Models
6. Encourage student use of models.
The mathematical process goals section of the 5th grade 2016 Curriculum Framework states the following:
"Students will represent and describe mathematical ideas, generalizations, and relationships using a variety of methods. Students will understand that representations of mathematical ideas are an essential part of learning, doing, and communicating mathematics. Students should make connections among different representations – physical, visual, symbolic, verbal, and contextual – and recognize that representation is both a process and a product."
Models or representations are important to the 5.4 standard to help students make sense of problem situations, as well as to help students compute and understand algorithms.
Thinking Blocks from Math Playground is one helpful site for exploring modeling. This site uses the bar model to represent the various addition, subtraction, multiplication, and division problem types. You may choose to use this site with students, or you may find that it's useful to deepen your understanding of unfamiliar problem structures.
Concrete Representational Abstract (CRA) Approach
CRA (also sometimes called Concrete Pictorial Abstract) is an approach to teaching math that moves students through the use of objects first, then models, then numbers as they are learning a new skill or concept. In the case of learning double digit multiplication, students might start with base 10 blocks or some other tangible array, then model problems on graph paper or with boxes. Finally, connections would be drawn between these representations and the partial products method. Whenever planning a new unit, consider how you will use the CRA approach to support student sense-making.
Want to learn more?
Learn about the "CRA Sweet Spot" from Christina Tondevold at Build Math Minds
Virtual Manipulatives
If you have time, check out the presentation See It, Move It, Grasp It: Math with Virtual Manipulatives from NCTM's 100 Days of Professional Learning, then explore the tools below.
