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Day 4: Finish Section 1.4 & Section 1.5
LAUNCH: Use the multiplication table. Explain why each fact is true.
1. 4(‐3) = ‐12
2. ‐4(‐3) = 12
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A little more work with multiplication tables: Where are...
1. the zeros?
2. the positives?
3. the negatives?
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Does 17, 24, 19, or 72 appear most frequently as an entry in the entire multiplication table? Explain.
Take it Further with Your Partner: Use the multiplication table. (5 min.)
*Which numbers between 0 and 150 appear the most frequently as entries in the multiplication table?
*What numbers between 0 and 150 appear the least frequently as entries in the multiplication table?
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Evaluate the expressions below and try to identify a pattern.
a. (‐1)2
b. (‐1)3
c. (‐1)4
d. (‐1)5
e. (‐1)347
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Section 1.5: The Basic Rules of Arithmetic
Important fact: represents the set of integers
{ } together with
the operations of ______________ & _____________________
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So...what are the rules when we use ?
Addition:
1.
2.
Multiplication:
1.
2.
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Developing Habits of Mind:
What are some ways you could find the sum of the numbers in the array?
5 5 5 5
5 5 5 5
5 5 5 5
Methods:
1.
2.
3.
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Three More Rules about
1. _______________________ : When you add _____ to any number,
you get the number itself.
2. _______________________ : When you multiply ______ to any
number, you get the number itself.
3. _______________________ : When this is added to its opposite, the
result is ______.
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Think About It:
What is the overall change to a number after you add 17, ‐5, 0, 5, 12, and ‐17 to it?
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With your partners work on the following for 5 minutes:
Are each of the following example equivalent? Show the numerical value of each to support your answer.
a. 5(3 + 7) and 5(3) + 5(7)
b. (‐5)(3 + 7) and (‐5)(3) + (‐5)(7)
c. (‐5)((‐3) + (‐7)) and (‐5)(‐3) + (‐5)(‐7)
d. a(b + c) and (a)(b) + (a)(c)
e. (‐2)(x + 5) and (‐2)(x) + (‐2)(5)
What's the property called?
Find a way to use the property to easily find the product of 27 and 102 without calculators or paper! Explain what you did in your notebook.
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How could we use an array to show the distributive property?
1. Show that 4(50 + 3) = 4(50) + 4(3)
50 50 50 50
3 3 3 3
2. What array would you use to show 6(40 + 7) = 6(40) + 6(7)
3. Could you use an array to show 3(109)?
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