Algebraic Thinking with Boom Cards

Teaching Algebraic thinking early and often is a core feature of the Common Core math standards (and standards with similar underlying foundations such as TEKS). Algebraic thinking is the ability to recognize and analyze patterns and relationships in a mathematical context. The Common Core/TEKS approach replaces an elementary curriculum focused primarily on calculation with a model more like that used elsewhere in the world (yes Canada you beat us too it!). We still have some time in the U.S. before we’ll see the adoption of the Common Core methodology influencing high school math scores: the first cohort to have Common Core standards from Kindergarten is just now entering 5th grade.

Newer research casts significant doubt on earlier findings that students are not developmentally ready for algebra until a certain age, suggesting that those finding were are a function of instructional shortcomings, not neurological limitations. Neuroscience has shown that introducing concepts such as variable notation (representing numbers with letters or shapes) is within the reach of even lower primary-grade students.

Did you know?

When performing mathematical thinking, our brains activate the occpital lobes, the frontal cortex, and our parietal lobes. The parietal lobes help us find our way home. They combine mental maps with proprioceptive feedback to perform real world geometry and trigonometry. In the educational context, the parietal system helps us transform sequential information into quasi-spatial information, transcending order to find meaning. It is used to comprehend spoken language, perceive melody, and perform mathematical reasoning. If your students have basic navigational skills or can hold a melody, they have the baseline for algebraic thinking.

Introducing Algebraic Thinking, a pathway to success

Students begin developing algebraic thinking when they learn to decompose numbers in kindergarten. By first grade, they are ready to begin working with variable notation when solving basic addition and subtraction problems. They are also introduced to the first set of abstract rules that help them decipher relationships: the commutative and associative properties of addition. They also explore the relationships between addition and subtraction and the meaning of the equal sign. Patterns of equal groups of objects are then introduced to lay the foundation for reasoning about multiplication.

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The foundations laid with patterns of repeated addition in second grade, expand in upper elementary into manipulations with multiplication and division. The commutative, associative and identity properties of multiplication are introduced. Prior work with variable notation sets students up for success in understanding division as an unknown-factor problem. Complexity accelerates into fourth and fifth grade, adding fractions and decimals into the mix. Students use algebraic thinking to explore comparative relationships and practice writing equations using variable notation. Pattern and relationship work continues, with a focus on the patterns of factors.

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With these solid foundations, students are ready to continue developing their skills into middle school, high school and beyond, working with expressions, equation, inequalities, and when ready, working with polynomials, rational functions, and more.

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Resources for Deeper Investigation

Bárbara M. Brizuela, Maria Blanton, Katharine Sawrey, Ashley Newman-Owens & Angela Murphy Gardiner, Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas, Mathematical Thinking and Learning, Vol. 17, Iss. 1, 2015.

Carolyn Kieran (Editor), Teaching and Learning Algebraic Thinking with 5-to 12-Year-Olds: The Global Evolution of an Emerging Field of Resarch and Practice, Springer International Publishing AG 2018.

Cathy Seely, A Journey in Algebraic Thinking, NCTM News Bulletin, Sept. 2004.

Give the Gift of Fundamentals: Why Sequencing is Critical

School breaks are a great time to assign optional practice on fundamentals. As Boom Cards will play on devices from smartphones to desktops, they provide an equitable method for helping students, catch up, stay up or move ahead.

Today Belinda Givens of BVG SLP talks about the fundamental skill of sequencing. Check out our store for more ideas for sequencing fundamentals.


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Sequencing: Why It’s So Critical

by Belinda Vickers Givens, MA, CCC-SLP

The ability to put things into sequential order is an extremely important precursor to organizing thoughts, retelling stories, following directions, reading comprehension, problem solving, and so much more.  It is a vital common core standard from as early as Kindergarten, primarily because it will prepare students for future academic success.  The sooner children are exposed to, and able to demonstrate mastery of sequencing, the better equipped they are for higher level critical thinking.  From putting numbers in order, alphabetizing words, recognizing a pattern, following directions, and even following a schedule, students are taught to sequence in EVERY subject.

As a Speech Language Pathologist, I work with students daily on organizing their thoughts for more effective communication.  A large part of thought organization involves being able to mentally put your ideas in order, before speaking, to effectively get your point across in a logical way that can easily be understood by your communication partner.  I find that my youngest scholars are most successful when they are presented with a visual that they are able to manipulate as they learn this vital skill.  Physically interacting with the content and moving pictures around allows them to visually see and better comprehend this concept.  As they progress towards being able to visually sequence an event or story, the goal is to graduate to fading the visual supports and ultimately independence without the need for verbal or visual cues.

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Presenting my students with picture cards for them to organize was very feasible as a face-to-face therapist, however, now that I’m working as a teletherapist (a service delivery model that allows Speech Language Pathologists to deliver therapy services remotely via the computer) gone are the days of tangible picture cards.  I love technology and embrace it with open arms as I have witnessed firsthand the enthusiasm and growth in my students when we are learning via a digital platform.  I have been very busy searching for and creating resources that capture my students’ attention to keep them engaged.

Boom Cards™ have been a HUGE hit with my students and I absolutely love the ease of use, interactive nature, and self-grading features of these digital task cards.  What I love most about them is that the cards I have created can easily be differentiated for use with all of my students regardless of their skill level.  With my lowest scholars, I can verbally provide them with increased cues or repetitions as necessary or scale back the cueing to provide less guidance as they gain independence.

 

I have started a series of Sequencing and Story Retell Boom Cards that are seasonal and timely to keep my students motivated and engaged all year long!

