https://file.aiquickdraw.com/mathbot/file/172910981412533r6ta09.jpg

Daphne's pattern involves beads and sticks. Her first pattern consists of 4 beads and 3 sticks, and she adds the same number of beads and sticks each time. Based on the image, we can analyze the patterns and answer the questions:

1. **Pattern analysis**:
   - Pattern 1: 4 beads and 3 sticks.
   - Pattern 2: 6 beads and 5 sticks.
   - Pattern 3: 8 beads and 7 sticks.

It appears that for each new pattern:
- She adds **2 beads**.
- She adds **2 sticks**.

2. **Finding the number of beads and sticks in the 4th pattern**:
   - Beads in the 4th pattern: 8 beads (from pattern 3) + 2 = **10 beads**.
   - Sticks in the 4th pattern: 7 sticks (from pattern 3) + 2 = **9 sticks**.

### Answers:
a) There are **10 beads** in the 4th pattern.  
b) There are **9 sticks** in the 4th pattern.

Would you like further details or have any questions?

Here are 5 related questions to deepen understanding:
1. How many beads would be in the 5th pattern?
2. How many sticks would be in the 6th pattern?
3. What is the general formula for the number of beads in the nth pattern?
4. What is the general formula for the number of sticks in the nth pattern?
5. If Daphne starts with 5 beads and 4 sticks in the first pattern, how would that change the sequence?

**Tip:** Look for a relationship between the pattern number and the increment of beads and sticks to find general formulas.

Daphne is making a sequence of patterns using beads and sticks. Her first pattern is made up of 4 beads and 3 sticks. She adds the same number of beads and the same number of sticks each time. a) How many beads are there in the 4th pattern? b) How many sticks are there in the 4th pattern?

Learn how to determine the number of beads and sticks in a sequence of patterns. This problem involves recognizing an arithmetic progression where the number of beads and sticks increases by a constant value in each step. Suitable for students in Grades 5-7.

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