2. Connecting Cubes Building Understanding Dispelling Misunderstanding

3. Leading Math Success Manipulatives should be used effectively and selectively as a means of facilitating the ongoing transition from the concrete (physical and visual) stage in student learning, to the more abstract knowledge and deep understanding. (Consortium of Ontario School Boards, 2003, p.29)

4. Introducing … Connecting Cubes

5. Virtual Tools 1) http://matti.usu.edu/nlvm/nav/vlibrary.html 2) http://illuminations.nctm.org/tools/isometric/isometric.asp

6. Developing Understanding Uses of Interconnecting Cubes: -Integers -Fractions -Patterning -Area -Volume -Slope -Histograms -Modeling Algebraic Rules

7. Building Crosses Purpose: To create the equation of a line from a table of values. Procedure: Create the following diagrams below with the linking cubes provided.

8. Enter the model number (X) and number of cubes (Y) in the table below: Model ## of CubesDifferences Find the equation of the line using the table above.

9. How many cubes are required to make model # 7? Show your work below. Build the cross for model # 7 to check your answer. What model # will have 17 cubes? Predict the model #: ______ Build the cross to check your prediction

10. Building Fences Johnny has 20 meters of fencing and wants to build the largest rectangular yard he can. Using cubes, make a model for this problem. Each cube represents 1 meter of fence. Complete the table using 5 different possibilities. LengthWidthPerimeterArea 282016

11. Compare your results with other groups. Square What was the shape had the maximum area? Now, try the same thing using 16 cubes. What shape had the maximum area? What suggestion can you give Johnny about the shape of his yard?

12. Possible Extensions: -Creating Scatterplots -Looking at relationships between volume and surface area.

13. Reflection Activity How could you use this manipulative to support learning in this strand?

14. Next Steps Try one of the activities or explore one of the websites from the LMS manipulative sheet Use the Think-Pair-Share strategy (page 96, Think Literacy: Mathematics)

15. Leading Math Success “The key to the successful use of manipulatives lies in the bridge - which must be built by the teacher - between the artifact and the underlying mathematical concepts.”