Curriculum for the high school grades (9-12) for the state of North Carolina (US) : Curriculum for the high school grades (9-12) for the state of North Carolina (US)
Objectives : Objectives This module explains the curriculum for the high school grades (9-12) for the state of North Carolina (US) Country: United States
State: North Carolina
Time Zone: Eastern Standard Time (GMT-5) till 11th March 2007
Subject: Mathematics
Topic: Integrated Mathematics 1 Language: English
Grade: Grade 9-12
Introduction : Students will be expected to
Describe and translate among graphic, algebraic, numeric, tabular, and verbal representations of relationships.
Use those representations to solve problems.
Appropriate technology, from manipulatives to calculators and application
Software, should be used regularly for instruction and assessment. Introduction
Contents : Integrated Mathematics 1 includes:
The opportunity to study traditional topics from algebra, geometry, probability, and statistics in a problem-centered, connected approach. Contents
Pre-requisites : What your student must already know?
Operate with real numbers to solve problems.
Use formulas to solve problems.
Find, identify, and interpret the slope and intercepts of a linear relation.
Visually determine the line of best fit for a given scatter-plot; explain the meaning of the line; and make predictions using the line.
Collect, organize, analyze, and display data to solve problems. Pre-requisites
Competency Goal 1 : Competency Goal 1 1.01 Write equivalent forms of algebraic expressions to solve problems.
a) Apply the laws of exponents.
b) Operate with polynomials.
c) Factor polynomials. Sample Problems: Solution: Factori z e: a + b a + b = (a 1/3 ) 3 + (b 1/3 ) 3 = (a 1/3 + b 1/3 ) (a 2/3 - a 1/3 b 1/3 + b 2/3 )
Competency Goal 1 : Competency Goal 1 Sample Problems: Solution:
Competency Goal 1 : Competency Goal 1 Sample Problems: Solution: Factorize: 2x3-14x2 + 20x
2x3-14x2 + 20x
= 2x(x2- 7x + 10)
= 2x(x2 - 5x - 2x + 10)
= 2x [x (x- 5) – 2 (x- 5)]
= 2x (x- 5) (x- 2)
Competency Goal 1 : 1.02 Use algebraic expressions, including iterative and recursive forms, to model and solve problems. Sample Problem: Competency Goal 1 Sum of two numbers is 35 and difference is 13. Find the numbers.
Let the numbers be x and y. Then
x + y = 35---------(i)
and, x – y = 13---------(ii)
Adding (i) & (ii) we get 2x = 48
Therefore, x = 24
Putting the value of x in (i) we get y = 35 – 24 = 11
Hence the numbers are 24 and 11. Solution:
Competency Goal 2 : Competency Goal 2 Sample Problem: 2.01 Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures. Find the curved surface area and the total surface area of a right circular cylinder with height 21 cm and base radius 7 cm.
Solution:
Competency Goal 2 : Competency Goal 2 Sample Problem: 2.02 Develop and apply properties of solids to solve problems. A spherical canon ball, 28 cm in diameter is melted and cast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal. Solution:
Competency Goal 3 : Sample Problem: Competency Goal 3 Make a vertical bar graph of the data. Compare the number of students who play the flute to the number of students who play the violin. 11
18
7
5 clarinet
flute
trumpet
violin Frequency Instrument
Competency Goal 3 : Competency Goal 3 Step 1 Decide on the scale and interval. The data includes numbers from 5 to 18.
So, a scale from 0 to 20 and an interval of 4 is reasonable.
Step 2 Label the horizontal and vertical axes.
Step 3 Draw bars for each instrument. The height of each bar shows the number of students who play that instrument.
Step 4 Label the graph with a title.
About twice as many students play the clarinet compared to those that play the flute Solution:
Competency Goal 3 : 3.02 Use theoretical and experimental probability to model and solve problems.
a) Use addition and multiplication principles.
b) Calculate and apply permutations and combinations.
c) Create and use simulations for probability models.
d) Find expected values and determine fairness. Sample Problem: Competency Goal 3 After her softball game, Aislyn can choose a drink from a cooler provided by one of the parents. There are 3 grape drinks, 5 lemon drinks, 4 lime drinks, and 8 orange drinks in the cooler. Aislyn reaches in the cooler and randomly takes a drink. What is the probability that the drink is either lemon or lime?
Competency Goal 3 : Competency Goal 3 Solution:
Competency Goal 3 : 3.03 Create linear and exponential models, for sets of data, to solve problems.
a) Interpret the constants, coefficients, and bases in the context of the data.
b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. Sample Problem: Competency Goal 3 Graph exponential function y = 3x - 4. Then state the y-intercept To find the y-intercept, let x = 0 and solve for y. y = 30 - 4 or -3
In this case, the y-intercept is -3. The constant is -4: 1 + (-4) = -3. Solution: x 3 x - 4 y - 2 3 - 2 - 4 - 3. - 1 3 - 1 - 4 - 3. 0 3 0 - 4 - 3 1 3 1 - 4 - 1 2 3 2 - 4 5
Competency Goal 4 : Competency Goal 4 4.01 Use linear functions or inequalities to model and solve problems; justify results.
a) Solve using tables, graphs, and algebraic properties.
b) Interpret the constants and coefficients in the context of the problem. Sample Problem: Trevor wants to buy a home theater system that costs $850. He has already put aside $370. If he is able to save $30 a month for this purchase, how many months will it take until he has at least enough money to buy the system? Solution:
Competency Goal 4 : Competency Goal 4 4.02 Use exponential functions to model and solve problems; justify results.
a) Solve using tables, graphs, and algebraic properties.
b) Interpret the constants, coefficients, and bases in the context of the
problem. Sample Problems: Solve: 55n + 1 = 125 n – 2 Solution: 5 5n + 1 = 125 n – 2 Original equation
5 5n + 1 = (53) n - 2 Rewrite 125 as 53 so
each side has the same base.
5 5n + 1 = 5 3n – 6 Power of a Power
5n + 1 = 3n – 6 Property of Equality for Exponential Functions
2n + 1 = –6 Subtract 3n from each side.
2n = –7 Subtract 1 from each side.
n = –3.5 Divide each side by 2.
The solution is –3.5.
Competency Goal 4 : Competency Goal 4 4.03 Use systems of linear equations or inequalities in two variables to model problems and solve graphically. Sample Problems: Use elimination to solve the system of equations. 2x + 7y = 1 5x - 7y = -22 Solution: 2x + 7y = 1 7y and -7y are additive inverses.
(+) 5x - 7y = - 22 Add the equations to eliminate the y terms.
7x + 0 = - 21
7x = - 21
x = - 3 Divide each side by 7.
The value of x is - 3.
Competency Goal 4 : Competency Goal 4 Solution: (contd.) Now substitute in either equation to find the value of y.
2x + 7y = 1
2(-3) + 7y = 1 Replace x with -3.
- 6 + 7y = 1
- 6 + 7y + 6 = 1 + 6 Add 6 to each side.
7y = 7
y = 1 Divide each side by 7
The value of y is 1.
The solution of the system is (-3, 1).