Problem of the Week
Problem
B
Quilt
Designs for Barns
Sometimes people decorate their barns with quilts. These barn quilts
are often designed in a square grid with a variety of colours and
patterns, and they usually have symmetry in such a way that if they’re
rotated they will look the same. In the \(6\) by \(6\) grids below, you are going to explore
and create some barn quilt designs. In each part, you can add straight
lines as needed.
What fraction of the barn quilt design below is black, and what
fraction is white? In the blank grid, design another barn quilt using
two colours and the same fractions.
The \(6\) by \(6\) quilt pattern is formed by nine \(2\) by \(2\) squares arranged into \(3\) rows and \(3\) columns. The quilt looks the same when
rotated by a quarter turn.
The \(2\) by \(2\) square in the centre is coloured
entirely black.
The four \(2\) by \(2\) squares in the corners are coloured
entirely white.
On the other four \(2\) by \(2\) squares, the two diagonals are drawn
dividing the square into four identical triangles. One pair of opposite
triangles is coloured white and the other pair is coloured
black.
What fraction of the barn quilt design below is black? Grey?
White? In the blank grid, design another barn quilt using three colours
and the same fractions.
The \(6\) by \(6\) quilt pattern is formed by nine \(2\) by \(2\) squares arranged into \(3\) rows and \(3\) columns. The quilt looks the same when
rotated by a quarter turn.
The \(2\) by \(2\) square in the centre is coloured
entirely white.
The four \(2\) by \(2\) squares in the corners are coloured
entirely black.
On the other four \(2\) by \(2\) squares, the two diagonals are drawn
dividing the square into four identical triangles. One pair of opposite
triangles is coloured white and the other pair has one black and one
grey.
What fraction of the following barn quilt design below is black?
Grey? Striped? White? In the blank grid, design another barn quilt using
four colours and the same fractions.
The \(6\) by \(6\) quilt pattern is formed by nine \(2\) by \(2\) squares arranged into \(3\) rows and \(3\) columns. The quilt looks the same when
rotated by a half turn.
The four \(2\) by \(2\) squares in the corners each have one of
the four smaller squares coloured grey and the other three coloured
white.
On the other five \(2\) by \(2\) squares, the two diagonals are drawn
dividing the square into four identical triangles.
In the \(2\) by \(2\) square in the centre, one pair of
opposite triangles is coloured grey and the other pair is
striped.
In the other four \(2\) by \(2\) squares, one pair of opposite triangles
is striped and the other pair has one black and one white.
