How the West Was One + Three x Four focuses on the order of operations, the importance of using parentheses, and problem solving strategies. The Old West theme is used as the students construct arithmetic expressions from the three numbers randomly generated by the spinners. The students may take a locomotive or stagecoach along the number line that passes through towns in the Old West. On each turn, the players must determine which combination of the three numbers, parentheses and the operations of addition, subtraction, multiplication, and division will produce the best move. The sheriff offers hints in order to suggest game strategies and/or expressions to guide the students’ improvement. The goal is to be the first to arrive in the last town and be welcomed by cheering people.

This unit was designed for an inclusive sixth grade math class. The class consists of fourteen special education students with varied needs and six regular education students. The special education teacher accompanies the regular education teacher 100% of the time, and the class is co-taught. The reading levels of the students range from beginning third grade to seventh grade. The math levels vary from third to sixth grade, with modifications needed to guide students with neurological impairments, specific learning disabilities, attention difficulties and behavioral issues.

Due to the availability of only one computer in the math room, the students will participate in How the West Was One + Three x Four on a rotating basis. The computer program will be used following a whole class introduction to the concepts involved in determining the order of operations and after a lesson (using a projection system) that shows how to use the software.

• Understand the need for a mathematical convention for the order of operations
• Evaluate expressions by determining the correct order in which to compute at least two different operations
• Manipulate parentheses to produce a specific result
• Analyze a problem , consider alternatives and select the best move in a problem solving situation
• Manipulate whole numbers to attain a specific result
• Strengthen computational skills using addition, subtraction, multiplication, and division of whole numbers

Software: How the West Was One + Three x Four by Sunburst Communications

Transparencies 1A - 1D & Printed handouts for activities 2 – 9 from How the West Was One + Three x Four

• Activity 2 should be completed independently. If a student encounters difficulty he/she could be peered up with a partner and reinforcement of this activity should be given at another time. Note the differences between the problems even though the numbers and operations used are the same. Reinforce how the use of parentheses changes the outcome of some of the problems, depending on where the parentheses are placed.
• Complete activity skill sheets 3 and 4 independently for practice. Bring whole class together in order to review and discuss the completion of the expressions, and how the insertion of parentheses altered the outcome of the problems.
• Upon successful completion of the activity skill sheets, allow the students to participate in a tournament against one another in How the West Was One + Three x Four. The game should take ten to twenty minutes. If a child encountered difficulty with the concept taught and was not successful at completing the previous activity sheets, he or she should be paired with a willing classmate and they will become a team. This student should also be given the opportunity to play at his/her level against the computer during a resource period or any other convenient time.
• While students are playing the game the other students should be completing the additional activity sheets (five through nine). Small group instruction may be needed for some of the children to learn the special properties of zero and one, to reinforce the order of operations, and the use of parentheses.
• After all of the students had one opportunity to play the game and complete the activity skill sheets, they will all receive a computer print out of an analysis of their performance. The students that would like to continue on and participate in another tournament will participate in future groups to discuss the strategies needed to make the best moves. Others may be encouraged to continue to play against the computer at his/her level in order to gain a better understanding of the concepts previously taught.

The computer records, participation in class, and the students’ performance of the activity skill sheets will all be used to assess the students’ knowledge. The teacher will observe, evaluate progress, and modify or enrich the content as needed. This will be accomplished by giving students the opportunity for additional computer time and/or supplemental skill sheets.

Supplemental Materials

Additional math texts or skill sheets, which focus on the order of operations, should be used for homework completion, additional classwork, and/or during a resource period.