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**Note**: some or all of the courses in the subjects
marked as "Transfer" can be used towards a transfer degree: Associate of Science
and Arts or Associate of Engineering Science at DACC. Transferability for
specific institutions and majors varies. Consult a counselor for
this information.

COURSE NUMBER: | MATH118 | |

COURSE TITLE: | Mathematics for Elementary Education I | |

DIVISION: | Sciences | |

IAI CODE(S): | M1 903 | |

SEMESTER CREDIT HOURS: | 4 | |

CONTACT HOURS: | 60 | |

STUDENT ENGAGEMENT HOURS: | 180 | |

DELIVERY MODE: | In-Person |

The study of concepts taught in elementary school with a focus on problem solving and reasoning. Topics include whole numbers, rational numbers, irrational numbers, basic number theory, arithmetic, number patterns, and algebra. This is the first of a two-course sequence (followed with MATH 119).

Place into MATH118 with approved and documented math placement test scores or by completing MATH108 (Intermediate Algebra) with a grade of C or better.

Upon completion of this course, students will be able to:

- Clearly relate, either in written or oral form, interpretations of solutions and the methods/steps, including all steps and reasoning on how the solution was achieved (using multiple forms of explanations such as expressions, equations, charts, tables, diagrams).
- Use all appropriate symbolic forms that elementary school students would encounter, verbally and in writing.
- Explain steps and solutions using multiple methods for mathematical concepts or processes, verbally and in writing, including
- base-ten system using words, diagrams, situations, and contexts.
- fraction concepts (including, but not limited to, size, identifying the whole, arithmetic of fractions and percents).
- addition, subtraction, multiplication, and division of all rational numbers.
- how to use and set-up ratios and proportions.
- aspects of basic number theory (including, but not limited to, factors, multiples, divisibility tests, prime numbers, greatest common factors, and least common multiples).
- basic algebraic reasoning to solve problems.

- Model the use of mathematical ideas using multiple methods including
- fraction concepts (including, but not limited to, size, identifying the whole, arithmetic of fractions and percents).
- addition, subtraction, multiplication, and division of all rational numbers.
- how to use and set-up ratios and proportions.

- Compare numbers (including decimals, fractions, and negative numbers) using multiple methods.
- Apply the use of all technology skills appropriate for the class, including the use of mathematical manipulatives.
- Use appropriate mathematical terminology

- Numbers and the Base-10 System - 4 hours
- Explain the base-ten system and how we use it with place values
- Describe how adjacent place values are related in the base-ten system
- Draw diagrams and show how to group objects based off the base-ten system
- Illustrate the base-ten system (including decimals) using bundling
- Explain how to plot points (including decimals and fractions) on number lines
- Explain the difference between positive and negative numbers and illustrate with examples
- Compare numbers (including fractions and negatives) using either inequalities, ordering from least to greatest, using place value, bundling, lengths, common denominators, common numerators, and/or by benchmarks
- Round numbers correctly
- Identify the characteristics of a good mathematical explanation

- Fractions - 9 hours
- Calculate/Determine fractional amounts of an object, collection, or quantity and justify the amount
- Determine which value is the whole in a problem/situation
- Use fractions to compare quantities
- Explain how to calculate equivalent fractions and why we need them
- Calculate common denominators for fractions and explain why we need them and what we are actually doing when we find common denominators
- Simplify fractions (both numerically and through diagrams)
- Solve basic percent problems (using equivalent fractions, percent tables, going through 1%, going through 1, math drawings, benchmark fractions, and/or mental calculations)

- Addition & Subtraction - 8 hours
- Write equations that correspond to mental calculations
- Write and solve word problems involving addition and subtraction with negative numbers
- Explain how to use a number line to add and subtract numbers (including negative numbers)
- Explain and illustrate how to use bundled objects and base-ten drawings to do addition and subtraction problems
- State the associative property of addition and give examples of how to use the associative property of addition to make mental addition easier
- State the commutative property of addition and give examples of how to use the commutative property of addition to make mental subtraction easier
- Describe how to view subtraction problems as addend problems
- Identify problematic keywords in math problems
- Use and explain how to use a number line to add and subtract non-negative numbers
- Write and identify Add To, Take From, Put Together/Take Apart, and Compare problems of all subtypes

