Download Prealgebra Curriculum Outline 2011

PRE-ALGEBRA
CURRICULUM OUTLINE
2011 - 2012
_________________________________________________________________________
OVERVIEW:
1. Order of Operations and Exponents
2. Number Theory
3. Fractions
4. Decimals
5. Proportions and Percents
6. Planar Geometry
7. Perimeter and Area
8. Square Roots, Radicals, and the Pythagorean Theorem
9. Volume and Surface Area
10. Positive and Negative Numbers
11. Introduction to Algebra
12. Graphing and Functions
OUTLINE:
Notes:
Each class is 50 minutes and meets 4 times per week.
Time frames are approximate and include assessments.
Asterisks (*) indicate optional topics.
Quarter 1:
UNIT 1: ORDER OF OPERATIONS AND NUMBER THEORY
1.
2.
3.
4.
5.
6.
7.
8.
9.
Approx. 8 classes
Calculate powers of numbers
Recognize and use common exponents
Understand place value as it relates to powers of 10
Multiply and dividing by powers of 10
Convert between standard form and scientific notation
Simplify numerical expressions with exponents using the order of operations.
Understand the difference between prime and composite numbers
Determine the prime factorization of a composite number.
Use divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 10.
UNIT 2: VARIABLE EXPRESSIONS AND EQUATIONS
Approx. 8 classes
1. Evaluate variable expressions using substitution.
2. Solve one-step equations using addition, subtraction, multiplication and division.
3. Convert everyday language into variable expressions.
UNIT 3: FRACTIONS
1.
2.
3.
4.
5.
Find equivalent fractions and simplifying fractions
Change improper fractions to mixed numbers (and vice versa)
Compare and order fractions and mixed numbers
Add, subtract, multiply and divide fractions and mixed numbers
Find a fraction of another number
UNIT 4: DECIMALS
1.
2.
3.
4.
5.
6.
7.
Approx. 8 classes
Approx. 8 classes
Convert fractions to decimals (and vice versa)
Compare and order decimals
Add, subtract, multiply, and divide decimals
Round decimals
Estimate with rounding and compatible numbers
Solve word problems with decimals
Mental math with decimals
Pre-Algebra
2011-2012 Curriculum Outline
Packer Collegiate Institute
Revised: September 2011
Page 2 of 5
Quarter 2:
UNIT 5: PROPORTIONS AND PERCENTS
1.
2.
3.
4.
5.
6.
7.
8.
9.
Approx. 16 classes
Convert fractions to decimals to percents, and the reverse.
Solve proportions using equivalent fractions and cross-multiplying.
Solve word problems involving proportions and ratios.
Solve word problems involving distance rate and time.
Use unit pricing to compare prices.
Find a percent of an amount.
Solve word problems involving percent change.
Use proportions to solve percent problems.
Compute simple interest.
UNIT 6: PLANAR GEOMETRY
Approx. 16 classes
1. Name points, lines, line segments, rays and planes.
2. Measure and construct angles using a protractor.
3. Use knowledge of parallel and perpendicular lines, corresponding, alternate interior,
supplementary and complementary angles to solve angle puzzles.
4. Classify polygons.
5. Classify triangles based on sides and angles.
6. Classify quadrilaterals.
7. Determine measurement of angles in triangles and quadrilaterals.
8. Determine the number of degrees in a polygon.
Pre-Algebra
2011-2012 Curriculum Outline
Packer Collegiate Institute
Revised: September 2011
Page 3 of 5
Quarter 3:
UNIT 7: PERIMETER AND AREA
1.
2.
3.
4.
5.
6.
7.
Approx. 10 classes
Convert measurements within metric system and customary system.
Find the perimeter of a polygon.
Use the perimeter to find the length of missing sides in regular and irregular shapes.
Find the circumference of a circle, both using 3.14 for pi and in terms of pi.
Find the radius or diameter of a circle if the circumference is given.
Find the area of a triangle, parallelogram, regular polygon or compound polygon.
Find the area of a circle.
UNIT 8: SQUARE ROOTS, RADICALS, PYTHAGOREAN THEOREM
Approx. 8 classes
1. Simplify radicals.
2. Use the Pythagorean Theorem to determine if a triangle is a right triangle and to find the
missing sides of triangles.
UNIT 9: VOLUME AND SURFACE AREA
Approx. 8 classes
1. Find the volume of a prism, including rectangular, triangular prisms and cylinders.
2. Use the Pythagorean theorem to find missing sides, and then finding the volume of a
triangular prism.
3. Find the volume of a pyramid, including rectangular, triangular pyramids and cones.
4. Find the surface area of rectangular and triangular prisms.
Pre-Algebra
2011-2012 Curriculum Outline
Packer Collegiate Institute
Revised: September 2011
Page 4 of 5
Quarter 4:
UNIT 10: POSITIVE AND NEGATIVE NUMBERS
1.
2.
3.
4.
5.
6.
Determine absolute value and evaluate expressions with absolute value.
Add and subtract integers.
Add and subtract positive and negative decimals and fractions.
Multiply and divide integers.
Multiply and divide positive and negative decimals and fractions.
Apply the order of operations to expressions involving positive and negative numbers.
UNIT 11: INTRODUCTION TO ALGEBRA
1.
2.
3.
4.
5.
6.
7.
8.
9.
Approx. 8 classes
Approx. 16 classes
Identify "like terms".
Use the distributive rule to simplify expressions.
Determine whether given answers are solutions to equations.
Simplify the expressions in an equation to obtain an equivalent equation.
Solve equations with addition or subtraction.
Solve equations with multiplication and division.
Solve equations with multiple transformations.
Solve equations with variables on both sides of the equation.
Use equations to solve word problems.
UNIT 12:
GRAPHING AND FUNCTIONS
Approx. 10 classes
1. Find and identify points on the coordinate plane.
2. Determine whether ordered pairs are solutions to a linear equation.
3. Make a table of values of points from a linear equation, and use them to determine the
graph.
4. Understand slope and y-intercept.
5. Relate the concept of slope to rise-over-run.
6. Graph an equation using the slope/intercept form.
7. Solve for y in terms of x.
8. Find the equation of a line from the graph.
Pre-Algebra
2011-2012 Curriculum Outline
Packer Collegiate Institute
Revised: September 2011
Page 5 of 5