Multiply Fractions by a Whole

TIMS Challenge

This DPP item can be used as a Problem of the Week. Students will need square-inch tiles, a ruler, and grid paper to complete this item.

1. Students use square-inch tiles to build models.
   
   
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4. The line meets the vertical axis at (0 years, 3 squares). That means the creature has 3 squares when it is born.
5. Possible responses: Going down the column, the first column gets larger by one each row. The column for the number of squares gets larger by 6 squares as you move down a row. All of the numbers are multiples of 3. Going across the rows, if you multiply the age by 6 and add 3, you get the number of squares.
1. 45 squares; Possible response: I added 6 squares to 39 because 7 is one more than 6 and the creature grows 6 squares each year.
2. 63 squares; Possible response: I made the table go to 10 rows. I added 6 to each number in the squares column to get the next one. When I got to 10 rows, the size was 63 squares. I used dotted lines on my graph. See graph above.
3. 123 squares; Possible response: I thought of adding 10 rows after I found the answer to Question 6B. I thought that would be like adding 6 ten times. That would be like adding 60 squares, so I added 60 to 63 and got 123 squares.
4. 153 squares; I used the pattern I saw going across the rows. I multiplied 25 times 6 and added 3.
   That's 150 + 3 = 153 squares.
7. Possible response: To get the number of squares, multiply the age by 6 and add 3. S = 6 × A + 3
8. S = 6 × 25 + 3 = 150 + 3 = 153; Yes, the answer is the same as 6D.
9. 100 years old; Possible response: I used my formula backwards. 603 − 3 = 600. 600 ÷ 6 = 100 years.