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Exploring Limitless Growth: On Math, Mindset and Metacognition
Exploring Limitless Growth: On Math, Mindset and Metacognition
[Jo Boaler]
[Jo Boaler]
Run Time: 52:32 - May, 2023
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This is episode two from Toddle's "School Leadership Project"
Listen to this incredible conversation about Jo Boaler's groundbreaking research on what truly makes a difference in math education. Learn about how we can all become leaders in transforming math classrooms into places where all students can thrive. Jo also gives you an exclusive sneak peek into the research she's conducting for her exciting new book.
Discover how to unleash the potential in every student, because math is for everyone.
** Related resources connected to the podcast
Jo's book she mentioned in the podcast
What’s in Store:
The importance of struggle and vulnerability for growth. She grounds her thinking in the newest research in neuroplasticity and our
brains, which shows that all learners (and leaders) have limitless capacity!
How math is currently assessed and discuss some promising alternatives. Hint* collaboration plays a pivotal role. Dive into Jo's newest research on mental models, expertise, and the importance of metacognition.
Mathematical Mindset Practices Rubric
Mathematical Mindset Practices Rubric
Many teachers ask what a growth mindset looks like in the classroom, and how it may be measured. Youcubed have developed a rubric that you can use to help students understand the importance of developing a growth mindset toward mathematics.
Basketball Data Analytics Unit
Basketball Data Analytics Unit
YouCubed is sharing a basketball unit for grades 4 (ish) and up.
Who is this unit of lessons for? Any student in grade 4 and above. One of the goals of these lessons is to show students that data is everywhere - you don’t have to be an athlete to be involved in sports. Sports Data Analytics is a huge field.
Who can teach these lessons? Any teacher - you DO NOT have to know basketball. Students will happily lead the discussions and explain the rules to each other. All the information needed is in the videos made by Stanford basketball players.
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The goal of these lessons is to allow students to explore and make decisions with data through basketball. The lessons culminate with students conducting their own data investigation - choosing their dream team.
This unit of lessons is an example of an approach called “teaching to big ideas” which I explain in the latest edition of EdWeek.
Figure Me Out?
Figure Me Out?
Here's a cool activity to do with your students at the beginning of the year. It's a good way to determine prior knowledge. It's differentiated because each student can choose the operations and complexity to answer the questions. You could use it again mid-year and end year by asking students to demonstrate what they learned throughout the year by using more sophisticated math.
How Old Is the Sheppard?
How Old Is the Sheppard?
How do you think 32 eighth grade students would respond to this nonsensical question: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?” Take a guess as to what percentage of them would give a numerical answer and then watch the video.
The video would be a wonderful provocation for parents who are frustrated by how differently math is taught now as compared to when they were in school. They speak like everything was so much better back then. It can be challenging to get parents to realize that maybe things weren't so great before. Whaty would your student's think of it? Read Robert Kaplinsky's blog explaining the video and it's outcomes.
Run Time: 3:07 - Dec 1, 2013
NRICH Outdoor Maths
NRICH Outdoor Maths
NRICH offers several outdoor math tasks for 5-11 year olds to experience at school. Offering outdoor mathematics can be motivating and intriguing for many learners. The tasks suggest several different ways in which we can engage children in mathematics outside...
You can watch a recording of the webinar in which the mathematical thinking which can be prompted by these activities is discussed.
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Math Progressions/Standards
Math Progressions/Standards
Tap/Click to image view the Big Ideas Website
In this article - New Data Science Standards Are Needed for a Data-Filled World. Here’s What is Proposed - Jo Boaler explains the reason behind creating the Big Ideas website and the importance of teaching children K-12 data literacy.
In this article - New Data Science Standards Are Needed for a Data-Filled World. Here’s What is Proposed - Jo Boaler explains the reason behind creating the Big Ideas website and the importance of teaching children K-12 data literacy.
The Importance of Data Literacy
The Importance of Data Literacy
Jo Boaler and the YouCubed team have created a website - Big Ideas - that focuses on the development of Data Literacy. The need for data literacy has increased in recent years, not only to prepare students for 21st century jobs and support an informed citizenry. This has implications throughout the school years: teachers of younger students have the important task of helping them develop data literacy, and as students move through the grades they can start to learn the exciting and new discipline of data science.
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The Big Ideas website offers ideas for the development of data literacy and data science through the grades! For each grade range, the website links to tasks and data talks that Youcubed has curated which are appropriate for addressing the content at that level. Data talks support student development in reading and understanding data visuals – an important form of data literacy. The ones found on the Big Ideas website are among the most popular data science resources and a full collection can be found HERE.
