ISEE Middle Level Mathematics Achievement Quiz: Number Pattern Rules

What this quiz covers

This quiz focuses on Number Pattern Rules, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level Mathematics Achievement.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Add 4 to the number of flowers in the previous ring. (correct answer)
2. Multiply the number of flowers in the previous ring by 4.
3. Add 5 to the number of flowers in the previous ring.
4. Multiply the previous ring's flower count by 2 and subtract 6.

Explanation: The problem states that each new ring has 4 more flowers than the previous one. This describes an arithmetic sequence with a common difference of 4. The sequence of flowers is 5, 9, 13, 17, ... To get from one term to the next, you simply add 4.

Question 2

1. Add 10 more than the point value of the previous level's reward to the current score. (correct answer)
2. Add 20 to the player's current score after every level.
3. Multiply the player's current score by 1.2 after each level.
4. Add 10 times the number of the completed level to the current score.

Explanation: The sequence of scores is 100, 120, 150, 190, ... The points added are +20, +30, +40, ... Each time, the reward increases by 10. So, to find the new score, you add an amount to the current score that is 10 greater than the amount added for the prior level.

Question 3

1. Subtract 54 from the previous number.
2. Divide the previous number by 3. (correct answer)
3. Take the square root of the previous number.
4. Subtract two-thirds of the previous number.

Explanation: To get from 81 to 27, you can divide by 3. To get from 27 to 9, you can divide by 3. To get from 9 to 3, you can divide by 3. The rule is to divide the previous number by 3. Choice D would work for the first step (81 - 54 = 27), but fails for subsequent steps (27 - 18 = 9, but 9 - 6 = 3, not the pattern continuation).

Question 4

1. Add 4 to the previous number.
2. Multiply the previous number by 2, then add 1. (correct answer)
3. Multiply the previous number by 3, then subtract 2.
4. Multiply the previous number by 2, then subtract 1.

Explanation: To find the rule, check the relationship between consecutive terms. From 3 to 7: (3 × 2) + 1 = 7. From 7 to 15: (7 × 2) + 1 = 15. From 15 to 31: (15 × 2) + 1 = 31. The rule is to multiply the previous number by 2 and then add 1.

Question 5

1. Add 2 each time
2. Multiply by 2 each time
3. Add the two previous numbers (correct answer)
4. Subtract 1 each time

Explanation: This question tests middle school mathematics skills, specifically identifying rules that govern number patterns. Understanding number patterns involves recognizing the rule that consistently applies to each number in a sequence, such as addition, subtraction, multiplication, or division. In this problem, the sequence 2, 3, 5, 8, 13 follows the Fibonacci pattern where each term is the sum of the two previous terms (2+3=5, 3+5=8, 5+8=13). The correct choice, 'Add the two previous numbers,' accurately describes this recursive rule. A common distractor, such as 'Add 2 each time,' fails because the differences between consecutive terms are not constant (they are 1, 2, 3, 5). Teaching strategies include showing students how to check if each term equals the sum of the two preceding terms and introducing them to this famous mathematical sequence. Remind students that some patterns require looking at relationships between multiple previous terms, not just consecutive pairs.

Question 6

1. Multiply by 2 each time
2. Add 4 each time (correct answer)
3. Subtract 4 each time
4. Add 6 each time

Explanation: This question tests middle school mathematics skills, specifically identifying rules that govern number patterns. Understanding number patterns involves recognizing the rule that consistently applies to each number in a sequence, such as addition, subtraction, multiplication, or division. In this problem, the sequence 6, 10, 14, 18, 22 shows that each number increases by 4 (10-6=4, 14-10=4, 18-14=4, 22-18=4). The correct choice, 'Add 4 each time,' accurately reflects the mathematical operation that defines the sequence. A common distractor, such as 'Multiply by 2 each time,' fails because multiplying 6 by 2 would give 12, not 10. Teaching strategies include having students find the difference between consecutive terms and checking their rule against every pair of numbers in the sequence. Remind students to verify their answer by applying the rule to generate the entire sequence from the first number.

