Subject: singapore math

Lesson Study- Keys to Developing Numbers Sense in Students


Reignite your passion for teaching and learning! Our lesson study is research in action around number sense. Teachers work as a member of a professional development community by researching, planning, delivering, reflecting and refining lessons for grades 1- 5. This collaborative model will establish a community that desires to learn from each other and grow under the mentorship of Dr. Yeap Ban Har and Sarah Schaefer, M.Ed.

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Getting Ready for Developing Roots

Developing Roots and Mathodology

We love seeing and hearing how you are getting ready for the start of the school year. What steps are you taking to be ready?

This was shared with us from a teacher in Georgia getting her kindergarten classroom ready for the start of Developing Roots!

“Organized the whole closet by chapters! So excited to get in front of it this year!!”- Melissa

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What Apps Does Sarah Use?

Apps Sarah uses at Mathodology

As schools begin to embrace technology in the classroom, one question that Sarah often receives is, “What apps do you use in your workshops and classrooms?”

With a multitude of apps available, it can be challenging to find the right app that can help teachers teach better and engage students more meaningfully.

Sarah shares her list of frequently-used apps below.

Drawing and Writing Tools

Algebra Balance (iOS $1.99)

Algebra Balance App and Apps Sarah uses at Mathodology

Bamboo Paper (free for iOS, Android and Windows)

Bamboo-Paper App and Apps Sarah uses at Mathodology

Turn your screen into a paper with Bamboo Paper! Draw and write effortlessly with the various pens and brushes available. The zoom function in this app allows you to write in small spaces and fit more notes onto a page. This app also allows you to add images to your notes and write on them. Notebooks created within the app can also be shared and exported to other mobile platforms and cloud services.

Noteshelf (iOS $9.99)

Noteshelf App and Apps Sarah uses at Mathodology

Personalize your notes with Noteshelf! Individual notebooks can be easily customized in Noteshelf using the extensive library of cover designs and page templates in the app. Writing and drawing tools are available to help you write notes and draw precise geometric shapes with ease. There are also several fonts to choose from within the app if you prefer to type.

In Noteshelf, notes can be written across pages, just like a physical notebook, making it easy to create sections. Noteshelf also allows you to insert photos and write on them. Another excellent feature is its audio recording function, which means you never have to worry about missing out on the nitty-gritty details. Making annotations and signing PDFs is also a useful feature in Noteshelf. Other features include scanning of documents, password protection of notes, and syncing with Evernote and cloud services.

Pencil Box (iOS $0.99)

Pencil-Box App and Apps Sarah uses at Mathodology

Pencil Box is a drawing tool that will help anyone who wants to draw with precision. To start, pick a drawing tool and begin drawing or import an image to draw on. Besides the many brushes and shapes available, Pencil Box also allows you to add and edit layers of your drawing, making it easy to add or delete parts of a drawing without having to start over.

Teaching Tools

Geometry Pad+ (iOS $6.99, Android $5.99)

Geometry-Pad and Apps Sarah uses at Mathodology

Geometry Pad+ is a dynamic app that allows you to construct geometric shapes, such as circles, squares, triangles, rhombuses, and parallelograms, with precision and ease. Beyond creating shapes, this app also allows you to mark out angles within shapes and draw arcs using the in-app tools. The app also comes with a measuring tool that can measure lines and other properties. Other shapes properties, such as perimeter and area, can be calculated using the in-app tools as well. All documents can be saved and exported, making it convenient for future use and reference.

GeoBoard (free for iOS, Windows, and web browsers)

Geoboard and and Apps Sarah uses at Mathodology

Learn about shapes in a fun and interactive manner! In Geoboard, bands can be stretched around pegs on a virtual board to create line segments and different types of polygons. Available on both mobile and web-based platforms, GeoBoard can also be used to illustrate area, perimeter, fractions, angles, and many other concepts. With three board types to choose from and multiple band colors to work with, this app is bound to bring a lot of fun to the classroom.

