Lesson 5
MN Standard: Students understanding of ope rations with whole numbers and
integers can also be enhanced as they examine the validity and utility of
properties of operations, such as commutative and associative properties of
addition and multiplication . Also, at this level we will look at the Identity,
Inverse, and Closure properties. Knowing these properties is not a major topic
at this point. We will run in them at various times in this class and they will
become familiar to you then.
1. Hand back Quiz #1 and answer questions about it.
2. Go over an example of each property with respect to
each addition and multiplication.
3. Hand out Investigation on Properties to be worked in
groups of 3.
Make sure you can justify you answers with example to the
properties Investigation. Either a positive or a negative example to justify
your answer.
Properties Investigation
1. Complete the tables not completed and answer the questions, Yes or No( circle
Y or N ) as to whether the property named applies in each case.
| X |
1 2 3 4 … |
+ |
1 2 3 4 . . . |
properties for + |
| 1 |
|
1 |
|
C |
Y or N |
| 2 |
6 |
2 |
5 |
A |
Y or N |
| 3 |
|
3 |
|
Id |
Y or N |
| 4 |
|
4 |
|
Iv |
Y or N |
.
.
. |
|
.
.
. |
|
Cl |
Y or N |
| Properties for above table x |
| C |
Y or N |
| A |
Y or N |
| Id |
Y or N |
| Iv |
Y or N |
| Cl |
Y or N |
| Properties for above table operation
* |
properties for # table |
| C |
Y or N |
C |
Y or N |
| A |
Y or N |
A |
Y or N |
| Id |
Y or N |
Id |
Y or N |
| Iv |
Y or N |
Iv |
Y or N |
| Cl |
Y or N |
Cl |
Y or N |
Key to Properties C = commutative , A = Associative,
Id = Identity, Iv = Inverse, Cl = closure
A take home number sense problem which is optional, and
will be given points based on how many turn in the Work sheet correct.
Show your work and be able to explain to the class how you
arrived at the solution . I will randomly call on a few who got the correct
answer to explain.
Dogs
There were a total of four dogs staying at my parent’s cabin this past Memorial
Day. Aries, Liberty, Yankee and Murray are excellent dogs, so we frequently
reward them with dog biscuits.
Saturday evening, I forgot to put away the box of
dog-biscuits.
Aries found the box first and decided to eat three more
than one-half of the biscuits. After Aries had finished snacking, Liberty found
and ate three more than one-half of the remaining biscuits. When Liberty was
finished eating Yankee found and ate three more than one-half of the remaining
biscuits. Finally, Murray found and ate three more than one-half of the
remaining biscuits.
When I awoke Sunday morning the entire box was empty. How
many dog-biscuits were in the box originally?
Source: Greg Sarles, Bemidji State U.
Another short quiz based on your text assignments 1-5 will
be given at the end of the next class period.
SUMMARY LESSON 5: This is meant as a brief
introduction to some of the properties of whole numbers – a little if
formalizing your mathematics that you will need for more advanced courses.
Lesson 6
MN Standards: Develop meaning for integers and re present and compare
quantities with them. Understand the meaning and effects of arithmetic
operations with integers.
Since so many have trouble with Integers, specifically
negative integers rather just give out the rules we will investigate them in
another and hopefully refreshing way.
1. Handout red and blue paper to everybody.
2. Get a partner
3. Fold and cut the papers into small squares or cubes
The red squares each represent a Hot(H) unit or +1.
The blue squares each represent a Cold (C) or -1.
4. Represent the number zero 3 different ways.
5. Represent the numbers 4, 6, -3,-5 each in three different ways.
6. Using Hot and Cold cubes show the operations
4 + 2, 4 – 2, -4 + -2 , 2 + -4 , 2 – 4, 4 + -2
Specify how the minus sign (-) is sometimes used as ‘take-away’ and sometimes
referred to as Cold.
7. Using Hot and Cold cubes illustrate multiplication
4 x 2 , 2 x -4, -4 x 2, -4 x -2, -3 x -3
8. Answer the questions do you see any patterns in multiplication that you
discover ?
9. Apply what we have learned in multiplication to division .
-8 / 4 =
-8 / -4=
8 /-4 =
Show how you answer is justified through multiplication.
Your text as signment will verify if you have learned how
to use the operations on integers. Check your answers in the back of the text.
10. The last 15 minutes again will be a short quiz #2 from your text
assignments.
SUMMARY LESSON 6: Hoping that the introduction of
Hot and Cold cubes helped with your understanding of Integers.
Lesson 7
1. Hand back and answer questions from Quiz #2.
2. Summarize and review Unit 1 -- the remainder of the
class will be in answering questions on this unit, and preparing for the Unit
Test the next Class period. The test will be 100 points and no calculator will
be available. If it is necessary to use a multiplication table, a penalty will
be assessed. Those penalty points can be regained by weaning yourself off those
tables by the end of the semester. Also, because this is a major area of your
basic skills and if you scored less than 70 points on the test, you need to get
some help on what you missed and take a test on only what you were weak on to
gain back up to 30 points. You will have to tell me in advanced when you are
ready for this test, so I can put it up in the Testing Center for you to take at
your convenience. You will need a picture ID to take it there.
3. When I return you test the next period after we have
taken it, I
Will survey the class to here your opinion as to how you liked the method of
teaching by using number sense ideas and investigations rather than just
lectures and more traditional methods . So I need you to be thinking about that
part too.
