE: My Favorite Book Worksheet

I found my inspiration for the math activity game boards from a professional development course I was introduced to recently, Teaching Math with Children’s Literature from Advancement Courses. Advancement Courses has over 200 graduate-level professional development courses in 19 different subject areas (K-12), and many of them are pre-approved depending on your state and district.

How handy! Courses cover both traditional academic topics as well as emerging trends and even teacher wellness. They even offer group discounts! Plus, you can save 20% off any course right now when you use the code SALARY20 at checkout.

Their website is super easy to navigate and find the perfect course for you. You can narrow down your search by location, subject, grade level and Common Core. You can even filter by popular courses to see what other teachers are taking!

I absolutely love cross-over topics in education where one lesson can cover two areas of learning, and Advancement Courses has many courses that fit the bill, including the Teaching Math with Children’s Literature course that was my inspiration for these activities. Two other courses that caught my eye were Reaching and Teaching Gifted Students in the Regular Classroom and Motivating Unmotivated Students (Research and Practice) .

All of the courses through Advancement Courses are online and self-paced so you can take up to 6 months to effectively complete your coursework. I love this because I enjoy taking the time to process and research ideas as I am working through a course. You can see all the professional development course options here .

More About Advancement Course Credits:

Advancement Courses offers over 200 online courses available for graduate credit through CAEP and regionally accredited university partners or for continuing education units (CEUs) that meet state requirements. Choose whether you need Graduate Credit or Continuing Education credit. Once your course is completed, you’ll receive a transcript or certificate of completion. Find out how you can save 20% off any course using the code SALARY20 at checkout!

Check out all of the available Continuing Education Courses for Teachers here! 

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How to Write a Math Report

Linda donahue.

Writing a math report follows the same basic procedure as writing any report or essay. Present your argument or thesis and then support it, thereby proving it, over the following paragraphs. One difference between a math report and other types of reports is that a math report will typically include graphs or other relevant charts or data in the body of the paper and not just in appendices. A math paper may also include a proof as part of its logical arguments.

Introduce your thesis in your opening paragraph. Your thesis is whatever you intend to prove using mathematical data. Construct the opening to address the topic on a broader level then narrow down the exact point you intend to make. Use the opening to introduce your project. Define your project's parameters and give any relevant, yet brief, background information.

In each of the following paragraphs, take one point and elaborate as to how it supports your thesis. This can be discussing the details of your project step-by-step. Relate the results of any tests or experiments, using corroborating evidence in the form of graphs or charts as appropriate. Each stage of the project should support or disprove your initial thesis statement. Remember, in a math report, your findings could be that the initial thesis was wrong.

Write a conclusion. Your math project or data should either prove or disprove your thesis. Draw a conclusion and present the results. This paragraph is much like a summary.

Cite all references used and include additional information, charts, graphs and data in appendices.

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An book report/review examples on mathematics book reports and reviews is a prosaic composition of a small volume and free composition, expressing individual impressions and thoughts on a specific occasion or issue and obviously not claiming a definitive or exhaustive interpretation of the subject.

Some signs of mathematics book reports and reviews book report/review:

• the presence of a specific topic or question. A work devoted to the analysis of a wide range of problems in biology, by definition, cannot be performed in the genre of mathematics book reports and reviews book report/review topic.
• The book report/review expresses individual impressions and thoughts on a specific occasion or issue, in this case, on mathematics book reports and reviews and does not knowingly pretend to a definitive or exhaustive interpretation of the subject.
• As a rule, an essay suggests a new, subjectively colored word about something, such a work may have a philosophical, historical, biographical, journalistic, literary, critical, popular scientific or purely fiction character.
• in the content of an book report/review samples on mathematics book reports and reviews, first of all, the author’s personality is assessed - his worldview, thoughts and feelings.

The goal of an book report/review in mathematics book reports and reviews is to develop such skills as independent creative thinking and writing out your own thoughts.

Writing an book report/review is extremely useful, because it allows the author to learn to clearly and correctly formulate thoughts, structure information, use basic concepts, highlight causal relationships, illustrate experience with relevant examples, and substantiate his conclusions.

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Report Card Comments for Math

Overall Performance and Improvement

Positive Comments:

___________ has a good attitude towards the math work at this grade level. Please continue to work on ___________ daily.

At this point, ___________ has successfully learned _____________. [He/she] is now able to start a daily practice of ____________.

___________ has a true enthusiasm and gift for math. His effort is reflected in his high grades. He is also an excellent classmate, as he frequently assists other students with concepts.

___________ has shown impressive progress in understanding complex math concepts. [His/her] consistent effort is commendable.

___________ has shown a clear improvement in [his/her] math skills this term. The consistent practice is paying off, keep it up!

___________ displays a positive approach towards problem-solving tasks in math. [His/her] willingness to tackle challenging problems is noteworthy.

Needs Improvement Comments:

___________ has worked hard in math this quarter. However, [his/her] progress has been slower than I would have liked. Can we meet to discuss some helpful strategies?

___________ would benefit from more practice with ___________. If possible, could you please spend some time daily on this skill?

It would be helpful if ___________ practiced _______________ daily.

___________ is struggling with motivation in learning math. I know [he/she] can put in more effort than [he/she] has been recently. If possible, could you please reinforce this?

___________ still needs strengthening in the concept of ___________.

___________ is having trouble with many of the basic math skills. Can we meet to discuss some helpful strategies?

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Understanding of Concepts

___________ shows excellent understanding of mathematical concepts, which is reflected in [his/her] problem-solving abilities.

___________ consistently demonstrates a deep comprehension of all math topics we've covered.

___________ has a strong grasp of mathematical concepts and can apply them creatively in different contexts.

___________ demonstrates a robust understanding of concepts, consistently making connections between different areas of math.

___________ effectively translates their understanding of mathematical concepts into accurate and efficient problem-solving.

