Simplifying Expressions – Adding – Magic Squares Worksheets increase in difficulty and are in a variety of sizes/formats.

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9𝑎 2𝑎 7𝑎 4𝑎 6𝑎 8𝑎 5𝑎 10𝑎 3𝑎 Rows, columns & diagonals all sum to the same value!

1 A B C 8𝑎 𝑎 6𝑎 9𝑎 5𝑥 9𝑥 13𝑥 11𝑥 −2𝑡 5𝑡 𝑡 D E F 𝑐 7𝑐 −3𝑐 5𝑑 2𝑑 −𝑑 6.5𝑑 In each square, the rows, columns and diagonals all total the same MAGIC expression! Can you complete the squares? A B C 8𝑎 𝑎 6𝑎 9𝑎 5𝑥 9𝑥 13𝑥 11𝑥 −2𝑡 5𝑡 𝑡 MAGIC Exp. = 15𝑎 MAGIC Exp. = MAGIC Exp. = 3𝑡 D E F 𝑐 7𝑐 −3𝑐 5𝑑 2𝑑 −𝑑 6.5𝑑 𝑎+8𝑏 𝑎+5𝑏 𝑎+9𝑏 𝑎+2𝑏 MAGIC Exp. = 3𝑐 MAGIC Exp. = MAGIC Exp. = G H 𝑑−5𝑒 𝑑−4𝑒 𝑑+4𝑒 𝑑+𝑒 𝑑+2𝑒 𝑑−𝑒 𝑑−3𝑒 𝑑+7𝑒 𝑑+8𝑒 𝑑−6𝑒 5𝑎−3𝑏 4𝑎−2𝑏 9𝑏−7𝑎 4𝑏−2𝑎 7𝑎−5𝑏 8𝑏−6𝑎 3𝑎−𝑏 8𝑎−6𝑏 6𝑏−4𝑎 1 MAGIC Exp. = MAGIC Exp. =

2 A B C D E F In each grid, the rows, columns and diagonals all total the same MAGIC expression! Can you complete them? A B 𝑎+𝑏 𝑎 𝑎−2𝑏 3𝑑−𝑐 2𝑐 5𝑐−3𝑑 2𝑑 MAGIC Exp. = 3𝑎+3𝑏 MAGIC Exp. = C D 7+4𝑥−6𝑦 3−2𝑦 8+5𝑥−7𝑦 1−2𝑥 −5.5𝑠 −2𝑡−5𝑠 10𝑡−8𝑠 MAGIC Exp. = MAGIC Exp. = 6𝑡−18𝑠 7𝑖+6𝑗−5𝑘 6𝑖+5𝑗−4𝑘 6𝑘−4𝑖−5𝑗 4𝑖+3𝑗−2𝑘 4𝑘−2𝑖−3𝑗 3𝑘−𝑖−2𝑗 𝑖+𝑘 5𝑖+4𝑗−3𝑘 8𝑘−6𝑖−7𝑗 E MAGIC Expression = 4𝑎−2𝑏−2𝑐 11𝑎−9𝑏+5𝑐 9𝑎−7𝑏+3𝑐 6𝑎−4𝑏 5𝑏−3𝑎−9𝑐 10𝑎−8𝑏+4𝑐 𝑎+𝑏−5𝑐 5𝑎−3𝑏−𝑐 4𝑏−2𝑎−8𝑐 F 2 MAGIC Expression =

Answers 1 A B C 8𝑎 𝑎 6𝑎 3𝑎 5𝑎 7𝑎 4𝑎 9𝑎 2𝑎 7𝑥 5𝑥 15𝑥 17𝑥 9𝑥 𝑥 3𝑥 13𝑥 In each square, the rows, columns and diagonals all total the same MAGIC expression! Can you complete the squares? A B C 8𝑎 𝑎 6𝑎 3𝑎 5𝑎 7𝑎 4𝑎 9𝑎 2𝑎 7𝑥 5𝑥 15𝑥 17𝑥 9𝑥 𝑥 3𝑥 13𝑥 11𝑥 −2𝑡 5𝑡 3𝑡 𝑡 −𝑡 2𝑡 −3𝑡 4𝑡 MAGIC Exp. = 15𝑎 MAGIC Exp. = 27𝑥 MAGIC Exp. = 3𝑡 D E F Answers 3𝑐 5𝑐 −5𝑐 −7𝑐 𝑐 9𝑐 7𝑐 −3𝑐 −𝑐 −2.5𝑑 8𝑑 0.5𝑑 5𝑑 2𝑑 −𝑑 3.5𝑑 −4𝑑 6.5𝑑 𝑎+8𝑏 𝑎+𝑏 𝑎+6𝑏 𝑎+3𝑏 𝑎+5𝑏 𝑎+7𝑏 𝑎+4𝑏 𝑎+9𝑏 𝑎+2𝑏 MAGIC Exp. = 3𝑐 MAGIC Exp. = 6𝑑 MAGIC Exp. = 3𝑎+15𝑏 G H 𝑑+9𝑒 𝑑−5𝑒 𝑑−4𝑒 𝑑+6𝑒 𝑑−2𝑒 𝑑+4𝑒 𝑑+3𝑒 𝑑+𝑒 𝑑+2𝑒 𝑑 𝑑−𝑒 𝑑+5𝑒 𝑑−3𝑒 𝑑+7𝑒 𝑑+8𝑒 𝑑−6𝑒 5𝑎−3𝑏 2𝑏 4𝑎−2𝑏 9𝑏−7𝑎 7𝑏−5𝑎 2𝑎 4𝑏−2𝑎 7𝑎−5𝑏 8𝑏−6𝑎 3𝑎−𝑏 3𝑏−𝑎 6𝑎−4𝑏 8𝑎−6𝑏 5𝑏−3𝑎 𝑎+𝑏 6𝑏−4𝑎 1 MAGIC Exp. = 4𝑑+6𝑒 MAGIC Exp. = 2𝑎+6𝑏

