# Using the Multiplication and Division Relationship to Solve

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## Objective

SWBAT develop fluency of solving multiplication and division problems.

#### Big Idea

Students can solve multiplication and division problems quickly by recognizing the relationship between the two operations.

## Warm-up

5 minutes

I am going to need one of my bright and brilliant students to come teach the rest of us about a word problem and how they can think about solving it.

I do a segment called ‘student teacher’ where students get to come up to the board and solve a problem for the rest of us. They are essentially teaching us how to think about the concept. I find with the common core that to build the deep understanding that is necessary, it is helpful to allow students to explain their thinking to others (MP1, MP6).

## Intro

5 minutes

I want to make sure that we all have ways we can think about multiplication and division that work for us. What works for me when I solve problems might not work for my friend who sits next to me. I want to see how many different ways you all think of division problems so that we can all learn from each other.

I write a few division problems on the white board and call up students to solve the problems. I allow them to solve without my corrections and then each person takes a turn explaining what they did. Other students may ask questions about the work to clarify.

Here I am really emphasizing standard 3.OA.C.7 where students are expected to fluently divide using appropriate strategies. I really emphasize that there is not just 1 way to solve problems so that students may draw on strategies that work best for them. Some of the strategies we have used are drawing models, skip counting, looking for known products in multiplication etc.

## Independent Practice

30 minutes

As you become stronger and faster at problem solving, especially when you don’t know if the problem is asking you to multiply or divide, you can rely on all of the tools and strategies we have learned to help make it easier to solve.

I use a combination of problems that all of the teachers on our grade level write that use our students' names and familiar objects. There are websites (mathstories.com and teacherspayteachers.com) that allow you to print word problems, but my team prefers to write our word problems. Examples include:

Ms. Smart brought 48 brownies into school today. She placed them in the teachers lounge with a sign that says 'please take 2'. If all teachers who visit the teachers lounge take 2, how many teachers will get brownies?

James and Maggie went bird watching on Saturday. They saw 3 different flocks on birds. Each flock had 7 birds in it. How many birds did they see on Saturday?

Students go back to their tables to work independently using story problem cards, which include multiplication and division problems. While students may understanding solving problems with numbers and symbols, it is often more difficult for them to perform these operations in the context of a word problem. They must practice applying what they know about multiplication and division within word problems to determine what the problem is asking them to do (3.OA.A.3).

While I am working with a small group students must "ask 3 before me" if they have a question, which means they must ask 3 of their classmates at their table for help before they raise their hand to ask me. I intentionally mix ability levels at each table so that this works effectively.

Small group:

While students are working I pull a small group. In small group I address their difficulty in setting up the problems (determining whether or not we are creating or breaking apart groups) and choosing an appropriate strategy to solve (drawing a model, skip counting, thinking about multiplication products). I use the same word problems the rest of the class is using. We read each problem sentence by sentence and jot notes about what we know about the problem (ie: Ms. Smart had 48 brownies. What do we know here? What are they telling us in this part?). I will lay out 48 counters/cubes or other manipulatives to show them that they represent her 48 brownies.

I have white boards, dry erase markers and counters to use to help with problem solving. I walk students through problems one step at a time and have students help me determine the type of problem we are working on.

## Close-Check for Understanding

5 minutes

Now turn your eyes to the screen because we are going to watch one of your classmates read us a word problem from the previous day. Take out your note card and be sure to show me all of your work when you solve it!

Here I show a video of a group reading their problem. Students solve the problem on a note card and hand it in to me as a check for understanding. I do a quick spot check, and any students who got it wrong will be pulled into another small group the following day.