___________ often struggles to apply mathematical concepts to solve problems. Additional practice could be beneficial.

___________ seems to have difficulty understanding some of the math concepts we've covered. Extra support may be helpful.

___________ frequently makes mistakes that indicate a misunderstanding of key math concepts.

___________ has trouble relating mathematical concepts to real-world applications. More practice in this area could be beneficial.

___________ often seems confused when trying to apply math concepts during problem-solving. Additional review and practice might help solidify understanding.

Problem Solving Skills

___________ consistently demonstrates strong problem solving skills in math.

___________ effectively applies various strategies to find solutions to complex math problems.

___________ shows a clear ability to break down problems and work through them step by step.

___________ often comes up with multiple approaches to solve a single problem, showing great flexibility in [his/her] thinking.

___________ consistently shows perseverance in solving challenging problems and doesn't give up easily.

___________ often struggles when faced with complex math problems and could benefit from extra practice.

___________ tends to give up quickly when faced with challenging problems. Encourage perseverance and trying different strategies.

___________ often overlooks important details in problems, leading to incorrect solutions. More careful reading and analysis could be beneficial.

___________ struggles with applying learned strategies to new problems. Continued practice is needed.

___________ has difficulty in breaking down complex problems into smaller, manageable steps. Working on this skill could improve [his/her] problem-solving abilities.

Arithmetic and Operations

___________ demonstrates strong skills in arithmetic and handles complex operations with ease.

___________ has shown impressive improvement in arithmetic operations this term. Keep up the good work!

___________ has a solid understanding of basic arithmetic concepts and applies them correctly in problem-solving.

___________ is able to accurately perform arithmetic operations, even under time pressure.

___________ excels in arithmetic operations and consistently produces accurate results.

___________ often makes errors in arithmetic calculations. More practice would be beneficial.

___________ struggles with complex arithmetic operations and could benefit from additional support.

___________ has difficulty remembering the steps in long division. Continued practice at home would be helpful.

___________ struggles with basic arithmetic operations. Regular practice will help reinforce these skills.

___________ tends to rush through arithmetic operations, leading to errors. Encourage them to take their time and double-check [his/her] work.

Arithmetic and Operations — Elementary School Comments

At this point, ___________ has successfully learned all of the addition facts through ten. [He/she] is now able to start regular practice of the subtraction facts through ten.

___________ has done well learning the multiplication table.

___________ understands the plus, minus, and equal signs, and uses them to make number statements.

___________ understands and uses basic facts of addition and subtraction.

___________ can use manipulatives to add and subtract.

___________ can [add/subtract/multiply/divide] basic fractions.

However, it would be helpful if ___________ practiced [his/her] multiplication facts regularly.

___________ has difficulty retaining math processes of addition, etc.

Arithmetic and Operations — Middle School Comments

___________ understands basic equations and can solve for one variable.

___________ understands basic equations and can solve for multiple variables.

___________ can [add/subtract/multiply/divide] advanced fractions and mixed numbers.

___________ understands and can solve [pre-algebraic/algebraic] expressions and equations.

___________ exhibits proficiency in using order of operations to simplify expressions.

___________ is successful at applying properties of operations when simplifying algebraic expressions.

___________ struggles with understanding the concept of ratios and proportional relationships.

___________ is showing improvement in solving real-world math problems involving percentages.

Numbers and Number Sense

___________ has a solid understanding of number concepts and applies them effectively.

___________ uses number sense to solve problems and justify solutions effectively.

___________ demonstrates a strong ability to identify and work with number patterns.

___________ has made significant progress in understanding and applying number concepts.

___________ consistently shows a clear understanding of place value in [his/her] work.

___________ is having difficulty understanding the concept of place value.

___________ struggles with identifying and working with number patterns.

___________ needs to work on [his/her] understanding of number concepts and their application.

___________ often confuses number facts and needs to practice more.

___________ needs to improve [his/her] ability to use number sense in problem-solving.

Numbers and Number Sense — Elementary School Comments

___________ can work with numbers up to ___ with understanding.

___________ is still reversing some numbers.

___________ understands place value up to _____.

___________ can use manipulatives to show place value to _____.

___________ can count to ______.

___________ relies heavily on concrete objects.

___________ is beginning to memorize the number facts.

___________ does not know [his/her] math facts well.

Numbers and Number Sense — Middle School Comments

___________ understands and can represent [basic/intermediate/advanced] fractions.

___________ understands the basic concepts of decimal notation.

___________ understands and can [add/subtract/multiply/divide] using decimal notation.

___________ knows how to identify and work with number patterns.

___________ demonstrates proficiency in the use of scientific notation.

___________ shows excellent understanding of square roots and exponents.

___________ is skilled in rounding and estimating large numbers.

___________ effectively applies the principles of probability in problem-solving scenarios.

Money and Measurement

___________ has shown a deep understanding of the concepts of money and measurement. [He/She] can accurately use different units of measurement and understand the value of different currencies.

___________ has done exceptionally well in understanding and applying the concept of measurements in practical situations.

___________ shows a strong ability to convert between different units of measurement.

___________ has demonstrated a strong understanding of the value of money and can make accurate calculations involving money.

___________ has a solid grasp on time measurements and can accurately tell the time using both digital and analog clocks.

___________ is struggling with the concept of measurements; further practice and understanding are required.

___________ needs to work on understanding the value of money and how to calculate with it.

___________ often confuses units of measurement and could benefit from additional practice.

___________ has difficulty with time measurements and could use more practice reading clocks.

___________ struggles with applying measurement concepts in practical scenarios and could benefit from additional real-world examples.

Money and Measurement — Elementary School Comments

___________ understands the basics of money and coins (pennies, dimes, nickels).

___________ understands the types of currency (pennies, dimes, nickels, quarters, dollars).

___________ understands how to use coins and bills of different denominations to pay for items and make change.

___________ understands and can use basic units of measure for length, width, and height, including [inches/feet/centimeters/meters].

