A focused Grade 4 learning session for Number and Shape Patterns using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can identify a pattern rule and use it to find what comes next.
Number and Shape Patterns means looking at attributes such as sides, angles, equal parts, and shape categories.
Question: Look at the table below. What is the rule for the pattern?
| Input | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|
| Output | \(5\) | \(10\) | \(15\) | \(20\) |
Why it works: 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
Answer: Multiply by \(5\)
Question: Complete the table using the rule "multiply by \(2\) then add \(1\)":
| Input | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|
| Output | \(3\) | \(5\) | \(7\) | \(\mathbf{?}\) |
Answer: \(9\)
Question: A pattern of stars is shown: How many stars are in Figure 4?
Answer: \(10\)
Question: A pattern of circles grows as shown: How many circles are in Figure 4?
Why it works: Circles in each figure: \(1, 3, 6\). The increases are \(+2\), then \(+3\). Next increase is \(+4\): \(6 + 4 = \mathbf{10}\) circles.
Answer: \(10\)
Number and Shape Patterns becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Attributes prove the shape name.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A pattern starts at \(3\) and follows the rule "add \(4\)." What is the \(5\)th term in the pattern?
Answer C: \(19\)
Start at \(3\) and apply "add \(4\)" four more times: \(3, 7, 11, 15, \mathbf{19}\). The 5th term is \(\mathbf{19}\).
Which number comes next in the pattern? \(2, 6, 10, 14, 18, \underline{\quad}\)
Answer 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: \(18 + 4 = \mathbf{22}\).
A pattern starts at \(50\) and follows the rule "subtract \(5\)." Which list shows the first four terms?
Answer 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.
Looking at this pattern, what is the rule?
\(8, 16, 24, 32, 40, \ldots\)
Answer D: Add \(8\)
Find the difference: \(16 - 8 = 8\), \(24 - 16 = 8\), \(32 - 24 = 8\). Each term increases by \(8\). \checkmark
A pattern follows the rule "add \(3\)." If the second term is \(10\), what is the first term?
Answer D: \(7\)
Work backwards: if "add \(3\)" gives \(10\), then the first term is \(10 - 3 = \mathbf{7}\).
Look at the table below. What is the rule for the pattern?
Answer 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
Which of the following shows a pattern where all numbers are even?
Answer 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
A shape pattern uses squares and circles. The pattern is: How many circles are in Figure 4?
Answer C: \(9\)
Count circles: Figure 1 has \(3\), Figure 2 has \(5\), Figure 3 has \(7\). Each time adds \(2\) circles. So Figure 4 has \(7 + 2 = \mathbf{9}\) circles.
Which pattern shows all multiples of \(4\)?
Answer 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
Complete the table using the rule "multiply by \(2\) then add \(1\)":
Answer D: \(9\)
Apply the rule "multiply by \(2\) then add \(1\)" to input \(4\): \((2 \times 4) + 1 = 8 + 1 = \mathbf{9}\).
A pattern starts at \(100\) and subtracts \(10\) each time. What is the \(6\)th term?
Answer D: \(50\)
Subtract \(10\) each time: \(100, 90, 80, 70, 60, \mathbf{50}\). The 6th term is \(\mathbf{50}\).
