Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
Equal and Balanced
Equal and Balanced
100 pounds = ? pounds
Materials for Book 1
• Eight blue pawns
• Two red cubes, numbered 0-5
• Two red cubes, numbered 5-10
• A laminated balance scale
• Put the other items back in the bag.
5
X = Check:
Lesson 1
What is the value for the blue pawn to balance the scale?
5 5
5 5 5=
8
X = Check: Lesson 1
Use trial and error to solve.
4 + 48 8
4 8 8=
8
X =
Check:
Lesson 1
2
Use trial and error method to solve. 1, 2, 3, etc.
6
14 14=
The blue pawn has a special name, “x”.
10
X = Check: Lesson 1
Please place number cubes facing upward so I can see the numbers when I pass by.
Black triangles are symbols for blue
pawns
9
X = Check:
Lesson 1
2
9 9=7
7 + 29 9
7
X = Check:
Lesson 1
3
7 7=2
2+2 + 37 7
X = Check:
Lesson 1
8
12 12=4
4 + 812 12
4+4+4
X = Check:
Lesson 1
2 4
4 4=1
1 + 1 + 24 4
X = Check:
Lesson 1
8 410
14 14=6
6 + 814 14
10 +4
X = Check:
Lesson 1
4
8 8=4
4 + 48 8
4 + 4
X = Check:
Lesson 1
72 7
14 14=4
4+4+4 + 214 14
7 + 7
X = Check:
Lesson 1
4 10
16 16=6
6+6 + 416 16
6 + 10
X = Check:
Lesson 1
210
18 18=6
6+6 +618 18
6+10+ 2
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
X =
Check:
Lesson 2
The pawn has a special name, “x.” Therefore, the problem
4
12 12=
2x + x = x + 8
8
X =
Check:
Lesson 2
3
10 10=
3x + 1 = x + 7
1 7
X =
Check:
Lesson 2
=
1. 2x = x + 3
3
3
6 6
X =
Check:
Lesson 2
=
2. 3x = x + 4
4
2
6 6
X =
Check:
Lesson 2
=
3. x + 4 = 2x + 3
34
1
5 5
X =
Check:
Lesson 2
=
4. 4x = 2x + 6
6
3
12 12
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
Lesson 3
• Try this one.
• 4x + 2 = 3x + 9
• “Would you like to learn an easier way of getting the answer than by using trial and error?”
Lesson 3
4x + 2 = 3x + 9
2 9
Legal Moves
X = 7
X =
Check:
Lesson 3
7
30 30=
4x + 2 = 3x + 9
2 9
Reset the original equation to check.
Lesson 3
1. 3x + 7 = 4x
Set up
X =
Lesson 3
1. 3x + 7 = 4x
7
Legal Moves
X = 7
Lesson 3
1. 3x + 7 = 4x
7
X = 7
Check: 28 28=
Lesson 3
2. x + 2 +2x = x + 10
Set up
X =
Lesson 3
2. x + 2 +2x = x + 10
2 10
Legal Moves
X = 4
Lesson 3
2. x + 2 +2x = x + 10
2 10
X = 4
Check: 14 14=
Lesson 3
3. x + 3x = x + x + 10
Set up
X =
Lesson 3
3. x + 3x = x + x + 10
10
Legal Moves
X = 5
Lesson 3
3. x + 3x = x + x + 10
10
X = 5
Check: 20 20=
Lesson 3
4. 2x + 3 + 3x = x + 11
Set up
X =
Lesson 3
4. 2x + 3 + 3x = x + 11
10
Legal Moves
X = 2
13
Lesson 3
4. 2x + 3 + 3x = x + 11
10
X = 2
13
Check: 13 13=
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
Lesson 4
1. x + 2x +5 = x + 19
Set up
X =
Lesson 4
1. x + 2x +5 = x + 19
Legal Moves
X = 7
5 10 459
Lesson 4
1. x + 2x +5 = x + 19
X = 7
5 10 459
Check: 26 26=
Lesson 4
2. x + 2x + 14 = 5x + 2
Set up
X =
Lesson 4
2. x + 2x + 14 = 5x + 2
Legal Moves
X = 6
10 2224
Lesson 4
2. x + 2x + 14 = 5x + 2
X = 6
10 2224
Check: 32 32=
Lesson 4
3. x + 4 + 2x = x + 20
Set up
X =
Lesson 4
3. x + 4 + 2x = x + 20
Legal Moves
X = 8
4 641010
Lesson 4
3. x + 4 + 2x = x + 20
X = 8
4 641010Check: 28 28=
Lesson 4
4. x + 2 + 2x = x + 12
Set up
X = 5
Lesson 4
4. x + 2 + 2x = x + 12
Legal Moves
X = 5
2 210
Lesson 4
4. x + 2 + 2x = x + 12
X = 5
2 210Check: 17 17=
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
Lesson 5
1. 4x – 2x + 4 = x + 10
Set up
X =
104
Lesson 5
1. 4x – 2x + 4 = x + 10
Legal Moves
X = 6
64 410
Lesson 5
1. 4x – 2x + 4 = x + 10
X = 6
64 410Check: 16 16=
Lesson 5
2. x + 3x - x = 30
10 10 5 5
X = 10
Check: 30 30=
Lesson 5
3. 8 + 2x + 3 - x = 2x + 1
Set up
X =
18 3
Lesson 5
3. 8 + 2x + 3 - x = 2x + 1
Legal Moves
X =
18 213
10
Lesson 5
3. 8 + 2x + 3 - x = 2x + 1
X =
18 213
10
Check: 21 21=
Lesson 5
4. x + 2x - x + 7 = 4x – x + 2
Set up
X =
27
Lesson 5
4. x + 2x - x + 7 = 4x – x + 2
Legal Moves
X =
2527
5
Lesson 5
4. x + 2x - x + 7 = 4x – x + 2
2527
X = 5
Check: 17 15=
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
Lesson 6
1. 2(x +3) = 10
Set up
X =
1033
Lesson 6
1. 2(x +3) = 10
Legal Moves
X =
433
610
2
Lesson 6
1. 2(x +3) = 10
433
610
X = 2
Check: 10 10=
Lesson 6
2. 2(x +3) = 9 + x
Set up
933
Lesson 6
2. 2(x +3) = 9 + x
Legal Moves
333
69
X = 3
Lesson 6
2. 2(x +3) = 9 + x
333
69
X = 3
Check: 12 12=
Lesson 6
3. 2(2x +1) = 3x + 8
Set up
X =
811
Lesson 6
3. 2(2x +1) = 3x + 8
Legal Moves
X =
611
28
6
Lesson 6
3. 2(2x +1) = 3x + 8
X =
6 616
6 16
6 6 6 28
6
Check: 26 26=
Lesson 6
4. 2(2x + 3) = x + 9
Set up
X =
933
Lesson 6
4. 2(2x + 3) = x + 9
Legal Moves
X =
333
69
1
Lesson 6
4. 2(2x + 3) = x + 9
X =
333
69
1
Check: 10 10=
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error
Lesson 2
Pawn = xLesson 3
Legal moves pawnsLesson 4
Legal moves #sLesson 5
Set-up subtractionLesson 6parentheses
Lesson 7Symbols only
Lesson 1Trial & Error