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Product of factors inquiry

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The product of the factors of 24 equals 24⁴.

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Inquiry prompt

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The product of the factors of 24 equals 24⁴.

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Inquiry prompt

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The product of the factors of 24 equals 24⁴.

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Lines of inquiry

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Patterns

Shade the factors of the numbers from 1 to 24. What patterns do you notice?

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Patterns

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1. Find the factors of these numbers:

2. Copy the table. Fill in the table by grouping numbers with the same number of factors. For example, 12 and 20 both have six factors. 3. Find more numbers so that all the cells in the table are filled.

Structured inquiry

Number of factors

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Six factors Find the numbers less than 100 which have exactly 6 factors and … One of the factors is 6 One of the factors is 10 One of the factors is 14 One of the factors is 15 One of the factors is 25 There are two answers for each questions. Explain how you did it.	Four factors A number has 4 factors, one of which is 9, what is it? A number is one less than a square number; it has 4 factors, one of which is 5; what could it be? A number has 4 factors, two of which add up to 10; what could it be? How many numbers could it be?	Four factors Can you find some pairs of consecutive numbers, both of which have 4 factors? Can you find a trio of consecutive numbers all three of which have 4 factors? Can you find a trio of consecutive odd numbers all of which have 4 factors?	Four factors What types of numbers have exactly 4 factors? Describe the two distinct families of numbers that have 4 factors. Can you explain why the families of numbers have 4 factors?

Structured inquiry

Four and six factors

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Six factors Find the numbers less than 100 which have exactly 6 factors and … One of the factors is 6 12, 18 One of the factors is 10 50, 70 One of the factors is 14 28, 98 One of the factors is 15 30, 45 One of the factors is 25 50, 75 There are two answers for each questions. Explain how you did it.	Four factors A number has 4 factors, one of which is 9, what is it? 27 A number is one less than a square number; it has 4 factors, one of which is 5; what could it be? 35 A number has 4 factors, two of which add up to 10; what could it be? How many numbers could it be? 21, 27	Four factors Can you find some pairs of consecutive numbers, both of which have 4 factors? 14 and 15, 26, 27 Can you find a trio of consecutive numbers all 3 having 4 factors? 33, 34, and 35 is the first case. Can you find a trio of consecutive odd numbers all of which have 4 factors?

Structured inquiry

Four and six factors

solutions

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Students’

questions

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	1
	1
	1
	1

	1
	1
	1
	1

	1
	1
	1
	1

	1
	1
	1
	1

	1
	1
	1
	1

	1
	1
	1
	1

Inquiry Maths

Prime numbers

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						16




	1




	1

Square numbers

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	1	2




	1	2




	1

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Composite numbers

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Alternative prompt

The product of the factors of 18 equals 18³.

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