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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.

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algebra and fractions

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 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
algebraic reasoning

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

Algebraic Reasoning
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
Three Strands of Algebraic Reasoning
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
Generalizing
finding games to teach math

Let's Be Pattern Detectives

  • NCTM Illuminations Activity - Patch Tool
Finding games to teach math
practice

Choose an activity from pages 244 to 248

  • Discuss in small group, illustrate if materials are available, and describe to the whole group
Practice
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?
Introducing Fractions
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
Common Core State Standards
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
Meanings of Fractions
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
Fractions are Numbers too
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
Create a Fraction Activity
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

Resources