Introduction
Ms Mac has extended her vacation and you have been asked to fill in for her. Next lesson you and your partner will need to present to the class a summary about the associative properties, commutative properties, identity properties and distributive properties.
Task
Since you are such an awesome, intelligent, entertaining pair you need to find a creative way to teach the students in your class about the properties. You can create a song/rap, design an electronic poster; prezi; powerpoint or come up with some other creative way to teach these properties. You will need to define the properties and make sure students will remember the differences between the properties. You also need to look at how the properties would be used to solve equations and expressions.
Process
The Process
Step 1: Define the properties. One of you will define the properties in red. The other one will defind the properties in blue. Below are several websites and Youtube clips where you can go to find definitions of the properties. You need to make sure your definitions are written in a manner that your classmates will understand.
Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Identity Property of Addition
Identify Property of Multiplication
Distributive Property
Inverse Property
http://www.youtube.com/watch?v=MOYNs-FXKfY
http://amathsdictionaryforkids.com/
http://www.mathsisfun.com/associative-commutative-distributive.html
https://www.khanacademy.org/math/pre-algebra/order-of-operations
http://www.youtube.com/watch?v=7HFRH_M1nAc
Step 2: Learn about the properties by playing the games below. Each of you will need to go to at least two of these sites. You must play the first game and copy and email your results to me.
http://www.aaamath.com/pro74b-propertiesmult.html#section3
http://www.softschools.com/quiz_time/math/properties/theme50.html
Step 3: Design the presentation you will use to teach about the properties. Make sure you show how the properties would be used to solve equations and simplify expressions. You may want to look at the evaluation tab to see what your grades will be based on.
Evaluation
Create a Summary
Here is your chance to demonstrate your level of understanding of the basic number properties. For this part of this unit of study you are to create a presentation showing all that you have learned. You may use whatever media you like for this presentation but the use of technology is highly encourage and will obtain the highest possible grades. Use your imagination, be creative and have fun. Whatever you decide to create be certain it proves your complete understand of the number properties.
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A- Exceeded |
B- Expected |
C- Satisfactory |
D- Below expectation |
E- Incomplete |
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Media |
Student(s) creates a video/prezi/ to demonstrate their learning. |
Student(s) creates an electronic poster, Presentation/ PowerPoint or some other publishing package to summarize this unit. |
Student(s) uses a word processing package to create a summary for this unit. |
Student(s) did not use technology and creates a handwritten poster, brochure, etc. |
Student(s) did not create a summary for this unit. |
|
Creativity |
Student(s)’ summary is very creative, unique, and neat.. |
Student(s)’ summary is creative, unique, neat and pleasing. |
Student(s)’ summary is unique, neat and pleasing however not very creative. |
Student(s)’ summary is not creative, unique and/or neat. Very little effort put forth to complete this summary. |
Student(s) does not create a summary. |
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Properties explained |
All eight properties are defined |
Seven or six properties are defined |
Five or four properties are defined |
three or two properties are defined |
one property is defined |
|
Examples |
Provides examples for all properties |
Provides examples for most of the properties |
Provides examples for a few of the properties |
Only provides a couple of examples |
Provides no examples |
|
Accuracy |
All information contained in summary is accurate. |
Most of the information contained in the summary is accurate. No more than one error notes. |
More than half the information contained in the summary is accurate. Two to four errors found. |
Less than half of the information contained in the summary is accurate. Between five and six errors found. |
More than six errors found in summary. Or No summary submitted. |
Conclusion
CONCLUSION
Through this task you have explored different mathematical properties. You have discovered how properties are used to solve equations and simplify expressions.
Your next step is to find other ways that these properties might be used and what other properties might be beneficial.
Credits
Mathematics K–10
In-text: (NSW, 2014)
Bibliography: NSW, Board of Studies. (2014). Mathematics K–10. [online] Syllabus.bos.nsw.edu.au. Available at: http://syllabus.bos.nsw.edu.au/mathematics/mathematics-k10/ [Accessed 9 Jul. 2014].
Teacher Page
For use with Year 7 Stage 4. Used to introduce the properties to be used in algebraic equations.
NSW Stage 4 syllabus outcomes
Computation with integers
OUTCOMES
A student:
- MA4-1WM
communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols
- MA4-2WM
applies appropriate mathematical techniques to solve problems
- MA4-3WM
recognises and explains mathematical relationships using reasoning
- MA4-4NA
compares, orders and calculates with integers, applying a range of strategies to aid computation
Content
- Students:
- Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
- use an appropriate non-calculator method to divide two- and three-digit numbers by a two-digit number
- compare initial estimates with answers obtained by written methods and check by using a calculator (Problem Solving)
- show the connection between division and multiplication, including where there is a remainder, eg 451÷23=191423 means that 451=19×23+14
- apply a practical understanding of commutativity to aid mental computation, eg 3 + 9 = 9 + 3 = 12,3 × 9 = 9 × 3 = 27
- apply a practical understanding of associativity to aid mental computation,eg 3 + 8 + 2 = (3 + 8) + 2 = 3 + (8 + 2) = 13, 2 × 7 × 5 = (2 × 7) × 5 = 2 × (7 × 5) = 70
- determine by example that associativity holds true for multiplication of three or more numbers but does not apply to calculations involving division, eg (80 ÷ 8) ÷ 2 is not equivalent to 80 ÷ (8 ÷ 2)(Communicating)
- apply a practical understanding of the distributive law to aid mental computation, eg to multiply any number by 13, first multiply by 10 and then add 3 times the number
- connect algebra with the commutative and associative properties of arithmetic to determine that a×b=b×a and (a×b)×c=a×(b×c) (Communicating)