Algebra and fractions
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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

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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


  • 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

Practice – Stop and Reflect

Finding games to teach math

  • Let's Be Pattern Detectives

  • NCTM Illuminations Activity - Patch Tool

Finding games to teach math

Properties of operations to teach children

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

Properties of Operations to Teach Children


  • 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)

Big Idea - Fractions

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


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


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