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