Here are 9 straight lines and 20 squares. Find the smallest number of lines needed to make exactly 100 squares. Once you’ve done this, investigate further. How many different ways can you make a particular number of squares?
Can you draw a square with 3 lines?
You can draw a square with three lines by considering side edge of a paper as a line.
How many lines are required to draw a square?
4 line segments kept perpendicular to each other can make a square. 4 line segments kept perpendicular to each other can make a square.
What is the minimum number of squares to be shaded so that the figure has a line of symmetry?
Shading 2 little squares: We’ll need to shade two squares along a line of symmetry or a pair either side of a line of symmetry. Remember the diagonal and the side-bisecting lines! Be careful not to double count some patterns because opposite corners can be made to look the same by 180 degree rotations!
What size rectangle contains exactly 100 squares?
4 \times 11 rectangle
In fact, a 4 \times 11 rectangle contains exactly 100 squares.
How many different ways can you make 64 squares?
How many ways can you arrange 64 squares in equal rows? So the answer is 7 different ways, potentially. However, the rules are a little unclear and you could argue that 64 rows of one or one row of 64 doesn’t count. Or you could argue that 2 rows of 32 is really the same as 32 row of 2, you just rotated it.
Can you draw a square with two straight lines?
Yes! You can! Take 2 straight lines first.
How many lines of symmetries are there in a square A 1 B 2 C 3 D 4?
4 lines
Consider a regular square ABCD as shown in figure the line of symmetry is also shown as 1, 2, 3, 4 which folds the square into two equal halves. So, the regular square has 4 sides so the regular square has 4 lines of symmetry which folds the square into two equal halves. So, this is the required answer.
What rectangle has two lines symmetry?
In a rectangle, when a line of symmetry is drawn along its length and one along the breadth, we get two lines of symmetry. By doing this we exactly get four equal and matching shapes. The diagonals of a rectangle cannot be taken as a line of symmetry as they do not form equal matching shapes.
Which two squares which when shaded will produce a figure with 2 lines of symmetry?
The empty grid only has 2 lines of symmetry, as shown below, so when Mathias shades 4 squares, these will be the 2 lines of symmetry. If Mathias shades one of the corner squares, then he must shade all of the corner squares, as shown below. That is one way to make a grid with 2 lines of symmetry by shading 4 squares.
Can a symmetrical pattern on a grid have more than two lines of symmetry?
1) Carrie says, “A symmetrical pattern on a grid cannot have more than two lines of symmetry.” Is she correct? No. Draw your own pattern, with lines of symmetry, on the square grid to prove your answer. Children should have drawn a simple pattern showing horizontal, vertical and diagonal symmetry like the example here.
How many straight lines are needed to make 100 squares?
Let’s try — Here are 10 straight lines and 17 squares. Here are 9 straight lines and 20 squares. Find the smallest number of lines needed to make exactly 100 squares. Once you’ve done this, investigate further.
What’s the minimum number of Squares you can cut from paper?
Given a paper of size, A x B. Task is to cut the paper into squares of any size. Find the minimum number of squares that can be cut from the paper. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution.
What is the number of squares required to cover a?
If a side of the rectangle has a gap, then this section of the edge must be an edge of the final square. Since the final square has size less than 11, this can only happen for one edge. We may suppose the size a and d squares leave a gap, so a + b = c + d = 11 and b + c = 13. Thus b = 11 − a, c = a + 2, d = 9 − a.
How many squares do you need for an 11 × 13 rectangle?
EDIT: There’s no tiling of the 11 × 13 rectangle with 5 squares even if you don’t require integer sides. It’s best to work up to 5 tiles one at a time. With one tile ( a × a) you can only tile an a × a rectangle. With two tiles, both must be a × a, and you get an a × 2 a rectangle.
