Making Algebra Play

Hands – on Algebra Lesson 1: Trial and Error Lesson 2: Special name for blue pawn Lesson 3: Legal move with “x” Lesson 4: Legal move with cubes Lesson 5: Subtraction of “x” in setup Lesson 6: Distributive property Lesson 7: Pictorial Lesson 8: Introduce * Lesson 9: White and Blue are opposite

Hands – on Algebra Lesson 10: New Legal Move with Zero Lesson 11: Adding Zero pairs Lesson 12: Adding same value Lesson 13: Remove number cubes first Lesson 14: Add Zero Pairs to Subtract Lesson 15: Recognize opposite of x as "star" Lesson 16: Pictorial Lesson 17: Adding and Subtracting Positive and Nagative Numbers Lesson 18: Using Green Cubes

Lesson 1: Solve by trial and error Both sides of a balance must equal. So what is the value of the blue pawn? 5 5

Lesson 1: Solve by trial and error x = 5 Check 5 = 5 5 5 The check step is required!!!

Lesson 1: Solve by trial and error Both sides of a balance must equal. So what is the value of each blue pawn? 8 4 4

Lesson 1: Solve by trial and error x = 4 Check 4 + 4 = 8 8 = 8 8 4 4 The check step is required!!!

Lesson 1: Your Turn Both sides of a balance must equal. So what is the value of each blue pawn? 2 8 6 6 6

The check step is required!!! Lesson 1: Your Turn X = 6 Check 6 + 6 + 2 = 8 + 6 14 = 14 2 8 6 6 6 The check step is required!!!

The check step is required!!! Lesson 1: Worksheet X = 5 Check 5 + 5 = 10 10 = 10 10 The check step is required!!!

The check step is required!!! Lesson 1: Worksheet X = 7 Check 7 + 2 = 9 9 = 9 2 9 7 The check step is required!!!

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Special name for blue pawn – “x” Lesson #2 Special name for blue pawn – “x”

Lesson 2: Special name for blue pawn “x” 2 x + x = x + 8 X = 4 Check 4 + 4 + 4 = 4 + 8 12 = 12 8 The check step is required!!!

Lesson 2: Special name for blue pawn “x” 3 x + 1 = x + 7 X = 3 Check 3 + 3 + 3 + 1 = 3 + 7 10 = 10 1 7 The check step is required!!!

The check step is required!!! Lesson 2: Your turn 4 x = 3x + 5 X = 5 Check 5 + 5 + 5 + 5 = 5 + 5 + 5 + 5 20 = 20 5 The check step is required!!!

The check step is required!!! Lesson 2: Worksheet 2 x = x + 3 X = 3 Check 2 (3) = 3 + 3 6 = 6 3 The check step is required!!!

The check step is required!!! Lesson 2: Worksheet 3 x = x + 4 X = 2 Check 3 (2) = 2 + 4 6 = 6 4 The check step is required!!!

The check step is required!!! Lesson 2: Worksheet x + 4 = 2x + 3 X = 1 Check 1 + 4 = 2(1) + 3 1 + 4 = 2 + 3 5 = 5 4 3 The check step is required!!!

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Lesson #3 Legal move with “x”

Lesson 3: Legal move 4 x + 2 = 3x + 9 Would you like to learn an easier way of getting the answer than by using trial and error? 2 9

Lesson 3: Legal move If I remove the same amount from both sides does the balance remain “balanced”? 2 9

Can I continue removing pawns? Lesson 3: Legal move Can I continue removing pawns? 2 9

Can I continue removing pawns? Lesson 3: Legal move Can I continue removing pawns? 2 9

Can I continue removing pawns? Lesson 3: Legal move Can I continue removing pawns? 2 9

Lesson 3: Legal move X = 7 2 9

Lesson 3: Legal move 4 x + 2 = 3x + 9 Check 4(7) + 2 = 3(7) + 9 28 + 2 = 21 + 9 30 = 30 2 9 The check step is required!!! You must go back to the original problem!!!

Lesson 3: Legal move 5 x + 2 = 2x + 14 Check 5(4) + 2 = 2(4) + 14 20 + 2 = 8 + 14 22 = 22 10 4 2 The check step is required!!! You must go back to the original problem!!!

Lesson 3: Legal move 2x + x + 4 = 4x + 1 Check 2(3) + 3 + 4 = 4(3) + 1 6 + 3 + 4 = 12 + 1 13 = 13 1 4 The check step is required!!! You must go back to the original problem!!!

Lesson 3: Legal move 3x + 7 = 4x Check 3(7) + 7 = 4(7) 21 + 7 = 28 28 = 28 7 The check step is required!!! You must go back to the original problem!!!

