Math worksheet for practicing counting in steps of 4, 8, 50, and 100 with interactive exercises.

Problem Analysis:

The image contains a worksheet titled "Counting in Steps of 4, 8, 50, and 100." It consists of several tasks related to counting sequences and identifying patterns. Below is a detailed breakdown and solution for each part of the problem.

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Task 1: Complete the following number sequences

We are given several incomplete number sequences and need to fill in the missing numbers based on the step size (e.g., 4, 8, 50, or 100).

#### Sequence 1:
- Given: \( 4, 16, 20 \)
- Step size: The difference between consecutive terms is \( 4 \).
- Missing term: The next term after 20 is \( 20 + 4 = 24 \).
- Completed sequence: \( 4, 16, 20, 24 \)

#### Sequence 2:
- Given: \( 100, 400, 500 \)
- Step size: The difference between consecutive terms is \( 300 \) (from 100 to 400).
- Missing term: The term before 100 is \( 100 - 300 = -200 \).
- Completed sequence: \( -200, 100, 400, 500 \)

#### Sequence 3:
- Given: \( 150, 200 \)
- Step size: The difference between consecutive terms is \( 50 \).
- Missing terms: The term before 150 is \( 150 - 50 = 100 \), and the term after 200 is \( 200 + 50 = 250 \).
- Completed sequence: \( 100, 150, 200, 250 \)

#### Sequence 4:
- Given: \( 16, 24 \)
- Step size: The difference between consecutive terms is \( 8 \).
- Missing terms: The term before 16 is \( 16 - 8 = 8 \), and the term after 24 is \( 24 + 8 = 32 \).
- Completed sequence: \( 8, 16, 24, 32 \)

#### Sequence 5:
- Given: \( 64, 88, 98 \)
- Step size: The difference between consecutive terms is not consistent. Let's analyze:
- From 64 to 88: \( 88 - 64 = 24 \)
- From 88 to 98: \( 98 - 88 = 10 \)
- This sequence does not follow a single step size. It appears to be irregular.
- Missing term: Since the pattern is irregular, we cannot determine a consistent step size. However, if we assume the next term follows the last difference (\( +10 \)), the next term would be \( 98 + 10 = 108 \).
- Completed sequence: \( 64, 88, 98, 108 \) (with the understanding that the pattern is irregular).

#### Sequence 6:
- Given: \( 400, 450 \)
- Step size: The difference between consecutive terms is \( 50 \).
- Missing terms: The term before 400 is \( 400 - 50 = 350 \), and the term after 450 is \( 450 + 50 = 500 \).
- Completed sequence: \( 350, 400, 450, 500 \)

#### Sequence 7:
- Given: \( 350, 500 \)
- Step size: The difference between consecutive terms is \( 150 \).
- Missing terms: The term before 350 is \( 350 - 150 = 200 \), and the term after 500 is \( 500 + 150 = 650 \).
- Completed sequence: \( 200, 350, 500, 650 \)

#### Sequence 8:
- Given: \( 36, 40 \)
- Step size: The difference between consecutive terms is \( 4 \).
- Missing terms: The term before 36 is \( 36 - 4 = 32 \), and the term after 40 is \( 40 + 4 = 44 \).
- Completed sequence: \( 32, 36, 40, 44 \)

#### Sequence 9:
- Given: \( 85, 80 \)
- Step size: The difference between consecutive terms is \( -5 \).
- Missing terms: The term before 85 is \( 85 - 5 = 80 \), and the term after 80 is \( 80 - 5 = 75 \).
- Completed sequence: \( 90, 85, 80, 75 \)

#### Sequence 10:
- Given: \( 700, 800 \)
- Step size: The difference between consecutive terms is \( 100 \).
- Missing terms: The term before 700 is \( 700 - 100 = 600 \), and the term after 800 is \( 800 + 100 = 900 \).
- Completed sequence: \( 600, 700, 800, 900 \)

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Task 2: Explain the mistake in this number sequence

The given sequence is:
\[ 500, 550, 600, 650, 700, 750, 800, 900, 950, 1000, 1050 \]

#### Analysis:
- The sequence starts with a consistent step size of \( 50 \):
- \( 500 \to 550 \): \( +50 \)
- \( 550 \to 600 \): \( +50 \)
- \( 600 \to 650 \): \( +50 \)
- \( 650 \to 700 \): \( +50 \)
- \( 700 \to 750 \): \( +50 \)
- \( 750 \to 800 \): \( +50 \)
- However, from \( 800 \) to \( 900 \), the step size changes to \( 100 \):
- \( 800 \to 900 \): \( +100 \)
- After \( 900 \), the step size returns to \( 50 \):
- \( 900 \to 950 \): \( +50 \)
- \( 950 \to 1000 \): \( +50 \)
- \( 1000 \to 1050 \): \( +50 \)

#### Mistake:
The inconsistency occurs at the transition from \( 800 \) to \( 900 \). The step size should remain \( 50 \) throughout the sequence. Therefore, the correct term after \( 800 \) should be \( 850 \), not \( 900 \).

#### Corrected sequence:
\[ 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050 \]

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Task 3: Priya drops these cards on the floor and they get muddled up. She wants to make a row of multiples of 8 to help her do her work. Can you find and order the cards she will need?

The given cards are:
\[ 56, 40, 72, 24, 8, 32, 22 \]

#### Analysis:
We need to identify which of these numbers are multiples of 8 and then order them.

- Multiples of 8:
- \( 56 \div 8 = 7 \) (multiple of 8)
- \( 40 \div 8 = 5 \) (multiple of 8)
- \( 72 \div 8 = 9 \) (multiple of 8)
- \( 24 \div 8 = 3 \) (multiple of 8)
- \( 8 \div 8 = 1 \) (multiple of 8)
- \( 32 \div 8 = 4 \) (multiple of 8)
- \( 22 \div 8 = 2.75 \) (not a multiple of 8)

- Valid multiples of 8: \( 56, 40, 72, 24, 8, 32 \)

#### Ordering the multiples of 8:
- Arrange the multiples in ascending order: \( 8, 24, 32, 40, 56, 72 \)

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Task 4: What is Emily’s number?

This task is not fully described in the image. If additional context or details are provided, I can solve it accordingly.

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Final Answers:

1. Completed sequences:
- \( 4, 16, 20, 24 \)
- \( -200, 100, 400, 500 \)
- \( 100, 150, 200, 250 \)
- \( 8, 16, 24, 32 \)
- \( 64, 88, 98, 108 \) (irregular pattern)
- \( 350, 400, 450, 500 \)
- \( 200, 350, 500, 650 \)
- \( 32, 36, 40, 44 \)
- \( 90, 85, 80, 75 \)
- \( 600, 700, 800, 900 \)

2. Mistake in the sequence:
- The term \( 900 \) should be \( 850 \) to maintain a consistent step size of \( 50 \).

3. Ordered multiples of 8:
- \( 8, 24, 32, 40, 56, 72 \)

4. Emily’s number:
- Not solvable without additional context.

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Boxed Final Answer:
\[
\boxed{8, 24, 32, 40, 56, 72}
\]