Course Description
This course serves as a pre-curser to Algebra A. Calculator activities are provided to stimulate student interest and to facilitate the introduction of math concepts which include whole numbers, properties and rules of operations, number theory, rational numbers, ratio, proportion, percentage, measurement, statistics and probability, real numbers, and graphing. Students will also study basic algebra principles such as algebraic expressions, polynomials, equations, and factoring.
Credits: 5
Course Content
Unit 1 - Whole Numbers and Number Theory
California Curriculum Standards
Students place value in whole numbers, use expanded notation to represent whole numbers, and practice addition, subtraction, multiplication and division of whole numbers: Number Sense 1.3, 1.5 (Grade 3), 1.1, 3.0, 3.1, 3.2, 3.3, 3.4 (Grade 4); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7)
Students use variables and work with equations with the addition, subtraction, multiplication, and division of whole numbers: Algebra & Functions 1.1(Grade 4), 1.2 (Grade 5) 1.1 (Grade 6), 1.1 (Grade 7); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7)
Students understand the Associative, Commutative, Identity, Inverse and Zero, and Distributive Properties with Whole Numbers Algebra & Functions 1.1 (Grade 2), 1.3 (Grade 7), 1.5 (Grade 3); Number Sense 2.6 (Grade 4)
Students understand the order of operations and the use of a calculator
Algebra & Functions 1.2 (Grade 4), 1.3 (Grade 5), 1.4 (Grade 6); Number Sense 3.1, 3.2 (Grade 4)
Students factor whole numbers and understand prime factors and exponents Number Sense 4.1 (Grade 4), 4.2 (Grade 4), 1.3, 1.4 (Grade 5), 2.4 (Grade 6); Algebra & Functions 1.4 (Grade 6)
Unit Objectives
Upon completion of this unit, the student will be able to:
- Understand the concept of place value in whole numbers.
- Perform the operations and solve word problems involving of addition, subtraction, multiplication and division of whole numbers.
- Use variables in the application of the addition, subtraction, multiplication and division of whole numbers.
Solve simple equations and word problems with variables applying the operations of addition, subtraction, multiplication and division of whole numbers.
- Apply the associative, commutative, identity, inverse, zero properties and the distributive rule in working with whole numbers.
- Learn the basic operation of a calculator and use a calculator to perform the operations of the addition, subtraction, multiplication and division of whole numbers.
- Find all factors of a given whole number and factor a whole number using prime numbers and exponents.
Find the greatest common factor (GCF) and the lowest common multiple (LCM) between two or more whole numbers.
- Use a calculator to compute numbers with exponents and use “power of ten” exponents to express whole numbers in expanded notation.
- Develop a mathematical vocabulary.
Unit 2 - Rational Numbers
California Curriculum Standards
Students will understand fractions, improper fractions, and mixed numbers
Number Sense 4.0 (Grade 2), 1.5, 1.7 (Grade 4), 2.0, 2.4, 2.3, 2.5 (Grade 5), 1.2 (Grade 7)
Students will simplify, add, subtract, multiply, and divide fractions and understand the use of a calculator in relation to such practices Number Sense 1.0, 2.0, 2.3, 2.4, 2.5 (Grade 5), 1.2 (Grade 7); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7); Algebra & Functions 1.4 (Grade 6)
Students will use variable and equations while adding, subtracting, multiplying, and dividing fractions as well as solving word problems Number Sense 2.0, 2.5 (Grade 5); Algebra & Functions 1.1 (Grade 4), 1.2 (Grade 5), 1.1 (Grade 6), 1.1 (Grade 7); Mathematical Reasoning
1.1, 1.2, 1.3 (Grade 7)
Students will understand concepts related to decimals including decimal numbers, converting fractions to decimals and decimals to fractions, the addition, subtraction, multiplication and division of decimals, and working with equations involving decimals Number Sense 1.6 (Grade 4), 1.0, 2.0, 2.1, 2.2 (Grade 5), 1.2, 1.3, 1.5 (Grade 7); Algebra & Functions 1.1, 1.4
(Grade 6), 1.1 (Grade 7); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7)
Unit Objectives
Upon completion of this Unit, the student will be able to:
- Understand the concept of a fraction – a whole and its parts.
- Convert mixed numbers to improper fractions and vice-versa.
- Find the product and quotient of two fractions.
