Thursday, March 10, 2016

Gallery Walks

One way of having students share and critique each other's math ideas is by hosting gallery walks. Prior to a gallery walk, students work on a problem or question and share their thinking, ideas and/or strategies in writing, usually on a large whiteboard or poster size paper that can be displayed in class. Then students walk around the room to reflect on responses from classmates, writing down ideas they agrre with, disagree with, or feel need to be clarified.  Following a gallery walk, we come together as and have a whole class discussion to review the concepts, including understandings and misunderstandings that are uncovered during the process.

The pics below are from a gallery walk during our last unit, involving adding and subtracting integers, and how to represent the concepts with visual models.  Enjoy!


When adding 2 integers, how do you know if the sum will be positive or negative?


This question requires students to use a chip model to better understand the idea of why subtracting a negative integer increases the value.


Students analyzing one group's response to a question...




These students are working collaboratively to answer one of the questions prior to the gallery walk.


Students are currently working on a project in which they are creating a series of cartoon characters. The project focuses on mathematical similarity, scale factor, and the relationship between scale factor in similar shapes and area.  Check back soon for more info and pics of student projects!

Wednesday, December 23, 2015

Terrific Tessellations

As a culminating project for our Shapes and Designs unit, Students worked in small groups of 2-4 to create a catalog of tessellations for a fictional flooring business.  Each student in a group was responsible for creating 2 tessellations for their group's catalog, as well as mathematical explanations as to why their shape or combination of shapes would tile a surface, accompanied by visual representations.  Click here to see the assignment sheet and grading rubric!

Here are some catalog covers....(Note some of the clever company names)









Below are some excerpts from various catalogs, including full page designs and explanations for why/how shapes create a tessellation. For a closer look, click on the picture.










As you can see, some students went into great detail in explaining their tessellations, including ways of finding angle sums, individual angle measures, and how/why they will tessellate.








Friday, December 4, 2015

Happy December!

To culminate the Shapes and Designs unit, students are working in groups on a project in which they work for a fictional company called Floored. Each team needs to create a catalog of  floor designs for a that can be made with various regular and irregular shapes.  Project Assignment Sheet and Grading Rubric

Below are a few pics of students working on some initial designs....


 






In addition to getting a start on this culminating project, students have been working on solving algebraic equations.  This mini-unit is much more procedural in nature than our core curriculum.  It involves learning steps in "balancing" equations and solving for unknown variables.  We start with manipulatives and visual images - pawns that represent "X" and scales that represent equations- and slowly ween away the visuals and manipulatives as students understand the concept and steps more abstractly. 
 Next week we will begin our new unit, Accentuate The Negative. Be sure to check back in a few weeks for pics from the students' floor design catalogs, as well as work we are doing in our new unit.

Friday, November 13, 2015

More Shapes and Designs






A student used an angle ruler to measure angles of a polygon during a class investigation




Students have been working on a variety of concepts throughout this unit.  Here's a brief summary:


  • How to sort polygons into classes according to the number, size, and relationship of their sides and angles
  • How to find angle measures by estimation, by use of tools like protractors and angle rulers, and by reasoning with variables and equations
  • Discovering formulas for finding the angle sum of polygons
  • The relationships of complementary and supplementary pairs of angles, and in figures where parallel lines are cut by transversals
  • How to apply angle-side measurement conditions needed for drawing triangles and quadrilaterals with specific properties
  • The tiling and rigidity or flexibility properties of polygons that make them useful in buildings, tools, art and craft designs and natural objects


HERE ARE SOME PICS OF THE ACTION!
These students are investigating which regular polygons will tile a surface (tessellate). Through conducting the investigation, students discover that regular polygons must have an angle measure that is a factor of 360 to fit around a vertex in order to tessellate.


As students investigated the concept, they traced the shapes and had to provide written explanations to accompany their diagram about why some polygons would tessellate and some would not.
These students are creating a representation to help them determine (and then prove) why some specific characteristics of triangles will produce a unique shape.



These students are analyzing work from a group in the class to determine if the 3 requirements given would create a unique triangle, or if more than one triangle could be created from the 3 requirements.

Students used polystrips to investigate whether whether or not a triangle can be formed by any 3 side lengths.
We took an opportunity during a double block to display our summer math projects.  During the "gallery walk", students looked for strengths in each other's work and compared strategies for solving problems.  And, we got to learn more about each other! Some pics from the gallery walk....


 







Friday, October 9, 2015

Welcome to 7th Grade Math!

To kick of the school year, all 7th grade students participated in an Identity Project.  Each core class integrated content to focus on identity - who are we each as individuals, who are we as a group, and how does each of our individual indentities and our group identity co-exist?  In math, we created rectangular "Identity Prisms".

Class lessons focused on how to determine surface area and volume of a rectangular prism, and how to create a flat net for a rectangular prism.  Students were told that their prism had to have a volume of 48 cubic inches.  Each face represented a piece of their individual identity.  The challenge was to create a prism in which you could represent which parts of your identity were the most important to you.  Therefore, students needed to figure out how to make the surface areas of each face either larger or smaller, depending on which part of their identity they were representing.



Students learned about surface area and volume first by using various rectangular prisms found in the classroom and finding their volumes and surface areas.  This led to discovery of formulas for both measures.


                                        Students working collaboratively during a work period



Some students used cubes as a way to justify using the formulas for volume and surface that they knew or discovered






                                                 
                                         Before creating their prisms, students drew out their nets - a flat                                                              version of their prisms - using grid paper or white boards.




                  
                                 



                                                    Working on the final product!