Three Part Lesson: Area

This is a summary of the three part math lesson we were fortunate to observe in Justus' Grade 5/6 classroom.

Part 1: Getting Started:

Justus made sure students were ready for the main problem by activating their prior knowledge with this simple activity.

He folded a piece of paper and asked students several questions such as:

What happens to the square when you fold it along the diagonal?

How do you know the two triangles are congruent?

What did the second line of symmetry do to the two triangles?

How do you know all four triangles are congruent?

Justus used folded paper along with the interactive white board throughout his questioning.

Part 2: Working on It

Justus chose a problem from a previous EQAO assessment.  He ensured that students understood the problem by completing a KWC with the whole class.

Once the class understood the problem, students worked in pairs to solve it.  Many pairings were mixed pairings of Grade 5 and 6 students.  Students chose their partners, as it was a common practice in the classroom.

Here are some of the student work we observed:

This pair used a ruler and measured the dimensions of the polygon.

This pair created a grid system and counted.

  

This pair created congruent triangles.

We observed many misconceptions in student thinking.

Base of the triangle is inaccurate

Inaccurate calculation of the area of the triangle

Part 3: Reflecting and Connecting

Based on his observations and the learning goal of the lesson, Justus chose several pairs to share their solution to the class.  Students were invited to ask each other questions throughout this process.

Part 3: Explicit Teaching and Feedback

To summarize the lesson, Justus provided oral feedback to the class regarding their thinking and organization of their solutions. 

 Since this was a diagnostic task before their unit, Justus did not do any explicit teaching, as he plans to start tomorrow's lesson with one of the misconceptions he observed.

Writing Workshop-Persuasive Letters

An important component of the literacy block is the writing workshop (also known as the writer's workshop).  Justus and his grade team have been working on persuasive letter writing for their teaching learning critical pathway.  In the initial task, he noticed that his class needed more direct instruction on the purpose of this form of writing to clarify the misconceptions and help them strengthen their arguments.


With a SMART Board in his classroom, he created a PowerPoint presentation to provide feedback and reflection from their first writing task.  He reviewed the form, looking closely at the purpose, audience and problem posed in the letter, asking students to think about what proposed solution they would offer.  He scaffolded his lesson and shared his expectations with the students for them to think about what arguments they can make to support their stance.  He has threaded in an example of a letter to review conventions and text features of a letter.  


From this lesson, students are crafting their own persuasive letter around an issue.

In addition to the lesson discussing the elements and form of writing, Justus uses success criteria with his students so that the expectations are clear and concise for them.  Seeing as this is a part of their pathway, the criteria was brainstormed and created with his grade team so that there is consistency from class to class.  

For more information about Success Criteria (and Learning Goals) click on the following link: Learning Goals and Success Criteria

Read Alouds/Think Alouds

During his literacy block, Justus weaves in many opportunities for his students to listen, learn and engage in different activities.

He uses a read aloud to share his thinking with his students and invites them to do the same in partners or a small group.  In this lesson, he is working on asking higher-level questions using the Q-Chart.  Using The Stranger, by Chris Van Allsburg, students are asked to jot down their questions on sticky notes.  As he reads, Justus stops periodically to think aloud and make his thinking explicit to help students.

When he finishes reading, students post their questions on the Q-Chart.

Guided Reading

Often times, guided reading is left out of many classrooms, especially junior ones, as the strategy is seen to be a primary one, and there are too many things to think about: what are the rest of the students doing, what texts do you use, how are small groups created, what is the teacher doing with that small group...

In Justus' class, he uses his independent reading time to meet and read with a small group.  While the rest of the class is reading quietly, he has a group meet with him to read.  In this session, he used a graphic novel to address text conventions.  In addition, he focused his small group lesson on the students' reading fluency and expression, pausing to dissect difficult words and their meaning and to check in for comprehension.

Here is a copy of the book the students in the group were reading:

While students read, Justus made anecdotal notes about their reading, focused on his goal for the lesson:

 

 

Justus has his reading groups organized and each one is responsible for handing in their reactions to what they are reading one day a week:

Remember, guided reading is not meant to be a time consuming process in the classroom.  Spending no more than 15 minutes with a group, focused on a reading skill or strategy with an appropriate text, can make a huge difference to students and their reading proficiency and comprehension.

