# 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 .

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