Patterns & Sequences
Fill in the missing number: 2, 4, 8, 16, ___
32
Is 7 prime or composite? Explain.
Prime. 1 x 7
What are the factor pairs of 12?
1 x 12, 2 x 6 and 3 x 4
What is 7 × 8?
56
Define "multiple" in one sentence and give an example.
Multiple: a number you get when you multiply a given number by an integer. Example: 15 is a multiple of 3
Write the next two numbers in the pattern: 5, 10, 15, 20, ___, ___
25, 30
Is 21 prime or composite? Give a quick justification using factors.
Composite. 1 x 21 and 3 x 7
A rectangle has side lengths 3 units and 4 units. What is its area?
Area: 12 units
Solve 48 ÷ 6 and identify the related multiplication fact
8; related fact 6 × 8 = 48.
What does "product" mean? Give a multiplication example.
Product: the answer to a multiplication problem. Example: product of 6 and 7 is 42.
A pattern of shapes repeats: square, triangle, triangle, circle, square, triangle, triangle, ___. Which shape comes next?
circle
Use a method to test whether 29 is prime and show which method you used.
Prime. 1 x 29
A rectangle has area 48 square units. List three possible whole-number side length pairs (width × length).
1 x 48, 2 x 24, 4 x 12, and 6 x 8
Use multiplication facts to find two factor pairs of 72
8×9 and 6×12 (plus 1×72, 2×36, 3×24, 4×18).
Define "common multiple" and give an example of a common multiple of 4 and 6.
Common multiple: a number that is a multiple of two or more numbers. Example: 12 is a common multiple of 4 and 6.
Create a number pattern that increases by multiplying the previous term by 3. Start with 1 and write the first five terms.
1, 3, 9, 27, 81
Tell whether 68 is a prime or composite.
Composite. 1 x 68, 2 x 34 and 4 x 17
Find all factor pairs of 36. Then name one rectangle (width × length) with area 36.
1 x 36, 2 x 18, 3 x 12, 4 x 9 and 6 x 6
Explain how knowing multiplication fluency to 10 × 10 helps you find whether 81 is divisible by 9 without dividing long division
If you know 9×9 = 81, then 81 is divisible by 9 because you can write 9×9 = 81; so quotient = 9.
Explain the difference between "factor" and "multiple" with examples.
Factor: a number that multiplies with another to make a product (e.g., 3 is a factor of 12). Multiple: a result of multiplying a number by an integer (e.g., 12 is a multiple of 3).
Describe a rule for the pattern: 3, 6, 12, 24, 48. Then give the 6th term.
96
Give me 1 prime number and 1 composite number, list all factor pairs of each number.
Answers may vary
Explain how factor pairs of a number help you list all possible integer side lengths for a rectangle with that area. Use 60 as your example.
Explanation: Factor pairs (a×b = n) give all whole-number side lengths. For 60: 1×60, 2×30, 3×20, 4×15, 5×12, 6×10.
A student says 14 is a factor of 84 because 84 ÷ 14 = 6. Use the relationship between multiplication and division to show another factor pair that includes 14 and explain.
If 84 ÷ 14 = 6, then factor pair is 14×6 = 84; another pair including 14 is 7×12 = 84 (show multiplication pairs; explain factors come in pairs).
Use these words correctly in one sentence: prime number, composite number, factor, multiple, product, area.
Example sentence: "The prime number 7 has only factors 1 and 7, while the composite number 12 has many factors like 3 and 4, and 3×4 equals the product 12, which is also a multiple used to compute the area of a 3-by-4 rectangle."