___________ understands and can use basic units of measure for volume, mass, and weight, including [ounces/pounds].

___________ understands and can use basic units of measure for distance of travel [and/or} time, including [feet/yards/miles, seconds/minutes/hours].

___________ understands and can use basic units of measure for temperature, including [Fahrenheit].

___________ knows how to tell time by reading a clock, and can effectively use seconds, minutes, and hours to describe time.

___________ can use a ruler to measure [inches/feet/yards].

___________ effectively uses common measurement tools including [ruler, protractor, scale, thermometer, clock] to solve measurement problems.

Money and Measurement — Middle School Comments

___________ understands the basics of financial literacy and the role of currency in personal and economic affairs.

___________ understands and can use basic units of measure for length, width, and height, including [meters].

___________ understands and can use basic units of measure for volume, mass, and weight, including [tons/kilograms].

___________ understands and can use basic units of measure for distance of travel [and/or} time, including [kilometers, hours].

___________ understands and can use basic units of measure for temperature, including [Centigrade].

___________ can use a ruler to measure [milimeters/centimeters/meters].

___________ has learned how to convert U.S. measurements to metric measurements, including [milimeters/centimeters/meters/kilometers, kilograms, Centigrade].

_______ has a strong understanding of geometric concepts and applies them effectively in problem-solving.

_______ shows an impressive ability to identify and work with shapes and angles.

_______ demonstrates a keen understanding of [2D and/or 3D] shapes.

_______ excels in applying geometric principles to real-world problems.

_______ consistently demonstrates a clear understanding of [area/perimeter/volume].

_______ often confuses different types of angles and shapes. More practice would be beneficial.

_______ is struggling with the concept of volume and could benefit from additional exercises.

_______ has difficulty understanding and applying the concept of area.

_______ struggles with identifying and applying geometric principles in problem-solving tasks.

_______ often makes errors when trying to calculate the perimeter of complex shapes.

Geometry — Elementary School Comments

_______ knows the basic shapes.

_______ understands the differences between 2-dimensional and 3-dimensional shapes.

_______ knows the basic angles and types of triangles.

_______ understands the basic concept[s] of [area/perimeter].

_______ understands the basic concept[s] of [volume/mass].

_______ understands and can use the basic concept[s] of [area/perimeter] to solve problems.

_______ understands and can use the basic concept[s] of [volume/mass] to solve problems.

Geometry — Middle School Comments

_______ understands and can use the basic concept[s] of [points/lines] to solve problems.

_______ understands and can use advanced geometric concepts to solve problems.

_______ demonstrates a strong ability to identify, compare, and analyze shapes and their properties.

_______ excels in calculating the area and volume of complex geometric figures.

_______ can apply the principles of symmetry, congruence, and similarity in geometric problems.

_______ displays a deep understanding of coordinate plane concepts and can plot points accurately.

_______ is proficient in using geometric formulas and theorems to solve algebraic equations.

Graphs and Charts

_______ can create graphs using simple data.

_______ understands several methods of graphing.

_______ can effectively synthesize and present complex data in [bar graphs, line graphs, pie charts, visualizations, tables], and explain correlations.

_______ skillfully interprets graphical data and uses it to inform problem-solving strategies.

_______ exhibits a strong ability to construct and analyze scatter plots and understands their relationship with linear equations.

_______ often struggles with interpreting data from graphs and charts. Working on this at home would be beneficial.

_______ needs to improve [his/her] ability to construct accurate and meaningful graphs from given data.

_______ frequently has difficulty understanding the correlation between variables in a scatter plot. More practice with this concept would be helpful.

_______ should work on using graphs and charts effectively to support problem-solving strategies.

_______ has trouble creating pie charts and bar graphs accurately. Continued practice in this area is needed.

Participation in Class

___________ actively participates in all class discussions and regularly contributes valuable insights.

___________ is always eager to answer questions in class, showing a great understanding of the subject.

___________ often takes the lead in group activities, demonstrating strong leadership skills.

___________ consistently engages with the lesson and asks thoughtful questions.

___________ effectively collaborates with peers during group work, demonstrating team spirit.

___________ rarely participates in class discussions. Encouraging more active engagement would be beneficial.

___________ often hesitates to ask questions, even when struggling with a concept. Remind them that asking for clarification is part of learning.

___________ tends to work alone during group activities. Encouraging teamwork might enhance their learning experience.

___________ often seems distracted during class. Focusing on the lesson can significantly improve their understanding.

___________ seldom contributes to class discussions. More active participation would be beneficial.

Work Habits

___________ shows a strong interest in math and actively engages in-class activities.

___________ regularly contributes to class discussions with insightful questions and comments.

___________ demonstrates a solid understanding of math concepts during group work and discussions.

___________ takes initiative to help others understand difficult math concepts.

___________ consistently completes math assignments on time and shows a high level of dedication.

___________ rarely engages in math-related discussions. Encourage more active participation.

___________ often appears distracted during math lessons. More focus would be beneficial.

___________ struggles to meet deadlines for math assignments. Better time management could help.

___________ rarely asks for help, even when struggling with math concepts. Encourage asking questions.

___________ tends to work independently, even during group activities. More teamwork is needed.

Use of Tools and Strategies

___________ effectively uses a variety of tools and strategies to solve math problems.

___________ consistently applies learned strategies to new math challenges.

___________ demonstrates a strong ability to choose suitable tools for different math tasks.

___________ is adept at using technology to enhance [his/her] understanding in math.

___________ skillfully applies a range of strategies to understand complex math concepts.

___________ struggles with selecting the appropriate strategy for problem-solving tasks.

___________ could benefit from a wider range of strategies to approach math problems.

___________ often relies on one strategy, even when it may not be the most efficient.

___________ has difficulty in using mathematical tools effectively.

___________ could improve in utilization of technology to aid in understanding math.

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Review of the math book.