Answers 2 A B C D E F In each grid, the rows, columns and diagonals all total the same MAGIC expression! Can you complete them? A B 𝑎+4𝑏 𝑎−3𝑏 𝑎+2𝑏 𝑎−𝑏 𝑎+𝑏 𝑎+3𝑏 𝑎 𝑎+5𝑏 𝑎−2𝑏 3𝑐−𝑑 4𝑐−2𝑑 3𝑑−𝑐 4𝑑−2𝑐 2𝑐 6𝑐−4𝑑 5𝑐−3𝑑 2𝑑 𝑐+𝑑 MAGIC Exp. = 3𝑎+3𝑏 MAGIC Exp. = 6𝑐 C D 7+4𝑥−6𝑦 𝑦−3𝑥 5+2𝑥−4𝑦 2−𝑥−𝑦 4+𝑥−3𝑦 6+3𝑥−5𝑦 3−2𝑦 8+5𝑥−7𝑦 1−2𝑥 −5.5𝑠 −2𝑡−5𝑠 8𝑡−7.5𝑠 10𝑡−8𝑠 2𝑡−6𝑠 −6𝑡−4𝑠 −4𝑡−4.5𝑠 6𝑡−7𝑠 4𝑡−6.5𝑠 Answers MAGIC Exp. = 12+3𝑥−9𝑦 MAGIC Exp. = 6𝑡−18𝑠 9𝑘−7𝑖−8𝑗 7𝑖+6𝑗−5𝑘 6𝑖+5𝑗−4𝑘 6𝑘−4𝑖−5𝑗 4𝑖+3𝑗−2𝑘 4𝑘−2𝑖−3𝑗 3𝑘−𝑖−2𝑗 𝑖+𝑘 2𝑘−𝑗 2𝑖+𝑗 3𝑖+2𝑗−𝑘 5𝑘−3𝑖−4𝑗 5𝑖+4𝑗−3𝑘 7𝑘−5𝑖−6𝑗 8𝑘−6𝑖−7𝑗 8𝑖+7𝑗−6𝑘 E MAGIC Expression = 2𝑖−2𝑗+6𝑘 3𝑏−𝑎−7𝑐 4𝑎−2𝑏−2𝑐 2𝑏−6𝑐 11𝑎−9𝑏+5𝑐 9𝑎−7𝑏+3𝑐 2𝑎−4𝑐 6𝑎−4𝑏 5𝑏−3𝑎−9𝑐 10𝑎−8𝑏+4𝑐 𝑎+𝑏−5𝑐 5𝑎−3𝑏−𝑐 4𝑏−2𝑎−8𝑐 6𝑏−4𝑎−10𝑐 7𝑎−5𝑏+𝑐 3𝑎−𝑏−3𝑐 8𝑎−6𝑏+2𝑐 F 2 MAGIC Expression = 14𝑎−6𝑏−10𝑐

