Patterns and Algebraic Thinking (10-12)

Patterns and Algebraic Thinking


  1. Algebra By Hand https://algebrabyhand.com/ – A set of manipulatives for students to manipulate; allows students to drag and drop terms and factors to help them visualize the algebra-solving process. Prevents students from skipping steps and chronicles their solving process with a coherent narrative that can be reviewed. It’s like algebra with training wheels − you can go in the wrong direction, but you can’t fall off the bike. Students need to have some basic knowledge of algebra before using this program.
  2. AlgebraLab http://www.algebralab.org/ – An online learning environment that focuses on topics and skills from high school mathematics that students must be able to draw upon in their introductory science courses. Since math is the language of science, science courses are often where students first realize “Oh, so this is why we learned that in algebra …”
  3. BetterLesson – Lesson ideas in the section called “Algebra”.
  4. Dad’s Worksheetshttps://www.dadsworksheets.com/ The worksheets below concentrate on algebraic thinking in some way. It is advised to take a look at the main website for other possible worksheets falling into your teaching area.
    • Exponents – Practice exponents worksheets introducing exponent syntax, calculation of simple exponents, powers of ten and scientific notation.
    • Factoring Calculator – To find the factors for a number, simply enter it at the top of the calculator and it will be decomposed instantaneously.
    • Linear Equations – Students identify the direction of slope, as well as calculating slope from points on the coordinate plane.
    • Order of Operations – The printable order of operations worksheets below will get you mastering your PEMDAS (BEDMAS) skills in no time.
    • Prime Factorization Calculator – Use this factorization calculator to produce a factor tree, or just determine the list of primes that divide a given integer.
    • Square Root Charts – Whether it’s a list of perfect square roots or a complete table of square roots from 1 to 100, the square root charts from this page will have your radicals covered.
  5. Edxhttps://www.edx.org/course/subject/math – Online math courses from MIT, ASU, and other leading math and science institutions. Get introductions to algebra, geometry, trigonometry, precalculus and calculus or get help with current math coursework and AP exam preparation.
  6.   Geogebra – https://www.geogebra.org/ – Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more. Find over 1 million free activities, simulations, exercises, lessons, and games for math.
  7. Get The Mathhttps://www.thirteen.org/get-the-math/ – Combines video and web interactivity to help middle and high school students develop algebraic thinking skills for solving real-world problems. Drawing on conventions of popular reality TV shows, viewers are encouraged to try challenges themselves using interactive tools provided on the website before returning to the video to see the solutions. 
  8. Gizmos https://www.explorelearning.com/ – Find the perfect Gizmo to get your students ready for success with Gr. 9 – 12 Patterns and Algebraic Thinking. Manage your classes and assess your grade 3-12 students in one place. Make planning easy with customizable, expert lesson materials.
  9. Graspable Math https://graspablemath.com/ – Assign algebra tasks to your students and see live feedback of their step-by-step work. Discover, create, and share engaging math activities for 4th to 12th graders.
  10. Inside Algebra – https://www.voyagersopris.com/math/inside-algebra/overview – Engages at-risk students in grades 8–12 through explicit, conceptually based instruction to ensure mastery of algebraic skills. A multisensory approach leverages hands-on and manipulative-based activities and pictorial representations to help students visualize concepts.
  11. Inside MathematicsHigh School Algebra Common Core Resources | Inside Mathematics – Find all high school algebra resources to guide and support mathematics teaching and learning. These resources are organized by mathematical strand and refer to specific Common Core math content standards.
  12. iSmartboard.com – Use these Smart Board games, activities and lessons to learn about Adding, Subtracting, Multiplying and Dividing, Exponents, Algebra, Variables, Order of Operations, Equations and Expressions. Note: Lots of ads to deal with on the page and everything is lumped into one listing.
  13. Khan Academyhttps://www.khanacademy.org/ – The most fundamental branch of math is having a clear idea on number sense and numeration. It consists of understanding place values and basic operations. 
  14. Math Worksheets 4 Kids – Number pattern worksheets contain reading patterns on number lines, showing the rule, increasing and decreasing pattern, writing the rules, geometric pattern, pattern with two-rules and more.  “Practice makes perfect,” prepare a stronger base for algebra with this assemblage of pre-algebra worksheets; featuring exercises on topics like order of operations, factors, exponents and more.
  15. MIT Open Courseware – https://ocw.mit.edu/high-school/ – Highlights for High School contains an abundance of resources that cover not only science and mathematics but also engineering, humanities, and social sciences. These resources are available under a Creative Commons license, so the material on the site can be integrated into classroom lesson plans, shared, reused, and remixed.
  16. National Council of Teachers of Mathematics (NCTM) – Most of the very helpful classroom resources and activities are for members only but there are a few lessons and activities (through Illuminations) that can be aqccessed without a membership.
    • How Should I Move? – This lesson is intended to introduce various function types, including linear, exponential, quadratic, and piecewise. Therefore, use this activity to pique students’ interest in functions and to allow them to deduce algebraic equations.
