Identify and list integers Use the number line to order integers Add subtract multiply and divide integers Use the number line to illustrate integer arithmetic Solve problems about integers ID: 630665
Download Presentation The PPT/PDF document "Integers – Learning Outcomes" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Integers – Learning Outcomes
Identify and list integers.Use the number line to order integers.Add, subtract, multiply, and divide integers.Use the number line to illustrate integer arithmetic.Solve problems about integers.
1Slide2
Identify and List Integers
Integers are the set of all whole numbers.
Recall the natural numbers:
2
The natural numbers are all integers.
We can say that the natural numbers are a subset of the integers:
Slide3
Identify and List Integers
Outcome check: can you identify the integers?
-4
3.14
90-1 000 000 42
Outcome check: list any ten integers and check with the person beside you.
3Slide4
Use the Number Line to Order Integers
Extend the natural number line to the left.This is where the rest of the integers are found.The number line gets more negative as you continue left.
4
Which is greater: 7 or -2?
Which is greater: -2 or 0?
Which is greater: 7 or -7?Slide5
Use the Number Line to Order Integers
The symbols “>” and “<“ are used to compare numbers.e.g.
means that 5 is less than 9.
e.g.
means that 9 is greater than 5.The arrow points to the lesser number.Outcome check: Use the “<“ or “>” symbols to compare the following pairs of numbers:
5
2, 3
6, 10
12, 02, -1
-15, 15
2, -3
-1000, 5
12, 6Slide6
Use the Number Line to Illustrate Arithmetic
Calculate each of the following and express it on a big enough number line:3 + 53 + -5
-3 + 5
-3 – 5
6Slide7
Use the Number Line to Illustrate Arithmetic
Outcome check: Calculate each of the following:-4 + 3
2 + 4
5 – 6
-2 – 3-4 + 5-3 – 24 – 6-5 + 51 – (-4)7Slide8
Use the Number Line to Illustrate Arithmetic
Outcome check: The table below shows the average temperature in Finland last year:
8
Month
Jan
Feb
Mar
AprMayJun
Temp-3-4-15914MonthJulAugSeptOctNovDecTemp17161161-2
By how much did the temperature change:
from May to June?
from November to December?
from March to May?
from January to March?Slide9
Multiply Integers
Copy this table into your copybook and complete it.9
12
12
What is the pattern as you go down the table?Slide10
Multiply Integers
Copy this table into your copybook and complete it.10
20
20
What is the pattern as you go down the table?
From these two tables, come up with a rule about multiplying a negative number and a positive number.Slide11
Multiply Integers
Copy this table into your copybook and complete it.11
-12
-12
What is the pattern as you go down the table?Slide12
Multiply Integers
Copy this table into your copybook and complete it.12
-20
-20
What is the pattern as you go down the table?
From these two tables, come up with a rule about multiplying two negative numbers together.Slide13
Multiply and Divide Integers
positive x positive = positivepositive x negative = negativenegative x positive = negativenegative x negative = positiveThe rules for signs are the same for dividing two integers.
13Slide14
Multiply and Divide Integers
Outcome check: Calculate:
14
5 x 6
-5 x 6
5 x -6
-5 x -6
(10)(4)
(-2)(16)7(-8)(-15)(-6)(-5)(6)(-3)(-16)(-2)(-5)
15
÷ 3
-24 ÷ 6
-39 ÷ -13
21 ÷ -7
16 ÷ 4
-99
÷ -33
-66 ÷ 11
144 ÷ -12
-16 ÷ -8
25 ÷ -5Slide15
Raise Integers to Powers
Recall that multiplication is repeated addition:e.g. 3 + 3 + 3 + 3 + 3 = 3 x 5There is a shorthand for repeated multiplication, called powers.e.g. 3 x 3 x 3 x 3 x 3 = 35
e.g. 2 x 2 x 2 x 2 = 2
4
Calculate:15
2
3
3
4(-5)2
(-3)
3
(-4)
4
(-2)
5Slide16
Use the Order of Operations
GEMDAS is used as normal for indices.G – groups (operations inside brackets, roots, modulus, numerators, denominators, …) are always strongest.E – exponents (powers, roots) are next.
MD – multiplication, division are the same strength.
AS – addition, subtraction are the same strength.
If a tie would cause different answers, work from left to right.16Slide17
Use the Order of Operations
17Outcome check:
Calculate: