Testinar Grade 4 math

Number and Shape Patterns

Students will generate, extend, and explain number and shape patterns using observable rules.

CH01-05 Operations and Algebraic Thinking
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A pattern starts at \(3\) and follows the rule "add \(4\)." What is the \(5\)th term in the pattern?

    1. \(15\)
    2. \(16\)
    3. \(19\)
    4. \(23\)

  2. Which number comes next in the pattern? \(2, 6, 10, 14, 18, \underline{\quad}\)

    1. \(20\)
    2. \(26\)
    3. \(24\)
    4. \(22\)

  3. A pattern starts at \(50\) and follows the rule "subtract \(5\)." Which list shows the first four terms?

    1. \(50, 45, 40, 35\)
    2. \(50, 55, 60, 65\)
    3. \(50, 45, 40, 30\)
    4. \(50, 40, 30, 20\)

  4. Looking at this pattern, what is the rule?
    \(8, 16, 24, 32, 40, \ldots\)

    1. Subtract \(8\)
    2. Add \(6\)
    3. Multiply by \(2\)
    4. Add \(8\)

  5. A pattern follows the rule "add \(3\)." If the second term is \(10\), what is the first term?

    1. \(6\)
    2. \(15\)
    3. \(13\)
    4. \(7\)

  6. Look at the table below. What is the rule for the pattern?

    Number and Shape Patterns visual for G4-C01-T05-Q006
    1. Divide by \(2\)
    2. Add \(4\)
    3. Multiply by \(4\) then add \(1\)
    4. Multiply by \(5\)

  7. Which of the following shows a pattern where all numbers are even?

    1. \(2, 5, 8, 11, 14\)
    2. \(4, 8, 12, 16, 20\)
    3. \(3, 6, 9, 12, 15\)
    4. \(1, 2, 3, 4, 5\)

  8. Which pattern shows all multiples of \(4\)?

    1. \(4, 8, 10, 16, 20\)
    2. \(2, 4, 6, 8, 10\)
    3. \(4, 8, 12, 16, 20\)
    4. \(3, 6, 9, 12, 15\)
Teacher and parent reference

Answer key and explanations

  1. C. \(19\)

    Start at \(3\) and apply "add \(4\)" four more times: \(3, 7, 11, 15, \mathbf{19}\). The 5th term is \(\mathbf{19}\).

  2. D. \(22\)

    First find the rule by looking at the gaps: \(6-2=4\), \(10-6=4\), \(14-10=4\), \(18-14=4\). So the rule is "add \(4\)." Apply it once more: \(18 + 4 = \mathbf{22}\).

  3. A. \(50, 45, 40, 35\)

    Apply "subtract \(5\)" starting at \(50\). Term 1: \(50\). Term 2: \(50 - 5 = 45\). Term 3: \(45 - 5 = 40\). Term 4: \(40 - 5 = 35\). So the first four terms are \(50, 45, 40, 35\), which matches choice A.

  4. D. Add \(8\)

    Find the difference: \(16 - 8 = 8\), \(24 - 16 = 8\), \(32 - 24 = 8\). Each term increases by \(8\). \checkmark

  5. D. \(7\)

    Work backwards: if "add \(3\)" gives \(10\), then the first term is \(10 - 3 = \mathbf{7}\).

  6. D. Multiply by \(5\)

    Check the rule: \(1 \times 5 = 5\), \(2 \times 5 = 10\), \(3 \times 5 = 15\), \(4 \times 5 = 20\). The rule is "multiply by \(5\)". \checkmark

  7. B. \(4, 8, 12, 16, 20\)

    Remember: even numbers end in \(0\), \(2\), \(4\), \(6\), or \(8\). Check each list: choice A has \(5\) and \(11\) (odd), choice C has \(3\), \(9\), \(15\) (odd), choice D has \(1\), \(3\), \(5\) (odd). Only choice B---\(4, 8, 12, 16, 20\)---has every term ending in an even digit, so every term is even. \checkmark

  8. C. \(4, 8, 12, 16, 20\)

    Multiples of \(4\) are: \(4, 8, 12, 16, 20, \ldots\) Check choice C: \(4 \div 4 = 1\), \(8 \div 4 = 2\), \(12 \div 4 = 3\). All divide evenly. \checkmark

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