# 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

opposite, missing addend.

• 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

and (b) the addition 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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