Multiplicative comparisons are a major leap in mathematical thinking for many students, especially when transitioning from basic multiplication to more complex, real-world applications.
But before we dive into teaching multiplicative comparisons, it’s crucial to lay a strong foundation. There are several key skills that students need to have mastered in order to fully grasp this concept.
In this post, we’ll explore the essential building blocks students need before they can succeed with multiplicative comparisons, along with strategies for reinforcing these skills in your classroom.
What Is a Multiplicative Comparison?
First, let’s clarify what multiplicative comparisons are. A multiplicative comparison involves comparing two quantities by showing that one is a multiple of the other. For example, instead of saying, “Lena has 4 apples, and Sara has 8 apples,” we’d say, “Sara has 2 times as many apples as Lena.”
This type of problem requires students to think about relationships between numbers in a more abstract way, rather than simply adding or subtracting quantities. It sets the stage for understanding more complex ideas like ratios, proportions, and algebra later on.
Some of multiplicative comparison statements I tend to use in my classroom are:
➡️Times as many
➡️Times more
➡️Times as much
➡️Times as large
What Skills Should Students Have Before Learning Multiplicative Comparisons?
To successfully teach multiplicative comparisons, we need to ensure students have a solid grasp of several key skills:
1. Understanding Basic Multiplication
It seems obvious, but students need to have a strong foundation in basic multiplication facts before they can dive into multiplicative comparisons. They should understand multiplication as repeated addition (e.g., 4 × 3 is the same as 4 + 4 + 4) and be able to quickly recall their multiplication facts.
Classroom Tip #1: Use engaging multiplication games, flashcards, or timed tests/drills to help students practice and reinforce their multiplication fluency. You can also incorporate visual aids like arrays or number lines to solidify their understanding of what multiplication represents.
Check out some multiplication fluency resources that my students love below!
2. Familiarity with Equal Groups
Multiplicative comparisons often hinge on the idea of “equal groups.” Students need to understand that multiplication is essentially creating equal groups of items.
For example, if we say, “4 times as many,” we are comparing 4 groups of something to 1 group.
Classroom Tip #2: Use manipulatives like counters, cubes, or drawing representations to show students how equal groups work in multiplication.
Ask them to physically group items and count the totals so they can visualize the relationship between the groups.
3. Distinguishing Between Addition and Multiplication
Many students tend to confuse addition and multiplication, especially when they first start working with multiplicative comparisons. They might interpret a problem like “3 times as many” as simply adding 3 to the number, rather than multiplying.
It’s important to help students understand the difference between additive and multiplicative thinking.
Classroom Tip #3: Give students plenty of practice with problems that contrast addition and multiplication. For example, have them solve side-by-side problems like “Sara has 3 more apples than Lena” vs. “Sara has 3 times as many apples as Lena.” This will help them see the difference between the two operations.
4. Mastering the Language of Multiplicative Comparisons
The language used in multiplicative comparison problems can trip students up if they aren’t prepared for it. Phrases like “twice as many” or “three times as much” might be new or confusing. It’s essential to ensure students are comfortable with this terminology before diving into full comparison problems.
Classroom Tip #4: Introduce this language early and often in your instruction. Use real-world examples (e.g., “You have 2 times as many crayons as your friend”) to model the language and give students plenty of opportunities to practice using it in context.
Putting It All Together: Prepping for Multiplicative Comparisons
Once your students have mastered these key skills, they’ll be ready to tackle multiplicative comparisons with confidence. The next step is introducing simple comparison problems that encourage them to apply what they’ve learned.
Start with basic problems using small numbers, like “Sara has 3 marbles, and Tom has 6. How many times as many marbles does Tom have as Sara?” Gradually work your way up to more complex, multi-step problems once they’ve gotten the hang of it.
Conclusion
Multiplicative comparisons can seem tricky at first, but with a strong foundation in multiplication and equal groups, your students will be ready to take on this challenge. Focus on reinforcing these prerequisite skills before diving into comparison problems, and your students will be well-equipped for success.
With a little patience and practice, multiplicative comparisons will become just another tool in their growing math toolbox!
By focusing on these foundational skills, you’re not only setting your students up for success with multiplicative comparisons, but you’re also helping them develop a deeper understanding of how multiplication works in the real world. Keep the lessons engaging, interactive, and connected to everyday experiences, and your students will thrive!
