Chapter 2 In t e gers
N8.5 Demonstrate understanding of multiplication and division of integers concretely, pictorially, and symbolically. • • • • • • • • • •
Indicators a. Identify and describe situations that are relevant to self, family, or community in which multiplication or division of integers would be involved. Model the multiplication of two integers using concrete b. materials or pictorial representations, and record the process used symbolically. Model the division of two integers using concrete materials c. or pictorial representations, and record the process used symbolically. Identify and generalize patterns for determining the sign of d. integer products and quotients. Generalize and apply strategies for multiplying and dividing e. integers. Create and solve problems involving the multiplication or f. division (without technology for onedigit divisors, with technology for twodigit divisors) of integers. Explain how the order of operations can be extended to g. include integers and provide examples to demonstrate the use of the order of operations. Create and solve problems requiring the use of the order of operations on integers.
Positive integer
Negative integer
Zero pairWhen a set of
A number that is on the right A number that is on the left one negative and one positive side of zero on a number line. side of zero on a number line. cancel themselves out in an equation.
Opposite integer
Zero property With
Distributive property
The integer numbers that addition, Zero does not effect shares the same distance from the number. With zero, left and right. multiplication, the answer is always zero.
when you have a(b+c), it can be written as ab+ac. The same happens for a(bc)= abac.
Quotient the answer when Product the answer when multiplying. dividing.
Order of Operations
BBRACKETS EEXPONENTS Grouping symbol When Commutative property the DDIVIDE working with a fraction, all the order of numbers being added MMULTIPLY AADDdoes not effect the answer work must be done in the (2+3=3+2). This is also true for SSUBTRACT numerator and the multiplying (4x5=5x4). denominators before you divide.
Tiles activity â€˘ Use different tiles to understand the way positive and negative numbers interact with each other
+
+

Number lines Positions on a number line can also help us to understand integers
Number lines can help us to do computations
Number lines can help us to do computations • Subtracting Integers
• • • • •
Subtract Add The Opposite Result + 9  +4 = +9 + 4 = +5 + 9  4 = +9 + +4 = +13 9  +4 = 9 + 4 = 13 – 9  4 = 9 + +4 = 5
. Indicator
Identify and describe situations that are relevant to self, family, or community in which multiplication or division of integers would be involved
Exploring integers
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Exploring integers
Indicator
Generalize and apply strategies for multiplying and dividing e. integers
ADDING AND SUBTRACTING INTEGERS â€˘ Using a number line
ADDING AND SUBTRACTING INTEGERS
ADDING AND SUBTRACTING INTEGERS
ADDING AND SUBTRACTING INTEGERS
Multiplying Integers
Multiplying Integers
Dividing Integers
Dividin g Intege rs
Order of operations s n o i t a r e p o f S s r o R e r O g e T e d t A r n C o i I e D e h d t IN u l c w n o i h o n t i a l d e p x d f o n t o â€˘ E e t s r x e e l e d p r e o m b a e n x h e t ca f e o d i e v s o u r p e h d t an e t a r g t n s i r n i o u q e r dem ions. s m e l s b n t o a o i r r t p e a r e op e v l p o o s f d o n r a e e d t r a o e r e C h t â€˘ f o e the us gers. e t n i n o
Order of operations
D . E . â€˘ B
. S . A .M.
"Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ... 7 + (6 Ă— 52 + 3) ... what part should you calculate first? Start at the left and go to the right? Or go from right to left? Warning: Calculate them in the wrong order, and you will get a wrong answer ! So, long ago people agreed to always follow certain rules when doing calculations, and they are:
What is the order?
Examples of BEDMAS in action
• Thanks to :
• http://mathbits.com/MathBits/TeacherResources/ For use of the images