New Mathematics Framework
New Mathematics Framework
A new Mathematics Framework for the State of California has just released for public comments. Jo Boaler was one of 5 writers of this new framework. The framework is worth some consideration by educators beyond California. Some highlights of the recommendations in the new proposed framework are these:
An asset-based, mindset infused approach, with a strong social justice orientation.
An approach to mathematics of “Investigating and Connecting” big ideas. It proposes that students do not spend time doing questions for the sake of doing them but investigate ideas with a purpose of “making sense of the world,” “predicting what could happen” or “impacting the future.” Sounds very PYP to me!
A new definition of fluency - neither number sense nor “fluency” are about speed, they are about flexibility.
K-12 chapters on two important areas of mathematics – number sense and data science and three Standards for Mathematical Practices.
Every grade, TK-10, now has a network map. The maps set out the big ideas and the connections between them. A document sharing the big ideas and network maps is available HERE.
The California Department of Education (CDE) shared ideas for integrating digital tools, with wonderful teacher vignettes and similar standards guidance for ELA/ELD. The full 500 page document is available HERE. You can also find all of these resources by visiting a new page on our website titled California Maths that is linked to a new item on our top menu called "California."
Learn more about this project from Jo Boaler HERE.
Math Websites
Math Websites
The NRICH Project
Click/Tap to ViewThe NRICH Project
The NRICH Project aims to enrich the mathematical experiences of all learners. The NRICH website hosts a large collection of math problems and solutions for teachers and students. An interesting section of the website is the Features section where students are presented with a problem which they are encouraged to solve using a variety of strategies and words. Live web-based sessions are scheduled where problem solutions for each feature are discussed. This is wonderful PD and could be used for feedback to students.
Primary Math Strategies & Resources
Primary Math Strategies & Resources
Primary Curriculum: Curriculum support for Primary teachers; Primary curriculum mapping; other resources
Supporting Students to Work Collaboratively: collections of resources, together with guidance, to help develop key mathematical thinking skills, and to nurture mathematical mindsets.
Developing Pupils' Mathematical Thinking: Mathematical Habits of Mind; Be a Mathematician!; Developing Problem Solving; Maths Club
Proof Through Words (FEATURES): Creating convincing arguments or "proofs" is a key mathematical skill which even the youngest learners can explore with NRICH
For Teachers: All primary Live problems; All primary Previous features
For Students: Shape Your Proof (maths.org)
See Events for Teachers and Students where the live problem solutions are discussed. Here you will find how to register for free for the online events for a chance to work on problems from their latest features. The hosts will consider the valuable mathematical thinking that the problems might prompt in your classroom and how they can be embedded into your everyday practice.
News and Recent Solutions: See solutions to recent primary problems; Sign up for our Newsletter
Early Years Math Strategies & Resources
Early Years Math Strategies & Resources
Early Years Curriculum: Early Years useful documents; Early Years activities; Early Years articles
Proof Through Words (FEATURES): Creating convincing arguments or "proofs" is a key mathematical skill which even the youngest learners can explore with NRICH
The latest activity encourages children to experience and talk about position and direction.
Children's Thinking: Article: Children's Thinking; Some examples of children's thinking
Professional Development
Professional Development
Student Games and Activities
Student Games and Activities
Feature packed math activities with activities and games suitable for learners to work on at home without a teacher. LINK
Activities for Ages 3-5 | Activities for Ages 5-7 | Activities for Ages 7-11 | Maths at Home
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Open Middle (Robert Kaplinski)
(Click/Tap to View)Open Middle (Robert Kaplinski)
What’s Open Middle?
What’s Open Middle?
The name “Open Middle” created by Robert Kaplinski might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:
a “closed beginning” meaning that they all start with the same initial problem.
a “closed end” meaning that they all end with the same answer.
an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.
Open middle problems generally require a higher Depth of Knowledge (Open Middle Math Depth of Knowledge Matrix) (Download Matrix Here) than most problems that assess procedural and conceptual understanding. They provide students with opportunities for discussing their thinking.
Here are Two Blogs to get you started: Why Are You Using That Problem? & Is Depth of Knowledge Complex or Complicated?
**Download a Student Work Sheet
Some additional characteristics of open middle problems include:
They generally have multiple ways of solving them as opposed to a problem where you are told to solve it using a specific method. Example
They may involve optimization such that it is easy to get an answer but more challenging to get the best or optimal answer. Example
They may appear to be simple and procedural in nature but turn out to be more challenging and complex when you start to solve it. Example
They are generally not as complex as a performance task which may require significant background context to complete. Example
You can even have your students create new problems and send them in to have them added to the website
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What’s Zearn Math?
