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