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### Algebra and Fractions

Dr. Laura McLaughlin Taddei

- 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.

- What are the big ideas of promoting algebraic reasoning (Van de Walle, Lovin, Karp, & Bay-Williams, p. 126, 2014)?

- Study of structures in number system de
- Study of patterns, relations and functions
- Process of mathematical modeling, including the meaningful use of symbols

- 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

- Choose an activity on pages 230 to 235 teach children generalizations – what tools would you use to teach this?
- Demonstrate and explain to the class

- Let's Be Pattern Detectives teach children generalizations – what tools would you use to teach this?
- NCTM Illuminations Activity - Patch Tool

- Please refer to Table 13.1 – how would you teach these properties of operations to children

- Choose an activity from pages 244 to 248 properties of operations to children
- Discuss in small group, illustrate if materials are available, and describe to the whole group

- What are the big ideas for exploring early fraction concepts? (page 251)

- 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?

- 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

- 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

- Partitioning – splitting or cutting a quantity equally whole that has been partitioned into equal parts
- 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

- 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

Van de can use to teach fractions to childrenWalle, 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

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