MCCCD Program Description

Basic Arithmetic

Course: MAT081

First Term: 2016 Fall

Lecture 4 Credit(s) 4 Period(s) 4 Load
Subject Type: Academic
Load Formula: S - Standard Load

Description: Primary emphasis on conceptual understanding of and solving problems involving whole numbers, integers, mathematical operations, decimals, decimal operations, fractions, percentages, angles and geometric figures. Use of systems of measure, similarity, proportionality and the Pythagorean theorem. Focus on mathematical language, connections, patterns and reasoning, and additive and multiplicative reasoning.

MCCCD Official Course Competencies
1. Construct number meanings for whole numbers and integers through real world experiences. (I, II) 2. Use multiple frameworks to describe the meaning of whole number. (I, II) 3. Use multiple solution strategies to solve a single problem. (I, II, III, IV, V) 4. Determine whether a result is reasonable in the context of a problem. (I, II, III, IV, V) 5. Use physical materials, pictures and diagrams to express mathematical ideas. (I, II, III, IV) 6. Use models, known facts, properties and relationships to reason mathematically. (I, II, III, IV, V) 7. Use patterns and relationships to analyze mathematical situations. (I, II, III, IV, V) 8. Model, solve, and interpret solutions to real world problems involving whole numbers and integers. (I, II, III, IV, V) 9. Reason additively and multiplicatively. (III, IV, V) 10. Derive number facts from known facts. (III, IV) 11. Model and discuss meaning for the operations in a variety of problem situations. (III, IV) 12. Relate the mathematical language and symbolism of operations to problem situations and informal language. (III, IV) 13. Illustrate and explain how addition, subtraction, multiplication and division are interrelated. (IV) 14. Construct fraction and decimal meanings through real world experiences. (VI, VII, VIII) 15. Relate the mathematical language and symbolism of number and operations to problem situations and informal language. (VI, VII, VIII, IX) 16. Use multiple solution strategies to solve a single problem. (VI, VII, VIII, IX) 17. Determine whether a result is reasonable in the context of a problem. (VI, VII, VIII, IX) 18. Use physical materials, pictures and diagrams to express mathematical ideas. (VI, VII, VIII, IX) 19. Use models, known facts, properties and relationships to reason mathematically. (VI, VII, VIII, IX) 20. Use patterns and relationships to analyze mathematical situations.(VII) 21. Relate decimals to place value concepts. (VII) 22. Model and discuss meaning for the operations on decimals in a variety of problem situations. (IX) 23. Distinguish appropriate uses of additive and multiplicative reasoning. (X, XI, XII) 24. Use multiple solution strategies to solve a single problem. (X, XI, XII) 25. Determine whether a result is reasonable in the context of a problem. (X, XI, XII) 26. Model, solve, and interpret solutions to real world problems involving fractions and percentages. (X, XI, XII) 27. Analyze and compare multiple models to establish the meaning of fractional equivalence. (XI) 28. Perform operations on fractions. (II) 29. Use multiple frameworks to describe the meaning of a fraction, including percentages. (XI, XII) 30. Convert between decimals, fractions, and percentages. (XI, XII) 31. Identify the unit quantified by each fraction/ratio/percent in context when problem solving. (XI, XII) 32. Solve ratio and proportion applications, including percentages. (XI, XII) 33. Analyze, compare and classify two-dimensional geometric figures by their definition, including squares, rectangles, triangles and circles. (XIII) 34. Identify types of angles (right, acute, obtuse). (XIII) 35. Model, solve and interpret solutions to real world problems. (XIII-XVIII) 36. Compare alternative solution strategies. (XIII-XVIII) 37. Communicate process and results in written and verbal formats. (XIII-XVIII) 38. Measure lengths by expressing the length as a number of copies of the standard length unit. (XIV) 39. Measure areas by tiling a surface with unit squares. (XIV) 40. Make connections between the array model for multiplication and area by understanding area as a geometric representation of multiplication. (XIV) 41. Measure volumes by packing an object with unit cubes. (XV) 42. Measure perimeter, circumference, area and volume with the ability to explain the use of any formulas. (XV) 43. Use unit conversions, including conversions from two-dimensions to three-dimensions. (XVI) 44. Evaluate similar figures by using the definition of similarity based on scale factor. (XVII) 45. Utilize the definition of proportionality. (XVII) 46. Evaluate proportions relating to geometric figures. (XVII) 47. Evaluate arithmetic expressions involving square roots, radical and irrational numbers. (XVIII) 48. Evaluate situations using the Pythagorean Theorem. (XVIII)
