Tasks | Early Adolescence | Rule of Order

Tasks - Year 8, 9

Rule of Order   by Glenys Stade, Hampton SHS

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Number	Calculate
Working Mathematically	Mathematical Strategies
Brief Description:	Using of graphic calculator to establish and apply Rule of Order.
Expected Outcomes:	Understand the need for and use of the Order of Operations. Using the number capacity of a graphic calculator.
Context:	Hampton Senior High School. Activities devised for a calculator workshop. Some have been trialed with a year 8 group.
Learning Activities/ Experience:	Time taken - 2 - 3 hours of class time. Although this activity could be done with any scientific calculator, for motivational purposes and to ensure students get an early start with practicing with a graphics calculator is desirable. A series of questions like: 2 + 3 x 4 12 3 x 2 64 8 + 7 x 2 (4-3) x (2+3) could be posed and students asked what they think the answers are. The answers can then be found using a graphics calculator. This should lead to discussion about the order of the operations. As this is further developed, the teacher can decide where and when the calculator should be used. I like them to use it to "mark" their work. During the course of this activity they will need to be shown power keys, brackets etc. on the calculator. Follow up activities include the worksheets: The 2222 problem The 1998 Problem or Four 4's on the listed resource p.9.
Resources:	Graphic Calculators Introduction to the Casio CFX-9850G Color Graphic Calculator by Lois Burke, Lani Hoza
Assessment & Evaluation:	The activity is used as a way of introducing an idea. One of the follow up activities could be used for assessment.

The 2222 Problem

The number 3 can be expressed by combining four 2s in the following manner (2 x 2) - (2 + 2) = 3

1. Try to create expressions for all the numbers form 1 to 10 involving four 2s, brackets and the operations +, -, x and /.

2. Are there any number that you cannot express this way?

Suppose you can use the decimal point as well : for example 2.2 - 0.2 - 2 = 4

3. Use the decimal point to help with any numbers you have not found yet?

Suppose you can use a number with 2s as its digits like 22 : for example 22 - 2 - 2 = 18

4. Try to find expressions for all the numbers from 11 to 20 (you can also use the decimal point).

5. Are there any numbers that you cannot express this way?

6. Try finding expressions for all the numbers from 1 to 20 using four 3s.

7. Try finding expressions for all the numbers from 1 to 20 using four 4s.

The 1998 Problem

Using the following rules, see if you can find numerical expressions for the numbers 1 to 20. You must use correct Rule of Order. A graphic calculator uses rule of order, so you can use it to check your expressions work.

• You must use all 4 digits (1, 9, 9, & 8) each time once and only once. (the digits may be used as powers)

• The digits may appear in the same order as they appear in 1998.

• You are allowed to place between the four digits any of the mathematical operations or symbols you know. (eg +, -, x, , brackets, etc.)

1 + (9 - 9)8 = 1	=2	=3
= 4	=5	=6
= 7	19 - 9 - 8 = 8	=9
= 10	=11	=12
= 13	=14	=15
= 16	=17	=18
= 19	=20