- Simplify or “reduce” a fraction to its simplest terms.
- Solve word problems with the multiplication and division of fractions.
- Use a calculator in the division of whole numbers with a quotient which is not a divisor (has a remainder) and to convert fractions to decimals, decimals to fractions, and perform the arithmetic operations involving numbers with decimals.
- Perform the operations of addition and subtraction of fractions and solve word problems with the addition and subtraction of fractions.
- Use variables in the application of the addition, subtraction, multiplication and division of fractions.
Solve simple equations and word problems with variables applying the operations of addition, subtraction, multiplication and division of fractions.
- Understand decimal notation and place value.
- Convert fractions to decimals and decimals to fractions.
- Perform the operations of the addition, subtraction, multiplication and division of numbers involving numbers with decimals.
- Solve simple equations and word problems involving numbers with decimals.
- Develop a mathematical vocabulary.
Unit 3 - Ratio, Proportion, Percentage, Measurement, Statistics, and Probability
California Curriculum Standards
Students will understand ratios and proportions and work with them in word problems, scale drawings, similar triangles, and DRT equations Number Sense 2.7 (Grade 3), 1.2, 1.3 (Grade 6); Algebra & Functions 2.1 (Grade 3), 2.0, 2.2 & 2.3 (Grade 6), 4.2 (Grade 7); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7); Measurement & Geometry 1.2, 1.3 (Grade 7)
Students will work with percentages including figuring base and rate, increase and decrease, and percentage formulas Number Sense 1.0 (Grade 5), 1.4 (Grade 6), 1.0, 1.3, 1.6, 1.7 (Grade 7); Algebra & Functions 1.4, 2.0, 2.1 (Grade 6)
Students will understand metric measurements of length, area, volume/capacity, and mass/weight, and to convert those measurements into different systems Algebra & Functions 1.4, 2.0, 2.1 (Grade 6); Measurement & Geometry 1.0, 1.1, 2.4 (Grade 7); Number Sense 1.0 (Grade 5)
Students will find Range, Mean, Median and Mode and figure probability of simple events Statistics, Data Analysis & Probability 1.0, 1.1, 1.4, 3.3, 3.4 (Grade 6)
Unit Objectives
Upon completion of this Unit, the student will be able to:
- Understand the concept of a ratio and express the relationship between two quantities as a ratio in two ways.
- Set up two ratios into a proportion and solve by using the product of the means and extremes.
Solve word problems using ratios and proportions.
- Use ratios and proportions in the applications of scale drawings and similar triangles.
- Use the formula D = RT, to solve word problems involving distance, rate (speed) and time.
- Use a calculator to solve problems involving proportions.
- Understand and use the concept of percentage.
- Given a fraction, decimal or percent, convert it into the other two number forms.
- Using base, rate and percentage, solve proportions involving percentage.
- Calculate the percentage increase or decrease of a numerical change.
- Solve word problems involving money issues like discounts, commissions, installment purchasing, interest and buying items at the school store.
- Using the percentage formula p = r x b and the interest formula I = P x R x T, solve word problems involving percentage and interest..
- Use a calculator to solve problems involving money.
- Converting from one metric unit of length to another, one metric unit of area to another, one metric unit of volume/capacity to another, one metric unit of mass/weight to another, units of length, area, volume/capacity and mass/weight in different systems of measurement, using a unit multiplier, and use a calculator to compute areas and volumes.
- Given a set of data, calculate the range, mean, median and mode of the data.
- Find the mean of grouped data and expressing the data in a frequency table and the probability of a simple event.
- Use the Counting Principle to determine the number of ways an event can occur.
- Do research on the use of mathematics in daily life and in careers.
- Develop a mathematical vocabulary.
