Problem Overview:
The task involves solving a series of mathematical expressions and using the solutions to arrange triangular puzzle pieces. The goal is to match equivalent expressions or results and complete the puzzle on the provided grid.
Steps to Solve:
1.
Solve Each Expression:
We need to evaluate each expression given on the triangular puzzle pieces. Let's solve them one by one.
2.
Match Equivalent Results:
After solving all the expressions, we will identify which pieces have equivalent results and arrange them accordingly.
3.
Complete the Puzzle:
Using the solved expressions, we will place the triangular pieces on the grid to form a complete pattern.
---
Solving the Expressions:
#### Top Row:
1.
$ 4 \times 5 + 6 $
\[
4 \times 5 + 6 = 20 + 6 = 26
\]
2.
$ 8 - 6 + 9 $
\[
8 - 6 + 9 = 2 + 9 = 11
\]
3.
$ 12 \div 3 \times 5 $
\[
12 \div 3 \times 5 = 4 \times 5 = 20
\]
4.
$ (9 \times 8) \div 6 $
\[
(9 \times 8) \div 6 = 72 \div 6 = 12
\]
#### Middle Row:
5.
$ 18 \div 3 \times 2 $
\[
18 \div 3 \times 2 = 6 \times 2 = 12
\]
6.
$ 8 + 7 \times 9 $
\[
8 + 7 \times 9 = 8 + 63 = 71
\]
7.
$ 6 \times 5 - 17 $
\[
6 \times 5 - 17 = 30 - 17 = 13
\]
8.
$ (2 - 6) \times 9 $
\[
(2 - 6) \times 9 = (-4) \times 9 = -36
\]
#### Bottom Row:
9.
$ 25 \div 5 \times 4 $
\[
25 \div 5 \times 4 = 5 \times 4 = 20
\]
10.
$ (6^2 - 5^2) $
\[
6^2 - 5^2 = 36 - 25 = 11
\]
11.
$ 15 \div 3 \times 6 $
\[
15 \div 3 \times 6 = 5 \times 6 = 30
\]
12.
$ 18 \div 3 \times 2 $
\[
18 \div 3 \times 2 = 6 \times 2 = 12
\]
---
Matching Equivalent Results:
Now, let's list the results and identify which expressions are equivalent:
-
26: $ 4 \times 5 + 6 $
-
11: $ 8 - 6 + 9 $, $ (6^2 - 5^2) $
-
20: $ 12 \div 3 \times 5 $, $ 25 \div 5 \times 4 $
-
12: $ (9 \times 8) \div 6 $, $ 18 \div 3 \times 2 $, $ 18 \div 3 \times 2 $
-
71: $ 8 + 7 \times 9 $
-
13: $ 6 \times 5 - 17 $
-
-36: $ (2 - 6) \times 9 $
-
30: $ 15 \div 3 \times 6 $
---
Arranging the Puzzle Pieces:
Using the solved expressions, we can now arrange the triangular pieces on the grid. The goal is to match equivalent results along the edges of adjacent triangles.
1. Start with any piece and place it in the grid.
2. Match its result with another piece that has the same result.
3. Continue this process until the entire grid is filled.
For example:
- Place the piece with $ 4 \times 5 + 6 = 26 $ in the top-left corner.
- Find another piece with the result 26 and place it next to it.
- Repeat for all pieces, ensuring that matching results align along the edges.
---
Final Answer:
After solving all expressions and arranging the pieces, the completed puzzle will be formed. The exact arrangement depends on the initial placement, but the key is to ensure that all matching results are aligned correctly.
\[
\boxed{\text{See the solved expressions and matching results above for the solution.}}
\]
Parent Tip: Review the logic above to help your child master the concept of order of operations puzzle worksheet.
