Find a way to partition the set of integers into 2 subsets. How do you know your subsets form a partition of the integers?

You will need to have some squares, you can cut out paper squares that are 1 inch by 1 inch, use cheez its, use starburst, saltine crackers, or any other object that is a square. Choose a certain number of squares that you want to work with - only restriction is that you must use at least 7 squares. Create a shape using the number of squares that you have chosen. This can be any shape that you are able to create with your set number of squares. Show how to determine the Area of the shape that you created - DO NOT use the Area formulas. Using the same shape, show how to determine the Perimeter of that shape you created - again DO NOT use the Perimeter formulas. Then take the squares that you are using and create a NEW shape. Show how to determine the Area of this new shape. Show how to determine the Perimeter of this new shape. Be sure to reference any differences or similarities that your students might notice about the two shapes.

Find the number of different partitions of a set having 5 elements and  find the number of different partitions of a set having 6 elements.

Write a set of integer numbers greater than equal to -201 but less than equal to 500 using set-builder notation only.

Write the set of integers that is greater than -3 but less than or equal to 5 using both notations.

Is it possible for two numbers to have the same least common multiple and greatest common devisor?

Find the number of positive integers not exceeding 1020 that are not divisible by 3, 17, or 35.

Find the total number of positive integers < 100 that are either odd or the square of an integer. In a class, 96% students have at least one smartphone, 98% have a calculator, and 95% have a calculator and at least one smartphone. What percentage of students in the class have neither a calculator nor a smartphone? Explain your results. No generic explanations.

How many partitions does the set {1,2,3, 4} have? List all the partitions.

List the integer of the elements of B = {7, v7, -20, 0, –, , 1.5, /16 8