A focused Grade 3 learning session for Arithmetic Patterns using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can identify and explain a number pattern.
Arithmetic Patterns means choosing a model, naming what each number means, and explaining the strategy.
Question: Look at this part of the \(2 \times 2\) multiplication table: Which pattern do you see in the row for 2?
| \(\times\) | 1 | 2 | 3 |
|---|---|---|---|
| 2 | 2 | 4 | 6 |
| 4 | 4 | 8 | 12 |
Why it works: The products 2, 4, 6 each increase by 2 because we multiply 2 by 1, then 2, then 3.
Answer: Goes up by 2 each time
Question: Looking at the number 12 in the table, which multiplications give 12?
| \(\times\) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 2 | 2 | 4 | 6 | 8 | 10 |
| 3 | 3 | 6 | 9 | 12 | 15 |
| 4 | 4 | 8 | 12 | 16 | 20 |
| 5 | 5 | 10 | 15 | 20 | 25 |
Answer: \(3 \times 4\) and \(4 \times 3\)
Question: Look at a column in the multiplication table: How much does each product increase?
| Number | Product |
|---|---|
| \(1 \times 6\) | 6 |
| \(2 \times 6\) | 12 |
| \(3 \times 6\) | 18 |
| \(4 \times 6\) | 24 |
Answer: By 6
Question: A toy costs $5. Two toys cost $10. Three toys cost $15. Four toys cost $20. How much do 5 toys cost?
Why it works: The cost goes up by $5 each time. Five toys cost \(5 \times 5 = $25\).
Answer: $25
Arithmetic Patterns becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which statement is true about the products of even and odd numbers?
Answer C: Even \(\times\) odd is always even
An even number times any other whole number is always even, because the result is a multiple of \(2\).
Sam skip counts by 3s: 3, 6, 9, 12, \ldots What is the next number in the pattern?
Answer C: 15
Each number increases by 3. Add 3 to 12 to get 15.
Look at this part of the \(2 \times 2\) multiplication table: Which pattern do you see in the row for 2?
Answer A: Goes up by 2 each time
The products 2, 4, 6 each increase by 2 because we multiply 2 by 1, then 2, then 3.
Mia writes this list of odd numbers: 1, 3, 5, 7, 9 What is the next odd number in the pattern?
Answer D: 11
Odd numbers go up by 2 each time. Add 2 to 9 to get 11.
A toy costs $5. Two toys cost $10. Three toys cost $15. Four toys cost $20. How much do 5 toys cost?
Answer D: $25
The cost goes up by $5 each time. Five toys cost \(5 \times 5 = $25\).
Eli multiplies: \(2 \times 4 = 8\), \(2 \times 6 = 12\), \(2 \times 8 = 16\). Why is every product an even number?
Answer D: Because we are always multiplying by 2, and multiplying by an even number always gives an even product
Multiplying any number by 2 gives an even result, because \(2 \times n\) means \(n\) groups of 2, and 2 is even. This pattern always holds: even \(\times\) any number \(=\) even.
Look at the rows in a multiplication table: What increases by 3 in the row for 3?
Answer D: The product each time
In the row for 3, the products are 3, 6, 9, 12, going up by 3 each time.
Which list shows skip counting by 4s?
Answer D: 4, 8, 12, 16, 20
Skip counting by 4 means adding 4 each time: \(4 + 4 = 8\), \(8 + 4 = 12\), etc.
Ben multiplies two odd numbers: \(3 \times 5 = 15\). What can you say about the product of two odd numbers?
Answer D: The product is always odd
Odd \(\times\) odd always gives an odd number. For example: \(1 \times 1 = 1\), \(3 \times 3 = 9\), \(5 \times 7 = 35\).
Kai skip counts by 6: 6, 12, 18, 24, 30. Which number should come next?
Answer C: 36
Add 6 each time: \(30 + 6 = 36\). This is skip counting by 6.
Looking at the number 12 in the table, which multiplications give 12?
Answer C: \(3 \times 4\) and \(4 \times 3\)
Both give 12. The multiplication table shows that \(3 \times 4 = 12\) and \(4 \times 3 = 12\).
