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Course Description
Basic Math B is designed to teach students basic mathematical concepts including fractions, mixed numbers, decimals, ratio, proportion, percent, and measurement. Students are given several opportunities to work with the principles and practice the applications. Concepts covered in each unit are reviewed in the next, to be sure students are building a solid foundation for future mathematical studies. This course helps students develop a concrete understanding of the mathematical concepts necessary to prepare for the math portion of the CAHSEE.
Credits: 5
Languages: English and Spanish
Released: 2010
Course Content
Unit 6 – Fractions
California Mathematics Content Standards:
- Number Sense 1.5: Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers; explain equivalency of fractions.
- Number Sense 1.7: Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
- Number Sense 2.0: Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.
- Number Sense 2.1: Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used in a given situation.
- Number Sense 2.1: Add, subtract, multiply, and divide rational numbers.
- Number Sense 2.2: Explain the meaning of multiplication and division of positive fractions and perform the calculations.
- Number Sense 2.2: Add and subtract fractions by using factoring to find common denominators.
- Number Sense 2.3: Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions, and express answers in simplest form.
- Number Sense 2.4: Understand the concept of multiplication and division of fractions.
- Number Sense 2.4: Determine the least common multiple and greatest common divisor of whole numbers; use them to solve problems with fractions.
- Number Sense 2.5: Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
- Number Sense 3.1: Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context.
- Mathematical Reasoning 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
- Mathematical Reasoning 1.2: Determine when and how to break a problem into simpler parts.
- Mathematical Reasoning 2.1: Use estimation to verify the reasonableness of calculated results.
- Mathematical Reasoning 2.2: Apply strategies and results from simpler problems to more complex problems.
- Mathematical Reasoning 2.3: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, and diagrams to explain mathematical reasoning.
Unit Objectives
Upon completion of this Unit, students will:
- Understand that fractions refer to parts of a set or whole.
- Explain different interpretations of fractions through drawings and real-life examples.
- Write fractions, identify the parts of a fraction, and express a fractional number written in words and vice versa.
- Distinguish between proper and improper fractions and mixed numbers.
- Convert improper fractions to mixed numbers and vice versa.
- Find the GCF and LCM given two or more whole numbers.
- Understand that the LCM is used to find the LCD in adding and subtracting fractions.
- Understand that the GCF is used to reduce fractions to their simplest form.
- Understand the equivalency of fractions.
- Find the sums, differences, products, and quotients of two or more fractions and express in reduced form.
- Solve word problems involving multiplication, division, addition, and subtraction of proper fractions.
Unit 7 – Mixed Numbers
California Mathematics Content Standards:
- Number Sense 1.5: Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers; explain equivalency of fractions.
- Number Sense 1.7: Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
- Number Sense 2.0: Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.
- Number Sense 2.1: Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used in a given situation.
- Number Sense 2.1: Add, subtract, multiply, and divide rational numbers.
- Number Sense 2.2: Explain the meaning of multiplication and division of positive fractions and perform the calculations.
- Number Sense 2.2: Add and subtract fractions by using factoring to find common denominators.
- Number Sense 2.3: Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions, and express answers in simplest form.
- Number Sense 2.4: Understand the concept of multiplication and division of fractions.
- Number Sense 2.4: Determine the least common multiple and greatest common divisor (factor) of whole numbers; use them to solve problems with fractions.
- Number Sense 2.5: Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
- Number Sense 3.1: Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context.
- Mathematical Reasoning 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
- Mathematical Reasoning 1.2: Determine when and how to break a problem into simpler parts.
- Mathematical Reasoning 2.1: Use estimation to verify the reasonableness of calculated results.
- Mathematical Reasoning 2.2: Apply strategies and results from simpler problems to more complex problems.
- Mathematical Reasoning 2.3: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, and diagrams to explain mathematical reasoning.
Unit Objectives
Upon completion of this Unit, students will:
- Understand that fractions refer to parts of a set or whole.
- Explain different interpretations of fractions through drawings and real-life examples.
- Write fractions, identify the parts of a fraction, and express a fractional number written in words and vice versa.
- Distinguish between proper and improper fractions and mixed numbers.
- Convert improper fractions to mixed numbers and vice versa.
- Understand that the GCF is used to reduce fractions to their simplest form.
- Understand the equivalency of fractions.
- Find the sums, differences, products, and quotients of two or more fractions and express in reduced form.
- Find the product, quotient, sums, and differences of two mixed number fractions and express in reduced form.
- Solve word problems involving multiplication, division, addition, and subtraction of mixed number fractions.
Unit 8 – Decimal Numbers
California Mathematics Content Standards:
- Number Sense 1.0: Students understand the place value and decimals to two places and how whole numbers and decimals relate to simple fractions.
- Number Sense 1.0: Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals and fractions.
- Number Sense 1.1: Estimate, round, and manipulate very large and very small numbers
- Number Sense 1.1: Compare and order positive fractions, decimals and mixed numbers.
- Number Sense 1.2: Order and compare whole numbers and decimals to two decimal places.
- Number Sense 1.2: Add, subtract, multiply, and divide rational numbers.
- Number Sense 1.3: Convert fractions to decimals and use these representations in estimations, computations, and applications.
- Number Sense 1.5: Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
- Number Sense 1.5: Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers; explain equivalency of fractions.
- Number Sense 1.6: Write tenths and hundredths in decimal and fraction notations and know the fractional equivalents for halves and fourths.
- Number Sense 1.7: Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal.
- Number Sense 2.0: Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of decimals.
- Number Sense 2.1: Add, subtract, multiply, and divide with decimals.
- Number Sense 2.2: Demonstrate proficiency with division, including division with positive decimals and long division with multi-digit divisors.
