Parts of the Square
Use the dot paper to show that 8  2 2 . Find 18 ,
20 , and
45 . Will your method
always work? Why or why not? Can you use your method to find 24 or 12 ?
Parts of the Square (Teacher Notes)
Purpose: Students will use what they have done with area of a square and side lengths to see
that some irrational numbers can be simplified to common radical forms like
task will also show how to combine irrational numbers so
8  2 2 . This
2 2 2 2.
Launch: Read the directions at the top of the student page. You might want to remind
students about the squares that they have worked with when introduced to irrational numbers.
Explore: If students are struggling, help them recall drawing a square with area 8, then they can
find that there are 4 squares with area 2. As students are working look for students that are
starting with area of the beginning number (8) and moving to breaking it into pieces of
lengths. You can also find students that are creating
2
2 lengths and putting two together to
find that 2 2 length would be 8 square units. Students should be developing a method to
determine how the radicals would simplify. Look for multiple strategies to have them share the
different methods.
Discuss: Have different students share the variety of methods they found for each of the
irrational numbers. Ask if their method will always work and test it with either 12 or 24 .
Have students share what is special about these numbers. You might want to have a few more
that are difficult to draw with integer dot paper as others to try.