FOLDABLE Solving Systems of Equations By Mrs Math * This foldable takes a while so not do it all in one class period. The students will burn out halfway through it. So break it up into two or three class periods.

Materials needed (per student) Construction paper or cardstock Graph Sheet (Slide 22) Ruler Scissors 2 or 3 markers

Construction Paper Fold

INSIDE  Draw  Draw Fold

INSIDE  Cut  Cut Stop at Fold

Graph Paper  Cut  Cut Fold  Cut  Cut

On top is construction paper Graph sheet is inside FOLD Staple Staple Staple FOLD

FRONT No Solutions Infinite Solutions 1 solution (x, y) Staple Staple

{ { { Inside TOP Solve by graphing: Solve by graphing: y = -1/3x + 3 y = 2x – 4 y = -4/3x + 5 y = -4/3x y = 3x – 1 Bottom

{ LEFT Top y = -1/3x + 3 y = 2x – 4 Bottom Solve by graphing: Solution: (3, 2)

{ MIDDLE Top y = -4/3x + 5 y = -4/3x Bottom Solve by graphing: No Solution

Solve by graphing: { Top y = 3x – 1 RIGHT Bottom Infinite Solutions

{ { { Inside TOP Fold Inside Bottom Solve by substitution: -5x + 5y = -5 x = -y + 5 2x – 4y = 1 x = 2y + 3 4x – 2y = -10 y = 2x + 5 Fold Inside Bottom

Solve by substitution: Top { -5x + 5y = -5 x = -y + 5 LEFT Fold -5(-y + 5) + 5y = -5 5y – 25 + 5y = -5 Bottom 10y – 25 = -5 +25 +25 10y = 20 10 10 y = 2 x = -y + 5 x = -(2) + 5 Solution: (3, 2) x, y x = -2 + 5 x = 3

Solve by substitution: { Top 2x – 4y = 1 x = 2y + 3 MIDDLE Fold 2(2y + 3) – 4y = 1 Bottom 4y + 6 – 4y = 1 0y + 6 = 1 6 = 1 Is this a true? NO No Solutions

Solve by substitution: { Top RIGHT 4x – 2y = -10 y = 2x + 5 Fold 4x – 2(2x + 5) = -10 Bottom 4x – 4x – 10 = -10 0x – 10 = -10 -10 = -10 Is this a true? YES Infinite Solutions

{ { { Inside TOP Fold Inside Bottom 5x + 2y = 12 -5x + 4y = -66 Solve by Elimination: Solve by Elimination: Solve by Elimination: { { 5x + 2y = 12 -5x + 4y = -66 { 3x – 5y = -6 -9x + 15y = 13 2x – 4y = 6 -3x + 6y = -9 Fold Inside Bottom

{ LEFT Top Bottom 5x + 2y = 12 -5x + 4y = -66 + Fold 6y = -54 6 6 Solve by Elimination: Top { 5x + 2y = 12 LEFT -5x + 4y = -66 + Fold 6y = -54 Bottom 6 6 y = -9 5x + 2y = 12 5x + 2(-9) = 12 5x - 18 = 12 +18 +18 5x = 30 Solution: (6, -9) 5 5 x, y x = 6

{ MIDDLE Top Bottom ( ) 3 3x – 5y = -6 -9x + 15y = 13 Fold 9x – 15y Solve by Elimination: Top { MIDDLE ( ) 3 3x – 5y = -6 -9x + 15y = 13 Fold 9x – 15y = -18 Bottom + -9x + 15y = 13 = -5 Is this true? No! No Solutions

{ RIGHT Top Bottom ( )3 2x – 4y = 6 -3x + 6y = -9 ( )2 Fold 6x – 12y Solve by Elimination: Top { RIGHT ( )3 2x – 4y = 6 -3x + 6y = -9 ( )2 Fold 6x – 12y = 18 Bottom + -6x + 12y = -18 = 0 Is this true? Yes! Infinite Solutions

Back SIDE F OL D NAME Period Date Subject

Helpful Information About Foldables Once the foldable is done you must have the students USE it on a follow-up activity such as a short quiz, BINGO game, or on a set of guided practice problems or students will NEVER use it. For grading purposes have students paper punch foldables to keep in their binder, put in their portfolio, or to hand in for a note-check. When making foldables its best to hand students just 2 or 3 different colored markers to make color changes to emphasize words or concepts but not so many that they get distracted. Always have at least one or two foldables cut out and ready for students who make mistakes. If a student is absent the day of the foldable then just print out the relevant Powerpoint slides for them to include in their notebook. (SLIDES 10 – 12, SLIDES 14 – 16, and SLIDES 18- 20)