Post on 02-Jan-2016
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Algebra and FractionsDr. Laura McLaughlin Taddei
Learning Outcomes
• Learning Goal: Students will develop and present various examples of developmentally appropriate math experiences for young children.
• Learning Goal: Students will develop, implement, assess, and modify curriculum and lessons for children from Pre-K through 4th grade using PA state standards and National standards if applicable.
• Learning Goal: Students will plan, implement, and adapt for all children appropriate developmental, cultural, and linguistic instructional practices and strategies.
Algebraic Reasoning
• What are the big ideas of promoting algebraic reasoning (Van de Walle, Lovin, Karp, & Bay-Williams, p. 126, 2014)?
Three Strands of Algebraic Reasoning
• Study of structures in number system• Study of patterns, relations and functions• Process of mathematical modeling, including the
meaningful use of symbols
Generalizing
• Activity 13.1 – One up One Down – how can this activity teach children generalizations – what tools would you use to teach this?
• How can you use the Hundreds chart to help children learn to generalize
Practice – Stop and Reflect
• Choose an activity on pages 230 to 235• Demonstrate and explain to the class
Finding games to teach math
• Let's Be Pattern Detectives• NCTM Illuminations Activity - Patch Tool
Properties of Operations to Teach Children
• Please refer to Table 13.1 – how would you teach these properties of operations to children
Practice
• Choose an activity from pages 244 to 248 • Discuss in small group, illustrate if materials are
available, and describe to the whole group
Big Idea - Fractions
• What are the big ideas for exploring early fraction concepts? (page 251)
Introducing Fractions
• Curriculum Focal Points and NCTM and Common Core recommend formal instruction of fraction concepts begin in third grade
• However, you can begin to build on children’s every day experiences to introduce fractions.
• How would you do this?
Common Core State Standards
• Partitioning geometric shapes into equal shares – can occur in first and second grade
• First grade children begin to partition circles and rectangles into two and four equal parts
• First graders should know the vocabulary – halves,fourths and quarters
Meanings of Fractions
• Introducing children to part-whole – shading part of a whole that has been partitioned into equal parts
• Equal Sharing – initial instruction on fractions should focus on this – children have experience with this – create an equal sharing problem
• Measurement – Common Core standards recommend limiting measuring in K-2 to whole units, however, fractions emerge naturally – this also includes time – telling time to half hour or quarter hour and relating an hour to 60 minutes
Fractions are Numbers too
• Partitioning – splitting or cutting a quantity equally• Connecting informal knowledge of fair sharing to more
formal fraction concepts is key to providing effective initial fraction instruction in K -2 grade
• Iterating – counting a repeated amount (unit or fraction)How many fourths are in one whole?
• Using models to teach fractions is important
Create a Fraction Activity
• Use the materials in the classroom to create an activity you can use to teach fractions to children
• Identify the standards• Demonstrate to the class• Complete a Teaching Children Math activity sheet
Resources
Van de Walle, J., Lovin, L., Karp, K., Bay-Williams, J. (2014). Teaching student-centered
mathematics. Second edition. Pearson Education.
Smith, S. (2013). Early childhood mathematics. Pearson Education