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# Math 1400 Learning Objectives

Chapter 6 Fractions

Chapter 6 overarching goals
Students will be able to:
• Communicate different representations of a fraction
• Compare two fractions.
• Model and perform computations with fractions.

Section 6.1
Students will be able to:
• State the definition of a fraction as a numeral that represents part of a whole and sketch pictures
that illustrate given fractions.
• State the definition of a fraction as a number that represents relative amounts and sketch pictures
all of which represent the same relative amounts and, hence, are represented by the same fraction
(as a number).
• State the definitions of the following terms: numerator, denominator, simplest form, cross
product, improper fraction, mixed number, complex fraction.
• State the definition of equality of fractions.
• Express a fraction in its simplest form.
• State the definitions of less than and greater than for fractions.
• Show how to compare fraction using common denominators.
• State and apply the cross multiplication property of inequality.
• State the definition of density and apply it to any given pair of fractions.

Section 6.2
Students will be able to:
• Show how to motivate the definition of addition and subtraction of fractions using concrete
models.
• Compute sums and differences of given pairs of fractions and provide rationale for your
computations.

Section 6.3
Students will be able to:
• Show how to motivate the definition of multiplication and division of fractions using concrete
models.
• Compute products and quotients of given pairs of fractions and provide rationale for your
computations.
• Describe three equivalent ways to find the quotient of two fractions.
• State the definitions of multiplicative inverse and reciprocal .

Chapter 7 Decimals, Ratio, Proportion, and Percent

Chapter 7 overarching goals
Students will be able to:
• Convert decimals to their fraction representation
• Represent, model and perform addition, subtraction, multiplication and division of
decimals.
• Solve problems using ration, proportion and percent.

Section 7.1
Students will be able to:
• Show how to motivate and represent decimals using a hundreds square and number line.
• Write a given decimal numeral in expanded form.
• Characterize the fractions with terminating decimal representations.
Order decimals using their (a) fraction representation and (b) decimal representation.
• Justify the “moving the decimal point” when multiplying or dividing by a power of 10.

Section 7.2
Students will be able to:
• Compute sums, differences, products, and quotients of numbers in decimal form (a) using the
standard algorithms and (b) using a calculator.
• Change any fraction to its decimal form.
• Convert given repeating decimals to their fraction form and characterize the fractions that have
repeating, nonterminating decimal representations.

Section 7.3
Students will be able to:
• State definitions of the following: ratio, proportion.
• Apply the definition of cross multiplication of equal ratios.
• Solve applied problems involving ratios and proportions.

Section 7.4
Students will be able to:
• Define n% for any fraction n and solve problems involving percents using a variety of methods:
grids, proportion, equation, calculator.
• Convert any fraction, decimal, or percent into any of the other two forms.
• Solve applied problems involving percents.

Chapter 8 Integers

Chapter 8 overarching goals
Students will be able to:
• Explain how to represent, model and perform addition, subtraction, multiplication and
division of integers.
• Solve problems involving negative exponents .

Section 8.1
Students will be able to:
• State the definition of the set of integers and represent integers (a) using colored chips and (b) on
the integer number line.
• Explain how to add integers using (a) a set model and (b) a measurement model.
• Define addition of integers via whole numbers and opposites.
• Explain and apply the opposite of the opposite and additive cancellation properties.
• Explain how to subtract pairs of integers using each of these approaches: take-away, adding the
• Distinguish between the terms “negative”, “opposite”, and “minus”.

Section 8.2
Students will be able to:
• Explain how to represent multiplication of integers using repeated addition and patterns.
• Define multiplication of integers via whole numbers and opposites.
• Define and apply the distributive property of integer multiplication over addition (subtraction).
• Explain and apply properties of integer multiplication.
• State and apply the multiplication cancellation property.
• Explain division of integers using the missing factor approach .
• State and apply the definitions of negative exponents and scientific notation.
• State the definitions of less than and greater than for integers using (a) the number line approach
• State and apply the properties of less than and greater than with respect to addition, subtraction,
and multiplication.
• Understand the concept of and methods for the multiplication and division of integers.
• Know the rules of signs for multiplication of integers
• Understand the ordering of integers.
• Know the number properties of integer multiplication.
• Understand and be able to work with negative exponents.

Chapter 9 Rational Numbers and Real Numbers, with and Introduction to Algebra

Chapter 9 overarching goals
Students will be able to:
• Explain and perform addition, subtraction, multiplication and division of rational
numbers.
• Be able to order rational numbers.
• Explain the subset relationships among the sets of rational numbers, irrational numbers,
terminating decimals, and repeating or nonrepeating nonterminating decimals.
• Be able to calculate nth roots.
• Solve linear equations and inequalities.
• Use graphs to solve problems.

Section 9.1
Students will be able to:
• State the definition of the set of rational numbers and the definition of equality of rational
numbers.
• Define addition of rational numbers.
• State the definition of subtraction of rational numbers.
• State the definition of multiplication of rational numbers.
• State the definition of division of rational numbers and explain how to divide rational numbers in
three different ways.
• Find sums, differences, products, and quotients of two rational numbers using both written and
calculator methods.
• Order rational numbers using the following methods: the number line, addition, common positive
denominators, cross multiplication property of inequality.
• Explain and apply properties of ordering rational numbers including the density property.

Section 9.2
Students will be able to:
• State the definition of the set of real numbers and explain the subset relationships among the sets
of rational numbers, irrational numbers, terminating decimals, and repeating or nonrepeating
nonterminating decimals.
• State the definition of the square roots and principal square root of a nonnegative real number and
determine square roots.
• State the definition of and calculate nth roots.
• State the definition of rational exponent.
• State and apply properties of rational exponents.
• State and apply the definitions of inequality and solution set of an inequality.
• Solve linear equations and inequalities.
• Apply properties of real number inequalities.

Section 9.3
Students will be able to:
• Construct and interpret graphs of the following kinds of functions: linear, quadratic , exponential,
cubic , step.
• Apply the vertical line test to determine if a graph is the graph of a function.
• Use graphs to solve problems.

Extra Topic 1 – p876
Students will be able to:
• Be able to use logic to represent and analyze arguments.
• Be able to use deductive reasoning to solve problems.

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