MATH 111 College Math for Early Childhood Education (5 credits)
Distribution Area Fulfilled Quantitative and Symbolic Reasoning (not all four-year colleges accept this as a QSR)
Prerequisite MATH 077, MATH 096 or MATH 098 or equivalent with a grade of at least 2.0 or satisfactory placement test score and eligible for ENGL& 101 .
A course for early childhood educators providing the mathematical foundations for quantitative concepts appropriate for children from birth through Grade 3. Topics include patterns, sequencing, number systems and computation, models for operations, problem-solving strategies, functions, geometry, measurement, and basic concepts of statistics and probability. Methods used are interactive, activity-based, and guided by national and state mathematics education standards. Emphasizes conceptual understanding, connections among topics, and communication of mathematical thinking.
1. Apply problem-solving strategies to problem situations, such as the use of models, pattern recognition, working backwards, “guess, check, and revise”, and organized tables.
Patterns and sequences
2. Recognize and describe patterns, such as those found in nature, sounds (music, rhythms), pictures, and objects. Create new patterns.
3. Create sequences of objects or numbers. Recognize and extend existing sequences, including arithmetic and geometric numeric sequences.
Numeration systems and operations with numbers
4. Discuss the components and properties of our base 10 number system, another base such as 5, and ancient numeration systems, including symbols used, place value, methods of computation, and advantages and disadvantages of the system.
5. Describe and apply a variety of cognitive models and concrete materials (manipulatives) to explore, illustrate, and justify quantitative relationships and computational methods.
6. Apply properties of the real number system to justify reasoning and to solve mathematical and real-world application problems involving whole numbers, integers, fractions, decimals, percents, and proportions.
7. Use number sense, estimation, and reasoning to evaluate the reasonableness of solutions.
Algebraic expressions, relations, functions, coordinate plane
8. Solve mathematical and realistic contextual problems by applying algebraic skills using expressions, formulas, linear equations, and inequalities.
9. Use two-dimensional coordinate geometry to specify locations and describe relationships.
10. Explore and analyze patterns, relationships, and functions using tables, graphs, and equations.
11. Describe and analyze rates of change including slope, rate of growth, and speed.
Geometric shapes, measurement, area, perimeter, volume
12. Analyze characteristics and properties of two- and three-dimensional geometric shapes. Apply the Pythagorean Theorem.
13. Build and manipulate representations of two- and three-dimensional objects using concrete models and drawings.
14. Describe relationships among two- and three-dimensional geometric shapes, including congruence and similarity. Use proportions to solve problems involving similar triangles.
15. Apply geometric concepts and modeling to solve mathematical and real-world problems.
16. Recognize measurable attributes of objects. Explore and apply various units and systems of measurement, including nonstandard, U.S., and metric (SI).
17. Select and use appropriate measurement units, techniques, and tools to find length, perimeter, area, volume, capacity, and weight. Compare and contrast shapes and objects by size.
18. Determine area, perimeter, and volume of two- and three-dimensional geometric shapes.
Statistics and probability
19. Design simple investigations and collect and organize data.
20. Display data in a variety of ways including graphs and charts.
21. Determine and analyze measures of center for sets of data (mean, median, mode).
22. Interpret data by observing patterns and departures from patterns in data displays. Discuss results.
23. Calculate the empirical probabilities of events after collecting relevant data.
24. Estimate the theoretical probability of simple events and the likelihood of real world events.
Connections and Communication
25. Connect mathematical ideas to the real world.
26. Recognize how mathematical ideas interconnect and build on one another to produce a coherent whole.
27. Communicate mathematical thinking coherently and clearly (using correct vocabulary) to peers, teachers, and others by, for example, leading activities involving the concepts of this course or presenting lessons to the class using appropriate materials.
28. Collaborate with classmates in order to achieve some of the learning outcomes of this course.
29. Relate national and state mathematics education standards for Pre-K to Grade 3 to mathematical content of this course.
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