What’s Zearn Math?
Zearn is the top-rated math learning platform that helps kids explore concepts, discover meaning, and make sense of math. It is free for classroom teachers and there is a pay option for schools. Zearn is striving for is large cultural change in student attitude, hoping to move toward a new normal where math isn’t perceived as uniquely scary. . To use you will need to create a free account.
Zearn can be used for differentiating instruction, discovering prior knowledge, review, personal inquiry and learning math content.
How it works - for students, teachers and administrators
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Byrdseed math archives host a variety of articles about developing high level math problems.
Here are a few examples:
Differentiate Math: Getting Started
Working with a student who is bored in math? Quickly finishing lessons? Needs something more? Here are three ways you can get started differentiating in math.
Differentiating in Math: Running Multiple Groups in One Class
100%, 100%, 100%. If you've ever taught gifted students math, you're probably familiar with those kids who can knock perfect scores out week after week. You've probably also questioned what good you're doing for those students. A differentiated math program may be just what you need.
Constructing Meaningful Math Projects
Here are four key attributes I look for when developing math projects: juicy data, interesting conflict, an expert's lens, and a final product.
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Graham Fletcher Website
(Click/Tap to View)Graham Fletcher Website
Graham Fletcher has served in education as a classroom teacher, math instructional lead, and currently as a math specialist. His work with the math progressions and problem-based lessons has led him to present throughout North America and beyond.
Graham is continually advocating for best practices in elementary mathematics by seeking new and innovative ways to support students and teachers in their development of conceptual understanding. He is the author of Building Fact Fluency: A Toolkit for Addition and Subtraction.
Twitter: @gfletchy
Facebook: https://www.facebook.com/gfletchy/
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Robert Kaplinski has been an educator since 2003 as a classroom teacher, teacher specialist for Downey Unified School District, instructor for the University of California, Los Angeles (UCLA), and presenter at conferences around the world.
He is also the author of Open Middle Math: Problems That Unlock Student Thinking, Grade 6-12, creator of the #ObserveMe movement, president of Grassroots Workshops, and runs the website Open Middle.
Blog Sections
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Math is Visual
(Click/Tap to View)Math is Visual
This website was created to assist in building a better conceptual understanding of mathematics through the use of visuals. The images, videos and resources shared here are intended to help all teachers, parents and students understand that Math Is Visual and we should take every opportunity to teach it that way.
This website was created to assist in building a better conceptual understanding of mathematics through the use of visuals. The images, videos and resources shared here are intended to help all teachers, parents and students understand that Math Is Visual and we should take every opportunity to teach it that way.
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Estimation 180
(Click/Tap to View)Estimation 180
ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together. Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.
ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together. Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.
Estimation 180 is the love of Andrew Stadel, a math educator who has also created many problem-based lessons including 3-Act problems.
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Youcubed provided a variety Math Problems/Tasks for all grades. Curated by Jo Boaler and Stanford Graduate School of Education | 100% free
Week of Inspirational Math(s): The Week of Inspirational Maths (WIM) resources are free lessons and videos about math and mindset designed to inspire students. They are ideal for the first week of school, to get students excited for the year ahead, but can be used any time. You can even build your own WIM week. Check out these pre-made playlists curated by the youcubed team for first grade, middle school and high school.
The site also has a free student online math course.
Data Talks: Data talks are short 5-10 minute classroom discussions to help students develop data literacy.
Mathematical Mindset Teaching Guide, Teaching Video and Additional Resources The guide contains five Mathematical Mindset Practices along with links to teaching videos. It has been designed for teachers to use in the process of self-reflection, or for coaches or administrators to use to encourage a mindset teaching culture.
Inspiring Math Success for all Students through Growth Mindsets and Innovative Teaching. Headed up by Jo Boaler, Youcube's main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math learning into accessible and practical forms.
Resources
Posters sharing messages about mindset and the beauty of mathematics
Data talks are short 5-10 minute classroom discussions to help students develop data literacy.
Courses
*Week of Inspiration Math (WIM)
Week of Inspirational Math(s). It's great PD and offers activities for students. All you do is choose your own maths adventure using. interactive tools to build a custom playlist of inspirational maths activities and messages!
Definitely worth checking out HERE
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Would You Rather Math
(Click/Tap to View)Would You Rather Math
Would You Rather Math presents students with two scenarios of a problem and asks them to choose one of them and then defend their answer. There is no right or wrong answer. It provides opportunities for students to strengthen their critical thinking skills by taking a stance and defending
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This blog was created by School District 38 (Richmond) in British Columbia, Canada. It has a Math/Science focus.