These cards include four complete short stories in each unit, multiple choice comprehension questions (to address story elements and answering “wh” questions), and interactive digital picture cards for students to sequence by dragging and dropping directly on the screen. I have also included visual cue cards with transition words to aid in story retell, as well as, an introduction to using context clues to address vocabulary by defining unfamiliar words.

My students have been very motivated by these lessons and are excited to manipulate the content directly on the screen.  I have found that I get the best outcomes for my students when they can interact with the material being presented.  They are not only engaged and enthused to actively participate, but they don’t require outside reinforcement to attend to the task and I can, therefore, maximize my time for increased trials.  They enjoy the ability to point and click their answer choices for immediate feedback and I really appreciate the fact that the Boom Cards are self-grading which saves me a substantial amount of time with data collection and progress monitoring.

I currently have a Fall and Winter themed unit available for purchase and will be releasing a Spring and Summer Sequencing and Story Retell unit very soon.  To find more of my digital interactive lessons, please visit my Boom Learning store HERE.


Belinda has been an American Speech-Language and Hearing Association (ASHA) Certified Speech Language Pathologist for 11 years.  She is licensed in FL, CA, WA, and VT and is a member of ASHA’s Special Interest Group 18 for Telepractice.  She currently works as a teletherapist serving PK – 12th grade students.  She holds her B.S. in Psychology with a minor in Education from Florida State University and her M.A. in Communicative Sciences and Disorders from the University of Central Florida.  She also earned an endorsement in Reading from UCF.

She is the co-owner of Infinity Rehabilitation, LLC with her husband who is an Occupational Therapist.  She is also the creator and owner of BVG SLP, which specializes in creating No- Prep, No-Print digital therapy materials that are great for use within teletherapy platforms or face to face therapy.  She is passionate about literacy and has written a children’s book (The Adventures of DemDem the Garbage Truck: Watch Out for the Bumps).  She tries to incorporate literacy into the majority of her therapy sessions. In addition to her Boom Cards store, you can find products from her at her Teachers Pay Teachers store.

Belinda is the mother to three amazing young boys and enjoys taking road trips, reading, crafting, and exploring.  She has been married for 15 years and resides with her family in Central Florida. Connect with her on Facebook and Pinterest

 

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Mathematics Materials for Third, Fourth and Fifth Grade

Common Core Aligned

Under the Common Core state standards, during grades third through fifth students work with mathematics using models, standard algorithms and in the context of word problems. By doing so, students develop a deep number sense that prepares them for algebra and beyond and the real world application of mathematics to everyday problems. Boom Learning has a range of materials to help you teach, review, assess or prep on these topics.

Operations

Between third and fifth grade, students are expected to master addition, subtraction, multiplication and division. For a fully developed number sense, they must be able to identify the unknown number in an equation, perform word problems, and understand the identity, commutative, and associative properties. Finally, they should be able to identify operations based patterns. Success with operations necessitates a firm foundation in place value. Authors Evil Math Wizard, Simone’s Math Resources, Wise Guys, Shelley Rees, LittleStreams, I Heart 4th Grade, White’s Workshop, Teachers Features, Mercedes Hutchens | Surfing to Success, and more provide a wide variety of operations Boom Cards.

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Fractions

For fractions, students in these grades first develop their concept of a fraction as a part of a whole, including learning to convert whole numbers to fractions. Working with models, such as fraction wheels and number lines, deepen students understanding of fractions. Students learn to recognize and generate equivalent fractions. Finally, students master applying the four operations to fractions, which prepares them for conversions and unit rate applications in middle school. Wise Guys, Simone’s Math Resources, Little Streams, Miss Mindy, I heart 4th grade, Crockett’s Classroom, Meredith Anderson – Momgineer and Pink Cat Studio make colorful and engaging fractions Boom Cards.

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Decimals

In fourth grade, students learn to relate decimals to fractions and the number line. They also learn to perform the four operations on decimals and to represent decimals using models. Finally, students learn to apply decimals in real world situations, which prepares them for percentages and interest in middle school. Look for decimals Boom Cards by Wise Guys, Shelley Rees, LittleStreams, I heart 4th grade, Simone’s Math Resources, and Stress-Free Teaching.

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Geometry, Measurement and Data

For geometry, students master the most common geometric shapes and begin to understand concepts of area and volume. For all three concepts, students master the concept of units and apply them to solving a variety of problems. Finally they begin to understand graphing as a way to represent mathematical problems. These skills prepare them for advanced geometric manipulations, conversions, probability, and statistics in middle school and beyond. Look for Boom Cards by Making the Grayd, Garden Full of Knowledge, Little Streams, Catia Dias, Amber from TGIF, and Fishyrobb.

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Assess and Review Middle School Mathematics

Whether you are assessing understanding, preparing for Common Core or similar standards-based tests, recommending summer retention or credit recovery, or are looking ahead to fall, we have a few resources to help your middle schoolers solidify core skills. You can find our collection of mathematics materials for middle schoolers here.

MiddSimoune's Math Resourcesle schoolers are expected to extend their understanding of operations to all rational numbers, including negative numbers. Everyday reasoning about the meaning of negative numbers provides a solid foundation. Simone’s Math Resources’s Comparing Integers can be used as a pre-test, assessment, or practice of student ability to understand the applicability of negative numbers to real world problems.

A firm grasp of absolute value is an essential foundation to performing operations on mixed negative and positive numbers. Miss Mindy has an Absolute Value lesson plus practice deck bundle. You can use it with the student who needs extra or with the student reading to jump ahead.

Middle schoolers must develop increasingly sophisticated skills in working with expressions and exponents. We have several items from Joan Kessler, LittleStreams, Simone’s Math Resources, Jean Adams, and Misty Miller to evaluate how well your students are working with Expressions and Exponents or to assign extra practice.

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