Math 1400 Learning Objectives

Math 140 Learning Objectives
Mathematics for Elementary Teachers: A Contemporary Approach, 7th Edition, Chapters 1-9
Musser, Burger & Peterson

Overarching, continuous course goals
Students will be able to:
• Use mathematical problem solving techniques .
• Use reasoning skills to interpret and solve problems.
• Use mental math and estimation skills to approximate sums , differences, products and quotients.
• Apply the order of operations.
• Determine, justify and apply different number properties such as closure, commutativity,
associativity, distributivity of multiplication over addition (subtraction), identity, and inverse for
whole numbers, integers, fractions, decimals , rational numbers, real numbers.

Chapter 1 Introduction to Problem Solving
Chapter 1
Students will be able to:
• Use inductive reasoning to solve problems

Chapter 2 Sets, Whole Numbers, and Numeration

Chapter 2 overarching goals
Students will be able to:
• Use Venn diagrams to solve problems involving sets
• Be able to represent numbers in different numeration systems
• Identify and represent functions in different ways

Section 2.1
Students will be able to:
• Describe the concept of a set, use set notation and define the following terms: counting numbers,
whole numbers, element, empty set, equivalent sets , one-to-one correspondence, finite set,
infinite set, universal set, disjoint sets, union, intersection, complement, ordered pairs, subset,
proper subset, Cartesian product.
• Solve problems using Venn Diagrams
• Represent relationships among sets using Venn Diagrams.

Section 2.2
Students will be able to:
• Communicate what numbers constitute the set of whole numbers
• Describe the relations of less than and greater than for whole numbers using sets.
• Express whole numbers using different numeration systems such as the Egyptian, Babylonian,
Roman, Mayan and Hindu-Arabic numerations systems.
• Compare the attributes (additive, subtractive, multiplicative, positional, place value) of the
different numerations systems listed above.

Section 2.3
Students will be able to:
• Write a Hindu-Arabic numeral in any base from two to ten in its expanded form and convert from
expanded form to the numeral represented.
• Convert a numeral from any base to base ten and vice versa.

Section 2.4
Students will be able to:
• State the definition and provide examples of a relation.
• Identify sequences as arithmetic, geometric, or otherwise. If arithmetic, find the common
difference ratio and the nth term. If geometric, find the common ratio and the nth term.
• State the definition of a function, the domain, range, and codomain of a function.
• Describe the differences and similarities between relations and function.
• Identify functions and represent functions graphically and as tables , formulas and ordered pairs.

Chapter 3 Whole numbers – Operations and Properties

Chapter 3 overarching goals
Students will be able to:
• Represent and model addition, subtraction, multiplication and division of whole numbers.
• Be able to solve problems involving exponents.

Section 3.1
Students will be able to:
• Represent addition of whole numbers using a set model and a measurement model.
• Represent subtraction of whole numbers using the take-away and missing addend approaches.
• Explain and illustrate the comparison model of subtraction.
• Represent addition and subtraction problems using multibase pieces and Cuisenaire rods.

Section 3.2
Students will be able to:
• Describe multiplication of whole numbers using repeated addition and rectangular array
approaches, using a set model and a measurement model.
• Represent division of whole numbers using the missing factor approach and the repeated
subtraction approach.
• Explain the difference between partitive and measurement division.
• Explain division problems involving zero using the missing factor approach.
• State the division algorithm and illustrate it using examples on the number line .

Section 3.3
Students will be able to:
• Describe less than and greater than with whole numbers using the operation of addition.
• Justify and apply the following properties of less than: transitivity, property of less than and
addition, property of less than and multiplication.
• State the definition of whole number exponents using repeated multiplication.
• Justify and apply the properties of exponents.
• Explain and use the order of operations to simplify arithmetic expressions.

Chapter 4 Whole Number Computations – Mental, Electronic, Written

Chapter 4 overarching goals
• Explain and illustrate traditional and nontraditional algorithms for addition, subtraction,
multiplication, and division of whole numbers.
• Be able to solve problems within different bases.

Section 4.1
Students will be able to:
• Describe scientific notation as it appears on scientific calculators.

Section 4.2
Students will be able to:
• Justify the standard addition algorithm using (a) concrete models and (b) place value and
properties of addition.
• Explain, illustrate and use (a) intermediate algorithms for addition that lead to the standard
algorithm and (b) the lattice method for addition .
• Justify the standard subtraction algorithm using (a) concrete models and (b) place value and
properties of subtraction.
• Explain, illustrate and use nontraditional algorithms for subtraction.
• Justify the standard multiplication algorithm using place value and properties of multiplication.
• Explain, illustrate and use (a) intermediate algorithms that lead to the standard multiplication
algorithm and (b) the lattice method for multiplication.
• Explain, illustrate and use long division algorithms (including the scaffold method) that lead to
the standard algorithm.
• Justify the standard long division algorithm using multibase pieces or place value and properties
of division.

Section 4.3
Students will be able to:
• Add, subtract, multiply and divide in bases 2 through 12.

Chapter 5 Number Theory

Chapter 5 overarching goals
Students will be able to:
• Be able to determine GCF and LCM of a given pair of numbers.
• Use the prime factorization of a number to determine if the number is prime or
composite, to find the number of factors the number has, and to find all the factors of the
number.

Section 5.1
Students will be able to:
• State and apply the definitions of the following terms: prime, composite, divides, factor, divisor,
factor tree, multiple, is divisible by, common factor, common multiple, greatest common factor
(GCF), least common multiple (LCM).
• State and apply the fundamental theorem of arithmetic.
• State and apply tests for divisibility by 2,3,4,5,6,8,9,10,11,12.
• Find the prime factorization of a given composite number.
• Determine if a given number is prime or composite.

Section 5.2
Students will be able to:
• Use the prime factorization of a number to find all of its factors.
• Use the prime factorization of a number to determine the number of factors the number has.
• Find the GCF of a given pair of numbers using the set intersection method, the prime
factorization method and the Euclidean algorithm.
• Find the LCM of a given pair of numbers using the set intersection method, the prime
factorization method and the build-up method.
• Relate the GCF and LCM of any two numbers to the product of the numbers .