Testinar Grade 3 math

Arithmetic Patterns

Students will identify, extend, and explain arithmetic patterns in addition and multiplication tables.

CH01-09 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.

Which statement is true about the products of even and odd numbers?
1. Even $\times$ odd is always odd
2. Even $\times$ even is always odd
3. Even $\times$ odd is always even
4. Odd $\times$ odd is always even
Sam skip counts by 3s: 3, 6, 9, 12, \ldots What is the next number in the pattern?
1. 13
2. 14
3. 15
4. 16
Look at this part of the $2 \times 2$ multiplication table: Which pattern do you see in the row for 2?
1. Goes up by 2 each time
2. Goes up by 1 each time
3. Goes up by 3 each time
4. Goes up by 4 each time
Mia writes this list of odd numbers: 1, 3, 5, 7, 9 What is the next odd number in the pattern?
1. 10
2. 13
3. 12
4. 11
A toy costs $5. Two toys cost $10. Three toys cost $15. Four toys cost $20. How much do 5 toys cost?
1. $24
2. $30
3. $26
4. $25
Eli multiplies: $2 \times 4 = 8$, $2 \times 6 = 12$, $2 \times 8 = 16$. Why is every product an even number?
1. Because 2 is an even number
2. Because we add the numbers together
3. Because all products are less than 20
4. Because we are always multiplying by 2, and multiplying by an even number always gives an even product
Look at the rows in a multiplication table: What increases by 3 in the row for 3?
1. The multiplier on the top
2. The table title
3. The column number
4. The product each time
Ben multiplies two odd numbers: $3 \times 5 = 15$. What can you say about the product of two odd numbers?
1. The product is always even
2. The product is always a multiple of 5
3. The product is always greater than 10
4. The product is always odd

Teacher and parent reference

Answer key and explanations

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 $2$.
C. 15
Each number increases by 3. Add 3 to 12 to get 15.
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.
D. 11
Odd numbers go up by 2 each time. Add 2 to 9 to get 11.
D. $25
The cost goes up by $5 each time. Five toys cost $5 \times 5 = $25$.
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.
D. The product each time
In the row for 3, the products are 3, 6, 9, 12, going up by 3 each time.
D. The product is always odd
Odd $\times$ odd always gives an odd number. For example: $1 \times 1 = 1$, $3 \times 3 = 9$, $5 \times 7 = 35$.