Number Lines (free for iOS and web browsers)

Number Lines App and Apps Sarah uses at Mathodology

Available as a mobile and web app, Number Lines helps you to customize number lines easily for your classroom. This app allows you to create number lines with whole numbers, fractions, decimals, and even negative numbers. Students can visualize number sequences and demonstrate strategies related to counting, comparing, adding, subtracting and much more. Elements of the number line can also be hidden to encourage creative thinking.

Pieces Basic (free for iOS and web browsers)

Number Pieces Basic App and Apps Sarah uses at Mathodology

This interactive app helps students learn about place value and develop their computation skills with multi-digit numbers. Number Pieces Basic is a great visual aid for teachers to use in classrooms to engage students as pieces can be dragged around to illustrate addition and subtraction problems. Equations and expressions can also be written using the text tool. The app can be used on-the-go on a mobile device or from a web browser on a computer.

is a great visual aid for teachers to use in classrooms to engage students as pieces can be dragged around to illustrate addition and subtraction problems. Equations and expressions can also be written using the text tool. The app can be used on-the-go on a mobile device or from a web browser on a computer.

Manipulative of the Week (free for iOS)

This app bundle provides a free manipulative every week and contains the 14 most popular manipulatives used by students and teachers. Some of the apps that Sarah uses frequently are listed below.

Algebra Tiles (iOS $1.99)

Algebra Tiles App and and Apps Sarah uses at Mathodology

Algebra Tiles provides an engaging experience for students to explore algebraic concepts. Using tiles to represent algebraic expressions, students can learn to add and subtract integers as well as solve algebraic equations.

Base Ten Blocks (iOS $1.99)

Base Ten Blocks App and and Apps Sarah uses at Mathodology

Base Ten Blocks are virtual blocks to help students learn about place value, addition, subtraction, regrouping and more. Students can work with blocks representing ones, tens, hundreds and thousands to explore addition, subtraction, multiplication and division strategies. The place value chart is especially useful when working with decimals as well.

Color Tiles (iOS $1.99)

Color Tiles App and and Apps Sarah uses at Mathodology

Use Color Tiles to build number frames, make shapes, find fractions and more. The user-friendly interface gives users the freedom to create and customize manipulatives to suit their learning needs. Color Tiles helps students to develop their computing skills while enabling them to learn how to sort and classify objects.

to build number frames, make shapes, find fractions and more. The user-friendly interface gives users the freedom to create and customize manipulatives to suit their learning needs. Color Tiles helps students to develop their computing skills while enabling them to learn how to sort and classify objects.

Cuisenaire® Rods (Number Rods) (iOS $1.99)

Cuisenaire Rods App and and Apps Sarah uses at Mathodology

Number rods can be placed along a number line to compare numbers and fractions. By adding and removing rods, students can visualize the addition and subtraction of integers and fractions. This app also enables students to view ratios and proportions at a glance.

Fraction Circles (iOS $1.99)

Fraction Circles App and and Apps Sarah uses at Mathodology

In Fraction Circles, fraction pieces can be moved, rotated, overlapped and put together. It is a versatile app as fractions, decimals and percentages can be used to label each fraction piece. Each fraction piece is color-coded, making it easy to identify and work with as well.

Fraction Manipulatives (iOS free)

Fraction Manipulative App and Apps Sarah uses at Mathodology

Hundred Board (iOS $1.99)

Hundred Board App and Apps Sarah uses at Mathodology

Linking Cubes (iOS $1.99)

Linking Cubes App and Apps Sarah uses at Mathodology

Linking Cubes are virtual multi-colored cubes that help students to visualize numbers in a pictorial manner. Students can learn how to add, subtract, multiply and divide using different colored cubes. Place value can also be represented using the place value background available in the app. The built-in graph background makes it easy to create graphs as well.

