Grades 1-2 Video Solutions 2024-2024_1-2

Video Transcription

Problem number 19. Which two pieces can be used to complete the grid without overlapping?  1 and 2, 1 and 3, 3 and 4, 2 and 4, or 2 and 3?  For this type of problem, if you notice that the pieces we can use have different areas,  here they're made up of different numbers of little squares,  we can get rid of the choices by figuring out how many little squares we need in total.  We can draw in the rest of the grid, and then we can count the white squares.  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, there are 17 of them. Let's look at the pieces. Piece 1 is made up of 1, 2, 3, 4, 5, 6, 7, 8, 9 little squares.  Piece 2 is made up of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 little squares. Piece 3 is 1, 2, 3, 4, 5, 6, 7 little squares. And piece 4, 1, 2, 3, 4, 5, 6, 7, 8, 8 little squares.  The only way we can get 17 small squares is to use piece 1 together with piece 4, because 9 plus 8 makes 17, or use piece 2 together with piece 3, because 10 plus 7 makes 17.  Notice that 1 and 4 is not one of the answer choices, so the answer will need to be 2 and 3.  Now let's see how they fit. Here's piece 2  and piece 3, and they fit perfectly without even having to rotate them. The answer is E, 2 and 3.

Video Summary

To solve the problem of completing the grid with two pieces that don't overlap, the goal is to make a total of 17 squares. By counting the squares in each piece, piece 1 has 9, piece 2 has 10, piece 3 has 7, and piece 4 has 8 squares. The combinations to reach 17 squares are piece 1 with piece 4 (9+8) or piece 2 with piece 3 (10+7). Since the combination 1 and 4 is not an answer choice, the solution is pieces 2 and 3, which together exactly fit 17 squares without rotation. The correct answer is option E, 2 and 3.

Keywords

grid completion

non-overlapping pieces

17 squares

piece combinations

solution option E