The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics , Clifford A. Pickover, 2009. 528 pp. illustrations, bibliography, index. $29.95 hardcover, ISBN: 978-1-4027-5796-9. Sterling Publishing Inc. 387 Park Ave. S., New York, NY 10016–8810. Phone: 212–532–7160, www.sterlingpublishing.com

I have often said that a good book is not merely written or compiled; it is crafted. That is, the book is designed for a specific audience and the textual and sensory format is carefully chosen for that audience. Clifford Pickover’s latest venture into the history of mathematics is such an endeavor. This is a wonderful book that presents an eclectic selection of mathematical concepts, personalities, and events that are chronologically organized from 150 million BCE to the year 2007. The author admits that this is a personal selection of happenings that stirred his curiosity. Still, I found this collection fascinating and most informative. Individual narratives are limited to one page and accompanied by a beautiful and often intriguing color illustration. Many of the illustrations are computer-generated. Indeed the illustrations are of such excellent quality and composition that they themselves provide a tour de force of mathematical ideas.

Even a very knowledgeable student of the history of mathematics will find much new information in this book. For example, I learned of James Alexander's (1888–1971) topological marvel, the horned sphere; Viggo Brun’s constant (1885–1978); and Emile Borel’s (1871–1956) normal numbers. Of course, many familiar topics such as the Golden Ratio, the abacus, and the tragic death of Hypatia are also included. Historically eminent mathematicians such as Pierre de Fermat (1601–1665), Giuseppe Peano (1858 –1932), Emmy Noether (1882–1935), and Kurt Gödel (1906–1978), along with many others, stare out at the reader from the illustrations. The entry for the year 1957 is about Martin Gardner (1914–2010). This is the year Gardner began his “Mathematical Games” column in Scientific American . The accompanying illustration (p. 409) shows Gardner standing before a bookshelf containing his many writings and is prefaced by the comment, “Martin Gardner stands by all his words.” This is a wonderful tribute to the man.

While the explanatory discussions are brief, they are sufficiently substantive to serve the subject in question and to pique further interest in the topic. While Pickover reaches out culturally to include such non-western contributions to mathematical progress as Al-Khwarizmi’s Algebra and al-Samawal’s The Dazzling , Chinese accomplishments remain ignored. At the very least , Jiuzang suanshu (Nine Chapters on the Mathematical Art, c. 100 BCE), possibly the most influential mathematics book of all time, could have been mentioned. Despite this oversight, The Math Book is an excellent, stimulating, and inspiring book, easily accessible for popular reading as well as scholarly perusal. The price is a true bargain for a work of this quality. The book is highly recommended for library and personal acquisition, and it also is a perfect gift for any young person interested in mathematics.

________________________

See also the MAA Review by Fabio Mainardi.

Frank J. Swetz (The Pennsylvania State University), "Review of [i]The Math Book[/i]," Convergence (November 2010), DOI:10.4169/loci003493

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42 Math Report Card Comments Examples and Template for Teachers

Preparing report cards for your math students? Let’s help you skip the most frustrating part with these math report card comment examples and templates.

You can use these comments to effortlessly write comments in minutes and save hours.

42 Math Report Card Comments

End of the year math report card comments.

• {year} has been great overall for {student’s name}. {he/she} has developed great study habits that have resulted in a significant improvement in her {math topic} this year.
• {student’s name} has shown a significant improvement in {math topic} this year. Please continue working on {math topic} over this summer to improve your skills.
• {he/she} will benefit greatly from reading the following math books this summer: {name of the books}.
• To improve {student’s name}’s math skills, {he/she} must improve {his/her} {math skill 1} and {math skill 2}.
• It was great to have {student’s name} in my math class this year.
• {student’s name} is a hard-working student. I have seen {his/her}progress this year in {mathematical topic} and it is impressive to see the progress {he/she} made.
• {student’s name} needs to improve on {mathematical topic 1} and {mathematical topic 2} this year if {he/she} wants to succeed in the {e.g. eighth} grade.
• {student’s name} should continue working on {mathematical topic} exercises this summer to improve his performance next year.
• While I didn’t get to know {student’s name} very well, I can certainly tell {he/she}’s a very bright student and has an excellent grasp of {mathematical topic}.

Related : Algebra report card comments

Math Report Card Comments for Struggling Students

• {student’s name} struggles with completing {his/her} math homework in a timely manner.
• {student’s name} is having a difficult time with {mathematical topic}. Practicing {mathematical topic} more would help {student’s name} overcome it.
• {student’s name} would benefit from {mathematical} exercise everyday.

Geometry Math Report Card Comments

Geometrical concepts math report card comment templates.

• {student’s name}has a good understanding of geometrical concepts.
• {student’s name}has a poor understanding of geometrical concepts.
• {student’s name}has an excellent understanding of geometrical concepts.

Triangle - Geometry Math Report Card Comment Templates

• {student’s name} struggles with the understanding of obtuse, acute, and right triangles.
• {student’s name} has a good understanding of obtuse, acute, and right triangles.
• {student’s name} has an excellent understanding of obtuse, acute, and right triangles.

Geometry Skill Level Math Report Card Comment Templates

• {student’s name} has a good understanding of {geometry skill(s)} and has an excellent understanding of various geometry concepts.
• {student’s name} has a good understanding of {geometry skill}, however {he/she} needs to improve upon {geometry skill 2} and {geometry skill 3}.
• {student’s name} has a very poor understanding of {geometry skills(s)} and should do {revision/exercises/etc} on a {daily/weekly} basis.

