Patterns and Algebraic Thinking (7-9)

Patterns and Algebraic Thinking

  1. Algebra By Hand – 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. BetterLesson – Lesson ideas in the section called “Algebra”.
  3. Dad’s Worksheets The worksheets below concentrate on patterns and algebraic thinking in some way. Take a look at the main website to see if there are other worksheets for the subject you are teaching.
    • Arithmetic Sequences – Practice finding the common difference for a sequence of numbers or finding arbitrary nth terms in an arithmetic sequence given its formula definition.
    • 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.
    • Geometric Sequences – Students practice determining if a sequence is geometric, finding ratios, finding the nth term of a geometric sequence and finding multiple subsequent terms of a sequence.
    • 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.
  4. Edx – 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.
  5. Formative Loop – Provide Gr. 1-8 students with five-minute math drills each day. Daily exercises are generated for each day of the week and are based on individual student progress. View the reports to find out if any kids are struggling, and provide remedial instruction as needed.
  6.   Geogebra – – 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 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 – Find the perfect Gizmo to get your students ready for success with Gr. 6 – 8 Patterns and Algebraic Thinking or Gr. 9 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 – 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. – 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.
  11. Khan Academy – 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. 
  12. Math 4 The Nines – The OAME Grade 9 Applied Project paid attention to the use of rich tasks in the classroom. The participants shared many of the tasks used with their own students with each other.
  13. 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.
  14. 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.
  15. 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.
  16. NRICH (Algebra) – Some exciting activities which use numbers in lots of different ways, including algebraic thinking.
  17. Number Spiral – 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.
  18. Numeracy Ninjas – A whole-school numeracy intervention run in Key Stage 3 (Gr. 7-9) mathematics lessons (but could possibly be used for Gr. 6 students with some alterations). Students complete a 5 min. skills test including: 30 questions – 10 each of mental numeracy calculation 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.
  19. PBS Learning Media – K-8 Mathematics ranges from counting cardinal numbers to linear equations and functions. Students can review the calculation of area, find the area of combined shapes and can be assessed on their understanding using Khan Academy. Similar units can be created on topics such as lines and angles, probability models, and the multiplication and division of fractions. Make sure to use the filter to isolate the right grade.
  20. Quick Math – 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.
  21. SoftSchools – Worksheets, quizzes and activities pertaining to the branch of algebraic thinking.
  22. S.O.S Mathematics – A very simplistic website with a directory of algebraic resources with various equations & functions.
  23. 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.
  24. The Centre for Education in Mathematics and Computing – This course covers the topics typically taught in Canadian Grade 7 and 8 Mathematics curricula and, in some instances, extends ideas beyond grade level.
    • Representing PatternsPart A (Lessons 1–6): Topics include representing sequences using tables, general terms and graphs, describing patterns using variables and expressions, extending sequences, and solving problems involving unknown quantities. Part B (Lessons 7–11): Topics include equivalent expressions for the general term of a sequence, describing relationships and patterns using equations, and decreasing and naturally occurring sequences.
    • Equations and the Pythagorean TheoremPart A (Lessons 1–5): Topics include using variables in expressions and equations, exploring linear relationships, and solving equations by inspection, trial and error and using visual models. Part B (Lessons 6–10): Topics include solving equations using algebraic techniques, comparing the differences between evaluating an expression and solving an equation, exploring equations with multiple variables and the Pythagorean Theorem.
    • Introduction to Functions (Gr.9) – Function notation. Domain and range. Transformations of functions. Inverses of functions. Inequalities, absolute values, and reciprocals.
  25. 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.
  26. Transmath – 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.
  27. Virtual Nerd – 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.
  28. YouCubed – 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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