Mathematics 10 Linear Relations
Specific Curriculum Outcomes
RF03 Demonstrate an understanding of slope with respect to: rise and run, line segments and lines, rate of change, parallel lines, perpendicular lines.
RF05 Determine the characteristics of the graphs of linear relations, including the: intercepts, slope, domain and range.
RF06 Relate linear relations expressed in: slope–intercept form (y = mx + b), general form (Ax + By + C = 0) and slope–point form (y – y1) = m(x – x1)) to their graphs.
RF07 Determine the equation of a linear relation, given: a graph, a point and the slope, two points and a point and the equation of a parallel or perpendicular line to solve problems. * RF07.06 Determine the equation of the line of best fit from a scatterplot using technology and determine the correlation is a departure from the WNCP curriculum and not in the textbook. Resources for this indicator can be found in the NS Curriculum Companion.
RF03 Demonstrate an understanding of slope with respect to: rise and run, line segments and lines, rate of change, parallel lines, perpendicular lines.
RF05 Determine the characteristics of the graphs of linear relations, including the: intercepts, slope, domain and range.
RF06 Relate linear relations expressed in: slope–intercept form (y = mx + b), general form (Ax + By + C = 0) and slope–point form (y – y1) = m(x – x1)) to their graphs.
RF07 Determine the equation of a linear relation, given: a graph, a point and the slope, two points and a point and the equation of a parallel or perpendicular line to solve problems. * RF07.06 Determine the equation of the line of best fit from a scatterplot using technology and determine the correlation is a departure from the WNCP curriculum and not in the textbook. Resources for this indicator can be found in the NS Curriculum Companion.
Activities

 One Solution, No Solutions, Infinite Solutions from Open Middle  Using Integers (without repeating any number), create equations of the form (__/__)x + __ = __x + (__/__) and fill in the spaces to create the following types of Linear Equations: one solution, no solutions and infinite solutions. As an added challenge see what the smallest integer interval of the numbers used that you can find.
 Creating Squares from wild.math.org  This game is played on a 5x5 piece of dot paper. Take turns claiming a dot. Whoever completes a square first is the winner. You can play against the computer or a friend. Also an opportunity to talk about parallel and perpendicular lines.
 The Crow and the Pitcher from Pam Wilson  A lesson based on an old fable about a crow that wants a drink of water but can't reach the bottom of the glass. Drop marbles in a tall glass to make the water rise. How many marbles will it take to rasie the water level to the top of the glass? Mary Bourasa also wrote a post about this lesson.
 Writing Linear Equations given Two Ordered Pairs from Nora Oswald  Each student is given an index card with a point on it. They find a partner and write the equation of the line that passes through both of their points. Then they find another partner and repeat the process. After a few partners they will realize that no matter what person they match with, the get the same line! Let the students figure out what is going on and tell you about it.


 Infinite Chocolate Bar video  This mindboggling video shows a 4 x 6 chocolate bar cut vertically, horizontally and diagonally into different parts after which one piece of chocolate is removed and put into a cup. The parts are then rearranged in a way that the bar doesn’t look like it’s missing a piece and still has 4 rows and 6 columns. Here is a video using a Geogebra demonstration showing how this works. An nice combination of linear function and area measurement outcomes. Here is a great video from Chris Danielson demonstrating how the trick works.
 Fill 'er Up! from Denis Sheeran  Look at the relationship between the estimated range on a car and the actual distance travelled on the odometer. How do they compare?
 Introducing Linear Equations Barbie Bungee Activity from Julie Reulbach  Have students create a Barbie Bungee Company and determine the number of rubber bands needed for a really exciting barbie bungee.

 Guess the Correlation Game  Silly fun 8bit game where you look at a scatter plot and guess R. With a little practice you can get really good at estimating the correlation just by looking at the scatterplot. Lots of fun.
 Target Practice Game  A game for 2 teams using two differently colored dice, paper, graph paper. On each turn, each team rolls the pair of dice to come up with a set of target points. They then come up with an equation, to hit as many of the target points in the graph of the equation as possible. On each round, you roll the same number of targets as the round number; ex. on round three, three targets. For each target scored, you get the same number of points as the round; ex. If you hit two targets on round three, you score 6 points. Play for at least five rounds. Variations: For variety, allow teams to make any given roll positive or negative. For challenge, include (0,0) as an extra target point in each round.
Desmos Activities
 Marbleslides: Lines from Desmos  In this superawesome and challenging activity, students click Launch to release marbles, which slide down the line, into the first quadrant, through the stars, and down off the bottom of the screen.
 Polygraph: Lines from Desmos  One student picks a line and answers questions and the other student asks yes or no questions to try to determine which line was chosen.
 Match My Graph: Linear Functions from Michael Fenton  Develop your students’ graphing abilities with this multiday series of linear function challenges. Can be done online with Desmos or with pencil and paper. Lots of great resources.
 Regressions on Desmos video from Bob Lochel  Bob Lochel explains how to work with data to find bestfit equations using linear regression in the Desmos online graphing calculator.
 Desmos Math Journey: Representations of Linear Functions from Bob Lochel  Bob uses an innovative way to break an investigation down into a series of Desmos graphs focusing on linear relations. In the activity, students begin using their understanding of linear relations and constant growth to determine missing values in a table. Students continue on to discover the importance of the m and b value in slopeintercept form.
 Balloon Pop using Desmos  I created a little game on Desmos for students to create linear functions to go through as many points as possible. Let me know what you think.
 Desmos Puppy House from Fawn Nguyen  Student create a dog house using linear equations on paper and then in Desmos.
 Desmos Art: Fries  Students draw a picture using straight lines, snap a photo and then try to duplicate the image in Desmos.