Area and Volume - Geometry Math Report Card Comment Templates

• When it comes to the perimeter, surface area, and volume - {student’s name} struggles to understand them.
• {student’s name}has a good understanding of perimeter, surface area, and volume.
• When it comes to perimeter, surface area and volume - {student’s name} understands {perimeter/surface area/volume}, but struggles to understand and calculate {perimeter/surface area/volume}.

Shapes - Geometry Math Report Card Comment Templates

• {student’s name} can differentiate between various shapes perfectly.
• {student’s name} can differentiate between some shapes, but not all. {he/she} needs to address it to reach a good level of understanding of geometric shapes.
• {student’s name} struggles with identifying geometric shapes and needs to work hard on it.

Application of Geometric Concepts - Math Report Card Comment Templates

• {student’s name} understands basic geometric concepts and can apply them very well to solve mathematical problems.
• While {student’s name} understands basic geometric concepts, {he/she} finds it difficult to solve mathematical problems focused around certain geometric concepts.
• {student’s name}struggles with understanding basic geometric concepts. {he/she} needs to work hard to understand {geometric concept(s)} in order to solve mathematical problems around these concepts.

Advanced Geometry - Math Report Card Comment Templates

• {student’s name} is excellent at learning advanced geometry concepts like {advanced geometry topic}.
• {student’s name} shows interest in learning advanced geometry concepts. I would recommend {book/course/class} for {student’s name} to learn these advanced concepts better.

General Math Report Card Comments

• {student’s name} pays attention to math, but is facing difficulty with understanding {math topic 1}, {math topic 2} and {math topic 3}.
• {student’s name} is struggling with math. I recommend that {he/she} improves {topic 1}, {topic 2} and {topic 3} by {studying/practicing} {suggestion 1} and {suggestion 2}.
• {student’s name} understands all mathematical concepts taught in class very well. {he/she} can communicate his understanding of these topics very well. {student’s name} also helps {his/her} peers when they hit roadblocks.
• {student’s name} when put {his/her} efforts delivers better results and learns more effectively. {student’s name} needs to be encouraged routinely so that {he/she} can put more effort into learning math with confidence.
• {student’s name} faces issues with concentrating when in class and as a result will face issues in learning advanced mathematical concepts in other grades.
• {student’s name} is often distracted during math class and never finishes their homework. It will be difficult for {him/her} to improve as we move towards harder mathematical topics like {topic 1} and {topic 2}.
• {student’s name} is attentive and learns well during math class. However, {he/she} isn’t practicing their math skills before the math tests which is reflected in lower grades. Starting practicing these questions a week or two before the math test will help {student’s name} get better grades.
• {student’s name} is facing issues with the following mathematical topics: {add topics here}. I would recommend you make sure that {he/she}works on their assignments to overcome these. Additionally, I will send out new monthly math assignments for students around {mathematical topic}, I would suggest that {student’s name} finish them a week before the math test too.
• {student’s name} has done a great job of understanding math concepts, math problem solving, and communication. I would recommend that {he/she} put a bit more effort into practicing more {mathematical topic} problems.
• {student’s name} has improved their math skills considerably. To improve {his/her} test scores in math, {he/she} needs to improve calculation speed.

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Some St. Patrick’s Day math

At today’s Gathering 4 Gardner social, Colm Mulcahy presented on two Irish figures in recreational mathematics with whom Martin Gardner corresponded: Victor Meally and Owen O’Shea. Owen O’Shea is the natural successor to Gardner’s “Professor I.J. Matrix” as a prolific generator of numerological coincidences — see for example The Magic Numbers of the Professor (2007). Victor Meally shows up occasionally in Gardner’s Mathematical Games columns, and also in “Problem 3.14” (appropriate for Pi Day!) in The Colossal Book of Short Puzzles and Problems (2006):

One of the satisfactions of recreational mathematics comes from finding better solutions for problems thought to have been already solved in the best possible way. Consider the following digital problem that appears as Number 81 in Henry Ernest Dudeney’s Amusements in Mathematics . (There is a Dover reprint of this 1917 book.) Nine digits (0 is excluded) are arranged in two groups. On the left a three-digit number is to be multiplied by a two-digit number. On the right both numbers have two digits each: \[158\times 23 = 79\times 46\] In each case the product is the same: 3,634. How, Dudeney asked, can the same nine digits be arranged in the same pattern to produce as large a product as possible, and a product that is identical in both cases? Dudeney’s answer, which he said “is not to be found without the exercise of some judgment and patience,” was 5,568: \[174\times 32 = 96\times 58\] Victor Meally of Dublin County in Ireland later greatly improved on Dudeney’s answer with 7,008: \[584\times 12 = 96\times 73\] This remained the record until a Japanese reader found an even better solution. It is believed, although it has not yet been proved, to give the highest possible product. Can you find it without the aid of a computer?

With the aid of a computer ( code ), it’s easy to confirm that that Japanese reader’s solution is indeed the best of the 11 basic solutions (and Meally’s the runner-up):

But now consider the ruminations of another Irishman, James Joyce’s Leopold Bloom, who in Chapter 17 of Ulysses recounts how he became aware of

the existence of a number computed to a relative degree of accuracy to be of such magnitude and of so many places, e.g., the 9th power of the 9th power of 9, that […] 33 closely printed volumes of 1000 pages each of innumerable quires and reams of India paper would have to be requisitioned in order to contain the complete tale of its printed integers […] the nucleus of the nebula of every digit of every series containing succinctly the potentiality of being raised to the utmost kinetic elaboration of any power of any of its powers.

There’s some confusion as to what number Joyce was really talking about (if any); but the mathematical community has apparently settled on \(9^{9^9}\), as seen in e.g. the “ Ulysses sequence” OEIS A054382 : \(\lceil\log_{10} 1^{1^1}\rceil, \lceil\log_{10} 2^{2^2}\rceil, \lceil\log_{10} 3^{3^3}\rceil,\ldots\)

The ninth element of this sequence — the number of decimal digits in \(9^{9^9}\) — is \(369\,693\,100\). If “closely printed” at the resolution of A Million Random Digits with 100,000 Normal Deviates , printed by the RAND Corporation (no relation) in 1955, the recording of the entire expansion of \(9^{9^9}\) would take up 148 thousand-page volumes. (Or, if you postulate a thousand physical pages, each printed on both sides: 74 volumes.)

