Term 2, TASK 1- Properties of Arithmetic

Task 1 is due on Monday, November 29th

TASK 1:

You will create a handbook for the properties of arithmetic:

1. Each page should list a single property.  Each property should be described in:

a.  words (at least 1 sentence)

b.  an example written using variables

c. at least 5 worked examples with numbers

d. a real life scenario for the property

***For the commutative and associative property prove why these properties do not apply to subtraction and division. 

***For the distributive property give an example of how it could be used to make arithmetic easier

2. The final page of the handbook should have a worked step by step example of a single problem that uses each of the properties.  There should be justification for each step. 

Knowledge: You need to show your knowledge of the following properties:  You should be able to identify, define and apply the following properties: 1. Zero 2. Identity 3. Commutative 4. Associative 5. Distributive Property 6. Symmetric 7. Transitive 8. Reflexive 9. Substitution 10. Inverse (addition and multiplication)

Reasoning:   Through this task you need to show your reasoning skills: __ the student is able to create unique examples with numbers and variables for each property __ the student is able to justify with reasons and examples why the commutative and associative properties do not apply to subtraction and division __ the student is able to prove how the distributive property could make a seemingly difficult multiplication problem easier __ the student is able to synthesize all of the properties into a single problem and justify how each step of the problem uses the property

Communication: -Within all your work make sure that you clearly communicate your understanding.  -All work is clearly labeled with your name/class/date and the title. -All written statements should include thorough justification. -All variables, symbols, abbreviations are clearly defined. -All work is shown in sequential order and each step is labeled.  -Each step of the work is clearly justified and easily understood.   -Solutions are given in statements or clearly summarized.  Ex. In order to cross the river with all the family members it will take 6 trips. -All units are clearly identified. Ex.  45kg  or 26 lbs. -ANY graphs, tables and charts included in the response clearly represent the solution or reasoning and meet the standard using the graphing rubric. -Written arguments and explanations include: appropriate and accurate scientific and mathematical vocabulary. -All written arguments follow the organization of claim, reason and evidence. -  Arguments include appropriate and sufficient evidence to support reasons and claims.