MCCCD Program Description

Investigating Quantity: Number, Operations and Numeration Systems

Course: MAT256

First Term: 2021 Spring

Lecture 4.0 Credit(s) 4.0 Period(s) 4.0 Load
Subject Type: Academic
Load Formula: S - Standard Load

Description: Explore number, numeration systems and operations on numbers. Techniques of problem solving with an emphasis on exploring a variety of strategies. Use a variety of visualization techniques to develop a conceptual understanding of these topics.

MCCCD Official Course Competencies
1. Identify and apply knowledge of various problem-solving strategies. (I) 2. Describe, extend, analyze, create and use algebraic reasoning to solve a variety of problems; to include working with number patterns and number properties. (I) 3. Analyze set properties and relationships including the use of set notation, set operations and verbal arguments. (I) 4. Develop, recognize, contrast and apply proportional reasoning to describe relationships between quantities and to solve problems. (I) 5. Describe, illustrate, justify and apply knowledge of number representations with positional and non-positional numeration systems. (I, II) 6. Illustrate and explain the structure of the Real number system. (II) 7. State, illustrate, explain, justify and apply properties of integers, e.g. even/odd, multiple/factor, divisibility tests, prime/composite. (II) 8. Illustrate and explain various mental and concrete models for addition, subtraction, multiplication and division with whole numbers, integers, and rational numbers. (III) 9. Illustrate and explain various contextual models for addition, subtraction, multiplication and division for use in authentic applications, e.g. for subtraction the take away, comparison and missing addend models. (III) 10. Illustrate, explain, justify and apply traditional and non-traditional algorithms of arithmetic. (III) 11. Analyze, describe, and justify the properties of operations with real numbers and the interconnectedness of addition, subtraction, multiplication, division, powers and roots. (III) 12. Develop through experience the Common Core Standards of Mathematical Practice. (I, II, III, IV)
MCCCD Official Course Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

MCCCD Official Course Outline
I. Problem solving and algebraic reasoning A. Problem solving strategies 1. Charts, tables and other numeric representations 2. Organized list 3. Draw a diagram 4. Use a variable (symbolic representations) 5. Act it out 6. Solve a simpler problem 7. Look for a pattern B. Sets and set operations C. Number patterns D. Ratio and proportion 1. Ratio versus rate versus unit rate 2. Proportional relationships versus non-proportional relationships 3. Percent II. Numeration systems A. Non-positional versus Positional number systems 1. Historical number systems 2. Base-10 and Base-b number systems B. Real number system 1. Whole numbers 2. Rational numbers a. Fraction b. Decimal 3. Integers 4. Irrational numbers C. Number theory 1. Factors, multiples, even and odd 2. Divisibility 3. Fundamental Theorem of Arithmetic (and Prime versus Composite) III. Operations A. Conceptual understandings 1. Concrete and visual models 2. Interconnectedness of operations B. Algorithms 1. Traditional 2. Nontraditional C. Properties 1. Properties of addition 2. Properties of multiplication IV. Common Core Standards of Mathematical Practice

MCCCD Governing Board Approval Date: November 24, 2020

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.