Understanding what value numbers have and having the ability to break them apart are important to being able to complete this activity. Being able to break down a number into its different place values, like the number 145 into 100 + 40 + 5, will help students become proficient in more difficult math concepts.
For this activity, have students break into groups of three. One student is the "calculator" (provide them with a calculator too); another student is the "caller"; and the third student is the "brain." The caller turns over two cards and asks for the sum of the cards -- jack, queens, kings and jokers can be assigned a value. The brain and the calculator both come up with the sum. The brain uses mental math strategies, while the calculator uses the calculator to find the sum. When either student has the answer, they call it out. The caller decides who called out the sum first. The caller keeps score using tally marks. By having the caller draw three cards, and having students find the product of two numbers, four numbers or three numbers, this game can be adjusted for any grade level.
Read aloud to the students "Betcha," by Stuart J. Murphy. The synopsis of this story is two boys want to participate in a contest at the local toy store. In the contest, they are to estimate how many jelly beans are in the jar displayed in the toy store window. The boys have different mental math techniques to find a solution to their problem.
Bring in a jar filled with any small item for your students to use their estimation skills. Ask the students to estimate the number of items you have placed in the jar. Instruct them to explain their strategy. Discuss the different strategies in class. At this point, take a smaller jar and fill it from the larger jar. Count with the class the number of items that filled up the smaller jar. Let the students adjust their estimates, now that they have more information.
The students use their mental math skills, as you apply an algebraic equation and give an output answer to the students suggested input. They develop algebra skills as they compute the formulas for the output you give them.
Have a selection of hats available. Hide a different algebraic formula in each hat, such as "n x n" or "(n + 1) x 3"; randomly ask the students to give you an input number, and apply the algebraic formula to the input number by replacing "n" with the number the student gave you. Give an output number. For example, if your specific formula is "n x n," when the student gives you the number 3, you respond with 9. Continue accepting input numbers and giving output answers, until someone can state the algebraic equation you have hidden in your hat and have applied it to all of the input numbers.
Being able to understand the value of rational numbers -- fractions, decimals and percentages -- is an easy skill to assess during mental math time. Explain to the students that you will give them a rational number; if it is more than one-half, they should stand up. If the number you give them is less than one-half, they should stay seated. It is easy to vary this strategy based on the grade-level of your students. You can change the target number or call out two rational numbers for the students to find the sum of, or give them a more difficult operation with rational numbers -- multiplication or division.