Suppose we allow solutions of Dudeney’s problem to contain powers: not merely \(abc\times de = gh\times ij\), but for example \(ab^c\times d^e = g^h\times i^j\). Then there are five more basic solutions possible, the largest of which is

The solutions are:

Clement Wood — compiler of The Best Irish Jokes (1926) — asserts, in the same Book of Mathematical Oddities (1927) which we previously mined in “Mathematical Golf” (2023-03-23), that there are only two solutions to the double equality

Wood is correct, and the administration of powers produces no further solutions to that puzzle.

A generative AI reset: Rewiring to turn potential into value in 2024

It’s time for a generative AI (gen AI) reset. The initial enthusiasm and flurry of activity in 2023 is giving way to second thoughts and recalibrations as companies realize that capturing gen AI’s enormous potential value is harder than expected .

With 2024 shaping up to be the year for gen AI to prove its value, companies should keep in mind the hard lessons learned with digital and AI transformations: competitive advantage comes from building organizational and technological capabilities to broadly innovate, deploy, and improve solutions at scale—in effect, rewiring the business  for distributed digital and AI innovation.

About QuantumBlack, AI by McKinsey

QuantumBlack, McKinsey’s AI arm, helps companies transform using the power of technology, technical expertise, and industry experts. With thousands of practitioners at QuantumBlack (data engineers, data scientists, product managers, designers, and software engineers) and McKinsey (industry and domain experts), we are working to solve the world’s most important AI challenges. QuantumBlack Labs is our center of technology development and client innovation, which has been driving cutting-edge advancements and developments in AI through locations across the globe.

Companies looking to score early wins with gen AI should move quickly. But those hoping that gen AI offers a shortcut past the tough—and necessary—organizational surgery are likely to meet with disappointing results. Launching pilots is (relatively) easy; getting pilots to scale and create meaningful value is hard because they require a broad set of changes to the way work actually gets done.

Let’s briefly look at what this has meant for one Pacific region telecommunications company. The company hired a chief data and AI officer with a mandate to “enable the organization to create value with data and AI.” The chief data and AI officer worked with the business to develop the strategic vision and implement the road map for the use cases. After a scan of domains (that is, customer journeys or functions) and use case opportunities across the enterprise, leadership prioritized the home-servicing/maintenance domain to pilot and then scale as part of a larger sequencing of initiatives. They targeted, in particular, the development of a gen AI tool to help dispatchers and service operators better predict the types of calls and parts needed when servicing homes.

Leadership put in place cross-functional product teams with shared objectives and incentives to build the gen AI tool. As part of an effort to upskill the entire enterprise to better work with data and gen AI tools, they also set up a data and AI academy, which the dispatchers and service operators enrolled in as part of their training. To provide the technology and data underpinnings for gen AI, the chief data and AI officer also selected a large language model (LLM) and cloud provider that could meet the needs of the domain as well as serve other parts of the enterprise. The chief data and AI officer also oversaw the implementation of a data architecture so that the clean and reliable data (including service histories and inventory databases) needed to build the gen AI tool could be delivered quickly and responsibly.

Our book Rewired: The McKinsey Guide to Outcompeting in the Age of Digital and AI (Wiley, June 2023) provides a detailed manual on the six capabilities needed to deliver the kind of broad change that harnesses digital and AI technology. In this article, we will explore how to extend each of those capabilities to implement a successful gen AI program at scale. While recognizing that these are still early days and that there is much more to learn, our experience has shown that breaking open the gen AI opportunity requires companies to rewire how they work in the following ways.

Figure out where gen AI copilots can give you a real competitive advantage

The broad excitement around gen AI and its relative ease of use has led to a burst of experimentation across organizations. Most of these initiatives, however, won’t generate a competitive advantage. One bank, for example, bought tens of thousands of GitHub Copilot licenses, but since it didn’t have a clear sense of how to work with the technology, progress was slow. Another unfocused effort we often see is when companies move to incorporate gen AI into their customer service capabilities. Customer service is a commodity capability, not part of the core business, for most companies. While gen AI might help with productivity in such cases, it won’t create a competitive advantage.

To create competitive advantage, companies should first understand the difference between being a “taker” (a user of available tools, often via APIs and subscription services), a “shaper” (an integrator of available models with proprietary data), and a “maker” (a builder of LLMs). For now, the maker approach is too expensive for most companies, so the sweet spot for businesses is implementing a taker model for productivity improvements while building shaper applications for competitive advantage.

Much of gen AI’s near-term value is closely tied to its ability to help people do their current jobs better. In this way, gen AI tools act as copilots that work side by side with an employee, creating an initial block of code that a developer can adapt, for example, or drafting a requisition order for a new part that a maintenance worker in the field can review and submit (see sidebar “Copilot examples across three generative AI archetypes”). This means companies should be focusing on where copilot technology can have the biggest impact on their priority programs.

Copilot examples across three generative AI archetypes

• “Taker” copilots help real estate customers sift through property options and find the most promising one, write code for a developer, and summarize investor transcripts.
• “Shaper” copilots provide recommendations to sales reps for upselling customers by connecting generative AI tools to customer relationship management systems, financial systems, and customer behavior histories; create virtual assistants to personalize treatments for patients; and recommend solutions for maintenance workers based on historical data.
• “Maker” copilots are foundation models that lab scientists at pharmaceutical companies can use to find and test new and better drugs more quickly.