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Lesson #4 Legal move with cubes

Lesson 4: Legal move with cubes 2x + 4 = 10 X = 3 Check 2( 3) + 4 = 10 6 + 4 = 10 10 = 10 4 6 10

Lesson 4: Legal move with cubes 4x + 5 = 2x + 13 X = 4 Check 4(4) + 5 = 2(4) + 13 16 + 5 = 8 + 13 21 = 21 5 5 10 3

Lesson 4: Legal move with cubes 2x + x + x +2 = 2x +10 X = 4 Check 2(4) + 4 + 4 + 2 = 2(4) + 10 8 + 4 + 4 + 2 = 8 + 10 18 = 18 2 8 10

Lesson 4: Legal move with cubes x + 3x + 3 = x +18 X = 5 Check 5 + 3(5) + 3 = 5 + 18 5 + 15 + 3 = 5 + 18 23 = 23 3 7 10 8

Lesson 4: Legal move with cubes x + 2x + 5 = x + 19 X = 7 Check 7 + 2(7) + 5 = 7 + 19 7 + 14 + 5 = 7 + 19 26 = 26 9 5 10 5

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Subtraction of “x” in the setup. Lesson #5 Subtraction of “x” in the setup.

Lesson 5: Subtraction of “x” in setup 5x - 3x + 2 = x + 5 X = 3 Check 5(3) – 3(3) + 2 = 3 + 5 15 – 9 + 2 = 8 8 = 8 2 3 5

Lesson 5: Subtraction of “x” in setup 2x + x - x + 1 = x + 9 X = 8 Check 2(8) + 8 - 8 + 1 = 8 + 9 16 + 8 – 8 + 1 = 17 17 = 17 1 8 9

Lesson 5: Subtraction of “x” in setup 4 + 3x – 2x + x = x + 5 X = 1 Check 4 + 3(1) – 2(1) + 1 = 1 + 5 4 + 3 – 2 + 1 = 6 7 – 2 + 1 = 6 5 + 1 = 6 6 = 6 4 5 1

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Distributive property Lesson #6 Distributive property

Lesson 6: Distributive property 2(x+4) = x + 12 X = 4 2(4+4) = 4 + 12 2(8) = 4 + 12 16 = 16 4 4 2 6 10 2

Lesson 6: Distributive property 2(2x+1) = 18 X = 4 Check 2(2(4)+1) = 18 2(8+1) = 18 18 = 18 1 1 16 17 18

Lesson 6: Distributive property 2(x+4) = x + 16 X = 8 Check 2(8+4) = 8 + 16 2(12) = 24 24 = 24 4 12 8 16 4

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Lesson #7 Pictorial

Lesson 7: Pictorial 4x + 3 = 3x + 9 x x x x x x x X = 6 Check 4(6) + 3 = 3(6) + 9 24 + 3 = 18 + 9 27 = 27 6 3 9

Lesson 7: Pictorial 4x + 3 = 3x + 9 X = 6 Check 4(6) + 3 = 3(6) + 9 24 + 3 = 18 + 9 27 = 27 6 3 9

Lesson # 8 Introduce *

Lesson 8: Introducing 2(3 +1) = 2 + 10 X = 2 Check 2(2+3) = 2 + 8 2(3 +1) = 2 + 10 X = 2 Check 2(2+3) = 2 + 8 2(5) = 2 + 8 10 = 10 3 3 5 2 8

Lesson 8: Introduce * 2(3* + 1) = 2* + 10 *=2 2(3(2) +1) = 2(2) +10 2(7)= 4 + 10 14 = 14

Lesson 8: Introduce * *=4 5* - 2* = * + 8 5(4) – 2(4)= 4 + 8 20 - 8 = 12 12=12

Lesson 8: Introduce * 3 + 2* = 2* - * + 4 4 1 3 X=1 3+ 2(1) = 2(1) -1 +4 3+2 =2-1+4 5=1+4 5=5

Lesson 8 Worksheet

Lesson 9: White and Blue are Opposites Evaluate Expressions

Lesson 9: x and * X + * = 0

*=4, evaluate: 3* + x - * + 1 Lesson 9: x and * X=2, evaluate: 2x + * x + * x + 5 *=4, evaluate: 3* + x - * + 1

Lesson # 10 New Legal Move with Zero Pairs

Lesson 10: Legal Move with Zero Pairs 3x + * = x + 4 X=4, *= -4 3(4) + -4 = 4 + 4 8 = 8 4

Lesson 10: Legal Move with Zero Pairs 2x + * + x = x + 5 X=5, *= -5 2(5) + -5 + 5 = 5 + 5 10 + 0 = 10 10 = 10 5

Lesson 10: Legal Move with Zero Pairs 4x + * + 1= 2x + 5 X=4, *=-4 4(4)+ -4 +1 = 2(4) + 5 16 + -3 = 8+5 13=13 1 4 5 1

