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: Introductory Mathematics Language: English
Grade: Grade 9-12
Introduction : Students will be expected to
Prepare for High School Mathematics.
Preparing the foundation of High school Algebra and Geometry.
Use of appropriate technology, from manipulatives to calculators. Introduction
Contents : Introductory Mathematics includes:
A survey of preparatory topics for high school mathematics, including the foundations for high school algebra and geometry. Contents
Pre-requisites : What your student must already know?
The Subject strands studied till Grade 8.
This includes Number and Operations, Geometry, Measurements, Data analysis & Probability and Algebra.
In Grade 9-12 the total strands are four. The Geometry and Measurement are clubbed together in the future classes. Pre-requisites
Competency Goal 1 : Competency Goal 1 1.01 Develop number sense for the real numbers.
a) Define and use irrational numbers.
b) Compare and order.
c) Use estimates of irrational numbers in appropriate situations. Sample Problems:
Competency Goal 1 : Competency Goal 1 Solution: Write as fractions with the same denominator. For and , the least common denominator is 24. Since or, .
Competency Goal 1 : 1.02 Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and
pencil. Sample Problem:
Sammy’s average in his history class was 0.855 or 85.5%. The grade average is calculated by dividing a student’s number of points by the total number of points possible. If there were 600 points possible, how many points did Sammy earn? Competency Goal 1
Competency Goal 1 : Competency Goal 1 Solution:
Competency Goal 2 : Competency Goal 2 Sample Problem: 2.01 Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed. Solution: 6 in
Competency Goal 2 : Competency Goal 2 Sample Problem:
A cylindrical tub contains 1540 cm3 of water. The radius of the tub is 7cm. Now a stone is dipped in the tub the height of the water is now 15cm. Find the volume of the stone. 2.02 Apply and use concepts of indirect measurement. Solution: Let the height of the water in the tub be h cm = 1540 cm 3 or, h = or, h = 10 cm Now, the height rose by 15 – 10 = 5 cm According to Archimedes Principal, the volume increased because of the stone is = p x 7 2 x 5 cm 3 = cm 3 = 770 cm 3
Competency Goal 2 : Competency Goal 2 Sample Problem 2.03 Represent problem situations with geometric models. A rectangular lawn is there as shown in the figure. The width of the road is 5 m. Find the area of the lawn excluding the road. Solution:
The area of the lawn including the road is = 40 X 60 cm2 = 2400 cm2
The area of the road parallel to the width is = 5 X 40 = 200 cm2
The area of the road parallel to the length is = 5 X 60 = 300 cm2
But, at the centre the square of 5 X 5 cm2 is duplicated by both the roads.
Hence the total area of the road is = 200 + 300 – 25 = 475 cm2
Therefore the area of the lawn excluding the road is = 2400 – 475
= 1925 cm2 Answer.
Competency Goal 2 : Competency Goal 2 Sample Problem 2.04 Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems. Anita and her father are building an addition on their home. A section of a new wall is 6 feet wide and 8 feet high. The are installing a diagonal brace to make sure that the vertical boards are perpendicular to the horizontal boards. How long does the brace need to be?
Competency Goal 2 : Competency Goal 2 Solution Use the Pythagorean Theorem to find the length of the brace.
a2 + b2 = c2 Pythagorean Theorem
62 + 82 = c2 a = 6, b = 8
36 + 64 = c2 Simplify.
100 = c2 Add.
= c Take the square root of each side.
10 = c Simplify.
The brace should be 10 feet long.
Competency Goal 2 : Competency Goal 2 Sample Problem:
Determine the scale factor for dilation with center C. Then determine whether the dilation is an enlargement, reduction, or congruence transformation. [where the green box is the transformation] 2.05 Identify, predict, and describe dilations in the coordinate plane.
Competency Goal 2 : Competency Goal 2 Solution:
Competency Goal 3 : 3.01 Collect, organize, analyze, and display data (including scatter plots) to solve problems. Sample Problem:
The scatter plot displays the heights of a group of girls of various ages.
a. How many girls are represented?
b. About how tall was the
11-year- old girl?
c. How much taller was the tallest girl than the shortest girl?
d. Which range of heights includes the most girls:
2-3 feet, 3-4 feet, or 4-5feet?
