How might we develop algebraic reasoning as well as fluency with fractions right from the start? What if we empower learners to support each other to visualize and verbalize relationships and patterns?
In Choral Counting, students support one another often in the whole-group setting to count, to see relationships and patterns, to build on someone else’s idea, and to ask different kinds of questions of the mathematics. (Franke, pag.)
How might we facilitate productive conversations around SMP 8 I can look for and express regularity in repeated reasoning?
These activities help us enact our commitments to equity. We know that a sense of belonging and investment, of being seen, known, and heard by teachers and classmates, is fundamental to creating schools where children and families feel welcome and where they flourish. Because these activities foreground student sense making and cultivate a joy for doing mathematics, they can be powerful tools for teachers to counter narrow views that only a few can identify with mathematics or that mathematics is disconnected from students’ home lives, their communities, and their own interests. (Franke, pag.)
What if we connect to learners’ prior knowledge by counting and connecting counting to numbers on a number line? Might we develop reasoning and understanding of fractions as numbers? What will learners notice and wonder?
3rd Grade Numbers and Operations – Fractions
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts.
4th Grade Numbers and Operations – Fractions
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
5th Grade Numbers and Operations – Fractions
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Franke, Megan L. Choral Counting & Counting Collections: Transforming the PreK-5 Math Classroom . Stenhouse. Kindle Edition.
“Grade 3 ” Number & Operations-Fractions¹.” Grade 3 ” Number & Operations-Fractions¹ | Common Core State Standards Initiative, www.corestandards.org/Math/Content/3/NF/.
“Grade 4 ” Number & Operations-Fractions¹.” Grade 4 ” Number & Operations-Fractions¹ | Common Core State Standards Initiative, www.corestandards.org/Math/Content/4/NF/.
“Grade 5 ” Number & Operations-Fractions.” Grade 5 ” Number & Operations-Fractions | Common Core State Standards Initiative, www.corestandards.org/Math/Content/5/NF/.
“Standards for Mathematical Practice.” Standards for Mathematical Practice | Common Core State Standards Initiative, www.corestandards.org/Math/Practice/.