Little Bit Studio Bugs & Buttons (iOS $2.99)

Little Bit Studio Bugs & Buttons App and and Apps Sarah uses at Mathodology

Number Frames (iOS free)

Number Frames App and Apps Sarah uses at Mathodology

Osmo Tangram (iOS free)

Osmo Tangram App and Apps Sarah uses at Mathodology

Pattern Blocks (iOS $1.99)

Pattern Blocks App and Apps Sarah uses at Mathodology

Pattern Blocks is the closest thing you can get to physical pattern blocks. With a wide selection of two-dimensional shapes, including hexagons and trapezoids, students can learn about geometry, patterns, fractions, and decimals in a fuss-free manner.

Place Value Disks (iOS $1.99)

Place Value Disks App and Apps Sarah uses at Mathodology

Rekenrek (iOS $1.99)

Rekenrek app and Apps Sarah uses at  Mathodology

Software Smoothie Felt Board App (iOS $2.99)

Software Smoothie Felt Board App and Apps Sarah uses at  Mathodology

Two-Color Counters (iOS $1.99)

Two Color Counters App and Apps Sarah uses at  Mathodology

Two-Color Counters is a minimalistic app for those looking for a simple yet effective way to understand numbers, integers, and fractions. Only two colors are used in this app as its focus is on illustrating operations concepts. Teaching ideas aligned to Common Core are also featured in this app.

Are you inspired? Try out these apps in your own teaching or learning journey and let us know the results!

Note: All prices stated are in USD.



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Introduction to Lesson Study


Are you interested in deepening your practice? Our lesson study will focus on the process of delivering effective mathematics lessons with a focus on content and delivery. Teachers work as a member of a professional development community by planning, delivering, reflecting and refining lessons for grades 1- 5. This collaborative model will establish a community that desires to learn from each other and grow under the mentorship of Dr. Yeap Ban Har & Sarah Schaefer, M.Ed.

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The Lovett School – Atlanta, GA

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Three- Dimensions to Differentiating Mathematics


Mathodology presents Three-Dimensions to Differentiating Mathematics Lessons

This two-day workshop focuses on how to break down math instruction during and after the lesson to support both struggling and advanced learners. Developing effective instructional strategies that allow teachers to fill in gaps and enrich thinking is key!

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Essential Ideas in Mathematics


New to the CPA approach, three-part lesson structure and bar modeling? Join Mathodology this summer to understand these methods and how effectively implementing them can increase student learning!

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think!Mathematics Annual Institute Charlottesville, Virginia – Registration


Date : 24th – 26th July 2019 Time : 8:00 am – 3:30pm Venue   The Covenant School, : 1000 Birdwood Road, Charlottesville, Virginia, 22903, United States Trainers : Dr Yeap Ban Har and Sarah Schaefer Cost : $900 (Register before May 1st for a 5% discount)   Be inspired and equipped with effective instructional strategies to meet various student needs within (more…)

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Developing Mathematical Roots (K +)


A new, exciting and innovative approach to teaching mathematics in the Kindergarten and Pre-Kindergarten years!

Expect to learn the whys and the hows behind the education of mathematics during the foundational years. By the end of these two days, you’ll be inspired and excited to apply your new ideas and tools, making mathematics in your classroom come alive for your students.

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Lesson Study with Dr. Yeap Ban Har Middletown, Delaware – Registration


Are you interested in deepening your practice? Our lesson study will focus on the process of planning effective mathematics lessons with a focus on content and delivery. Teachers work as a member of a professional development community by planning, delivering, reflecting and refining lessons for grades 1- 3. This collaborative model will establish a community that desires to learn from each other and grow under the mentorship of Dr. Yeap Ban Har & Sarah Schaefer, M.Ed.