Unit 4 - Real Numbers
California Curriculum Standards
Students will work with real numbers and understand the number line, absolute value, adding, subtracting, multiplying and dividing integers, and solve word problems and equations involving integers. Number Sense 1.8 (Grade 4), 1.5 (Grade 5), 1.4, 2.3 (Grade 6), 1.4, 2.3, 2.5, (Grade 7), Algebra & Functions 1.3 (Grade 5), 1.1 (Grade 6), 1.2, 1.3 (Grade 7); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7)
Students will understand rational numbers including how to add, subtract, multiply and divide rational numbers, simplify and solve algebraic expressions with rational numbers, and will find, approximate, and simplify square roots Number Sense 1.1, 1.4 (Grade 6), 1.2, 1.4, 2.4 (Grade 7); Algebra & Functions 1.1 (Grade 6), 1.1, 1.4 (Grade 7); Mathematical Reasoning 1.1, 1.2, 1.3 (Grade 7); Algebra I 2.0; Measurement & Geometry 3.3 (Grade 7)
Students will graph real numbers on the number line, understand ordered pairs on the coordinate plane, and graph horizontal and vertical lines Number Sense 1.1 (Grade 6); 1.4, 2.4 (Grade 7); Algebra & Functions 1.4, 1.5 (Grade 5)
Unit Objectives
Upon completion of this Unit, the student will be able to:
- Learn the basics of a coordinate or number line, graphing integers.
- Add, subtract, multiply, and divide integers.
- Understand absolute value and how it applies to positive and negative numbers (signed numbers).
- Solve equations and word problems using addition, subtraction, multiplication, and division of integers.
- Multiply integers with grouping symbols.
- Use the correct order of operations when performing the basic operations with integers.
- Use a calculator to solve problems involving integers and to compute with rational numbers.
- Learn to graph rational numbers and square roots on a number line.
- Learn to add, subtract, multiply and divide rational numbers.
- Simplify algebraic expressions with rational numbers and solve equations using rational numbers.
- Understand square roots and find their approximate values.
- Simplify square roots.
- Solve word problems using the Pythagorean Theorem.
- Learn to graph all real numbers (rational and irrational) on a number line and to graph ordered pairs and horizontal and vertical lines on a coordinate plane.
- Develop a mathematical vocabulary.
Unit 5 - Basic Algebra
California Curriculum Standards
Students classify and write algebraic expressions, use exponents in algebraic expression, and adding like algebraic terms Algebra & Functions 1.1, 1.4, 2.1, 2.2 (Grade 7); Algebra I 10.0
Students will understand polynomials and monomials, adding and subtracting polynomials, multiplying monomials and terms with exponents, and multiplying terms with signed numbers Algebra I 10.0; Algebra and Functions 2.2 (Grade 7)
Students will multiply binomials (FOIL) and divide monomials by numbers, terms with exponents, fractions by common factors, and polynomials by monomials Algebra I 10.0; Algebra and Functions 1.4 (Grade 6), 2.2 (Grade 7)
Students will solve one, two, three, and four step equations, gather variable and constant terms, simplify expressions with grouping symbols, simplify polynomials, and practice monomial factoring in polynomials Algebra & Functions 1.1, 1.4 (Grade 6), 4.1 (Grade 7); Algebra I 4.0, 5.0, 10.0, 11.0, 12.0; Mathematical Reasoning 1.1, 1.2, 1.3, 2.1 (Grade 7)
Students will graph solutions to equations and to inequalities on a number line, understand and graph the slope of a line, and understand and graph the equations of a line. Algebra and Functions 1.5, 3.3, 4.1 (Grade 7); Number Sense 1.1 (Grade 6); Algebra I 6.0, 7.0
Unit Objectives
Upon completion of this Unit, the student will be able to:
- Classify polynomials as a monomial, binomial or trinomial.
- Write algebraic expressions given words indicating certain arithmetic operations.
- Express a number in exponential form and find the numerical value of numbers in exponential form.
- Write algebraic expressions with variables in exponential form.
- Perform the addition of “like” algebraic terms and the addition and subtraction of polynomials, combining “like” terms.
- Multiply and divide monomials by constants (numbers), algebraic terms containing exponents, and terms with signed numbers.
- Use grouping symbols when multiplying algebraic terms.
- Multiply binomials, using the FOIL method.
- Divide polynomials by monomials.
- Solve problems with a calculator.
- Solve one-step, two-step, and three-step equations and equations with grouping symbols (four-step).
- Simplify algebraic expressions by combining “like” terms and algebraic terms with grouping symbols.
- Simplify polynomials, combining “like” terms and factor polynomials, using simple monomial factoring.
- Graph solutions to equations and inequalities on a number line.
- Understand the characteristics of a line, like slope, x-intercept and y-intercept.
- Calculate the slope of a line given two points.
- Understand equations of lines, finding key information from the equation.
- Given an equation of a line, graph the line by plotting points and using the key information acquired from the equation.
- Develop a mathematical vocabulary.