    • Supreme Court Handshake – How many handshakes occur when a group of n people shake hands exactly once with every other person in the group?
    • Handshakes (Interactive) – This interactive will help with the “Supreme Court Handshakes” lesson if students struggle.
    • Tessellation Creator – A tessellation is a repeating pattern of polygons that covers a plane with no gaps or overlaps. What kind of tessellations can you make out of regular polygons?
    • Bunny Times – Become confident in facts up to 12 x 12 using visual models that stress the conceptual aspects of multiplication.
    • Factorize – Visually explore the concept of factors by creating rectangular arrays.
    • Pan Balance – Numbers – Use this tool to strengthen understanding and computation of numerical expressions and equality.
  17. New South Wales Government – Education Patterns and Algebra section – Algebra is a branch of mathematics that deals with general statements of relations, utilising letters and other symbols to represent specific sets of numbers and values and their relationships to one another. Patterns are important in the early stages of the development of algebraic thinking. Some very good suggestions on how to attack these disciplines starting in the primary grades.
  18. NRICH (Algebra) – Some exciting activities which use numbers in lots of different ways, including algebraic thinking.
  19. Number Spiralhttps://numberspiral.com/ – Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center. A list of contents listed on the left sidebar.
  20. Numeracy Ninjashttp://www.numeracyninjas.org/ – Although this program is targeted towards Gr. 7-9 students, it could be used to brush up on existing skills. Students complete a 5 min. skills test: 30 questions total – 10 each of mental math strategies, times tables and key numeracy skills. There was a minor interruption with downloading resources on the website so they set up a temporary folder through Facebook.
  21. PBS Learning Mediahttps://www.pbslearningmedia.org/subjects/mathematics/ – Bring math concepts to life through interactive games animations and engaging media resources for secondary school students.
    • High School Algebra – A mathematical journey that starts with evaluating simple single variable expressions, continues with linear systems, and challenges them with graphing multi-variable equations. 
    • High School Functions – Resources encourage students to explore this relationship with an interactive Valentine’s Day scenario, a Cyberchase video analyzing how quickly money can grow when exponential growth is applied and Khan Academy resources can be used to review and assess concepts taught. Additional topics include linear, quadratic, and exponential models, periodic phenomena, and extending the domain of functions using the unit circle.
  22. Quick Math http://quickmath.com/ – The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction. The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
  23. SoftSchoolshttps://www.softschools.com/math/algebra/ – Worksheets, quizzes and activities pertaining to the branch of algebraic thinking.
  24. S.O.S Mathematicshttp://www.sosmath.com/algebra/algebra.html – A very simplistic website with a directory of algebraic resources with various equations & functions.
  25. Texas Instruments – This directory of resources will likely involve some form of Texas Instruments technology but the classroom activities certainly will be different from the normal process of teaching patterns and algebraic thinking.
  26. The Centre for Education in Mathematics and Computing – Courses cover the topics typically taught in Canadian Grade 9-11 and Grade 12 Mathematics curricula.
    • Introduction to Functions Function notation. Domain and range. Transformations of functions. Inverses of functions. Inequalities, absolute values, and reciprocals.
    • Number Sense and Algebraic Expressions – Exponent laws. Manipulating expressions including polynomials, radical and rational expressions. Investigating prime factorization.
    • Advanced Functions and Pre-Calculus (Gr. 12) – Introduces functions with many terms and notations that will be encountered. A large portion deals with sketching functions using transformations. Concludes with a look at inverses.
    • Calculus and Vectors (Gr. 12) – Students will examine values of the average rate of change over an interval to approximate the instantaneous rate of change at a point. The concept of a limit will be formally defined, graphing of a function and the properties of limits to evaluate limits of a variety of functions.

  27. The Get-it Guide – Math tutorials with slideshows and a follow-up worksheet to help focus on the key steps required for solving the math problem, determine the steps of the solution path you understand and identify the steps of your solution path you do not yet understand. Develop mathematical resilience when solving problems. Read and talk about the math problem you are trying to solve.
  28. Transmathhttps://www.voyagersopris.com/math/transmath/overview – A comprehensive math intervention curriculum that targets middle and high school students who lack the foundational skills necessary for entry into algebra and/or who are two or more years below grade level in math.
  29. Virtual Nerdhttps://www.virtualnerd.com/ – Developed as a supplemental learning resource for teachers and students with over 1,500 video lessons focusing on middle school and high school mathematics – especially for algebra and geometry.
  30. YouCubedhttps://www.youcubed.org/algebra/ – This 4-week curriculum unit has been developed to introduce algebraic concepts at any grade level. It draws upon algebraic research showing that it is more helpful for students to learn algebra through studying pattern growth where a variable represents a case number, and can vary, before learning about “solving for x.” 



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