Q1: What is the next number in this pattern? 5, 10, 15, 20, _____ (a) 22 (b) 25 (c) 30 (d) 24
Solution:
Ans: (b) Explanation: This pattern uses the rule "add 5" each time. Starting with 5: 5 + 5 = 10, 10 + 5 = 15, 15 + 5 = 20, and 20 + 5 = 25. This is a pattern counting by fives.
Q2: Which rule describes the pattern? 3, 6, 9, 12, 15 (a) Add 2 (b) Multiply by 2 (c) Add 3 (d) Subtract 3
Solution:
Ans: (c) Explanation: Looking at consecutive numbers: 3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12, and 12 + 3 = 15. The pattern rule is "add 3" to get from one term to the next. This is the three times table.
Q3: What number is missing in this pattern? 40, 35, 30, _____, 20 (a) 28 (b) 27 (c) 25 (d) 22
Solution:
Ans: (c) Explanation: This is a decreasing pattern with the rule "subtract 5." From 40: 40 - 5 = 35, 35 - 5 = 30, 30 - 5 = 25, and 25 - 5 = 20. The missing number is 25.
Ans: (b) Explanation: In option (b), each number is multiplied by 2: \(3 \times 2 = 6\), \(6 \times 2 = 12\), \(12 \times 2 = 24\). Options (a), (c), and (d) all use addition rules, not multiplication.
Q5: What is the 6th term in this pattern? 7, 14, 21, 28, 35, _____ (a) 40 (b) 41 (c) 42 (d) 49
Solution:
Ans: (c) Explanation: The pattern uses the rule "add 7" each time. This is counting by sevens: 7, 14, 21, 28, 35. The next number is \(35 + 7 = 42\).
Q6: Which shape comes next in this repeating pattern? Circle, Square, Triangle, Circle, Square, _____ (a) Circle (b) Square (c) Triangle (d) Rectangle
Solution:
Ans: (c) Explanation: This is a repeating pattern with the core unit: Circle, Square, Triangle. After Circle and Square, the next shape must be Triangle to complete the repeating unit.
Q7: What is the pattern rule for this sequence? 100, 90, 80, 70, 60 (a) Subtract 5 (b) Subtract 10 (c) Add 10 (d) Divide by 10
Solution:
Ans: (b) Explanation: Each term decreases by 10: 100 - 10 = 90, 90 - 10 = 80, 80 - 10 = 70, and 70 - 10 = 60. The pattern rule is "subtract 10."
Q8: If a pattern starts at 4 and uses the rule "add 6," what are the first four numbers? (a) 4, 8, 12, 16 (b) 4, 10, 16, 22 (c) 4, 6, 8, 10 (d) 4, 10, 14, 18
Solution:
Ans: (b) Explanation: Starting with 4 and adding 6 each time: \(4 + 6 = 10\), \(10 + 6 = 16\), \(16 + 6 = 22\). The sequence is 4, 10, 16, 22. Options (a) and (c) add different amounts.
Section B: Fill in the Blanks
Q9: A pattern that uses the same core unit over and over is called a __________ pattern.
Solution:
Ans: repeating Explanation: A repeating pattern is one where the same group of elements or numbers appears again and again in the same order.
Q10: In the pattern 2, 4, 8, 16, 32, each number is found by __________ the previous number by 2.
Solution:
Ans: multiplying Explanation: Each term is created by multiplying the previous term by 2: \(2 \times 2 = 4\), \(4 \times 2 = 8\), \(8 \times 2 = 16\), \(16 \times 2 = 32\).
Q11: The pattern 50, 45, 40, 35, 30 is an example of a __________ pattern because the numbers get smaller.
Solution:
Ans: decreasing Explanation: A decreasing pattern or descending pattern is one where each number becomes smaller than the one before it.
Q12: The instruction that tells you how to get from one number to the next in a pattern is called the pattern __________.
Solution:
Ans: rule Explanation: The pattern rule describes the operation (such as add, subtract, multiply, or divide) used to move from one term to the next.