1 1 A B C A B C 8𝑎 𝑎 6𝑎 9𝑎 5𝑥 9𝑥 13𝑥 11𝑥 −2𝑡 5𝑡 𝑡 8𝑎 𝑎 6𝑎 9𝑎 5𝑥 9𝑥 13𝑥 In each square, the rows, columns and diagonals all total the same MAGIC expression! Can you complete the squares? In each square, the rows, columns and diagonals all total the same MAGIC expression! Can you complete the squares? A B C A B C 8𝑎 𝑎 6𝑎 9𝑎 5𝑥 9𝑥 13𝑥 11𝑥 −2𝑡 5𝑡 𝑡 8𝑎 𝑎 6𝑎 9𝑎 5𝑥 9𝑥 13𝑥 11𝑥 −2𝑡 5𝑡 𝑡 MAGIC Exp. = 15𝑎 MAGIC Exp. = MAGIC Exp. = 3𝑡 MAGIC Exp. = 15𝑎 MAGIC Exp. = MAGIC Exp. = 3𝑡 D E F D E F 𝑐 7𝑐 −3𝑐 5𝑑 2𝑑 −𝑑 6.5𝑑 𝑎+8𝑏 𝑎+5𝑏 𝑎+9𝑏 𝑎+2𝑏 𝑐 7𝑐 −3𝑐 5𝑑 2𝑑 −𝑑 6.5𝑑 𝑎+8𝑏 𝑎+5𝑏 𝑎+9𝑏 𝑎+2𝑏 MAGIC Exp. = 3𝑐 MAGIC Exp. = MAGIC Exp. = MAGIC Exp. = 3𝑐 MAGIC Exp. = MAGIC Exp. = G H G H 𝑑−5𝑒 𝑑−4𝑒 𝑑+4𝑒 𝑑+𝑒 𝑑+2𝑒 𝑑−𝑒 𝑑−3𝑒 𝑑+7𝑒 𝑑+8𝑒 𝑑−6𝑒 5𝑎−3𝑏 4𝑎−2𝑏 9𝑏−7𝑎 4𝑏−2𝑎 7𝑎−5𝑏 8𝑏−6𝑎 3𝑎−𝑏 8𝑎−6𝑏 6𝑏−4𝑎 𝑑−5𝑒 𝑑−4𝑒 𝑑+4𝑒 𝑑+𝑒 𝑑+2𝑒 𝑑−𝑒 𝑑−3𝑒 𝑑+7𝑒 𝑑+8𝑒 𝑑−6𝑒 5𝑎−3𝑏 4𝑎−2𝑏 9𝑏−7𝑎 4𝑏−2𝑎 7𝑎−5𝑏 8𝑏−6𝑎 3𝑎−𝑏 8𝑎−6𝑏 6𝑏−4𝑎 1 MAGIC Exp. = MAGIC Exp. = 1 MAGIC Exp. = MAGIC Exp. =

2 2 A B A B C D C D E E F F In each grid, the rows, columns and diagonals all total the same MAGIC expression! Can you complete them? In each grid, the rows, columns and diagonals all total the same MAGIC expression! Can you complete them? A B A B 𝑎+𝑏 𝑎 𝑎−2𝑏 3𝑑−𝑐 2𝑐 5𝑐−3𝑑 2𝑑 𝑎+𝑏 𝑎 𝑎−2𝑏 3𝑑−𝑐 2𝑐 5𝑐−3𝑑 2𝑑 MAGIC Exp. = 3𝑎+3𝑏 MAGIC Exp. = MAGIC Exp. = 3𝑎+3𝑏 MAGIC Exp. = C D C D 7+4𝑥−6𝑦 3−2𝑦 8+5𝑥−7𝑦 1−2𝑥 −5.5𝑠 −2𝑡−5𝑠 10𝑡−8𝑠 7+4𝑥−6𝑦 3−2𝑦 8+5𝑥−7𝑦 1−2𝑥 −5.5𝑠 −2𝑡−5𝑠 10𝑡−8𝑠 MAGIC Exp. = MAGIC Exp. = 6𝑡−18𝑠 MAGIC Exp. = MAGIC Exp. = 6𝑡−18𝑠 7𝑖+6𝑗−5𝑘 6𝑖+5𝑗−4𝑘 6𝑘−4𝑖−5𝑗 4𝑖+3𝑗−2𝑘 4𝑘−2𝑖−3𝑗 3𝑘−𝑖−2𝑗 𝑖+𝑘 5𝑖+4𝑗−3𝑘 8𝑘−6𝑖−7𝑗 7𝑖+6𝑗−5𝑘 6𝑖+5𝑗−4𝑘 6𝑘−4𝑖−5𝑗 4𝑖+3𝑗−2𝑘 4𝑘−2𝑖−3𝑗 3𝑘−𝑖−2𝑗 𝑖+𝑘 5𝑖+4𝑗−3𝑘 8𝑘−6𝑖−7𝑗 E E MAGIC Expression = MAGIC Expression = 4𝑎−2𝑏−2𝑐 11𝑎−9𝑏+5𝑐 9𝑎−7𝑏+3𝑐 6𝑎−4𝑏 5𝑏−3𝑎−9𝑐 10𝑎−8𝑏+4𝑐 𝑎+𝑏−5𝑐 5𝑎−3𝑏−𝑐 4𝑏−2𝑎−8𝑐 4𝑎−2𝑏−2𝑐 11𝑎−9𝑏+5𝑐 9𝑎−7𝑏+3𝑐 6𝑎−4𝑏 5𝑏−3𝑎−9𝑐 10𝑎−8𝑏+4𝑐 𝑎+𝑏−5𝑐 5𝑎−3𝑏−𝑐 4𝑏−2𝑎−8𝑐 F F 2 2 MAGIC Expression = MAGIC Expression =

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