This “mind-reading” effect is accessible to students in grades 4 and up. It requires mental division by four which may create a need/desire for an efficient strategy to divide by 4 such as divide by 2 twice. This is a nice way to practice mental mathematics and it empowers kids to do mathematics to bring some joy and wonder to others.

The video below shows what this performance might look like.

The lesson:

After performing, give students a copy of several calendar pages to use as they investigate this problem. Students should draw a box around a 2 x 2 array of dates. Students should work with a partner to discuss what they notice about the numbers in the box. They can look for patterns, or anything interesting they find out about the numbers they boxed.

When students share, others will want to check to see if what they said is also true about the numbers they boxed. Keep a class list of what students notice, so they can see if the conjectures they make work with all boxed numbers.

Some things students may notice:

• The diagonal numbers added together are the same (3 + 11 = 4 + 10).
• The top numbers and the bottom numbers are 7 apart (3 + 7 = 10; 4 + 7 = 11).
• The sum is always a multiple of 4.
• The sum is always even.
• If you know one number, you can figure out the rest.

Students may also wonder:

• What math could I do to get a number in the box?
• How can I get from the sum to at least one of the box numbers? or
• How can I get from at least one of the box numbers to the sum?

There is actually more than one solution to this problem. As students try different computations to solve, refer them back to what they notice. Ask least helpful questions such as:

• What does it mean if a number is even?
• If a number is a multiple of four, then __________?
• Which of the notices do you think might be most helpful?

Have students share their solutions (there may be more than one that works) and discuss the benefits of each. Check each solution strategy to see if it works with any set of 4 boxed numbers. Provide students an opportunity to practice the strategy that works best for them. Give those who wish an opportunity to perform this for others (administrators, other teachers, other classes, parent math night, etc.). Ask students to perform this for their own families as well.

Below is one solution, but there are many others.

Extensions:

• Box a 3×3 array on a calendar. What patterns do you see in these boxes. What if you add the 8 outer numbers inside the box? What relationship does that have to any of the numbers in the box?
• What if you boxed a row of 5 numbers? Could you find the numbers if you were given the sum?