1. Instructional Strategies
MAP2D
Quarter 3
Instructional Strategies
Grade 6

2. Chapter 7/8 Statistics and Probability Chapter 9 Geometric Figures
MAP2D
Chapter 6
Percents
Chapter 7/8 Statistics and Probability Chapter 9 Geometric Figures

3. Instructional Strategies Chapter 6 Percents
MAP2D
Instructional Strategies Chapter 6 Percents

4. Percent is defined as per hundred
Ratios to Percents! 8
2 0
Ratio
DECIMAL 1
Percent
Percent is defined as per hundred

5. Using an Equation to Solve Percent Problems
What number is 40% of 5?
x =
2 is 40% of 5
*NS 1.4 Percent of a Number Section 6.4

6. Using an Equation to Solve Percent Problems
What number is 40% of 5?
x =
2 is 40% of 5
*NS 1.4 Percent of a Number Section 6.4

7. Using a Proportion to Solve Percent Problems
What number is 40% of 5?
Part (is)
Whole (of)
Percent
100 = x 5 40
100 =
2 is 40% of 5
*NS 1.4 Percent of a Number Section 6.4

8. Using a Proportion to Solve Percent Problems
What number is 40% of 5?
Part (is)
Whole (of) %
100
Circle the PERCENT 1st
Circle everything to the right
Circle the everything to the left = x 5 40
100 =
2 is 40% of 5
*NS 1.4 Percent of a Number Section 6.4

9. Real Life Percent Problems Using Equations
The original price of a new bicycle is $ If the bicycle is marked down 15%, what is the new price?
 ADD or SUBRTACT that amount depending on the situation
 What is the question? Discount? Or New Price?
 Multiply the original amount by the percent
$138.00
20.70
$117.30
138
Original Price
Rate
Discount/Tip/Tax
Final Price
$138.00
15%
20.70
$117.30
x .15
690
The new price of the bike is $117.30
+1380
20.70
*NS 1.4 Percent of a Number Section 6.5

10. Real Life Percent Problems Using Proportions
The original price of a new bicycle is $ If the bicycle is marked down 15%, what is the new price? x 15
Part (is)
Percent
 Set up a proportion
 Multiply the cross products
 ADD or SUBRACT from the total depending on the situation
138
100
Whole (of)
100
Original Price
Rate
Discount/Tip/Tax
Final Price
$138.00
15%
20.70
$117.30
The new price of the bike is $ = $117.30
X=20.7
*NS 1.4 Percent of a Number Section 6.5

11. Interest = Principal  Rate  Time
Simple Interest
Interest = Principal  Rate  Time
Interest: the amount of money paid to you on savings, or paid by you on money borrowed
Principal: the initial amount of money
Rate: the percent charged or paid (must be changed to a decimal or fraction)
Time: measured in years

12. Simple Interest (Percent as a fraction)
You have $40 in a savings account earning 2% interest per year. How much interest will you earn in 5 years?
Write the formula
Step 1
I = PRT
Step 2
Substitute the values and cancel out
I = 4  2  5
Step 3
Simplify 10
Step 4
Answer the question
$4 interest

13. Simple Interest (Percent as a fraction)
You have $500 in a savings
account earning 2% interest per year.
How much interest will you earn in 5 years?
Write the formula
Step 1
I = PRT
Step 2
Substitute the values and cancel out
Step 3
Simplify
I = 5  2  5
Step 4
Answer the question
$50 interest

14. Simple Interest (Percent as a decimal)
You have $500 in a savings
account earning 2% interest per year.
How much interest will you earn in 5 years?
Write the formula
Step 1
I = PRT
Step 2
Substitute the values
I = 500  0.02  5
Step 3
Simplify
I = 50
Step 4
Answer the question
$50 interest

15. Instructional Strategies Chapter 7/8 Statistics and Probability
MAP2D
Instructional Strategies Chapter 7/8 Statistics and Probability

16. Probability of an Event
The probability of an event equals:
yellow blocks
(yellow)
blocks in the bag 1
P(Y) = 2

17. Representing Outcomes
1st Die
2nd Die
Outcome 1 2 3 4 5 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
36 Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events. 1 1 2 3 4 5 6 2 1 2 3 4 5 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6 3 1 2 3 4 5 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
What are all the possible outcomes when 2 dice are rolled? 4 1 2 3 4 5 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6 5 1 2 3 4 5 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6 6

18. Representing Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events.
36 Outcomes
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
What are all the possible outcomes when 2 dice are rolled?
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

19. Representing Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events.
Outcomes
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) 1 2 3 4 5 6
What are all the possible outcomes when 2 dice are rolled?

