Algebra and Fractions

1. Algebra and Fractions Dr. Laura McLaughlin Taddei

2. 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. Learning Outcomes

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

4. Study of structures in number system • Study of patterns, relations and functions • Process of mathematical modeling, including the meaningful use of symbols Three Strands of Algebraic Reasoning

5. 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 Generalizing

6. Choose an activity on pages 230 to 235 • Demonstrate and explain to the class Practice – Stop and Reflect

7. Let's Be Pattern Detectives • NCTM Illuminations Activity - Patch Tool Finding games to teach math

8. Please refer to Table 13.1 – how would you teach these properties of operations to children Properties of Operations to Teach Children

9. Choose an activity from pages 244 to 248 • Discuss in small group, illustrate if materials are available, and describe to the whole group Practice

10. What are the big ideas for exploring early fraction concepts? (page 251) Big Idea - Fractions

11. 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? Introducing Fractions

12. 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 Common Core State Standards

13. 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 Meanings of Fractions

14. 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 Fractions are Numbers too

15. 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 Create a Fraction Activity

16. 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 Resources