Standards for Mathematical Practices with Fractions

Implementing the Standards for Mathematical Practice- Grades K-5 High Five Institute August, 2013

Fishing Tasks Use pictures and equations to solve • You catch 65 fish during a 5 day fishing trip. Each day you catch 2 more fish than you do the day before. How many fish did you catch each day? • You catch 8 fish on the first day of a 5 day fishing trip. You catch a total of 90 fish total. During the week you catch a certain amount more fish than you did the day before. How many fish did you catch each day?

Fishing Tasks • Approaches? • Representations? • Equations?

Fishing tasks • How would you modify for your grade?

• Before students explore the task? • As students are exploring? • After students have explored the task?

Standards for Mathematical Practice • Which ones were “at play” while you worked on this task? • Think about the 8 Practices… where does each of the “at play” practices fit? What would it look like? – Before the task? – During the task? – After the task?

• How can the teacher support these?

Pattern Block Explorations • Put 2 joint hexagons together to make a shape. This new shape represents a garden. You want to split the garden up into triangles, rhombi, or trapezoids. Cover the new shape as many different ways as possible. Record your solutions in a table.

Triangle

Rhombus

Trapezoid

Hexagon

Standards for Practice? • What would students have to do?

Extending Pattern Blocks • Cover your new shape with 4 trapezoids. If we were going to trade all the trapezoids for triangles how many triangles would we need? Use your blocks to prove it. Explain to your partner how you know that you are right. • What if we were only trading 3 trapezoids? 2 trapezoids? 1 trapezoid?

Trapezoid

Triangle

Extending Pattern Blocks • Cover your new shape with 4 trapezoids. If we were going to trade all the trapezoids for blue rhombi how many rhombi would you need? Use your blocks to prove it. Explain to your partner how you know that you are right. • What if we were only trading 3 trapezoids? 2 trapezoids? 1 trapezoid?

Trapezoid

Rhombi

Pattern Blocks Trading • Why can we trade pattern blocks? • What does “trading” pattern blocks help students with?

• Where are the Mathematical Practices?

Pattern Blocks • If 2 blue rhombi connected is 1 whole, then what is the value of: • 1hexagon? • 1 trapezoid? • 5 connected triangles, 10 connected triangles • 3 connected hexagons, 6 connected hexagons • Make a model so that the trapezoid = 3/8. • Make a larger shape out of 4 smaller shapes so that the amount of yellow in your larger shape is less than half.

Pattern Block Puzzles • Mathematical Practices? Where are they? • How can teachers support the Practices?

Tasks and the Practices • Cognitively-demanding tasks • Doing Mathematics – Students pick the strategy to a complex task, solve it, and explain their strategy orally or in writing

• Procedures with connections – Students solve a procedural task 2 different ways2 algorithms, 1 algorithm and 1 representation, etc.

Resources • InterMath- http://intermath.coe.uga.edu/ • NCDPI Mathematics Wiki – K-2 tasks – 3-5 tasks

• Illustrative Tasks • Inside Mathematics

Questions? • [email protected] • http://elemath.pbworks.com