20. Let's Find the Median
35, 40, 81, 39, 40
Put the numbers in order from least to greatest: , 39, 40, 40, 81
MEDIAN: The MIDDLE number of the data.
Hint: If there is no middle number, add the two numbers in the middle and divide by 2.
35, 39, 40, 40, 81
Median = 40

21. 35, 40, 81, 39, 40 Let's Find the Mode 35, 39, 40, 40, 81 Mode = 40
Put the numbers in order from least to greatest: , 39, 40, 40, 81
MODE: The number that occurs MOST often in the data.
Hint: Sometimes there is no mode or sometimes there are more than one mode, called bimodal.
35, 39, 40, 40, 81
Mode = 40

22. 35, 40, 81, 39, 40 Let's Find the Mean 35+ 39 + 40 + 40 + 81 = 235
Put the numbers in order from least to greatest: 35, 39, 40, 40, 81
MEAN: Sum of the numbers divided by the quantity of the numbers in the data set..
= 235
Mean = 47

23. Each member of the population has an equal chance of being selected.
Random
A teacher needs to interview 6 students. The teacher chooses the students by various methods. This is a random sample because everyone has an equal chance of being picked.
Each member of the population has an equal chance of being selected.

24. Systematic
A teacher needs to interview 6 students. She randomly picks a student in her class, then selects every 3rd student. This is a systematic sample because every 3rd person was chosen. A pattern was used to pick the people.
A member of the population is selected at random, and then others are selected by using a pattern.

25. Members of the population volunteer to respond to a survey.
Self-selected
A teacher needs to interview 6 students. Six students volunteer to be a part of the survey. This is a self-selected sample because students volunteered to fill out the survey.
Members of the population volunteer to respond to a survey.

26. The most-available members of the population are chosen.
Convenience
A teacher needs to interview 6 students. The teacher chooses the students at table This is a convenience sample because they all were sitting at the same table.
The most-available members of the population are chosen.

27. Instructional Strategies Chapter 9 Geometric Figures
MAP2D
Instructional Strategies Chapter 9 Geometric Figures

28. Adjacent and Vertical Angles
Adjacent Angles :
angles that are next to each other. 1 2 3
 1 and 2 are adjacent angles.
Vertical Angles :
angles that are opposite of one another.
 1 and 3 are vertical angles.

29. Adjacent Angles Adjacent Angles : angles that are next to each other.5 4
 1 and 2 are adjacent angles. 6 3
 2 and 3 are adjacent angles. 2
Which other angles are adjacent to one another? 1

30. Vertical Angles Vertical Angles :
angles that are opposite of one another. 1 4
 1 and 3 are vertical angles. 2 3
 2 and 4 are vertical angles.

31. Vertical Angles a° b° a = b
Vertical angles are the angles opposite each other when 2 lines cross. a° b°
Vertical angles are congruent.
a = b

32. Vertical Angles c° d° c = d
Vertical angles are the angles opposite each other when 2 lines cross. c° d°
Vertical angles are congruent.
c = d

33. Adjacent Angles “Adjacent” means “next to”.
Adjacent angles are next to each other, sharing one side.

34. Complementary angles add up to 90°.

35. Supplementary angles add up to 180°.

36. Triangle Sum Property 1 2 3
For any triangle, the sum of the measures of the interior angles is always 180º. 1 3 2 1 2 3

37. Solve for a Missing Angle in a Triangle
73º xº
1. Write the equation:
m1 + m2 + m3 = 180º
2. Fill in the angle measures
m1 + m2 + m3 = 180º
90º
73º x
163º + x = 180º
3. Solve the equation for the missing value.
163º+x –163º= 180º–163º
x = 17º

38. Let's Learn How to Find Missing Angle Measures of a Triangle !
THE SUM OF THE ANGLES OF ANY TRIANGLE IS 180 !
To find the number of degrees in the missing angle add the two angles given and subtract from 180 .
= 155
= 25
125 30 ?
EXAMPLE
The 3rd angle measures 25

39. Solve for a Missing Angle in a Triangle
73º xº
1. Write the equation:
m1 + m2 + m3 = 180º x
2. Fill in the angle measures
m1 + m2 + m3 = 180º
90º
73º
163º + x = 180º
163º–163º+x = 180º–163º
3. Solve the equation for the missing value.
x = 17º

40. Classifying Triangles
All triangles have 2 names. They are classified by their angles, then their sides.
Tick marks are used to show that the sides of the triangle are equal in length.
Angles
Sides
Scalene
NO equal sides
Obtuse
Acute
2 equal sides
Isosceles
Right
Equilateral
3 equal sides

41. Classifying Triangles
All triangles have 2 names. They are classified by their angles, then their sides.
Angles
Sides
Scalene
Obtuse
NO equal sides
Angles
Sides
Scalene
Acute
Isosceles
Obtuse
Equilateral
Right
Acute
2 equal sides
Isosceles
Right
3 equal sides
Equilateral

42. Classifying Quadrilaterals
>>
Both opposite sides are parallel
Both opposite angles are congruent
>
>
Parallelogram with 4 right angles
>>
Parallelogram
Rectangle
Remember some quadrilaterals can have more than one name because they share properties. For examples squares are both a rhombus and a rectangle.
>>
Trapezoid
Parallelogram with 4 congruent sides and 4 right angles
Parallelogram with 4 congruent sides
>
>
>
Exactly one pair of opposite sides is parallel
>>
Rhombus
Square
>
Trapezoid
Grade 5 Angle Measures in Triangles 9.8