From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

CONTENTS OF CURRICULUM UNIT 17.05.02

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Content Objectives
  4. Teaching Strategies
  5. Classroom Activities
  6. Resources
  7. Appendix
  8. Endnotes

Solving Problems Multiple Ways: Using Arithmetic and Literature - Hooray!

Brittany F. McCann

Published September 2017

Tools for this Unit:

Teaching Strategies

Whole Group Discussion

Before starting a whole group discussion on problem solving, I plan to first have the students sit for 1-3 minutes in silent reflection on the question and gather their thoughts. This way, once the discussion starts, each student can bring an idea to the group.

I’ve found that students need direct instruction about how to have a class discussion. My favorite way to model this is by choosing a silly topic and modeling the correct and incorrect way to contribute to a discussion. For example, if I start class by telling the students, “Barbie is the greatest toy ever created!”, there is always one student who will disagree and voice their opinion. When I reply with, “I’m the teacher, so what I say is right!” the students get even more excited for this discussion. This is a perfect place to pause and talk about positive talk. In my reply, I was not adding anything to the discussion. We also discuss that it is perfectly ok to disagree in a discussion, but you need to state why you disagree. As a class, we make sentence models for how to begin sentences in a class discussion. They may change slightly, but they typically stay within the same four phrases for accountable talk:

“I agree with you because…”

“I disagree with you because…”

“I would like to add on to that point…”

“I have a question about what you said…”

In the beginning, the teacher needs to lead the discussion and make sure everyone gets a turn to speak. As time goes on, the teacher can release some of his or her tasks to the students (taking notes about what is said, keeping track of who has had a turn to share their thoughts, calling on students, etc).

“What Makes You Say That?”

In his book Making Thinking Visible, Ron Ritchhart describes the “What makes you say that?” (WMYST?) routine. This routine helps students identify the basis for their thinking by asking them to elaborate on the thinking that lies behind their responses.10 It seems easy enough, but when used consistently in the classroom it creates an atmosphere of using evidence for reasoning. I like to use this routine in my classroom because it encourages the students to justify their answers. There is a common joke in my classroom that you cannot simply choose a number from the sky - you have to be able to backup your answer. Richart states that this question (WMYST?) should not sound like a challenge or a test, but convey a curiosity regarding how the learner is constructing understanding of a complex idea.11 In my classroom, I have it on a poster and model it from day one, sometimes even pointing to it to remind students I’m looking for their thinking. As time goes on, I will start to hear it in student conversations when doing group work or whole class discussions.

Teaching the Teacher

When I was a student, one of my favorite things do was to catch an error made by the teacher. Now that I am the teacher, one of my favorite things to do is sprinkle in errors into random lessons so that my students can catch them too!

These errors have to be with skills that the students have had a lot of practice with and are nearing mastery. This gives the teacher time to discover common misconceptions and present them to the class. I always make sure that I explicitly teach common misconceptions, and as a class we discuss why they are incorrect.

My favorite example is with subtraction. In third grade, students spend weeks learning subtraction strategies. In the fourth grade, they should have subtraction mastered, but many still struggle. I would write the following problem on the board and talk through my steps:

4714

-2533

_____

2221

“Ok, I’m going to start on the right. Four minus three is one, one minus three is two, seven minus five is two, and four minus two is two. So my answer is two thousand, two hundred twenty-one.” Almost instantly, a student should catch my error (one minus three is not two). This can start a class discussion and students can teach the teacher. This is extremely rewarding when students start to repeat the skills they have learned during class lessons. In fourth grade, students are allowed to use calculators. I tell the students to always check their work with a calculator, but to solve it first without one. If no students catch the error, I will have them check the teacher’s work with a calculator.

A side note: the more animated the teacher is, the more excited the students get. I like to pump up my acting skills and make claims like, “The chalk did it, not me!” and “The calculator must be broken!” It also gives students, especially ones who struggle, a chance to see that teachers make mistakes too!

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