Lesson 10 Worksheet

Lesson # 11 Adding Zero Pairs to Solve Equations

Lesson #11: Adding Zero Pairs 2x = * + 6 X=2, * = -2 2(2) = -2 + 6 4=4 6

Lesson #11: Adding Zero Pairs 3x = * + 4 X=1, * = -1 3(1) = -1 + 4 3=3 4

Lesson 11: Adding Zero Pairs 3x = 2* + 15 X=3, * = -3 3(3) = 2 (-3) + 15 9 = -6 + 15 9 = 9 10 5

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Lesson # 12 Adding the same value to both sides

Lesson #12: Adding Same Value 2x = * + 6 X=2, * = -2 2(2) = -2 + 6 4=4 6

Lesson #12: Adding Same Value 3x = * + 4 X=1, * = -1 3(1) = -1 + 4 3=3 4

Lesson #12: Adding Same Value 3x = 2* + 15 X=3, * = -3 3(3) = 2 (-3) + 15 9 = -6 + 15 9 = 9 10 5

Lesson # 13 Remove Number Cubes First

Lesson 13: Move Number Cubes 1st 2x + * + 3 = 2* + 15 X=4, *=-4 2(4) + -4 +3 = 2(-4) +15 4 + 3 = -8 + 15 7=7 3 7 10 5

Lesson 13: Move Number Cubes 1st 3 * + x + 5 = * + 12 * + 12 = 2x + 6

Lesson # 14 Add Zero Pairs in order to Subtract in Setup

Lesson 14: Add zero pair to subtract star 2x - * = 12 X=4, *=-4 2(4) – (-4) = 12 8 + 4 = 12 12=12 10 2

Lesson 14: Add zero pairs to subtract star X - 3 * + 2 = 8 – 2x X= 1 *= -1 1- 3(-1) + 2 = 8 – 2 (1) 1- (-3) +2 = 8 -2 4 + 2 = 6 6=6 2 6 8

Lesson 14: 5x + 3 = 2x + 24 10 1 4 10 3

Lesson # 15 Recognize opposite of x and *

Lesson 15: Opposite of x and * 2x + (-x) + 3 = 2(-x) + 15 X=4, - x= -4 2(4) + -4 + 3 = 2(-4) + 15 8 + -1 = -8 + 15 7=7 3 10 2 5

Lesson 15: Opposite of x and * 2 ( -x) + (-x) = 10 + (-x) X=-5, -x=5 2(5) + 5 = 10 + 5 10 + 5 = 15 15=15 10

Lesson 15: Opposite of x and * 3(-x) – (-x) + 5 = 8 + (-x) -x=3, x=-3 3(3) – (3)+5 = 8 + (3) 9 – 3 + 5 = 11 6+5 = 11 11=11 5 3 8

Lesson 15 Worksheets

Lesson 16: Pictorial

Lesson 16: Pictorial 2x = * + 6 2x + * + 3 = 2* + 15

Lesson 16: Pictorial X - 3* + 2 = 8 – 2x 2x = * + 6

Lesson 17: Adding and Subtracting Positive and Negative Numbers

Lesson 17: Adding and Subtracting Positive and Negative Numbers (+2) + (-2) = 0 2 2 -10 -5 0 5 10

Lesson 17: Adding and Subtracting Positive and Negative Numbers (-3) + (-5) = -8 3 5 8 -10 -5 0 5 10

Lesson 17: Adding and Subtracting Positive and Negative Numbers (-3) + (+5) (-3) + (+5) = +2 3 2 5 3 -10 -5 0 5 10

Lesson 17: Adding and Subtracting Positive and Negative Numbers (-3) + (+5) = +2 3 5 2 -10 -5 0 5 10

Lesson 17: Adding and Subtracting Positive and Negative Numbers (-10) – (-5) (-10) – (-5) = -5 5 10 -10 -5 0 5 10

Lesson 17: Adding and Subtracting Positive and Negative Numbers (+5) – (-3) (+5) – (-3) = +8 5 3 3 -10 -5 0 5 10

Lesson 18: Simple Algebraic Equations using Green Cubes X + 3 = -5 X= -8 -8 + 3 = -5 -5 = -5 3 3 5 3 -10 -5 0 5 10

Lesson 18: Simple Algebraic Equations using Green Cubes 2x + (-5) = -7 X= -1 2(-1) + (-5) = -7 -2 + -5 = -7 -7= -7 5 7 2 -10 -5 0 5 10

Lesson 18: Simple Algebraic Equations using Green Cubes * - 3 = -6 * = -3 -3 -3 = -6 -6 = -6 3 3 3 6

Lesson 18: Simple Algebraic Equations using Green Cubes 3* - (-2) = 8 *=2 3(2) – (-2) = 8 6- (-2) = 8 8=8 2 2 6 8