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Multiplicative Comparisons – Tips and Resources for Student Success

August 2, 2022 by Krejci Creations

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. This means Jane is 3 times as old as her sister (i.e. 15 = 3 x 5). Therefore, 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: 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. 

This video is part of my digital anchor chart resource that plays video tutorials when students click or scan the QR codes!

Pictorial: Once you’ve modeled with fraction tiles, transition to having students use a pictorial model, specifically a bar model. 

multiplicative comparisons

This visual model helps students understand the relationship between the two quantities.

Abstract: Finally, students are ready to solve problems without a model, which is the abstract approach. They can write an equation (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 “3 times something doesn’t equal 32”. 

They must work through the CPA approach to discover why the equation would be 4 x n = 32 instead.

Therefore, I use the same strategy as in the first example: fraction tiles, bar models, and writing equations.

This example is part of my Editable Multiplicative Comparison PowerPoint Lesson. What’s unique about my PowerPoint lessons is they include printable and digital resources to use after the lesson for additional practice, such as a Google Form Assessment and small group activity!

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. These 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.

multiplicative comparison task cards

If you’re a fan of task cards, check out Episode 14 of Elementary Math Chat! I share 5 of my favorite ways to use and repurpose task cards to help you get the most out of these resources. 

episode 14 task cards

I share ideas for choice boards, partner activities to pair them with, and how to use them with cooperative learning structures.

In addition, I explain how to use them in your whole group instruction and within a Google Form assessment.

Okay, back to multiplicative comparisons…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”.

These worksheets can be used for small group instruction, intervention time, included in choice boards, or assigned as homework.

multiplicative comparisons worksheets

Practice makes 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!

free multiplicative comparisons

Until next time,
Happy Teaching!

-Annamarie

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.

Filed Under: 1-Digit Multiplication, Anchor Charts, blog posts, Teaching Strategies Tagged With: 1 digit multiplication, multiplication, multiplicative comparisons, word problems

A New Twist on Anchor Charts: QR Codes with Video Tutorials

December 1, 2019 by Krejci Creations

For years I had a love/hate relationship with anchor charts. I knew how beneficial they could be, but I just couldn’t grasp the logistics of posting and storing them. I’d scope out other classrooms and search endlessly on Pinterest for ideas, but what worked for others didn’t work for me. 

Because of this, I gave up on anchor charts completely. It wasn’t until I realized how much my students needed these reminders that I reconsidered. They were learning a new math skill every single day! Of course, they were going to forget some along the way. I was determined to find a solution.

To Post or Not To Post

For starters, I didn’t know how to properly store my anchor charts, nor did I have the time and energy to figure it out. As a result, they piled up on top of my cabinets and collected dust. Ohhhhh, the dust. In addition, I’d have to pull them all down just to find the one I needed.

Another problem was wall space, or the lack thereof, so I would only post charts related to current topics. Those, however, weren’t the only skills students were forgetting. My mind went down a rabbit hole. Should I post anchor charts from earlier in the year, or should I just post them all? Would that be too overwhelming? I found faults with each option, so coming up with a solution was a challenge.

On top of all that, not every student was able to look at an anchor chart and remember what to do. They needed a thorough example worked out and explained by me. I finally came up with a solution: mini anchor charts with an interactive twist. My love for alliteration inspired me to call them “reference rings”!

Bringing Anchor Charts to Life

With the addition of a simple QR code, I’ve brought these anchor charts to life. My students no longer have to wonder how I arrived at the answer. By scanning the QR code, they now see an example modeled and explained by me. 

All of my videos use manipulatives/visuals when possible and focus on conceptual learning. They have been a lifesaver! So, who exactly are these videos for?

Anchor Charts for Absent Students

Most recently, a student of mine was absent and missed my lesson on simplifying fractions. The next day, he felt behind and expressed how much he hated simplifying fractions. Statements like this are so hard to hear as a teacher!

A few days later, we did a review activity that included simplest form. He completed it with ease! I told him how impressed I was that he overcame his battle. He replied, “I watched the simplest form reference ring video a few times, and now I’m an expert.” He felt proud and relieved that he had mastered this difficult concept. I was thrilled!!!

Anchor Charts for Struggling Students

Not all students master a skill after a 30-minute whole group lesson; that’s what small group instruction is for. Even with this additional support, there are often a few students who still won’t fully understand,

I encourage these students to watch a reference ring video after they leave my group. Sometimes this is exactly what they need: one-on-one instruction. Reference rings are especially helpful when students are struggling but don’t want to interrupt my small group. We make reference rings part of our “Ask 3 Before Me” rule!

anchor charts with task cards

Anchor Charts for Enrichment

On the other hand, some students learn concepts so quickly that it’s hard to keep up with them. They soak up any knowledge they can get and run with it. Those students in particular have loved watching my reference ring videos on future topics. Several have even pretested out of chapters because of this!

4th grade anchor charts

These interactive anchor charts can also be displayed as a bulletin board using the full-size version. I typically post only the charts related to the current unit and include a few review skills. The mini anchor charts remain posted and available at all times since they don’t take up much space.

printable large anchor charts bulletin board

Want to try a reference ring set for yourself? Grab the Place Value FREEBIE, or shop the BUNDLE which includes 70 tutorial videos for 4th grade math!

Until next time,
Happy Teaching!

-Annamarie

 

Filed Under: Anchor Charts, blog posts, Digital Resources Tagged With: 4th grade math, anchor charts, math resources, math tutorials, QR codes, test prep

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