Lesson 2

Using Mental Math to Divide

Est. Class Sessions: 1

Daily Practice and Problems

Teacher Notes
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TIMS Challenge

This problem can serve as a Problem of the Week. Encourage all students to work on the questions in order and to get as far as they can.

  1. Possible patterns: The shape numbers grow by ones. They are the counting numbers. The size in squares goes up by 3 from one row to the next. Looking across the rows, if you multiply the shape number by 3 and add 1, you get the size in squares.
  2. You can always get the next size by adding 3 squares to the shape before it.
  3. Strategies will vary. One possible explanation is given for each.
    1. Shape 10 has 31 squares. I added to my data table until I got to Shape 10.
    2. Shape 20 has 61 squares. I know that I add 3 squares for each shape, so adding for 10 more shapes, you add 30 squares. 31 + 30 = 61 squares.
    3. Shape 25 has 76 squares. I used the same strategy that I did for B. 61 + 15 = 76 squares.
  4. Possible responses: To get the size in squares, multiply the shape number by 3 and add 1. Using symbols: S = 3 × N + 1.
  5. Using my rule: 3 × 25 + 1 = 76. Yes, it is the same answer I got in Question 5C.
  6. Shape 100 has 301 squares. If you multiply 100 by 3 you get 100 and adding 1 more, you get 301 squares.

D. Find the Pattern

Write complete answers on a separate sheet of paper.

  1. Draw the next two shapes. You may want to use square-inch tiles to build the shape or draw them on grid paper.
  2. Complete the data table.
  3. Describe patterns. Look down the columns and across the rows.
  4. Show or tell how you can find the next value for the size in squares (S) without drawing the shape and counting squares.
  5. How many squares (S) does each of the following shapes have? Show or tell how you know.
    1. Shape 10
    2. Shape 20
    3. Shape 25
  6. Use words or symbols to describe a rule for finding the size in squares (S) for any shape number (N).
  7. Use your rule to find the size of Shape 25. Did you get the same answer you got in Question 5C? Why or why not?
  8. What shape number has 301 squares? Show or tell how you know.