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Lesson Study with Dr. Yeap Ban Har Charlotte, North Carolina – Registration


Are you interested in deepening your practice? Our lesson study will focus on the process of planning effective mathematics lessons with a focus on content and delivery.  Teachers work as a member of a professional development community by planning, delivering, reflecting and refining lessons for grades 1- 3.  This collaborative model will establish a community that desires to learn from each other and grow under the mentorship of Dr. Yeap Ban Har & Sarah Schaefer, M.Ed.

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Developing Mathematical Roots (K +)


A new, exciting and innovative approach to teaching mathematics in the Kindergarten and Pre-Kindergarten years!

Expect to learn the whys and the hows behind the education of mathematics during the foundational years. By the end of these three days, you’ll be inspired and excited to apply your new ideas and tools, making mathematics in your classroom come alive for your students.

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Lesson Study with Dr. Yeap Ban Har Middletown, Delaware


Are you interested in deepening your practice? Our lesson study will focus on the process of delivering effective mathematics lessons with a focus on content and delivery. Teachers work as a member of a professional development community by planning, delivering, reflecting and refining lessons for grades 1- 3. This collaborative model will establish a community that desires to learn from each other and grow under the mentorship of Dr. Yeap Ban Har & Sarah Schaefer, M.Ed.

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Lesson Study with Dr. Yeap Ban Har Charlotte, North Carolina


Are you interested in deepening your practice? Our lesson study will focus on the process of delivering effective mathematics lessons with a focus on content and delivery.  Teachers work as a member of a professional development community by planning, delivering, reflecting and refining lessons for grades 1- 3.  This collaborative model will establish a community that desires to learn from each other and grow under the mentorship of Dr. Yeap Ban Har & Sarah Schaefer, M.Ed.

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think!Mathematics Annual Institute


Be inspired and equipped with effective instructional strategies to meet various student needs within the classroom. Led by Dr Yeap Ban Har and Sarah Schaefer, this 3-day course will provide insights into creating environments that promote deep learning where students and teachers are excited to reason, communicate, and think mathematically.

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Advanced Singapore Methods


Join Sarah and Ban Har for this two-day institute in sunny Florida! This course will challenge teachers to reflect on current practices and evaluate what effect instructional decisions have on student learning.

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Add by Counting On

Students using the think!Mathematics program reinforce the count on strategy.  Games/activities can be used during the guided practice part of a lesson.  Students are encouraged to count on from the larger number.

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Math PD for Early Elementary Jacksonville Beach, Florida


A new, exciting and innovative approach to teaching mathematics in the Kindergarten and Prekindergarten years! 

You have a unique opportunity to participate in an institute that will introduce you to Mathodology’s brand new curriculum Developing Roots. Work alongside the authors to see how lessons were developed and understand how each supports the ways our young mathematicians think and learn.   Each lesson incorporates a three-part format—first, students explore a given task; next, they practice through a hands-on activity; last, they reflect on their learning through the use of a journal. 

You’ll see the way lessons spiral and methods are offered in order to develop your own abilities to differentiate tasks to meet every one of your students where they are. Most excitingly, you’ll see how your classroom can transform into an environment filled with inviting activities that inspire the natural curiosity and love for learning mathematics. 

Expect to learn new ideas for creating centers and shelf work in your classroom that support and assist in developing an ideal learning culture. You will hear from teachers that are currently working in the program. You’ll study a variety of lesson formats from Small Groups to Whole Group to Partner Work that foster student communication through conversation, collaboration and journaling. 

Expect to learn the whys and the hows behind the education of mathematics during the foundational years. Be prepared to take a fresh look at assessment and how to translate student work into evidence of learning.  By the end of these three days, you’ll be inspired and excited to apply your new ideas and tools, making mathematics in your classroom come alive for your students.

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Essential Ideas in Mathematics Singapore Approach


Join Sarah and Ban Har for this three-day institute in sunny Florida! This course is what you need to learn the pedagogy behind Singapore Mathematics Programs from experts in the field. You’ll understand the research behind a spiral curriculum and the methods used to solve problems.

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