6th Grade Math Puzzles - Free Printable

Problem Description:

The task involves solving Newton's Number Puzzle 6A, where each number in the track is made by adding the previous two numbers. The puzzle provides examples and a series of tracks with missing numbers that need to be filled in.

Key Rules:

1. Each number in the track is the sum of the two preceding numbers.
2. The first two numbers in each track are given, and the rest must be calculated based on the rule.

Solution Approach:

We will solve each track step by step using the given rule. Let’s go through each track systematically.

---

#### Track 1:
- Given: `3`, `-5`
- Next number: \( 3 + (-5) = -2 \)
- Next number: \( -5 + (-2) = -7 \)
- Next number: \( -2 + (-7) = -9 \)

Completed Track 1:
`3`, `-5`, `-2`, `-7`, `-9`

---

#### Track 2:
- Given: `0.7`, `0.4`
- Next number: \( 0.7 + 0.4 = 1.1 \)
- Next number: \( 0.4 + 1.1 = 1.5 \)
- Next number: \( 1.1 + 1.5 = 2.6 \)

Completed Track 2:
`0.7`, `0.4`, `1.1`, `1.5`, `2.6`

---

#### Track 3:
- Given: `6`, `-2`
- Next number: \( 6 + (-2) = 4 \)
- Next number: \( -2 + 4 = 2 \)
- Next number: \( 4 + 2 = 6 \)

Completed Track 3:
`6`, `-2`, `4`, `2`, `6`

---

#### Track 4:
- Given: `8`, `-5`
- Next number: \( 8 + (-5) = 3 \)
- Next number: \( -5 + 3 = -2 \)
- Next number: \( 3 + (-2) = 1 \)

Completed Track 4:
`8`, `-5`, `3`, `-2`, `1`

---

#### Track 5:
- Given: `3`, `-4`
- Next number: \( 3 + (-4) = -1 \)
- Next number: \( -4 + (-1) = -5 \)
- Next number: \( -1 + (-5) = -6 \)

Completed Track 5:
`3`, `-4`, `-1`, `-5`, `-6`

---

#### Track 6:
- Given: `1.3`, `0.7`
- Next number: \( 1.3 + 0.7 = 2.0 \)
- Next number: \( 0.7 + 2.0 = 2.7 \)
- Next number: \( 2.0 + 2.7 = 4.7 \)

Completed Track 6:
`1.3`, `0.7`, `2.0`, `2.7`, `4.7`

---

#### Track 7:
- Given: `0.5`, `1.1`
- Next number: \( 0.5 + 1.1 = 1.6 \)
- Next number: \( 1.1 + 1.6 = 2.7 \)
- Next number: \( 1.6 + 2.7 = 4.3 \)

Completed Track 7:
`0.5`, `1.1`, `1.6`, `2.7`, `4.3`

---

#### Track 8:
- Given: `7`, `-3`
- Next number: \( 7 + (-3) = 4 \)
- Next number: \( -3 + 4 = 1 \)
- Next number: \( 4 + 1 = 5 \)

Completed Track 8:
`7`, `-3`, `4`, `1`, `5`

---

#### Track 9:
- Given: `1.3`, `3.4`
- Next number: \( 1.3 + 3.4 = 4.7 \)
- Next number: \( 3.4 + 4.7 = 8.1 \)
- Next number: \( 4.7 + 8.1 = 12.8 \)

Completed Track 9:
`1.3`, `3.4`, `4.7`, `8.1`, `12.8`

---

#### Track 10:
- Given: `-6`, `-9`
- Next number: \( -6 + (-9) = -15 \)
- Next number: \( -9 + (-15) = -24 \)
- Next number: \( -15 + (-24) = -39 \)

Completed Track 10:
`-6`, `-9`, `-15`, `-24`, `-39`

---

#### Track 11:
- Given: `-6`, `-12`
- Next number: \( -6 + (-12) = -18 \)
- Next number: \( -12 + (-18) = -30 \)
- Next number: \( -18 + (-30) = -48 \)

Completed Track 11:
`-6`, `-12`, `-18`, `-30`, `-48`

---

#### Track 12:
- Given: `0.7`, `5`
- Next number: \( 0.7 + 5 = 5.7 \)
- Next number: \( 5 + 5.7 = 10.7 \)
- Next number: \( 5.7 + 10.7 = 16.4 \)

Completed Track 12:
`0.7`, `5`, `5.7`, `10.7`, `16.4`

---

Final Answer:

Each track is completed as follows:

1. `3`, `-5`, `-2`, `-7`, `-9`
2. `0.7`, `0.4`, `1.1`, `1.5`, `2.6`
3. `6`, `-2`, `4`, `2`, `6`
4. `8`, `-5`, `3`, `-2`, `1`
5. `3`, `-4`, `-1`, `-5`, `-6`
6. `1.3`, `0.7`, `2.0`, `2.7`, `4.7`
7. `0.5`, `1.1`, `1.6`, `2.7`, `4.3`
8. `7`, `-3`, `4`, `1`, `5`
9. `1.3`, `3.4`, `4.7`, `8.1`, `12.8`
10. `-6`, `-9`, `-15`, `-24`, `-39`
11. `-6`, `-12`, `-18`, `-30`, `-48`
12. `0.7`, `5`, `5.7`, `10.7`, `16.4`

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \ 3, -5, -2, -7, -9 \\
2. \ 0.7, 0.4, 1.1, 1.5, 2.6 \\
3. \ 6, -2, 4, 2, 6 \\
4. \ 8, -5, 3, -2, 1 \\
5. \ 3, -4, -1, -5, -6 \\
6. \ 1.3, 0.7, 2.0, 2.7, 4.7 \\
7. \ 0.5, 1.1, 1.6, 2.7, 4.3 \\
8. \ 7, -3, 4, 1, 5 \\
9. \ 1.3, 3.4, 4.7, 8.1, 12.8 \\
10. \ -6, -9, -15, -24, -39 \\
11. \ -6, -12, -18, -30, -48 \\
12. \ 0.7, 5, 5.7, 10.7, 16.4 \\
\end{array}
}
\]