Sample Tags
Math Resources/Articles
(Click/Tap to View)Math Resources/Articles
Discovering Effective Approaches to Teaching Multiplication | Voyager Sopris Learning | April 15, 2024 | Once mastering addition and subtraction, students advance to multiplication. With each child's unique learning style, teachers must employ various resources and strategies for effective instruction, explored in this guide. - **Thank you to Ms. Cooper and her homeschool students for recommending this valuable math resource.
How to Teach Kids About Money | Annuity.org | 25 Aug 2023 | Educating children about finances at an early age establishes the groundwork for them to become adept at managing money in the future. This article offers parents insights into the significance of financial literacy and offers guidance on instilling prudent spending and saving habits in their children, helping them cultivate a balanced attitude towards money.
2 Ways to Encourage Reflection on Math Concepts | Edutopia | 2 July 2021 | Open-ended questions guide students to participate and to think mathematically, which cements their learning.
XtraMath - a free online program that helps students improve their math fact fluency
Facilitating Rich Math Tasks Remotely Podcast: Graham Fletcher talks about remote ways to facilitate 3-Act Math Tasks. Learn ways that allow you to connect with your students, create spaces for them to share their ideas, and engage students in productive math thinking from home.
Delta Learn Online Primary Math for Fun: A curated list of sites that parents can use to support their child in deepening their understanding of numbers through online and offline games and activities at home.
Mathology Little Books: Simple online tool with rich math activities
Math At Home - Daily Math Activities and other printable resources. The Daily Math Activities introduces math routines and exploring math in the home. Great examples and ideas provided for easy to implement learning.
SD38 Math Resources: A starter collection of K-7 weekly plans, instructional routines, math games, resources to share with parents and a link to additional vetted online resources.
Pirate Math Equation Quest: (K-3) an extension of the Pirate Math program developed by Vanderbilt University. Includes: single-digit and double-digit additive and multiplicative word problems that include four schemas: Total, Difference, Change, and Equal Groups. It is now available online for free, including the manuals and training videos. Download now while it’s available.
Delta Learn Online Math for Fun: (Gr 4-7) A curated list of sites that parents can use to support their child in practicing math and problem-solving at home through online and offline games and activities.
Nelson Canada: (Gr 4-7) Access to all of Nelson’s Math & Science resources.
SD38 Math Resources: (Gr 4-7) A starter collection of K-7 weekly plans, instructional routines, math games, resources to share with parents and a link to additional vetted online resources.
Math Resource Books
Math Resource Books
Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics
By: Jo BoalerMath-ish: Finding Creativity, Diversity, and Meaning in Mathematics
Jo Boaler's "Math-ish" is a thought-provoking and refreshing take on mathematics that challenges many of the myths and fixed mindsets surrounding the subject. Jo Boaler, a Stanford mathematics education professor, draws upon cutting-edge research to make a compelling case for rethinking how math is taught and perceived.
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Amazon.com: ISBN13 -978-0063340800 / HarperOne (May 7, 2024)/ 304 pages
The central premise is that math is a creative, multi-dimensional field that is far richer and more diverse than the narrow, rigid way it is often presented in classrooms. Jo argues convincingly that the compulsion to find the "one right answer" stifles the mathematical creativity, inquiry, and sense-making that should be the heart of math learning.
Through engaging stories and examples, the book illustrates how classrooms should move away from rote memorization and step-by-step procedures toward open-ended exploration, visual thinking, and connecting math concepts to real-world applications. Jo provides research showing the benefits of this approach, from boosting students' enthusiasm and self-concept to developing crucial abilities like problem-solving and quantitative literacy.
A key theme is the importance of recognizing the diversity of mathematical talent and dispelling stereotypes about who can excel in math. Jo celebrates the myriad forms mathematical thinking can take, from analytic to creative to artistic, giving readers a richer appreciation for the field's breadth.
While advocating for needed reforms, the book empowers readers to develop positive math mindsets and provides simple strategies for building number sense and math confidence. Boaler's passion for her subject shines through in her accessible, conversational writing style.
Overall, "Math-ish" makes a persuasive case not just for changing math instruction, but for changing society's limiting attitudes toward mathematics. It's an eye-opening work that will leave readers with a renewed appreciation for the boundless possibilities of mathematical thinking.
Some Strategies for Teachers from Jo Boaler's Book
Use open-ended questions and tasks that have multiple approaches and entry points.
Incorporate visual representations like drawings, graphs, and manipulatives.
Ask students to explain and justify their mathematical thinking verbally and in writing.
Facilitate discussions where students share different problem-solving strategies.
Connect math concepts to real-world contexts that are meaningful for students.
