Algebra and Fractions Dr. 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 4 th 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