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. Represent and Model Whole Numbers in Multiple Ways A. Place value and base-10 B. Discrete models C. Continuous models D. Contextual applications II. Represent and Model Integers in Multiple Ways. A. Discrete models B. Continuous models C. Contextual application III. Represent and Model Addition, Subtraction, Multiplication and Division on Whole Numbers and Integers in Multiple Ways A. Addition: Combining two parts to make a whole B. Subtraction: Comparison, Take-Away, Missing Addend C. Multiplication: Repeated Addition, Accumulated Distance,Area, Copies, Groups, Cartesian Product D. Division: Partitioning Model, Repeated Subtraction, Missing Factor E. Contextual Applications F. Continuous and Discrete models IV. Utilize the Interrelatedness of the Four Binary Operations and Their Properties When Performing Single or Multiple Binary Operations A. Addition and subtraction as inverses, multiplication and division as inverses, multiplication as repeated addition,division as repeated substraction B. Fact families to develop associative, commutative,distributive, inverse and identity properties C. Order of Operations V. Use Factorization as a method of decomposing or recomposing a number multiplicatively as two or more factors A. Multiples, common multiples and least common multiples B. Factors, common factors and greatest common factors C. Prime factorization D. Relationship and connections between Least Common Multiple (LCM) and Greatest Common Factor (GCF). VI. Fraction Sense A. Represent unit fractions 1/b on a number line. B. Represent a fraction a/b on a number line. C. Interpret a/b in myriad forms including rate, ratio,part-whole, quotient and number of copies of a unit fraction D. Utilize multiple strategies for comparing fractions without converting fractions to decimal form. E. Express whole number as fraction and recognize fractions that are equivalent to whole numbers. F. Explain why fraction a/b is equivalent to fraction (n x a)/(n x b) using visual models. VII. Decimal Sense A. Compare two decimal numbers to hundredths reasoning about the size of the two numbers. B. Compare two decimals to thousandths based on meanings of the digits and their respective place values. C. Read and write decimals to thousandths using base-ten numerals, number names and expanded form. D. Recognize that in a multi-digit number a digit in one place value has place value 10 times the digit to the right and 1/10th the digit to the left. E. Use place value understanding to round decimals to specified place value. VIII. Connections between Fractions and Decimals A. Use place value to write fractions with denominators of 10 or 100 as decimals. B. Convert fraction to decimal using division. C. Convert (terminating) decimals to fractions. IX. Decimal Operations A. Explain patterns in the number of zeros when multiplying or dividing by powers of 10. B. Add, subtract, multiply and divide multi-digit decimals to hundredths place fluently using standard algorithms. C. Utilize order of operations to simplify expressions containing decimals. X. Types of Mathematical Reasoning A. Additive reasoning B. Multiplicative reasoning C. Distinguish between additive and multiplicative reasoning D. Applications XI. Fractions A. Definitions B. Equivalent Fractions C. Operations D. Applications XII. Proportions and Percentages A. Ratios and rates B. Proportions C. Percentages D. Percent Increase/Decrease E. Applications XIII. Angles and Geometric Figures by Their Definitions A. Triangles, Quadrilaterals, Circles B. Angle Measure XIV. Measure as a Multiplicative Comparison A. One-dimensional (length) B. Two-dimensional (area) C. Three-dimensional (volume) XV. Measure Perimeter, Circumference, Area and Volume XVI. Systems of measure A. Converting 1-dimensional measures B. Converting 2-dimensional measures C. Converting 3-dimensional measures XVII. Similarity and Proportionality XVIII. Square Roots, Radicals and Irrational Numbers A. Definitions B. Pythagorean Theorem C. Use and interpret the calculations in the Pythagorean Theorem

MCCCD Governing Board Approval Date: April 26, 2016

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.