Here are the step-by-step solutions for each problem on the worksheet.
Problem 1
Pattern: $\star, \heartsuit, \checkmark, \uparrow$
The pattern repeats every
4 figures. To find any figure, we divide its position number by 4 and look at the remainder.
* Remainder 1 = 1st figure ($\star$)
* Remainder 2 = 2nd figure ($\heartsuit$)
* Remainder 3 = 3rd figure ($\checkmark$)
* Remainder 0 (no remainder) = 4th figure ($\uparrow$)
a) What is the 21st figure?
Divide 21 by 4:
$21 \div 4 = 5$ with a remainder of
1.
Since the remainder is 1, it is the 1st figure in the pattern.
Answer: $\star$
b) What is the 43rd figure?
Divide 43 by 4:
$43 \div 4 = 10$ with a remainder of
3.
Since the remainder is 3, it is the 3rd figure in the pattern.
Answer: $\checkmark$
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Problem 2
Pattern: $\star, \text{Star-with-smile}, \rightarrow, \wedge$
The pattern repeats every
4 figures.
a) What is the 29th figure?
Divide 29 by 4:
$29 \div 4 = 7$ with a remainder of
1.
Since the remainder is 1, it is the 1st figure in the pattern.
Answer: $\star$
b) What is the 52nd figure?
Divide 52 by 4:
$52 \div 4 = 13$ with a remainder of
0.
Since there is no remainder, it is the last (4th) figure in the pattern.
Answer: $\wedge$
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Problem 3
Pattern: $\blacklozenge, \square, \bigcirc$
The pattern repeats every
3 figures. We divide by 3 to find the position.
* Remainder 1 = 1st figure ($\blacklozenge$)
* Remainder 2 = 2nd figure ($\square$)
* Remainder 0 = 3rd figure ($\bigcirc$)
a) What is the 15th figure?
Divide 15 by 3:
$15 \div 3 = 5$ with a remainder of
0.
It is the last (3rd) figure in the pattern.
Answer: $\bigcirc$
b) What is the 23rd figure?
Divide 23 by 3:
$23 \div 3 = 7$ with a remainder of
2.
It is the 2nd figure in the pattern.
Answer: $\square$
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Problem 4
Pattern: A, G, C, E, L
The pattern repeats every
5 letters. We divide by 5 to find the position.
* Remainder 1 = A
* Remainder 2 = G
* Remainder 3 = C
* Remainder 4 = E
* Remainder 0 = L
a) What is the 28th letter?
Divide 28 by 5:
$28 \div 5 = 5$ with a remainder of
3.
The 3rd letter in the pattern is C.
Answer: C
b) What is the 61st letter?
Divide 61 by 5:
$61 \div 5 = 12$ with a remainder of
1.
The 1st letter in the pattern is A.
Answer: A
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Final Answer:
1. a) $\star$ b) $\checkmark$
2. a) $\star$ b) $\wedge$
3. a) $\bigcirc$ b) $\square$
4. a) C b) A
Parent Tip: Review the logic above to help your child master the concept of repeating pattern worksheet 4th.