Some industrial companies, for example, have identified maintenance as a critical domain for their business. Reviewing maintenance reports and spending time with workers on the front lines can help determine where a gen AI copilot could make a big difference, such as in identifying issues with equipment failures quickly and early on. A gen AI copilot can also help identify root causes of truck breakdowns and recommend resolutions much more quickly than usual, as well as act as an ongoing source for best practices or standard operating procedures.

The challenge with copilots is figuring out how to generate revenue from increased productivity. In the case of customer service centers, for example, companies can stop recruiting new agents and use attrition to potentially achieve real financial gains. Defining the plans for how to generate revenue from the increased productivity up front, therefore, is crucial to capturing the value.

Upskill the talent you have but be clear about the gen-AI-specific skills you need

By now, most companies have a decent understanding of the technical gen AI skills they need, such as model fine-tuning, vector database administration, prompt engineering, and context engineering. In many cases, these are skills that you can train your existing workforce to develop. Those with existing AI and machine learning (ML) capabilities have a strong head start. Data engineers, for example, can learn multimodal processing and vector database management, MLOps (ML operations) engineers can extend their skills to LLMOps (LLM operations), and data scientists can develop prompt engineering, bias detection, and fine-tuning skills.

A sample of new generative AI skills needed

The following are examples of new skills needed for the successful deployment of generative AI tools:

• data scientist:
• prompt engineering
• in-context learning
• bias detection
• pattern identification
• reinforcement learning from human feedback
• hyperparameter/large language model fine-tuning; transfer learning
• data engineer:
• data wrangling and data warehousing
• data pipeline construction
• multimodal processing
• vector database management

The learning process can take two to three months to get to a decent level of competence because of the complexities in learning what various LLMs can and can’t do and how best to use them. The coders need to gain experience building software, testing, and validating answers, for example. It took one financial-services company three months to train its best data scientists to a high level of competence. While courses and documentation are available—many LLM providers have boot camps for developers—we have found that the most effective way to build capabilities at scale is through apprenticeship, training people to then train others, and building communities of practitioners. Rotating experts through teams to train others, scheduling regular sessions for people to share learnings, and hosting biweekly documentation review sessions are practices that have proven successful in building communities of practitioners (see sidebar “A sample of new generative AI skills needed”).

It’s important to bear in mind that successful gen AI skills are about more than coding proficiency. Our experience in developing our own gen AI platform, Lilli , showed us that the best gen AI technical talent has design skills to uncover where to focus solutions, contextual understanding to ensure the most relevant and high-quality answers are generated, collaboration skills to work well with knowledge experts (to test and validate answers and develop an appropriate curation approach), strong forensic skills to figure out causes of breakdowns (is the issue the data, the interpretation of the user’s intent, the quality of metadata on embeddings, or something else?), and anticipation skills to conceive of and plan for possible outcomes and to put the right kind of tracking into their code. A pure coder who doesn’t intrinsically have these skills may not be as useful a team member.

While current upskilling is largely based on a “learn on the job” approach, we see a rapid market emerging for people who have learned these skills over the past year. That skill growth is moving quickly. GitHub reported that developers were working on gen AI projects “in big numbers,” and that 65,000 public gen AI projects were created on its platform in 2023—a jump of almost 250 percent over the previous year. If your company is just starting its gen AI journey, you could consider hiring two or three senior engineers who have built a gen AI shaper product for their companies. This could greatly accelerate your efforts.

Form a centralized team to establish standards that enable responsible scaling

To ensure that all parts of the business can scale gen AI capabilities, centralizing competencies is a natural first move. The critical focus for this central team will be to develop and put in place protocols and standards to support scale, ensuring that teams can access models while also minimizing risk and containing costs. The team’s work could include, for example, procuring models and prescribing ways to access them, developing standards for data readiness, setting up approved prompt libraries, and allocating resources.

While developing Lilli, our team had its mind on scale when it created an open plug-in architecture and setting standards for how APIs should function and be built.  They developed standardized tooling and infrastructure where teams could securely experiment and access a GPT LLM , a gateway with preapproved APIs that teams could access, and a self-serve developer portal. Our goal is that this approach, over time, can help shift “Lilli as a product” (that a handful of teams use to build specific solutions) to “Lilli as a platform” (that teams across the enterprise can access to build other products).

For teams developing gen AI solutions, squad composition will be similar to AI teams but with data engineers and data scientists with gen AI experience and more contributors from risk management, compliance, and legal functions. The general idea of staffing squads with resources that are federated from the different expertise areas will not change, but the skill composition of a gen-AI-intensive squad will.

Set up the technology architecture to scale

Building a gen AI model is often relatively straightforward, but making it fully operational at scale is a different matter entirely. We’ve seen engineers build a basic chatbot in a week, but releasing a stable, accurate, and compliant version that scales can take four months. That’s why, our experience shows, the actual model costs may be less than 10 to 15 percent of the total costs of the solution.

Building for scale doesn’t mean building a new technology architecture. But it does mean focusing on a few core decisions that simplify and speed up processes without breaking the bank. Three such decisions stand out:

• Focus on reusing your technology. Reusing code can increase the development speed of gen AI use cases by 30 to 50 percent. One good approach is simply creating a source for approved tools, code, and components. A financial-services company, for example, created a library of production-grade tools, which had been approved by both the security and legal teams, and made them available in a library for teams to use. More important is taking the time to identify and build those capabilities that are common across the most priority use cases. The same financial-services company, for example, identified three components that could be reused for more than 100 identified use cases. By building those first, they were able to generate a significant portion of the code base for all the identified use cases—essentially giving every application a big head start.
• Focus the architecture on enabling efficient connections between gen AI models and internal systems. For gen AI models to work effectively in the shaper archetype, they need access to a business’s data and applications. Advances in integration and orchestration frameworks have significantly reduced the effort required to make those connections. But laying out what those integrations are and how to enable them is critical to ensure these models work efficiently and to avoid the complexity that creates technical debt  (the “tax” a company pays in terms of time and resources needed to redress existing technology issues). Chief information officers and chief technology officers can define reference architectures and integration standards for their organizations. Key elements should include a model hub, which contains trained and approved models that can be provisioned on demand; standard APIs that act as bridges connecting gen AI models to applications or data; and context management and caching, which speed up processing by providing models with relevant information from enterprise data sources.
• Build up your testing and quality assurance capabilities. Our own experience building Lilli taught us to prioritize testing over development. Our team invested in not only developing testing protocols for each stage of development but also aligning the entire team so that, for example, it was clear who specifically needed to sign off on each stage of the process. This slowed down initial development but sped up the overall delivery pace and quality by cutting back on errors and the time needed to fix mistakes.