Question 7

1. Multiply by 2 each time
2. Add 5 each time (correct answer)
3. Subtract 5 each time
4. Add 4 each time

Explanation: This question tests middle school mathematics skills, specifically identifying rules that govern number patterns. Understanding number patterns involves recognizing the rule that consistently applies to each number in a sequence, such as addition, subtraction, multiplication, or division. In this problem, the sequence of numbers presented follows a specific rule that students must identify from the options provided. The correct choice, 'Add 5 each time,' accurately reflects the mathematical operation that defines the sequence. A common distractor, such as 'Multiply by 2 each time,' fails because it suggests a different operation than the one used in the sequence. Teaching strategies include practicing with different types of sequences and encouraging students to verbalize the rule they identify. Remind students to check their rule against each number in the sequence to ensure consistency.

Question 8

1. Add 5 to the previous number, then double the result.
2. Add a number that doubles each time, starting with 5.
3. Multiply the previous number by 2, then add 1. (correct answer)
4. Multiply the previous number by 3, then subtract 3.

Explanation: The stem specifies that the same two operations are applied each time. Let's test choice C. For 4 to 9: (4 × 2) + 1 = 9. For 9 to 19: (9 × 2) + 1 = 19. For 19 to 39: (19 × 2) + 1 = 39. For 39 to 79: (39 × 2) + 1 = 79. This rule works for the entire sequence. Choice B also describes the pattern correctly (differences are 5, 10, 20, 40), but it does not use the 'same two operations' each time, as the number being added changes.

Question 9

1. Add the two previous numbers to find the next number. (correct answer)
2. Double the previous number and subtract 1.
3. Add 2 to the previous number.
4. Add an increasing odd number to the previous number.

Explanation: This is a Fibonacci-like sequence. Check the rule: 1 + 3 = 4. 3 + 4 = 7. 4 + 7 = 11. 7 + 11 = 18. The rule is to add the two preceding terms to get the next term.

Question 10

1. Multiply the previous peak height by $\frac{1}{2}$. (correct answer)
2. Subtract 64 cm from the previous peak height.
3. Subtract half of the original height from the previous peak height.
4. Divide the original height by the bounce number.

Explanation: The problem describes a geometric decay. The heights are 128, 64, 32, 16, ... Each term is half of the previous term. This is equivalent to multiplying by $\frac{1}{2}$ or dividing by 2. Choice A correctly states this rule.

Question 11

1. Subtract 5 from the previous number.
2. Multiply the previous number by -1 and subtract 31.
3. Add a decreasing positive number to the previous term.
4. Add 5 to the previous number. (correct answer)

Explanation: To find the rule for this arithmetic sequence, find the common difference between consecutive terms. -13 - (-18) = -13 + 18 = 5. -8 - (-13) = -8 + 13 = 5. -3 - (-8) = -3 + 8 = 5. The rule is to add 5 to the previous number.

Question 12

1. Add 1 to the previous number.
2. Add the two previous numbers and subtract 5.
3. Add a number that is 1 greater than the number added to make the previous term. (correct answer)
4. Add consecutive odd numbers, starting with 1, to the previous term.

Explanation: Look at the differences between the numbers: 6 - 5 = 1. 8 - 6 = 2. 11 - 8 = 3. 15 - 11 = 4. The number being added increases by 1 each time. So, the rule is to add a number that is 1 greater than the number added to the previous term.

Question 13

1. Multiply the previous term by a decreasing factor.
2. Add the square of the previous term's position number.
3. Add the two previous terms and subtract 1.
4. Add the next consecutive perfect square, starting with adding 4. (correct answer)

Explanation: First, find the differences between the terms: 6 - 2 = 4. 15 - 6 = 9. 31 - 15 = 16. 56 - 31 = 25. The differences are 4, 9, 16, 25, which are the perfect squares $2^2, 3^2, 4^2, 5^2$. The rule is to add the next consecutive perfect square.

Question 14

1. Double the previous number, then subtract 3.
2. Alternately subtract 1, then add 2.
3. Alternately add 2, then divide by 4.
4. Alternately add 2, then subtract 3. (correct answer)

Explanation: Check the operations between consecutive terms. 2 to 4 is +2. 4 to 1 is -3. 1 to 3 is +2. 3 to 0 is -3. 0 to 2 is +2. The pattern alternates between adding 2 and subtracting 3.

