This lesson, led by Mr. Hul, focuses on writing products as sums and sums as products. It begins with a problem involving dividing money between George and Ben using a ratio, solved through tape diagrams. The lesson progresses to explaining rectangular arrays and their application in representing expressions. The distributive property is introduced and applied to calculate areas and expand expressions. Advanced examples and exercises are provided to reinforce the concepts, emphasizing visualization techniques like tape diagrams and arrays.

In the exercise involving George and Ben, if the total amount of money is $56 and the ratio is 3:4, how much does George receive?

• $16

• $24

• $32

• $40

When representing the sum 3 + 2 using a tape diagram, how many total squares are used?

• 6

• 3

• 4

• 5

In a rectangular array representing 3 * (x + 2), how many times is the sum (x + 2) repeated?

• 1

• 4

• 2

• 3

What is the distributive property formula for a * (b + c)?

• a * b + a * c

• a + b + c

• a * b * c

• a + b * c

Using the distributive property, what is the expanded form of 3 * (x + 2)?

• 3x + 2x

• x + 6

• 3x + 6

• 3x + 2

If x = 5, what is the value of 5 * (8x + 3) using the distributive property?

• 200

• 275

• 215

• 250

What is the result of substituting x = 5 into the expression 2x + 2?

• 10

• 12

• 14

• 16

How can the expression 6x + 15 / 3 be rewritten using the distributive property?

• 6x + 3

• 6x + 5

• 2x + 15

• 2x + 5

In the tile problem, if each side of the square is 5, how many tiles are needed including the corners?

• 28

• 24

• 20

• 16

What is the simplified form of the expression 4 * (x + y + z)?

• 4x + 4y + 4z

• x + y + z

• 4x + y + z

• x + 4y + 4z