- Number Sense 3.3: Solve problems involving addition, subtraction, multiplication and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole number multipliers and divisors.
- Number Sense 3.4: Know and understand that fractions and decimals are two different representations of the same concept.
- Mathematical Reasoning 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
- Mathematical Reasoning 1.2: Determine when and how to break a problem into simpler parts.
- Mathematical Reasoning 2.1: Use estimation to verify the reasonableness of calculated results.
- Mathematical Reasoning 2.2: Apply strategies and results from simpler problems to more complex problems.
- Mathematical Reasoning 2.3: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, and diagrams to explain mathematical reasoning.
Unit Objectives
Upon completion of this Unit, students will:
- Understand that fractions refer to parts of a set or whole.
- Write fractions, identify the parts of a fraction, and express a fractional number written in words and vice versa.
- Distinguish between proper and improper fractions and mixed numbers.
- Convert improper fractions to mixed numbers and vice versa and fractions to decimal numbers and vice versa.
- Identify the place values of mixed decimal numbers.
- Read and write decimal numbers in words and numeric form.
- Compare the values of numbers in decimal form.
- Round decimals to a named place value.
- Find the sum, difference, product, and quotient of two or more decimal numbers.
- Solve word problems involving multiplication, division, addition, and subtraction of decimal numbers.
- Solve word problems involving finding the average of two or more numbers.
Unit 9 – Ratio, Proportion, And Percent
California Mathematics Content Standards:
- Algebra & Functions 1.4: Write and solve one-step linear equations in one variable.
- Algebra & Functions 2.0: Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions.
- Algebra & Functions 2.2: Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
- Number Sense 1.0: Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents.
- Number Sense 1.2: Interpret and use ratios in different contexts to show the relative sizes of two quantities, using appropriate notations.
- Number Sense 1.3: Use proportions to solve problems. Use cross-multiplication as a method of solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.
- Number Sense 1.3: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
- Number Sense 1.4: Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
- Number Sense 1.7: Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
- Mathematical Reasoning 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
- Mathematical Reasoning 1.2: Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
- Mathematical Reasoning 1.3: Determine when and how to break a problem into simpler parts.
- Mathematical Reasoning 2.1: Use estimation to verify the reasonableness of calculated results.
- Mathematical Reasoning 2.2: Apply strategies and results from simpler problems to more complex problems.
- Mathematical Reasoning 2.3: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, and diagrams to explain mathematical reasoning.
Unit Objectives
Upon completion of this Unit, students will:
- Understand the concepts of ratio, rate, percent, percentage,
- Find the ratio and the rate between two numbers or quantities.
- Understand proportions and solve for an unknown proportion.
- Identify the means and extremes in a proportion.
- Convert fractions and decimals to percents and vice versa.
- Find the percentage given the percent and base.
- Find the percent given the percentage and base.
- Find the base given the percent and the percentage.
- Solve word problems involving ratios, rates, proportions, discounts, sales tax, commissions, simple interest, and installment purchasing.
Unit 10 – Measurement
California Mathematics Content Standards:
- Algebra and Functions 2.1: Convert one unit of measurement to another.
- Measurement & Geometry 1.0: Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.
- Measurement and Geometry 1.1: Measure the area of rectangular shapes by using appropriate units.
- Measurement and Geometry 1.1: Understand the concept of a constant such as π; know the formulas for the circumference and area of a circle.
- Measurement and Geometry 1.1: Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems.
- Measurement and Geometry 1.2: Recognize that rectangles that have the same area can have different perimeters.
- Measurement and Geometry 1.2: Know common estimates of and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.
- Measurement and Geometry 1.3: Understand that rectangles that have the same perimeter can have different areas.
- Measurement and Geometry 1.3: Understand the concept of volume and use the appropriate units in common measuring systems to compute the volume of rectangular solids.
- Measurement and Geometry 1.3: Know and use the formulas for the volume of triangular prisms and cylinders; compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.
- Measurement and Geometry 1.4: Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.
- Measurement and Geometry 1.4: Differentiate between, and use appropriate units of measures for, two- and three-dimensional objects.
- Measurement and Geometry 2.0: Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale.
- Measurement and Geometry 2.1: Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures.
- Number Sense 1.1: Estimate, round, and manipulate very large and very small numbers.
- Number Sense 1.2: Add, subtract, multiply, and divide rational numbers and take positive rational numbers to whole-number powers.
- Number Sense 1.3: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
- Number Sense 2.0: Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.
- Mathematical Reasoning 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
- Mathematical Reasoning 1.2: Determine when and how to break a problem into simpler parts.
- Mathematical Reasoning 2.1: Use estimation to verify the reasonableness of calculated results.
- Mathematical Reasoning 2.2: Apply strategies and results from simpler problems to more complex problems.
- Mathematical Reasoning 2.3: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, and diagrams to explain mathematical reasoning.
Unit Objectives
Upon completion of this Unit, students will:
- Understand the similarities, differences, advantages, and disadvantages between the US Customary and SI International systems of measurement.
- Measure lines and objects with rulers calibrated in the two systems of measurement.
- Measure angles with a protractor.
- Convert units of length from one unit of measurement to another in both systems of measurement.
- Find the area of rectangles and squares in both systems of measurement and convert units of area from one unit to another in both systems.
- Convert units of liquid and dry measurements and volume/capacity from one unit to another in both systems.
- Convert units of mass from one unity to another in both systems.
- Express measurements in expanded form.
- Use addition, subtraction, multiplication, and division with units of measurement.
- Solve word problems involving length, perimeter, circumference, area, volume/capacity, and mass/weight.
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