Mai has a sheet of stickers with 23 rows and 8 stickers in each row.

1. Does Mai have more or less than 100 stickers? Explain your reasoning.
2. How many stickers does Mai have? Explain or show your reasoning.

Find the value of \(7 \times 64\). Use a diagram if it is helpful.

1. Use the diagram to find the value of \(8 \times 573\).

   

   Diagram, rectangle partitioned vertically into 3 rectangles. Left rectangle, vertical side, 8, horizontal side, 5 hundred. Middle rectangle, horizontal side, seventy. Right rectangle, horizontal side, 3.

2. Find the value of \(4 \times 3,\!516\).

   

1. Use the diagram to find the value of \(47 \times 62\).

   

   Diagram, rectangle partitioned vertically and horizontally into 4 rectangles. Top left rectangle, vertical side, 40, horizontal side, sixty. Top right rectangle, horizontal side, 5. Bottom 2 rectangles, vertical side, 7.

2. Is this diagram helpful to finding the value of \(47 \times 62\)? Explain your reasoning.

   

   Diagram, rectangle partitioned vertically and horizontally into 4 rectangles. Top left rectangle, vertical side, 34, horizontal side, 48. Top right rectangle, horizontal side, 14. Bottom 2 rectangles, vertical side, 13.

The diagram and calculations show two ways for finding the value of \(2,\!518 \times 6\).

Diagram, rectangle partitioned vertically into 4 rectangles. Left rectangle, vertical side, 6, horizontal side, 2 thousand. Left middle rectangle, horizontal side, 5 hundred. Right middle rectangle, horizontal side, 10. Right rectangle, horizontal side, 8.

multiply. 2 thousand 5 hundred 18 times 6. 7 rows. First row: 2 thousand 5 hundred 18. Second row: multiplication symbol, 6. Horizontal line. Third row: 48. Fourth row: 60. Fifth row: 3 thousand. Sixth row:  plus 12 thousand. Horizontal line. seventh row: 15 thousand 1 hundred 8

1. How does each part of the vertical calculation relate to the diagram?
2. Find the value of \(3,\!172 \times 5\) using a method of your choice.

Here is an incomplete calculation that uses partial products of \(65 \times 43\).

1. Write multiplication expressions that the numbers 15, 180, 200, and 2,400 each represent. Then find the value of \(65 \times 43\).

   

   multiply. sixty 5 times 43. 6 rows. First row: sixty 5. Second row: multiplication symbol, 43. Horizontal line. Third row: 15. Fourth row: one hundred 80. Fifth row: two hundred. Sixth row: plus two thousand 4 hundred. Horizontal line.

2. Find the value of the product \(45 \times 38\).

Here is how Elena calculates the value of \(723 \times 3\).

1. Where does the 9 in Elena's calculation come from? What about the 6?
2. Where do the 2 and the 1 in calculation come from?
3. Use Elena's method to find the value of \(534 \times 2\).

There are 4,218 students in school district A. School district B has 3 times as many students as school district A. How many students are in school district B? Explain or show your reasoning.

Clare checks her answers for some products. Without doing the computation again, she knows that these answers are incorrect. How might Clare have known?

1. \(5 \times 5,\!783 = 27,\!914\)
2. \(7 \times 8,\!419= 54,\!253\)
3. \(9 \times 9,\!999= 99,\!999\)

Here is Mai's strategy to find the value of \(9 \times 8,\!235\).

1. Explain why Mai's method works.
2. Use Mai's method to find the value of \(9 \times 6,\!789\).
3. Find the value of \(9 \times 6,\!789\) using a strategy you learned. How is Mai's method like yours? How is it different?