Encourage students to work collaboratively and learn from each other's perspectives.
Frame mistakes as valuable learning opportunities, not something to be avoided.
Build in time for exploring patterns, making conjectures, and looking for generalizations.
Incorporate math games, puzzles and low-floor/high-ceiling tasks.
Provide frequent opportunities for self-assessment and reflective journaling.
Share stories of diverse mathematicians to counter stereotypes.
Have students create their own word problems and math challenges.
Use formative assessments focused on reasoning over procedures and memorization.
Build in creative extensions and open-ended projects related to the math concepts.
Understanding the Math We Teach and How to Teach It, K-8
By: Marian SmallUnderstanding the Math We Teach and How to Teach It, K-8
Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.
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Amazon.com: ISBN-13 : 78-1625313355 / Stenhouse Publishers (August 26, 2019)/ 648 pages
Both Comprehensive and Readable: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language
Focus on Student Thinking: The book's tools, models. and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children's book
Implementing Standards in Ways That Make Sense: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8 helps to explain the "whys" of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics
Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."
Also, check out these two blogs about the book.
Mathematical Mindsets:
Mathematical Mindsets:
Unleashing Students' Potential through Creative Mathematics, Inspiring Messages and Innovative Teaching (2nd Ed)
By: Jo Boaler Unleashing Students' Potential through Creative Mathematics, Inspiring Messages and Innovative Teaching (2nd Ed)
In the newly revised Second Edition of Mathematical Mindsets, distinguished Stanford math education professor Jo Boaler demonstrates what it takes to help students become high achievers in mathematics. Filled with brand-new material and updated references, the book integrates a social justice perspective and new research regarding the teaching of data science and math gathered over the past five years.
“Jo Boaler calls out the mindsets that can limit a student’s aptitude for math and ways to change them. More than just a replacement set of positive messages, Jo’s book elaborates practical, research-tested strategies for teaching, assessment, practice, and homework—all to help a student learn and love to learn mathematics.” —Dan Meyer
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Amazon.com: ISBN-13 : 978-1119823063 / Jossey-Bass; 2nd edition (February 23, 2022) / 320 pages
Reverse mathematics trauma and find a universal blueprint for math success.
In Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching mathematics education expert and best-selling author Jo Boaler delivers a blueprint to banishing math anxiety and laying a foundation for mathematics success that anyone can build on.
Perfect for students who have been convinced they are naturally "bad at math," the author offers a demonstration of how to turn self-doubt into self-confidence by relying on the "mindset" framework.
Mathematical Mindsets is based on thousands of hours of in-depth study and research into the most effective—and ineffective—ways to teach math to young people. This new edition also includes:
Brand-new research from the last five years that sheds brighter light on how to turn a fear of math into an enthusiastic desire to learn
Developed ideas about ways to bring about equitable grouping in classrooms
New initiatives to bring 21st century mathematics to K-12 classrooms
Mathematical Mindsets is ideal for K-12 math educators. It also belongs on the bookshelves of the parents interested in helping their K-12 children with their math education, as well as school administrators and educators-in-training. Here is a one-page explainer about how parents can help their child get excited about mathematics.
Teaching Student-Centered Mathematics:
Teaching Student-Centered Mathematics:
Developmentally Appropriate Instruction for Pre K-2 (Vol. 1) & Gr. 3-5 (Vol. 2) with Enhanced Pearson eText - Access Card Package (Vol. 1) & (Vol. 2) - 3rd Ed.
Developmentally Appropriate Instruction for Pre K-2 (Vol. 1) & Gr. 3-5 (Vol. 2) with Enhanced Pearson eText - Access Card Package (Vol. 1) & (Vol. 2) - 3rd Ed.
By: John Van de Walle, Karen Karp, LouAnn Lovin, Jennifer Bay-Williams
Note: These packages includes the Enhanced Pearson eText and the bound book version.
These books & eText help students make connections between mathematics and their worlds―and helping them feel empowered to use math in their lives. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM’s teaching practices, and engaging families.
The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions.
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Improve Mastery and Retention with the Enhanced Pearson eText
Improve Mastery and Retention with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content. The Enhanced Pearson eText is:
Engaging. The new interactive, multimedia learning features were developed by the authors and other subject-matter experts to deepen and enrich the learning experience.
Convenient. Enjoy instant online access from your computer or download the Pearson eText App to read on or offline on your iPad® and Android® tablet.*
Affordable. Experience the advantages of the Enhanced Pearson eText along with all the benefits of print for 40% to 50% less than a print bound book.
*The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads.
*The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7” or 10” tablet, or iPad iOS 5.0 or later.
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