Eileen Briggs

Pricco – Third Grade

November 14, 2005

Lesson Plan Framework

For Project 3

I. THINKING ABOUT WHAT YOU WANT STUDENTS TO THINK ABOUT, WHAT PROBLEM TO CHOOSE, AND HOW TO PRESENT IT:

What mathematical ideas or “paradoxes” do I want students to think about?

  • Combinations
  • Multiplication
  • Relationship between combinations and multiplication
  • Multiplication, instead of repeated addition

What Problem or Activity might help me to get them thinking about this? (Explain this enough so I can understand what the problem is and what the students will be doing.)

We will be doing a multiplication problem dealing with combinations. Here is the problem:

“I just found a hundred-dollar bill on the ground. Now it’s time for a shopping spree! While shopping I buy four shirts: one striped, one polka dot, one white, and one plaid. I also buy three pairs of pants: pinstripe, black, and white. Now I need help putting together outfits. Please show me all the different combinations of outfits that I can make! Don’t worry about making the outfits match.”

When you’re finished putting together the outfits decide what multiplication sentence (or expression) can be used to represent this problem.

Why does this expression make sense?

For an addition problem and if we have time, we may do this problem:

At the local ice cream parlor they offer sugar, waffle, and regular cones. They offer vanilla, chocolate, strawberry, fudge ripple and orange sherbet for ice cream flavors. How many different combinations of ice cream cones can we make? Please make a chart or table to illustration this problem.

What experiences, knowledge, and skills do almost all of my learners have that will be relevant to doing this activity or problem?

  • Prior knowledge of combinations
  • Addition (including repeated addition)
  • Introduction to multiplication

Why would this problem is a good one for my learners?

It will help push them in the right direction from addition to multiplication.

Clothes and ice cream are real life examples that will be relevant to their lives.

What vocabulary will I need to teach before they start work?

  • Combinations
  • Multipliers
  • Product
  • Table/chart

Materials:

Worksheets and overhead

Rules and expectations I want to establish before we start:

We are going to give them a few minutes to work individually and then when we let them know it’s time, they can work with their group.

II ANTICIPATING AND PLANNING FOR DIFFICULTY:

What parts of the problem may challenge some of my learners? (be as specific as you can—what do you know about particular children that will help you to anticipate difficulties? Which children had difficulty with the problem solving we did a few weeks ago?)? (In other words, write “Miguel is likely to…” rather than just “Children may drop their blocks…”)

  • Ryan (and others) may want to stick with addition and won’t try using multiplication.
  • Lawrence and Michelle may not understand how these problems are related to multiplication.
  • Sierra may want to draw pictures when it isn’t necessary.
  • Brandon may not see how the manipulates relate to the numbers in the problem.

What will I do to make it possible for children who struggle in math, the ones i know had trouble before, to engage in a way that helps them to learn mathematics?

  • Before we begin, allow the students to ask questions.
  • Start with a simpler problem.
  • Show them how to draw a chart to represent the problem.
  • Have a student who does understand explain it to the student who is struggling.

If I realize that the task is too hard for the group, how can I make it easier but still mathematically worthwhile (and how can I adapt it for a child who needs an easier version of a similar task?)?

  • See above strategies.
  • Ask them to explain to you what part of the problem they do understand, and which part they don’t.

If I realize that the task is too easy for this group, how can I make it harder and even more mathematically worthwhile (and what extensions can I provide for the child who finishes quickly?)?

  • Increase the quantities in the problem.
  • Add shoes to the problem.
  • Ask the student to explain their solution to you or to another student.

What questions can I ask that will help children engage with the task, that will help me to understand their thinking, that will help them to find a way to begin, but that will not tell them what to do? (list as many good questions as you can think of – you will be glad you did this preparatory work).

  • What is the problem asking you to do? Can you explain it to me?
  • Do you have any ideas on how to start the problem? If so, what are they?
  • How did you get that answer?
  • Can you do this in a different way?
  • Why did you start the problem there?
  • What do you think the next step should be?
  • Can you group those numbers any differently?
  • What is a strategy that you’ve used in another problem that might work for this problem as well?

III. LESSON SEQUENCE (Reread Van de Walle, pp 41-48):

Before (what will I do to get the students ready and excited about working on this? How will I make sure they know how to work on it? What will I do to establish expectations for behavior, for how we will work with any tools, and for explaining answers?):

The problem itself should excite the students. Finding a hundred-dollar bill would be good luck for anyone. Also, when they see the worksheet and realize that they will be cutting out clothes and using them to solve the problem, this will get them even more excited about the problem.

We’ll tell the students that we know that they all have very good addition skills. In this problem we’d like to see them try a more challenging problem using their advanced addition skills. We will also remind them that although they have done a similar combination problem before, we would like to see them solve this problem in a different way (using multiplication instead of addition).

During: (questions that will help me to understand what children are doing; hints and suggestions for children who are stuck; look at V. de W’s suggestions for this part of your lesson pp 45-46)

The first thing we will do is let the students go and work on their own and with their groups. This is important in allowing them to figure out their own ways of solving a problem. Another thing that we will do during the lesson is to listen actively. This means that we will pay attention to the questions asked and depending upon what those are, we will then aid in any way we can and also ask other open ended questions that will ask the students to explain their thinking. We can ask questions like, “What was your thinking here?” or “how did you get that answer?” Other questions we could ask are, “Where did you get that answer from?” or “Is there another way to look at that or to go about solving the problem?”

We could also have them attempt to solve the problem using a smaller number of items, maybe 2 shirts and 2 pants. If they are struggling to see how this problem relates to multiplication, we could use an array to show 4 x 3. Or we could line up all the outfit selections into a table that has the shirts along the top and the pants along the left side. This is a good visual way to show the students how this problem uses multiplication.

After: What will you do to make the discussion worthwhile? Plan ways to get ideas from as many children as possible; list probes you can ask that will get children to explain their thinking so others understand it. Consider several ways that the discussion might go and make a plan for each scenario.

We will have each group decide among themselves who wants to present for each group, this way they will be prepared to present and every student in the group will be able to contribute to the presentation. We will also try to encourage a student who doesn’t usually volunteer to present for their group.

We will have each student from each group present their strategy using pictures, tables, charts, or any other way they used to solve the problem. After each person presents we will ask the class if everyone understands and agrees with the strategy. When every group has presented, we will ask the whole class if anyone has any other strategies that have not yet been presented.

IV. HOW WILL I FIGURE OUT WHAT THE CHILDREN HAVE GOTTEN OUT OF THE LESSON?

  • Read their explanations of “why does this math expression make sense?”
  • Watch their reactions to other strategies – see if they agree or disagree.
  • Observe if they use multiplication before we suggest it to them.
  • See if they understand that repeated addition is the same as multiplication.