Ensure data quality and focus on unstructured data to fuel your models

The ability of a business to generate and scale value from gen AI models will depend on how well it takes advantage of its own data. As with technology, targeted upgrades to existing data architecture  are needed to maximize the future strategic benefits of gen AI:

• Be targeted in ramping up your data quality and data augmentation efforts. While data quality has always been an important issue, the scale and scope of data that gen AI models can use—especially unstructured data—has made this issue much more consequential. For this reason, it’s critical to get the data foundations right, from clarifying decision rights to defining clear data processes to establishing taxonomies so models can access the data they need. The companies that do this well tie their data quality and augmentation efforts to the specific AI/gen AI application and use case—you don’t need this data foundation to extend to every corner of the enterprise. This could mean, for example, developing a new data repository for all equipment specifications and reported issues to better support maintenance copilot applications.
• Understand what value is locked into your unstructured data. Most organizations have traditionally focused their data efforts on structured data (values that can be organized in tables, such as prices and features). But the real value from LLMs comes from their ability to work with unstructured data (for example, PowerPoint slides, videos, and text). Companies can map out which unstructured data sources are most valuable and establish metadata tagging standards so models can process the data and teams can find what they need (tagging is particularly important to help companies remove data from models as well, if necessary). Be creative in thinking about data opportunities. Some companies, for example, are interviewing senior employees as they retire and feeding that captured institutional knowledge into an LLM to help improve their copilot performance.
• Optimize to lower costs at scale. There is often as much as a tenfold difference between what companies pay for data and what they could be paying if they optimized their data infrastructure and underlying costs. This issue often stems from companies scaling their proofs of concept without optimizing their data approach. Two costs generally stand out. One is storage costs arising from companies uploading terabytes of data into the cloud and wanting that data available 24/7. In practice, companies rarely need more than 10 percent of their data to have that level of availability, and accessing the rest over a 24- or 48-hour period is a much cheaper option. The other costs relate to computation with models that require on-call access to thousands of processors to run. This is especially the case when companies are building their own models (the maker archetype) but also when they are using pretrained models and running them with their own data and use cases (the shaper archetype). Companies could take a close look at how they can optimize computation costs on cloud platforms—for instance, putting some models in a queue to run when processors aren’t being used (such as when Americans go to bed and consumption of computing services like Netflix decreases) is a much cheaper option.

Build trust and reusability to drive adoption and scale

Because many people have concerns about gen AI, the bar on explaining how these tools work is much higher than for most solutions. People who use the tools want to know how they work, not just what they do. So it’s important to invest extra time and money to build trust by ensuring model accuracy and making it easy to check answers.

One insurance company, for example, created a gen AI tool to help manage claims. As part of the tool, it listed all the guardrails that had been put in place, and for each answer provided a link to the sentence or page of the relevant policy documents. The company also used an LLM to generate many variations of the same question to ensure answer consistency. These steps, among others, were critical to helping end users build trust in the tool.

Part of the training for maintenance teams using a gen AI tool should be to help them understand the limitations of models and how best to get the right answers. That includes teaching workers strategies to get to the best answer as fast as possible by starting with broad questions then narrowing them down. This provides the model with more context, and it also helps remove any bias of the people who might think they know the answer already. Having model interfaces that look and feel the same as existing tools also helps users feel less pressured to learn something new each time a new application is introduced.

Getting to scale means that businesses will need to stop building one-off solutions that are hard to use for other similar use cases. One global energy and materials company, for example, has established ease of reuse as a key requirement for all gen AI models, and has found in early iterations that 50 to 60 percent of its components can be reused. This means setting standards for developing gen AI assets (for example, prompts and context) that can be easily reused for other cases.

While many of the risk issues relating to gen AI are evolutions of discussions that were already brewing—for instance, data privacy, security, bias risk, job displacement, and intellectual property protection—gen AI has greatly expanded that risk landscape. Just 21 percent of companies reporting AI adoption say they have established policies governing employees’ use of gen AI technologies.

Similarly, a set of tests for AI/gen AI solutions should be established to demonstrate that data privacy, debiasing, and intellectual property protection are respected. Some organizations, in fact, are proposing to release models accompanied with documentation that details their performance characteristics. Documenting your decisions and rationales can be particularly helpful in conversations with regulators.

In some ways, this article is premature—so much is changing that we’ll likely have a profoundly different understanding of gen AI and its capabilities in a year’s time. But the core truths of finding value and driving change will still apply. How well companies have learned those lessons may largely determine how successful they’ll be in capturing that value.

The authors wish to thank Michael Chui, Juan Couto, Ben Ellencweig, Josh Gartner, Bryce Hall, Holger Harreis, Phil Hudelson, Suzana Iacob, Sid Kamath, Neerav Kingsland, Kitti Lakner, Robert Levin, Matej Macak, Lapo Mori, Alex Peluffo, Aldo Rosales, Erik Roth, Abdul Wahab Shaikh, and Stephen Xu for their contributions to this article.

This article was edited by Barr Seitz, an editorial director in the New York office.

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