Math Problem Solving Part 5: Multiplication and Division Comparisons

by C. Elkins, OK Math and Reading Lady

As I promised, here is a post about another multiplication and division story structure.

The dinosaur is about twice as tall as the human. The dinosaur is about 12 times wider than the human.

While the previous structure I mentioned dealt with equal groups, this one deals with comparisons.  Like with addition / subtraction comparison problems, I will show some ways to use double bars to illustrate these. (I just added a FREEBIE – a 2-pg. pdf showing the pictures of the problems shown below – get it now Equal groups comparison problem pics)

Notice some of the questions associated with these stories. They sound a lot like questions used in other story structures — this is why I advise against statements like, “If it asks how many in all, add the numbers together.” Notice how this method guides a student as they go from pictorial to abstract. You can also represent these types of problems with cubes or money manipulatives if you need a concrete example.

This problem shows a multiplying process.

  1. Read the problem. Ask who and what this story is about (Joe and Brent – Joe has more $ than Brent). Notice  there is no additive or subtractive process, but one has more – the other has less. This is a signal to use comparison bars to help solve.
  2. Make a vertical line (to help line up the bars evenly on the left side. Draw the bar with the known amount. (Joe has $22.)  Label the second bar (Brent).

3. Since the story said Brent has 3 time more, draw 3 bars equal to the size of Joe’s bars.

4. Since Joe’s bar is $22 and the bars by Brent’s name are equal in size, all of Brent’s bars should be labeled with $22.

5.  To find out how much Brent has, solve by repeated addition or multiplication.

6.  IF the question was slightly different (How much do Joe and Brent have all together?), then the above steps would have to be followed by 1 more step (adding the two amounts together).

* If students had been taught earlier to “Add when the question asks How many in all” then the child would likely add $22 + 3 to get their answer.  That signals no conceptual understanding of what the problem is all about:  One has more, the other has less.

The following example involves the division of a bar to help solve it. Continue reading

Math Problem Solving Part 4: Equal Groups

by C. Elkins, OK Math and Reading Lady

Are you ready for a way to help students solve multiplication and division word problems? I have developed a template that will help students record the given facts and think through the process involving equal groups. There are 3 basic types of equal groups problems:

  • # of groups and # in each group are known
  • # of groups and total are known
  • # in each group and total are known

Pictured here is an illustration of the strategy which can be used for multiplication and division problems. Get my FREE packet right here: Equal groups strategy with template.

One of the most important steps I recommend when working with equal groups problems is for students to brainstorm things that typically come in equal groups. There is a great book titled “What Comes in 2’s, 3’s, and 4’s” which can set the stage. It’s a picture book, but helpful to get kids’ brains warmed up.  Here are some visuals I made to illustrate the point. Click here for your FREE copy. They are included in this set of Equal groups pictures and list template

Kids may need your help to think of things to add to the list. See some hints below. This template and a full list is included in the above FREE download. Continue reading