Nrich how many rectangles

It might be useful to gather the results of the students as they work, to help them to see patterns and encourage them to conjecture what the results will be for other rectangles. What effect does this have on the total number of squares? Do they notice anything special? Main menu Search. Hide Menu. You may also like Square Areas Can you work out the area of the inner square and give an explanation of how you did it?

Dissect What is the minimum number of squares a 13 by 13 square can be dissected into? Main menu Search. Hide Menu. You may also like Framed Seven small rectangular pictures have one inch wide frames. Tilted Squares It's easy to work out the areas of most squares that we meet, but what if they were tilted? Four or Five The diagram shows a large rectangle composed of 9 smaller rectangles.

Can They Be Equal? Laura and Amy say: We have been working systematically to list all the possible rectangles, e. Then we decided that we would try using decimals to see if we could find any more as we were getting stuck.

One of us found out that a rectangle of sides 10 and 2. After we found this rectangle someone else in the class managed to spot a pattern linking the numbers. Start at the square with sides 4 by 4. Main menu Search. Hide Menu. Problem Getting Started Student Solutions Teachers' Resources You may also like Bracelets Investigate the different shaped bracelets you could make from 18 different spherical beads.

Cut and Make Cut a square of paper into three pieces as shown. Days and Dates Investigate how you can work out what day of the week your birthday will be on next year, and the year after How Many Rectangles?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas. You can find more short problems, arranged by curriculum topic, in our short problems collection.