Common Core standards were adopted by the vast majority of states in 2010. For teachers, it was out with the old and in with the new. Change can be hard, and this “new math” created quite a stir among teachers and parents. One of the new standards added to 4th grade math was multiplicative comparisons, and boy were they a challenge to teach! After many years, I have found what works (and what doesn’t), when teaching multiplicative comparisons.

## Multiplicative Comparisons-A Shift in Thinking

The big shift for 4th graders is to understand multiplication in the reverse order that they learned in previous years. For example, they first learned that 5 x 3 = 15. Now, it’s often written as 15 = 3 x 5, which is much harder to process. Further, students learn to read this equation as “15 is 3 times as many as 5”.

Why the change? It better aligns with the context of real-world scenarios. For instance, Jane is 15 years old. Her sister is 5 years old. Therefore, Jane is 3 times as old as her sister (i.e. 15 = 3 x 5). Thus, it’s important to implement word problems as you teach this skill.

## Multiplicative Comparisons: Product Unknown

There are two types of multiplicative comparisons: product unknown and factor unknown. For both types, it’s helpful to use a CPA approach (concrete-pictorial-abstract). Concrete means students are using hands-on materials to build conceptual understanding. I use the blank side of fraction tiles and have students label them with dry-erase markers. Because fraction tiles are already broken into equal-sized pieces, they are the perfect manipulative for this concept.

Click on the play button below to see how I use fraction tiles to find the unknown product.

Once you’ve modeled with fraction tiles, transition to having students use a pictorial model, specifically a bar model. This visual model helps students understand the relationship between the two quantities.

Finally, students are ready to solve problems without using a visual model, which is the abstract approach. They can write an equation (either multiplication or division) to solve for the unknown factor.

## Multiplicative Comparisons: Factor Unknown

This is the more challenging of the two comparisons. Many students struggle to see the multiplicative relationship when the factor is unknown. In the example below, students might read the problem and become confused because “4 times something doesn’t equal 15”. They must work through the CPA approach to discover why the equation would be 5 x n = 15. Therefore, I use the same strategy as in the first example: fraction tiles, bar models, and writing equations.

This video shows you how I teach this skill from start to finish.

Once you’ve taught both types of multiplicative comparisons, plan a day to review both types of problems. This allows students to see the similarities and differences between the two.

## Multiplicative Comparison Resources

You’ll need a variety of activities to get you started. Boom Cards are my favorite resource because of their self-checking feature. When practicing a new skill, it’s essential students have immediate feedback. This is the wow factor in Boom Cards! Students can use any electronic device with internet access to complete these digital task cards.

Want to know more about Boom Cards? Read my BLOG POST with details on how to use them in your classroom.

Task cards are my go-to resource for small group instruction. For starters, students can focus on one question at a time. In addition, it’s simple for me to check their work. I normally have students solve 3-5 task cards at my small group table.

I’m going to say something controversial in the teacher world. Giving students a worksheet for extra practice is totally fine! If they have a purpose, then they fit under my umbrella of “purposeful practice”. Worksheets can be used for small group instruction, intervention time, included in choice boards, or assigned as homework.

## Practice Make Progress

I wish there was a magic wand I could wave to get students to better understand multiplicative comparisons. In reality, it just takes practice…LOTS of practice. Furthermore, remember to give yourself grace when things don’t go as planned. I spiral back to this skill all year long, especially right before state testing. A little bit of review goes a long way.

To help get you started, grab this FREE deck of Boom Cards!

Until next time,

### Happy Teaching!

P.S. For more 1-digit multiplication resources, shop my TPT store. You’ll find over 40 resources to choose from, including games, worksheets, task cards, and digital Boom Cards.