Activity Overview
Students attain a basic understanding of numbers and number operations, developing number sense, and gaining fluency in arithmetic computation. They also learn to use the calculator to explore the mathematical principles behind the standard multiplication algorithm for multidigit numbers.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 9 - 20 from the attached PDF file
During the Activity
Distribute the pages to the class.
Follow the activity procedure:
1-2-3-4-Challenge
Use the four digits 1, 2, 3, 4, and any or all of the four operations: +, -, x, to form one or more expressions for each of the values 1 through 12
Test your expressions on the calculator
View expressions created for each value, and explore algebraic properties by comparing two different expressions for the same number
Enter the expression for 12: 3 + 4 x 2 + 1 in the TI-108 calculator and MathMate, TI-10, or TI-15 calculator
Observe that the TI-108 uses arithmetic logic - it computes in the order in which the operations are entered and displays the result as 15, and MathMate, TI-10, TI-15, and most other TI calculators use algebraic logic and employ the algebraic order of operations and display the result as 12
Note that multiplying or dividing by 1 keeps the same number, adding or multiplying increases values, while subtracting and dividing decreases values
Create the Greatest Product
Using the five digits 1, 2, 3, 4, and 5 create a three-digit number and a two-digit factor that give the greatest product
Try the problem again with the digits 2, 4, 6, 7, and 9
Observe that the greatest product is formed by placing the greatest digit in the tens place of the two-digit factor
Try the problem again with the digits 0, 3, 5, 6, 8, and compare the results
Using calculators to assess whole number and operation sense
Test a wide variety of sets of three consecutive whole numbers in order to look for a pattern in their sums
Observe that the sums are divisible by 3
Use the calculator to solve real world problems involving whole numbers and operations with whole numbers
After the Activity
Review students results and re-teach concepts as necessary.