Achievement Chart Categories

One of the ways Justus ensures that his students understand how he evaluates their mathematical understanding is by sharing the achievement chart categories with them.

This benefits students by helping them understand that:

- mathematical understanding is more than knowledge and understanding (facts, procedures)

- the report card mark is based on consistency across all four categories

Finally, Justus is able to provide feedback based on a specific category.

Three Part Lesson: Mean

This is the three-part problem solving math lesson we observed in Justus' Grade 5/6 class during our visit.

Background of the Students/Class

Prior to this lesson, students had experience determining the mode, median, and mean of a set of numbers.  This lesson was a consolidation of the Data Management unit and served as a review before the unit test.

Justus uses the three-part lesson format regularly and aims to use the math congress consolidation strategy at least once a week.  In his words, 'the kids cheer when it's a congress day!".

The Lesson

Part 1: Activation of prior knowledge/schema

Justus wrote a group of numbers on the blackboard.  Students were asked to calculate the mean and the median of the set.  Students were given the choice to use a calculator to do this.

The goal of this part of the lesson was to ensure that students were able to calculate the mean of a set of data accurately.  Since the class was able to do this, Justus moved on to the problem.

Part 2: Working on It

Each student was given a copy of the problem to read on their own or possibly start solving it.

Grade 6 EQAO: Spring 2010 (#9)

Justus ensured that everyone understood the problem by completing a KWC chart with the class.  

Students worked in pairs to solve the problem.  Justus shared with us that since most of his students were around the same level, he allows them to choose their partner.  He finds that this strategy works for his class because his students are always on task and produce quality work.

During this time, Justus circulated and chose specific pairs to share their thinking with the whole class during the math congress.

Part 3: Reflecting and Connecting (Consolidation)

Prior to the math congress, Justus prefers to put all  of the student thinking on display.  This is a strategy he uses to manage the combined grade.  Students are exposed to the difference in the complexity/level/detail of each grade level's work. 

Once this was done, pairs were asked to share their thinking with the whole class.  Justus prefers that one member of a pair/triad present to invite active participation by all.  Here are three solutions that were shared with the whole class.

Sample #1: This solution was shared because of the error (misconception).  Two pairs shared the same thinking so Justus wanted it addressed during the congress.

Sample #2: This pair was asked to share their thinking because it was unique to the class (no one else thought of it like this, including all the teachers in the room!)

After this sharing was done, the rest of the class was invited to ask questions, make comments/connections etc.

Feedback:

Justus uses the consolidation portion of the lesson to give students/whole class feedback about their solution and/or thinking.  

The feedback he gave the class included specific comments about:

- organization of calculations

- crossing out work/thinking  

- justification (some groups did not do it)

Explicit Teaching

Since every pair was able to solve the problem in an effective way, Justus did not have to explicitly teach the concept of mean.  Rather, he focused on clarifying a particular misconception in student work, such as Sample #1.

By the end of the lesson, Justus concluded that his students understood the concept of mean and were ready for their unit test.

Characteristics of Non-Fiction Text

This is the anchor chart Cynthia created with her class after she read a piece of text (The First Civilization).

Integrated Social Studies and Writing Project

One of the many strategies Cynthia uses to teach a combined grade is to integrate curriculum topics.  In this project, students had to do some research about an explorer.

Prior to this project, they learn about the features of graphic novels (narration boxes, speech bubbles, styles and sizes of lettering, frames, perspective, expressions, motion lines etc.)

Here are some pictures of a product one student was working on:

Picture Book Writing Project

For this writing project, Cynthia started with the book 'Smoky Night' by Eve Bunting.

In the book, different textures are used.

The book begins with a crisis.  Students had to write a similar story but based on something true that happened.  They had to interview family members to find out information to form the basis of their story.  

Here are some pictures of the final product:

There were a lot of mini-lessons that needed to happen to get students ready to publish.  Cynthia said this project took about a month to complete.

The great thing about a project like this is that it's a completely integrated unit so you can afford to spend the time on it.

The best part of having students make books is that they can go into your classroom library.

The books were created in the first term but they're still a hit in the classroom today!

Self-Portrait Art Activity

When we first saw these, we thought students just drew a self-portrait. When we looked closer, we saw it was way cooler than that!

Students drew a portrait of themselves then wrote things they liked etc. around the contours of their face.

Cynthia then photocopied the paper onto a transparency.  Students painted a background in warm or cool colours for the transparency.