Q13: In the pattern 1, 4, 7, 10, 13, the pattern rule is add __________.
Solution:
Ans: 3 Explanation: Looking at the differences between consecutive terms: \(4 - 1 = 3\), \(7 - 4 = 3\), \(10 - 7 = 3\), \(13 - 10 = 3\). The pattern rule is add 3.
Q14: If a pattern increases by the same amount each time, it is called an __________ pattern.
Solution:
Ans: increasing (or growing) Explanation: An increasing pattern or growing pattern is one where each number becomes larger, typically by adding or multiplying a constant value.
Section C: Word Problems
Q15: Emma is saving money each week. In Week 1 she has $8, Week 2 she has $12, Week 3 she has $16, and Week 4 she has $20. If this pattern continues, how much money will Emma have in Week 6?
Solution:
Ans: Step 1: Identify the pattern rule. The amounts are 8, 12, 16, 20. Step 2: Find the difference: \(12 - 8 = 4\), \(16 - 12 = 4\), \(20 - 16 = 4\). The rule is add $4 each week. Step 3: Continue the pattern: Week 5: \(20 + 4 = 24\) dollars, Week 6: \(24 + 4 = 28\) dollars. Final Answer: $28
Q16: A library arranges books on shelves in this pattern: 15 books on the first shelf, 20 books on the second shelf, 25 books on the third shelf, and 30 books on the fourth shelf. How many books will be on the seventh shelf if the pattern continues?
Solution:
Ans: Step 1: Identify the pattern: 15, 20, 25, 30. The rule is add 5 books per shelf. Step 2: Continue the pattern: Shelf 5: \(30 + 5 = 35\) books Shelf 6: \(35 + 5 = 40\) books Shelf 7: \(40 + 5 = 45\) books Final Answer: 45 books
Q17: Carlos is making a tile pattern for his art project. He uses 3 tiles in Row 1, 6 tiles in Row 2, 12 tiles in Row 3, and 24 tiles in Row 4. What is the pattern rule, and how many tiles will he need for Row 5?
Solution:
Ans: Step 1: Examine the pattern: 3, 6, 12, 24. Step 2: Find the rule: \(3 \times 2 = 6\), \(6 \times 2 = 12\), \(12 \times 2 = 24\). The rule is multiply by 2. Step 3: Apply to Row 5: \(24 \times 2 = 48\) tiles. Final Answer: 48 tiles
Q18: A farmer plants trees in rows. The first row has 50 trees, the second row has 45 trees, the third row has 40 trees, and the fourth row has 35 trees. If the pattern continues, how many trees will be in the sixth row?
Solution:
Ans: Step 1: Identify the pattern: 50, 45, 40, 35. This is a decreasing pattern. Step 2: Find the rule: \(50 - 45 = 5\), \(45 - 40 = 5\), \(40 - 35 = 5\). The rule is subtract 5 trees per row. Step 3: Continue the pattern: Row 5: \(35 - 5 = 30\) trees Row 6: \(30 - 5 = 25\) trees Final Answer: 25 trees
Q19: Maya is creating a bead pattern with colors: Red, Blue, Green, Red, Blue, Green, Red, Blue, Green. What color will the 15th bead be?
Solution:
Ans: Step 1: Identify the repeating pattern core: Red, Blue, Green (3 beads repeat). Step 2: Divide the position by the pattern length: \(15 \div 3 = 5\) with remainder 0. Step 3: A remainder of 0 means the pattern completes exactly, so the 15th bead is the last color in the core pattern: Green. Final Answer: Green
Q20: A school is planning field trips. They took 120 students in January, 110 students in February, 100 students in March, and 90 students in April. If this pattern continues, how many students will go on the field trip in June?
Solution:
Ans: Step 1: Identify the pattern: 120, 110, 100, 90. The rule is subtract 10 students each month. Step 2: Continue the pattern: May: \(90 - 10 = 80\) students June: \(80 - 10 = 70\) students Final Answer: 70 students
The document Worksheet (with Solutions): Math Patterns is a part of the Grade 4 Course Math Grade 4.
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