- Multiplication & Division - 22 hours
- Correctly use the scaffold method of division
- Correctly use the standard long division algorithm
- Write equations that correspond to mental calculations
- Write array, ordered pair, and multiplicative comparison word problems for a given multiplication problem (including word problems)
- Explain multiplication using the area model
- State the commutative property of multiplication and explain how we can use it to subdivide rectangles/arrays
- State the associative property of multiplication and explain how we can use it to subdivide groups of objects in two different ways
- State the distributive property
- Explain why the distributive property is valid (subdividing arrays/objects/rectangles)
- Relate multiplication problems to arrays & subdivide the array to correspond to the partial-products algorithm
- Explain why the partial-products algorithm is valid
- Write and solve word problems for given numerical problems (including integers, fractions, and decimals) using equations, logic, and math drawings
- Explain why and how decimal multiplication works
- Explain the rules for multiplying and dividing positive and negative numbers
- Use exponents to express powers
- Write and recognize division word problems for both interpretations of division (how many groups and how many in each group)
- Explain the difference between dividing by 0 and dividing 0 by a number
- Write division calculations to solve problems
- Solve division problems with math drawings, tables, double number lines, and algorithms
- Explain why we can rewrite division as fractions
- Recognize when problems are best answered as a decimal, fraction, mixed number, whole number with remainder, or rounded
- Describe how the whole-number-with-remainder answer to a division problem is related to the mixed number answer and why this relationship holds
- Explain how to add and subtract decimals and why the algorithm works
- Describe how to add and subtract fractions, including explaining why we use the process of common denominators
- Write math problems involving fractions with addition and subtraction
- Determine if a given word problem fits a specific fraction addition or subtraction problem

- Ratio & Proportion - 9 hours
- Describe ratios in terms of composed unit or batch and fixed number of parts
- Write equivalent ratios using tables, double number lines, or calculations
- Compare qualities of quantities in different ratios
- Solve ratio problems (using reasoning, strip diagrams, ratio tables, double number lines, and unit rates)
- Identify and write unit rates
- Explain what a unit rate means in terms of a context
- Explain why we can solve proportions by setting two fractions equal to each other
- Recognize and give examples of inversely proportional relationships
- Explain the difference between inversely proportional relationships and proportional relationships
- Solve problems using inversely proportional relationships
- Calculate and explain percent increase and percent decrease in several ways
- Calculate quantities from a given percent increase or decrease
- Solve problems involving percent increase or decrease

- Number Theory - 5 hours
- State the meaning of factor and state the meaning of multiple
- Determine all factors of a given number and explain how to find them
- Determine multiples of a given number and explain how to calculate them
- Write and solve word problems that can be solved by finding all of the factors of a number
- Write and solve word problems that can be solved by finding several multiples of a number
- Describe and use the divisibility tests for 2, 3, 4, 5, 9, and 10, and explain why they work
- State the meaning of a prime number
- Determine if a number is prime and explain how to tell
- Factor a counting number into a product of prime numbers
- State the meaning of Greatest Common Factor
- State the meaning of Least Common Multiple
- Explain the difference between the GCF and LCM
- Using the definition, determine the GCF of a set of numbers
- Using the definition, determine the LCM of a set of numbers
- Write and solve word problems that can be solved by calculating the GCF and/or LCM of a set of numbers
- Use the standard division algorithm to explain why fractions have decimal representations that either terminate or repeat
- Given a terminating or repeating decimal, write it as a fraction
- Explain how the different number systems are related and identify how they are different

- Algebraic Thinking - 5 hours
- Write equations and make math drawings to represent problems
- Formulate numerical expressions from scenarios
- Define the term variable
- Correctly define variables within the context of a problem and identify incorrect variable definitions
- Generate and recognize equivalent expressions
- Recognize when expressions are not equivalent
- Formulate equations arising from scenarios/word problems
- Solve equations through reasoning and algebraically

Mathematics for Elementary Teachers. 5th Edition. Beckmann

Graph Paper

Colored Pencils/pens

Web access required.

Students will be evaluated with homework, class quizzes, chapter tests, instructional projects, and a comprehensive final examination.

Grading CriteriaTests Final Exam Problem Sets Projects/Reflections |
50% 20% 15% 15% |

Grading Scale

90-100 80-89.9 70-79.9 60-69.9 below 60 |
A B C D F |

Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

Fall 2019