How to Equip Your Students to Better Understand Multiplication, Part Three

How to Equip Your Students to Better Understand Multiplication, Part Three

Beverly and LillyI never liked word problems as a student. It was difficult for me to figure out which procedure to use, but I really didn’t like problems like this:

Robert is three times as old as his younger brother Mark. Mark is 7 years old. How old is Robert? 

As I reflect on my experience, I realize I memorized everything for school. I was good at filling out my worksheets and getting the right answer, but I didn’t know the concept behind the procedures I used. Deep understanding happens with a web of connections in a students’ mathematical knowledge. It is so important for students to see how things are connected.

Today I will be blogging about the third and final situation for multiplication called Comparison. If you are just joining me, you may want to check out Part One and Part Two. You may recognize the title Comparison because it is also a situation for addition and subtraction.

Addition and Subtraction Comparison  Multiplicative Comparision
If we look at a set of 3 and a set of 9, we can compare it two ways. In addition and subtraction we ask the question “What number when added to one set equals the other set?” (What number when added to 3 equals 9?) In multiplication, we ask the question “How many groups of one set do we need to equal the other set?” How many groups of 3 do we need to equal 9?

These questions have been adapted from the K-5 Operations and Algebraic Thinking Progression. The key for students is seeing the multiplicative relationship among the numbers. I will show you two ways for students to express this that I found in NC States Division and Multiplication Learning Trajectories. Click here to read a blog my colleague, Dr. Richard Theissen, wrote about this fabulous tool.

Lets look at a problem:

Zayla has 3 dolls. Her sister Rose has four times as many dolls. How many dolls does Rose have?

Students can use a Division/Multiplication Box to help them see the relationship. They may think about the relationship as multiplication or division so I have given you an example of both. Click on one of the examples to download a blank box.

Example Multiplication-Division Box       Example Division-Multiplication Box

Students can also use a number line to express the multiplicative relationship. Each jump is the iterated unit. In this example the unit is 3.

Multiplicative Comparison Number Line

Both of these tools will help students look for patterns and build understanding of multiplicative comparison. How have you helped your students understand these word problems that illustrate the multiplicative comparison relationship among the numbers?

How to Equip Your Students to Better Understand Multiplication, Part One

How to Equip Your Students to Better Understand Multiplication, Part Two

3 Responses to How to Equip Your Students to Better Understand Multiplication, Part Three

  1. Thank you for explanations of the two tools. The number line amazes me each time I explore it. Can’t wait to share them with my students!…oh- those pesky story problems!!!!

    • Yes they can be challenging for students, but we have to keep giving them positive experiences. Word Problems are the intersection of the real world and the world of mathematics, and students need them to know how to use mathematics in the real world. The number line continues to amaze me as well. It is a tool that needs to be used more in classrooms because it covers such a wide range of concepts.

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