Teachers Resources and Additional Activities for RF10 (solving systems of linear equations):

When Will They Be Equal?

• Class Starters - A collection of thinking problems relating to systems of equations that could be used as a class starter or warm-up question. Each question is a separate slide on a Google Slides document.

• Desmos Activity: Racing Cars (English, French) - Students predict where a pair of cars will meet by using tables, graphs, and/or equations.

• Desmos Activity: Solutions to Systems of Linear Equations (English, French) - Students explore equations and graphs of linear functions to conclude that the point of intersection of a system of linear equations represents the solution to the system.

• Venn Diagram Puzzles - Use an image of a Venn Diagram to visualize the solution to a system of equations. A variety of puzzles. Here is also a Venn Diagram puzzle practice handout for students to complete either virtually or printed off.  (From Michael Pershan's Blog - Teaching With Problems).

• Desmos Activity: Make Them Balance (English, French)- This lesson uses hangers to explore solutions to equations and systems of equations while making connections to a graphical representation.

• System of Equations Puzzles (Desmos Activity, Google Slide Deck) - An introduction to solving systems of linear equations where students solve puzzles that represent systems of equations pictorially.  They could be used as an introduction to systems using puzzles prior to adding abstracting with symbols.

• Stacking Cups - A 3 Act Task where students stack two different sized cups of different heights.  Where will they be the same height? 

• Tie Knots in Rope - Students tie knots in a rope, and measure the length of the rope each time, then repeat with a rope of a different thickness in order to collect data.  Studetns model this relationship symbolically and graphically, then make predictions about the number of knots needed in order to make the ropes the same length. (From Alex Overwijk - Slam Dunk Math).  Also see Knot Again! from Jon Orr at mrorr-isageek.com.

• Linking Cube Towers - Students create towers of multi-link cubes.  The roll one die to determine the starting number and another die to determine how many cubes the tower grows each step.  Then they make a second tower... are the towers ever the same height at the same step?  Mary shares a great handout that goes along with this activity. Additional details from Mary Bourassa.

Solving Systems of Linear Equations Graphically

• Desmos Activity: Graphing Systems of Equations Introduction - Students explore graphing systems of equations in order to find the point of intersection, from equations in y = mx + b form. 

• Desmos Activity: Systems of Two Linear Equations (English, French) - Students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution".  This activity uses the sum and product of numbers, and could set-the-stage for why there is only one factor pair that can be used when factoring expressions in the form a x^2 + bx + c or x^2 + bx + c in future units of study.

• Desmos Activity: Whack - A - Mole - Students graph systems of equations in y = mx + b form, then determine which mole is whacked using the point of intersection.

• Desmos Activity: Line Zapper (English, French) - In this lesson, students "zap" lines by identifying their solutions. Students begin by zapping individual lines and then turn their attention to systems of linear equations where a single "zap" aimed at a point of intersection will capture multiple lines at once. 

• Solving Systems of Equations Graphically handout -  8 problems for students to practice graphing two linear systems to find the point of intersection.

• Pixel Art (Eng, Fre) -  *added Feb2025*  Solving Systems of Equations Graphically

• Linear Equations Card Sort - Each group of students gets a stack of cards with 8 graphs, 8 systems of equations (in standard form) and 8 intersection points. Groups put each correct combination of graph-system-intersection together. Cards are in random order so that students can cut them out.

• Piling Up Systems of Linear Equations - Students use a scale to weight a number of different items so that students can figure out how much each item weighs.  For example, The weight of 4 bottles of glue and 5 glue sticks is 679 grams.  The weight of 3 bottles of glue and 12 glue sticks is 680 grams.  Knowing this, students can figure out how much each item weighs. From Kyle Pearce.

Solving Systems of Equations Pictorally and Algebraically

• Solving Systems of Linear Equations with Manipulatives - An introductory lesson on solving systems of linear equations using manipulatives.  Students worked in groups of 2 or 3 and used manipulatives to model problems (From Mary Bourassa Blog - M^3 (Making Math Meaningful).