Competency Goal 3
Competency Goal 3 : Competency Goal 3 Solution:
a. Seventeen girls are represented.
b. The 11-year-old girl was about 54 inches or 4 feet 6 inches tall.
c. The shortest girl was 24 inches or 2 feet tall, and the tallest girl was 60 inches or 5 feet tall, so the tallest girl was 36 inches or 3 feet taller than the shortest girl.
d. Most girls are in the height range of 3 -4 feet.
Competency Goal 3 : 3.02 Approximate a line of best fit for a given scatter plot; explain the meaning of the line as it relates to the problem and make predictions. Sample Problem:
The table shows the results of a survey showing the
average amount of time twelve teenagers exercised
per week and their scores on a fitness test on which
the maximum possible score is 60.
a. Draw a scatter plot and estimate a line of best fit.
b. Is there a positive or negative correlation
between the amount of time spent exercising
and scores on the fitness test?
c. Based on this data, about what score would you expect a teenager who exercises 10 hours a week to score on
the fitness test?
d. Based on this data, about how many hours a week
would you expect a teenager who gets a fitness test
score of 40 to exercise? Competency Goal 3
Competency Goal 3 : Competency Goal 3 Solution: a. Your line of best fit may differ because of
estimation.
b. The correlation is positive because fitness test
score increases as the number of hours of
exercise increases. The line of best fit slopes up
and to the right.
c. A teenager who exercises 10 hours per week
might score about 55.
d. A teenager who gets a score of 40 might
exercise about 6 hours a week.
Competency Goal 3 : 3.03 Identify misuses of statistical and numerical data. Sample Problem: Competency Goal 3 A survey asked a group of students to name their favorite type of pet. Choose and make an appropriate display for the situation. Solution:
Competency Goal 4 : Competency Goal 4 4.01 Develop an understanding of function.
a) Translate among verbal, tabular, graphic, and algebraic representations of functions.
b) Identify relations and functions as linear or nonlinear.
c) Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
d) Interpret and compare properties of linear functions from tables, graphs, or equations. Sample Problems:
Make a function table for the rule y = x – 2. Use input values of –1, 3, and 5. Then graph the function.
Solution:
Step 1 Record the input and output in a function table. List the input and output as ordered pairs.
Competency Goal 4 : Competency Goal 4 Solution: (contd.) Step 2: Graph the ordered pairs on the coordinate plane. The x-coordinates represent the input values. The y-coordinates represent the output values.
Step 3: The points appear to lie on a line. Draw the line that contains these points.
The line is the graph of y = x – 2. For any point on this line, y = x − 2.
Competency Goal 4 : Competency Goal 4 4.02 Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept. Sample Problems: Find the slope of the line. The slope of the line is 2.
Solution:
Competency Goal 4 : Competency Goal 4 4.03 Solve problems using linear equations and inequalities; justify symbolically and graphically. Sample Problems:
Karli has $12 to spend at the grocery store. She must buy 1 gallon of milk and some bags of snacks. The gallon of milk costs $3. How many bags of snacks can she buy if each bag costs $2.25? Solution: Variable Let s = the number of bags of snacks. Words Cost of the milk plus cost of the snacks equals $12. Equation 3 + 2.25 s = 12 3 + 2.25 s = 12 [ Write the equation. ] - 3 = - 3 [ Subtract 3 from each side. ] 2.25 s = 9 [ Simplif y. ] s = 4 [ 9 ¸ 2.25 = 4 ] Karli can buy 4 bags of snacks.
Competency Goal 4 : Competency Goal 4 4.04 Solve problems using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.
Solve 7n – 3 = 5n – 5.
7n – 3 = 5n – 5 [Write the equation.]
7n – 5n – 3
= 5n – 5n – 5 [Subtract 5n from each side.]
2n – 3 = –5 [Simplify.]
2n – 3 + 3 = –5 + 3 [Add 3 to each side.]
2n = –2 [Simplify.]
n = –1 [Mentally divide each side by 2.]
The solution is –1. Solution: Sample Problems:
Competency Goal 4 : Competency Goal 4 Sample Problems:
Simplify –3a + 2b + 5a – 4b.
The like terms in this expression are –3a and 5a, and 2b and –4b.
–3a + 2b + 5a – 4b [Write the polynomial.]
= –3a + 2b + 5a + (–4b) [Definition of subtraction]
= (–3a + 5a) + [2b + (–4b)] [Group like terms.]
= 2a + (–2b) or 2a – 2b [Simplify by combining like terms.] Solution: