Geometry Pre-Assessment & Summative Assessment

Pictured below is a pre-assessment a student in my class wrote about what he/she knew about Geometry at the beginning of the unit.   These assessments helped guide my planning of this unit.  I pictured a few of these in a blog a few weeks back here.

Below the pre-assessment is a summative assessment taken three weeks later.   I again asked the students to tell me everything they knew about Geometry.   Together the class brainstormed a few key words on the board prior to responding but no definitions were given.

February 2nd, 2012 

The same students response three weeks later on Feb. 24th.  He/She wrote both the page above and below.

Marshmallow/Toothpick GeoPanes

Today I brought in heaps of marshmallows and toothpicks.   This activity works best if the marshmallows are a bit stale.  I opened the bags of marshmallows yesterday and left them out overnight so they would be more crunchy and stay in the toothpicks better.

We have been learning about 3-D shapes and have played with many of the solid 3-D shapes. Today I had the students build some of the 3-D
shapes they were familiar with such as the cube, square based pyramid, and rectangular prism.   We spent a lot of time talking about the properties of prisms and pyramids.   I was very pleased to hear the students use the term congruent to describe prisms as having "two congruent bases".


I have taught this lesson many times and it is always a hit with the students.  At the end of the lesson I drew each 3-D figure on the board and had the students use a felt marker to mark the marshmallows and toothpicks as they counted the number of vertices (corners) and edges each of the shapes had.   I suggested they mark them with felts because sometimes I have found in the past that students tend to make simple mistakes counting and re-counting the vertices.

Many of the students explored other prisms such as this pentagonal prism, octagonal prism, and the hexagonal prism.  Another example of this lesson can be found on a mentor's blog HERE.

The Four Triangle Problem

Last week my students worked hard to solve a Marilyn Burns (a highly respected Mathematical Educator)  lesson called The Four Triangle Problem.

In groups, the students had to find all the possible arrangements using four triangles, two of each colour, and tape together the four-triangle shapes they made.   In each arrangement, each triangle must touch the side of at least one other triangle and follow the rule that the sides that touch must be the same length and match exactly.

In my many years of teaching, no one group has ever discovered all 14 non-congruent shapes... that is, until this year.   One groups did discover all 14 shapes.

Many of you know I love math but this lesson is one of my favourites.   It elicits mathematical language and introduces regular and irregular polygons.   As well, students learn the term "congruent" when they see that shapes that can be flipped or rotated to fit exactly onto another shape are actually the same shape or in mathematical language, "congruent".

After the students have had a full block to make the shapes, I ask the groups to volunteer to bring up the shapes.   I glue them onto a blank piece of chart paper.   As I glue them I am classifying the shapes but do not share my sorting rule with the class until the end of the lesson.   Usually at that point one of the students has caught onto to what I am doing and volunteers to tell the class.   The above chart was the one the students constructed this year.

Learning from Lenny... Post #1

Parents of students in Division 5, you may have heard the students talk about Lenny and might be wondering who is "Lenny"?  

Lenny is in grade 10 who attends Steveston-London Secondary School. He is part of the “Spectrum” enrichment program at the school.  The Spectrum program is designed for enriched learning and assigns each student a project called the Enrichment Exploration Project (EnEx). This project starts in grade 8 and continues until grade 10.  The purpose of the EnEx project is to explore students' passions  outside of school and learn invaluable life lessons. This year, the EnEx project consists of finding a mentor, meeting with the mentor a number of times, observing the mentor, and then designing a project to do based on what he has learned from observing. The project is supposed to be a mini version of the mentor’s job. 

Lenny's passion was education and he decided that he wanted to learn more about what it meant to be a teacher and through his project he hopes to explore all of the many roles of a teacher.   He posted that he was looking for a mentor on Richnet (Richmond Educators site) and I offered to be of assistance.   So far Lenny has spent 1 and half full days in the class.   He has observed, asked questions, engaged with students, assisted in lessons, and this week he took his first endeavour at teaching.   

What I discovered is that Lenny is a naturally born teacher!   Given the fact that he is a Grade 10 student and has not been formally taught how to teach, I was astounded with his immense knowledge of what makes an effective educator.   Last week I gave him a book called Polygons and told him that I would like him to read it to the class and if he wished, he could try to plan and teach a follow up activity.   During the course of the week, he emailed me his ideas for the lesson and to my surprise his lesson needed no tweaking.   It met the objectives of investigating polygons, was highly interactive and engaging, students were to work collaboratively, and he even included a worksheet that he would use for assessment!   I must meet Lenny's teachers as Lenny's first lesson was equal to and surpassed many first lessons I have seen beginning teacher candidates create.   Not sure exactly what they are doing over there in the Spectrum Program, but given the results of their students (example of Lenny) is it highly effective!

Below are some picture of the book he read, the worksheet he created, an images of the students actively seeking the polygons during their "shape hunt" with a partner.  

I am very much looking forward to my ongoing relationship with Lenny.   I have a strong feeling that he is going to teach me as much as I will teach him.   He will be returning next week to investigate 3-D shapes with my class.  

Introduction to Geometry

My former Math 11 teacher would never believe me today if I were to tell him that one of my favourite subjects to teach is Math.  I think what I love most about math is that the lessons can be so hands on and engaging.    Today we started a new unit on Geometry.  I began the lesson having the children do a quick 2 minute write or draw addressing the question "What is Geometry".  This pre-assessment will help to guide my planning for the unit.   I am not worried how much the students know at this point, but instead will be more interested to see growth when we respond to this question again in a few weeks.

Next, I used a lesson created by a "Math Guru" in my district.   I have attached the link to her posting of the same lesson here  We began by reading The Greedy Triangle, by Marilyn Burns.  This cute story follows a triangle who unsatisfied with his shape, requests the local shapeshifter to add another side and angle to him so that he can become a quadrilateral.   This pattern repeats and as he continues to add more angles and sides we see him transform into pentagons, hexagons, heptagons, octagons, nonagons, and decagons.  

 While I read the story, my students explored making the various shapes using large fuzzy pipe cleaners (they were a real hit!).   These pipe cleaners can be found at Michaels.  They absolutely loved this activity.  As they continued to work with the materials, adding sides and angles, they demonstrated a concrete understanding of 2-D shapes.

To summarize the lesson, I had the students write in their math journals.  I showed examples of each of the shapes as asked them to write about each one.   I wrote the question on the board, "What makes a triangle a triangle?".   We discussed the properties of triangles and this brought forth much of the geometry language we will be using over the new few weeks.   Above is a sample from a journal.