What works in upper elementary? APEC

In Ontario, students write the EQAO assessments of mathematics and language in grades three and six. I have been a grade six teacher for the majority of my career and have been through many, many years of student testing. One thing I noticed over the years was that students did not come to me in sixth grade knowing how to answer open ended, extended response questions. Students find questions like this on the CASI reading assessments as well.

I started looking for ways to help increase student understanding of how to structure a good response.  A "mentor" for responding to open ended, extended response questions.  Students will find these types of questions in both language and mathematics.  For example, from the 2013 EQAO reading test "Explain why the narrator states that “The only ice cube I want to see again is the one in my glass of juice.” Use specific details from the text to support your answer." and from the mathematics test "A store has 11.2 kg of potatoes. Maria buys 572 g of potatoes from the store and Colin buys 1.42 kg of potatoes from the store. 

After these two purchases, how many grams of potatoes does the store have left? Show your work."

After introducing APEC at my school, many of the teachers in my school have started teaching it.  Even though most of the students coming to me are familiar with this structure, I still spend time each year modelling how to use APEC as an effective method for responding to open ended, extended response questions (including problem solving in mathematics).

Recently someone on Facebook commented that they were marking EQAO and that the coordinators of the marking told them that the "connection" part some students were including was "irrelevant" and that student should NOT be taught to respond by making connections.  I went on record stating that I did not agree with this stance.  If you look at the reading curriculum in Ontario, you will see "making connections" is a HUGE part of the reading expectation 1.6 "extending understanding".  I agree that students need to master how to "make inferences about text using stated and implied ideas from the text" but they also need to EXTEND their thinking, and this is what expectation 1.6 asks them to do. 

I model how to write effective responses all year long.  Whether it is as descriptive feedback after students write CASI in the fall, or during literature response groups, I make sure that we look at how to "show what we know" by constructing strong responses.

I have written about how I use APEC in mathematics before. If you would like to read more about it you can view it at this post.

When I was reading the Facebook posts about using APE (or ACE, or APEC) I started looking for my APEC freebie I had posted a few years ago.  I could NOT find it anywhere, so I decided to make some new cute posters for my classroom.  If you have read my profile, you will know I am the proud owner of two beautiful Boston Terriers, so I included the adorable Boston Terrier clip art created by Scrappin Doodles on my new posters.

If you would like a copy of this FOREVER FREEBIE just click on the image below.

 

How do you teach students to improve their responses in math and language?  I am always looking for fresh, new and effective ideas.

Math Must Read Mentor Texts

Teachingisagift is again linking up with Stacia and Amanda at Collaboration Cuties for Must Read Mentor Texts.  I love how writing these posts makes me think about my favourite books and then write about how I use them in my classroom!

CLICK ON THE IMAGE TO VISIT COLLABORATION CUTIES MUST READ MENTOR TEXTS.

Many years ago I came across the book "A Grain of Rice" by Helena Clare-Pittman.  I was intrigued by the story and I loved that it linked to mathematics.  

The book is a simple variation on the old grains on a chessboard example of exponential growth.  As a reward for concocting a potion which saved the life of the princess, humble farmer Pong Lo asks for the Emperor's daughter's hand in marriage.  The Emperor is willing to offer Pong Lo anything he wishes, except for the hand of his daughter, the princess.  

Pong Lo then surprises the Emperor by making a basic request. He asks for a single grain of rice doubled every day for 100 days. The Emperor is baffled, yet he complies.  He soon discovers that Pong Lo uses his math skills and ingenuity to make all his wishes come true.

From Helena Clare Pittman's website:

"The peasant, Pong Lo, falls in love with the princess, Chang Wu, presenting, of course, the problem of class, for starters. But this peasant is "more than a little" clever, gifted and determined. With the conviction of love in his heart he defies tradition and common sense, becoming indispensable to the workings of the emperor's palace, and dear to emperor's love of good food and to his daughter's heart. The story unfolds from there and rests on Pong Lo's wit, and knowledge of arithmetic progression. This book has been in print since 1986, used in school curriculums since 1994, and is a love story on a royal scale."

This story is a great introductory lesson to the patterning and algebra strand in the Ontario Curriculum for mathematics.  I also like to use it prior to this lesson I wrote about INTERACTIVE MATH NOTEBOOKS.  The mathematical focus for this lesson the exponential growth of the powers of 2.

Prior to reading the story, I ask the students to consider this question: "Would you rather have $0.10 each day for 10 days or would you rather receive a penny on the first day and double that amount everyday for 10 days?   I allow students to think about the question but not give me any responses at this point.

I then begin to read the story and stop on the page where Pong Lo asks for a grain of rice which will double every day for one hundred days.

I then revisit the question I posed about the money.   With a partner I ask the students to determine how much money they would receive, depending on which decision they made.  We debrief the strategies used, and the answers the students come up with.  I like to use this as a bit of a diagnostic assessment of strategies students use.

I then ask the students to determine how much rice Pong-Lo would have at the end of 100 days. Again they work with their partners.  I like to use the KWC (Know, Want to Know and Conditions) model to have students work on the problem in partners.  I have them go through each step included in the table you see below.

K:  What do I KNOW?  Based on the problem, I know that...

W:  What do I WANT to do, find, or figure out? I am trying to find or figure out...

C: CONDITIONS.  Are there are special conditions? (e.g. that Pong Lo requests a single of grain rice which doubles each day for 100 days)

Next I use the APEC sheet to have students work through the process to come up with a reasonable answer.  

There is no right or wrong way for the students to use the table, but they must fill out all sections.  I find that gifted students often are able to come up with the correct answer but they cannot show how they know they are correct, and they have trouble explaining their thinking and/or making connections.  Using APEC gets my students thinking about the entire problem solving process and how the concepts they have been learning about connect to other math concepts, to themselves and to the world around them.

CLICK ON THE IMAGE ABOVE TO DOWNLOAD
YOUR OWN FREE COPY.

Prior to finishing the story but after the students are finished working on the problem they share their thinking, discuss the process and the answer.

I then finish reading the story to the students and we talk about what that much rice would look like. How would Pong Lo store it all?  What could he store it in?   Exploring a variety of measurement concepts are a natural extension to these questions.

Another extension I have used with my students is to have them create their own story related to the concept, powers of 2.  This can be used as an excellent cross curricular connection to language arts, visual arts and technology.

Head over to Collaboration Cuties now to read about more great Must Have Mentor texts!