Question 15

1. Subtract 2 from the previous number.
2. Subtract an amount that doubles with each step, starting with 2.
3. Subtract the next consecutive even number, starting with 2. (correct answer)
4. Divide the previous number by 2 and add a changing value.

Explanation: Examine the differences between terms: 50 - 48 = 2. 48 - 44 = 4. 44 - 38 = 6. 38 - 30 = 8. The amounts being subtracted are consecutive even numbers (2, 4, 6, 8). The rule is to subtract the next consecutive even number.

Question 16

1. Add 0.25 to the previous number.
2. Multiply the previous number by 1.5.
3. Add the two preceding numbers. (correct answer)
4. Add 0.25, then 0.50, then 0.75, and so on.

Explanation: This pattern follows a Fibonacci-like rule. Check by adding the two previous terms to get the next: 0.5 + 0.75 = 1.25. 0.75 + 1.25 = 2.0. 1.25 + 2.0 = 3.25. The rule is to add the two preceding numbers.

Question 17

1. Add 2 each time
2. Subtract 3 each time
3. Subtract 3, then add 5, repeat (correct answer)
4. Multiply by 2, then subtract 1

Explanation: This question tests middle school mathematics skills, specifically identifying rules that govern number patterns. Understanding number patterns involves recognizing the rule that consistently applies to each number in a sequence, such as addition, subtraction, multiplication, or division. In this problem, the sequence 10, 7, 12, 9, 14 follows an alternating pattern: subtract 3 (10-3=7), then add 5 (7+5=12), subtract 3 (12-3=9), then add 5 (9+5=14). The correct choice, 'Subtract 3, then add 5, repeat,' accurately describes this alternating operation pattern. A common distractor, such as 'Add 2 each time,' fails because it doesn't account for the decreasing values at positions 2 and 4. Teaching strategies include having students track whether each step increases or decreases and by how much, creating a visual pattern of operations. Remind students that some sequences use alternating rules rather than a single consistent operation.

Question 18

1. Add 2, then add 3, then add 4.5 to the previous term.
2. Multiply the previous term by 1.5. (correct answer)
3. Add 2 to the previous term, then multiply by 1.25.
4. Multiply the previous term by 2 and subtract 2.

Explanation: This is a geometric sequence. To find the common ratio, divide a term by the previous term. 6 ÷ 4 = 1.5. 9 ÷ 6 = 1.5. 13.5 ÷ 9 = 1.5. The rule is to multiply the previous term by 1.5.

Question 19

1. 162
2. 108
3. 243 (correct answer)
4. 84

Explanation: This question tests middle school mathematics skills, specifically identifying rules that govern number patterns. Understanding number patterns involves recognizing the rule that consistently applies to each number in a sequence, such as addition, subtraction, multiplication, or division. In this problem, the sequence 3, 9, 27, 81 follows a multiplication pattern where each term is multiplied by 3 to get the next term (3×3=9, 9×3=27, 27×3=81). The correct choice, 243, is obtained by multiplying 81 by 3. A common distractor, such as 162, might come from doubling 81 instead of tripling it. Teaching strategies include encouraging students to identify the relationship between consecutive terms by dividing each term by the previous one. Remind students that when they identify a pattern rule, they should verify it works for all given terms before applying it to find the missing number.

Question 20

1. Add 2, then add 3, repeat (correct answer)
2. Add 3 each time
3. Subtract 2, then subtract 3, repeat
4. Multiply by 2 each time

Explanation: This question tests middle school mathematics skills, specifically identifying rules that govern number patterns. Understanding number patterns involves recognizing the rule that consistently applies to each number in a sequence, such as addition, subtraction, multiplication, or division. In this problem, the sequence 9, 11, 14, 16, 19 follows an alternating pattern where we add 2 (9+2=11), then add 3 (11+3=14), then add 2 (14+2=16), then add 3 (16+3=19). The correct choice, 'Add 2, then add 3, repeat,' accurately describes this alternating addition pattern. A common distractor, such as 'Add 3 each time,' fails because the differences alternate between 2 and 3, not a constant 3. Teaching strategies include creating a table showing the differences between consecutive terms to reveal the alternating pattern. Remind students to look for patterns in the differences when the sequence doesn't follow a simple single-operation rule.