Instructional Strategies MAP2D Quarter 3 Instructional Strategies Grade 6
Chapter 7/8 Statistics and Probability Chapter 9 Geometric Figures MAP2D Chapter 6 Percents Chapter 7/8 Statistics and Probability Chapter 9 Geometric Figures
Instructional Strategies Chapter 6 Percents MAP2D Instructional Strategies Chapter 6 Percents
Percent is defined as per hundred Ratios to Percents! 0 . 2 5 4 1 . 0 0 8 2 0 Ratio DECIMAL 1 Percent Percent is defined as per hundred
Using an Equation to Solve Percent Problems What number is 40% of 5? x = 0.40 5 2 is 40% of 5 *NS 1.4 Percent of a Number Section 6.4
Using an Equation to Solve Percent Problems What number is 40% of 5? x = 0.40 5 2 is 40% of 5 *NS 1.4 Percent of a Number Section 6.4
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
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
Real Life Percent Problems Using Equations The original price of a new bicycle is $138.00. 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
Real Life Percent Problems Using Proportions The original price of a new bicycle is $138.00. 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 $138.00 - 20.7= $117.30 X=20.7 *NS 1.4 Percent of a Number Section 6.5
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
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
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
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
Instructional Strategies Chapter 7/8 Statistics and Probability MAP2D Instructional Strategies Chapter 7/8 Statistics and Probability
Probability of an Event The probability of an event equals: yellow blocks (yellow) blocks in the bag 1 P(Y) = 2
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
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)
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?
Let's Find the Median 35, 40, 81, 39, 40 Put the numbers in order from least to greatest: 35, 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
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: 35, 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
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.. 35+ 39 + 40 + 40 + 81 = 235 Mean = 47
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.
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.
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.
The most-available members of the population are chosen. Convenience A teacher needs to interview 6 students. The teacher chooses the students at table 1. This is a convenience sample because they all were sitting at the same table. The most-available members of the population are chosen.
Instructional Strategies Chapter 9 Geometric Figures MAP2D Instructional Strategies Chapter 9 Geometric Figures
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.
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
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.
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
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
Adjacent Angles “Adjacent” means “next to”. Adjacent angles are next to each other, sharing one side.
Complementary angles add up to 90°.
Supplementary angles add up to 180°.
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
Solve for a Missing Angle in a Triangle 73º xº 1. Write the equation: m1 + m2 + m3 = 180º 2. Fill in the angle measures m1 + m2 + m3 = 180º 90º 73º x 163º + x = 180º 3. Solve the equation for the missing value. 163º+x –163º= 180º–163º x = 17º
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 . + 30 = 155 180 - 155 = 25 125 30 ? EXAMPLE The 3rd angle measures 25
Solve for a Missing Angle in a Triangle 73º xº 1. Write the equation: m1 + m2 + m3 = 180º x 2. Fill in the angle measures m1 + m2 + m3 = 180º 90º 73º 163º + x = 180º 163º–163º+x = 180º–163º 3. Solve the equation for the missing value. x = 17º
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
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
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