Which 3 go together?

1. Noah draws a diagram and writes expressions to multiply 2 numbers.

   

   Diagram, rectangle partitioned vertically into 3 rectangles. Left rectangle, vertical side, 7, horizontal side, 1 hundred, area 7 hundred, colored red. Middle rectangle, horizontal side, 20, area 1 hundred 40, colored yellow. Right rectangle, horizontal side, 4, area 28, colored green. Beneath the diagram, 7 hundred plus 1 hundred 40 plus 28 equals 8 hundred sixty 8.

   
   
   
   

   How does each expression represent Noah’s diagram?

2. Noah learns another way to record the multiplication.

   

   

   multiply. 1 hundred 24 times 7. 4 rows. First row: 1 hundred 24, the 2 is highlighted yellow. Second row: multiplication symbol, 7, highlighted yellow. Horizontal line. Third row: 28, side note 7 times 4. Fourth row: 1 hundred 40, side note 7 times 20.

   

   multiply. 1 hundred 24 times 7. 6 rows. First row: 1 hundred 24, the 1 is highlighted red. Second row: multiplication symbol, 7, highlighted red. Horizontal line. Third row: 28, side note 7 times 4. Fourth row: 1 hundred 40, side note 7 times 20. Fifth row: plus 7 hundred, side note 7 times 1 hundred. Horizontal line. Sixth row: 8 hundred sixty 8.

   Make sense of each step of the calculations and record your thoughts.

3. Complete the diagram to find the value of . Use Noah’s recording method to check your work.

   

   Diagram, rectangle partitioned vertically into 3 rectangles. Left rectangle, vertical side, 5, horizontal side, 3 hundred. Middle rectangle, horizontal side, 80. Right rectangle, horizontal side, 4.

   

Noah and Mai want to find the value of . They record their steps in different ways.

Multiply. 2 thousand 9 hundred forty 7 times 6. 6 rows. First row: 2 thousand 9 hundred 47. Second row: multiplication symbol, 6. Horizontal line. Third row: forty 2. Fourth row: 2 hundred forty. Fifth row: 5 thousand 4 hundred. Sixth row: plus 12 thousand. Horizontal line.

Multiply. 2 thousand 9 hundred forty 7 times 6. 6 rows. First row: 2 thousand 9 hundred forty 7 . Second row: multiplication symbol, 6. Horizontal line. Third row: 12 thousand. Fourth row: 6 thousand 4 hundred. Fifth row: 2 hundred forty Sixth row: plus forty 2. Horizontal line.

1. How are these notations alike? How are they different?
2. Use a diagram to show what each of the partial products 42, 240, 5,400 and 12,000 represent. Then find the value of .

3. Find the value of each expression. Use the algorithm that Noah used for at least one expression. Show your thinking using diagrams, symbols, or other representations.