# 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. A-Plus Math (Varsity Tutors)https://www.varsitytutors.com/aplusmath – Interactive math resources for teachers, parents, and students featuring free math worksheets, math games, math flashcards, and more. (The interactive worksheets also have a print option.)
3. BetterLesson – Lesson ideas in the section called “Algebra”.
4. Dad’s Worksheets https://www.dadsworksheets.com/ 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.
• Number Lines – The number line PDFs on this page include various ranges (10, 12, 15, 20, 15 and 100) in both starting from zero as well as negative ranges.
• Number Patterns – The number patterns worksheets for basic operations.
• 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.
• 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.
• Basic Operations:
5. Formative Loophttps://formativeloop.com/ – 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 – 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. Gizmos https://www.explorelearning.com/ – Find the perfect Gizmo to get your students ready for success with Gr. 4-5 Patterns and Algebraic Thinking or Gr. 6 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.
8. 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.
9. Help Teachinghttps://www.helpteaching.com/free-math-worksheet-game-generators.htm – Quickly generate printable arithmetic worksheets for drilling and practice! Just set the difficulty, problem type, and number of questions desired, and generate a worksheet that can be downloaded or printed.
10. 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.
11. 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.
12. MathFROGhttps://cemc2.math.uwaterloo.ca/mathfrog/ – A website of mathematics fun resources and online games for grades 4, 5, and 6 students, teachers and parents in all the math strands.
13. MathsChasehttps://www.mathschase.com/ – They use Al to suggest questions to best test your ability, and it will advance as you become more skilled. Has over a 100 different tests covering a huge range of maths skills for K-6 students. Monitor your progress and get awards for completing differents games and levels.
14. Math Seedshttps://www.3plearning.com/software/mathseeds/ – Develops beginning numeracy skills with captivating activities covering number sense, addition, subtraction, and multiplication for K-4 students. Get the most out of class time with simple and teacher-friendly software.
15. Mathsframe – Although this website aims at providing math resources and worksheets for K-6 students, algebraic thinking is only available to Grade 6 students at this time.
16. 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.
17. 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.
• Growing Patterns
• 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.
• Patch Tool – These square patches are then repeated and connected to produce a larger pattern. Create your own patch using the shapes in the tool.
• Shape Tool – Create any geometric shape imaginable. (Can use this for tessellations.)
• Dynamic Paper – Need a number line that goes from ‑18 to 32 by 5’s? Or a set of pattern blocks where all shapes have one-inch sides? You can create all those things and more.
• 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.
• Times Table – This tool allows you to practice multiplying single-digit numbers.
• 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?
• Egg Carton Designs – Constructing Arrays to Begin a Study of Multiplication
• Using the Factor Game Interactive
• Bunny Times – Become confident in facts up to 12 x 12 using visual models that stress the conceptual aspects of multiplication.
• Handshakes – In general, how many handshakes occur when there are n people?
• 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.
18. 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.
19. NRICH (Number Patterns) – Some exciting activities which use numbers in lots of different ways, including algebraic thinking.
20. Numeracy Ninjashttp://www.numeracyninjas.org/ – 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.
21. 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.
22. Reflex Math https://www.reflexmath.com/ – Using fact families and delivering the right facts at the right time for each individual student, it meets students where they are. It is adaptive and individualized to work for grades 2-6 students with different needs, skills and goals.
23. S.O.S Mathematicshttp://www.sosmath.com/algebra/algebra.html – A very simplistic website with a directory of algebraic resources with various equations & functions.
24. Texas Instruments – This directory of K-5 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.
25. The Centre for Education in Mathematics and Computing https://www.cemc.uwaterloo.ca/resources/cemc-digital.html – With CEMC Digital, students and teachers can discover new ideas and dive deep into problem solving. The online resources are developed by expert CEMC educators and provide enrichment opportunities to students from Grades 4 to 12 with a mix of online games, video lessons, exercises and challenge problems.
• MathFROG (outlined more in-depth in list above)
• Emmy Noether Circles – Each Circle is a set of six problems, plus hints, suggestions, and solutions. The problems can be used individually, or as a set, as time permits. Circles are available in the charts below both as complete sets and divided into problems identified by curriculum strand.
• Problem of the Week – Designed to provide students with an ongoing opportunity to solve mathematical problems. Each week, problems from various areas of mathematics will be posted and e-mailed to teachers for use with their students from grades 3 and up.
• Math Circles – A free weekly enrichment activity for grade 6 to 12 students organized by the Faculty of Mathematics of the University of Waterloo. Math Circles materials, including presentation outlines, practice problems, and solutions, will be posted weekly. Registration for Fall 2021 Math Circles will take place online, beginning on Wednesday, September 15, 2021.
26. 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.
27. Times Tables Rock Starshttps://ttrockstars.com/ – It can be used in the classroom as whole-group instruction, a math center, or homework.  Multiplication facts can be assigned to the whole class or individual students and adjustments can be made in the student setup section. Both print worksheets or online interactions are available.
Although there is a charge to use the actual program, the interactive tools tab is free
and can be very useful in the classroom.
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. Worksheet Genius – Ready-made worksheets in different areas of number sense:
• Number Lines – These simple number lines focus on counting in steps of 2, 3, 4 etc. They support the student by supplying the first few numbers, so the pattern is simple to work out and then continue. Further down, the number lines focus on counting backwards and identifying links between numbers. They re-enforce both subtraction skills, recall and number bonds.
• Addition – Counting On strategy, using place value, horizontal and vertical adding worksheets.
• Subtraction – Counting Back strategy, using place value, horizontal and vertical subtracting worksheets.
• Multiplication – Using place value, horizontal or vertical multiplying worksheets.
31. WorksheetWorks – A collection of worksheet generators that provide various quick and easy worksheets when something is needed for K-6 students in a pinch.
• Basic Math Facts – addition, subtraction, multiplication, division and mixed operations.
• Basic Math Facts Activities – Basic math drills, word problem, integer sequences, magic squares, Math Maze, Mystery Number and Basic Operations bingo.
32. Xtra Mathhttps://home.xtramath.org/ – An online math fact fluency program that helps students develop quick recall and automaticity of their basic math facts. Students with a strong foundation of basic math facts will have an easier time when they begin to tackle more advanced math, like fractions or algebra.
33. 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.”