• Solving Systems by Elimination - This activity demonstrates how the elimination method for solving systems cam be represented pictorially. (From Mary Bourassa Blog - M^3 (Making Math Meaningful)

• System of Equations Anchor Chart - Anchor Charts are most effective when they are co-created with students.  This example from Katrina Newell can be used to support student decision making around selection of solving strategy (graphing, substitution, elimination). 

• Linear Equations Sticky Note -  A systems of linear equations problem with part of the problem hidden under a sticky note. What’s under the sticky note? What could equations 1 and 2 be? What else? How do you know?  (Shared by Chris Hunter).

• System of Equations Dot-to-Dot - A self-checking activity where students solve 18 systems of equations. Each solution gives them an (x, y) coordinate. Connect these points together to create a picture.

• Evaluating Energy Efficiency Claims -  A 20 Watt CFL light bulb package states that you will have $44 in energy savings by using this light bulb compared to a 75 Watt incandescent light bulb.  Is that $44 claim reasonable or bogus when you compare it against a bulb that uses 75 watts? How much does a kilowatt-hour cost in your town? And what exactly is a kilowatt-hour? What would happen if you switched every incandescent bulb in your house/school/neighborhood to an energy efficient bulb? (From Geoff Krall's Blog -  Emergent Math)

• Paper Bag Mystery - Students are given a mystery bag, stapled shut, with two different types of objects inside. Students record the weight and number of items of a sealed paper bag. Using this information to create and solve a system of equations. The answers will tell students how many of two different types of objects are in the mystery bag. At the end of class, open the bags to check the answers. Students record their work on a record sheet.  This activity was inspired by Mary Bourassa's Candy Lab.

• Systems of Equations Odd One Out Activity - Students are given 8 systems and 9 possible solutions. Students work to discover which of the solutions is the "odd one out".

• Systems of Equations Review Questions - Students can select problems from three different levels of difficulty.

• Desmos Activity: Polygraph (English, French) - A partnered guessing game that is designed to spark vocabulary-rich conversations about systems of linear equations. Students are matched into pairs and assigned Picker and Guesser roles. The Picker selects a card; the Guesser asks yes/no questions for the Picker to answer in order to narrow the field of cards down to one.

• Systems of Equations - One Solution Open Middle problem - Using the integers from -9 to 9 only one time each, create a system of three-equations such that the solution is (1,1).  You could use the same format to ask for 0 solutions, 2 solutions, 3 solutions, or as many solutions as possible.

Unit 3 Cumulative Review

• Systems of Equations Add 'Em Up Activity - *Updated April 2025* In an "Add 'Em Up" activity, students are given a set of problems. When all the problems are complete, the sum (or in this case slope) of their answers should match the number in the center.

• Detention Buy Out - A 3 Act Task where students will consider three "Detention Buy-Out's" that can be paid to their administration in order to avoid serving detention (From Kyle Pearce's Blog - Tap Into Teen Minds).  This task is also available as a  Desmos Activity .

• System of Equations Math Passport Activity - A series of four stations where students work individually, in pairs or small groups to complete the problems at each station. After successfully completing a station, students will get their teacher to "stamp" their passport and then move to the next station.

• System of Equations Escape the Apartment Activity -  This Google Slides virtual "escape room" reviews content from both unit 6 and unit 7. Student travel through rooms in the building "choose your own adventure" style until they find the key to escape.  Share this presentation link with students and provide them with this recording sheet.  When students get to the end, they can retrace their steps looking for a letter hidden in each room. If the letter spells out a word, they know they have not made any mistakes as the moved through the rooms.

• Desmos Activity: Unit Three Systems of Equations Review - Includes verifying solutions to linear systems, solutions on a graph, graphing systems of equations, and solving systems of equations algebraically.

• Unit 3 Student Self-Assessment and Review - Students self-assess their ability to demonstrate the outcomes from Unit 7. Practice questions from the textbook are identified and links to extra practice and review are included.