manipulatives Archives - Shelley Gray

Five Simple Activities to Help Your Students Build Fraction Sense

Shelley Gray — Wed, 28 Aug 2024 16:58:28 +0000

Do your students possess fraction sense? Fraction sense involves a deep, conceptual understanding of fractions as numbers. This goes far beyond simply shading parts of a whole or identifying numerators and denominators. It involves true, flexible understanding.

Errors in fraction calculations can often be traced back to poor fraction sense. For example, think of a student who might add three-fourths and three-fourths and get six-eighths.

This student is likely getting mixed up with a rule that he learned for adding the numerators only when adding two fractions with the same denominator.

But we don’t want our students to rely on a meaningless rule or procedure. We want them to actually understand fractions.

So how do we ensure that our students develop this fraction sense rather than having to rely on meaningless rules?

Here are five simple activities you can incorporate into your classroom to help your students build their fraction sense.

Use Manipulatives and Visual Models

Fractions are an abstract concept for many kids, especially since they may not have much real-life experience with fractions yet. But concrete manipulatives can be a game-changer, making fractions easy to visualize and understand.

I love the circular foam fraction pieces for students to explore concepts like fraction addition/subtraction and equivalent fractions. They also make improper and mixed fractions simple to visualize.

Another amazing manipulative for fractions is Cuisinaire rods. Look at the examples below for just a couple ways these can be used.

Another visual that I love for fractions is bar models. Bar models can be used to make simple calculations more conceptual, or as an effective problem-solving tool. See this post on Instagram for more information on how to use them.

Paper Folding

Simple paper-folding activities can take fraction concepts from abstract to concrete for your students. There is some prep involved to get these paper pieces ready for students, but the actual act of your students creating the fraction pieces will be well worth it.

To prepare for this activity each student will need several different square pieces of paper. I like to have different colors. In this picture, I used black as one whole. Then students can fold the blue piece in half. Each of these pieces represents one-half. The pink piece was folded in half, and then in half again. These represent one-fourth.

The act of folding and cutting is powerful, because it helps reinforce that one-fourth is half of one-half, one-eighth is half of one-fourth, etc.

BUT! Here’s the important part. You may be tempted to have students label the pieces as 1, 1/2, 1/4, etc. However, using them unlabelled will allow for far more deep thinking. For example, consider how these tasks might look:

If the black piece represents 4, what does the blue piece represent? How about the pink piece?
Show one-half in three different ways.
How does the orange piece relate to the black piece?

As you can see, using these pieces unlabelled will allow for some tremendous opportunities to rationalize and think deeply about fractions.

Conduct Whole Class or Small Group Fraction Talks

Simply talking about fractions can have a profound impact on students’ understanding. This can be done in a whole class or small group setting and requires no prep or special materials.

For example, you could simply draw an image on the board, like the one here, and ask students what they notice about the drawing.

If students are stuck for ideas, prompts like these could help get the conversation started:

What equations could we write to represent this drawing?
How are these circles the same and different?

If you own my Math Conversations number talk resources, you’ll also find some great fraction talk slides in there.

Think of all the possiblities that students might come up with for this question. Maybe it represents 8 groups of one-fourth.

Maybe it represents two wholes and 8 groups of three-fourths.

When we start looking at how students might group the circles to add them together, there are loads of different options.

Count By Fractions

Just like we can count by 1s, 2s, or 5s, we can count by fractions! This helps students see fractions as numbers.

I’ve made a few videos that you can use in your classroom to help your students make connections between the fractions and the visual representations. See all available videos here.

Make Fractions Meaningful and Relevant to Real Life

There is no better way to encourage true understanding than to relate fractions to how they are actually used in real life. Just think of all the amazing fraction skills we learn by baking! Here are just a few other examples of real-life experiences we can use to help our students understand fractions:

Sports statistics
Discounts at a store or restaurant
Time (half of an hour, etc.)

If you’d like a ready-made math project to help your students understand how fractions are used in real life, here are a couple of my favorites.

Or see all real-life math projects here.

The big idea here is giving our students the opportunity to actually SEE the fractions. Visuals and manipulatives make fractions so much easier to understand, and if we are teaching without them, we are likely creating gaps in understanding.

The post Five Simple Activities to Help Your Students Build Fraction Sense appeared first on Shelley Gray.

Using Bar Models to Effectively Solve Math Word Problems

Shelley Gray — Mon, 04 Mar 2024 14:08:11 +0000

Have you tried Model Drawing in your classroom? I recently read the book 8 Step Model Drawing by Bob Hogan and Char Forsten. I have always been a fan of bar models, but this book was an eye opener as to just how effective they are as a problem solving tool. The authors state that about 80% of word problems that students encounter can be effectively solved using models like these.

My mind has been spinning with all of the other potential uses for bar models beyond basic problem-solving.

As I continued to read more about model drawing, it became clear to me that they can be connected beautifully to so many different math manipulatives. I think every teacher should know about model drawing, so I decided to put together a 10-part video series with ideas you can take directly back to your classroom. These videos will incorporate both math manipulatives and model drawing for different problems including fractions, multiplication, division, and more! As the videos are posted on Instagram, TikTok, Facebook, and YouTube, I’ll also add links here so you can find them easily.

Or sign up here to have the link delivered to your inbox.

I hope you enjoy this video series! If you’d like to know even more about model drawing, be sure to check out Step-by-Step Model Drawing as well as 8-Step Model Drawing.

Day 1: Using Models and Manipulatives to Solve Fraction Problems

Bar models are naturally an incredible visual for fraction problems. Fractions can often be such an abstract concept for our students, and models can transform them to easy-to-understand.

View this video below or on these social media outlets:

Instagram

Facebook

Day 2: Using Models and Manipulatives to Solve (More) Fraction Problems

I decided to focus on fractions for 2 out of the 10 videos in this series, because models are so effective for visualizing fraction problems. The problem below is one of my favorites because it makes a 2-part, more complex problem so simple to visualize.

View this video below or on these social media outlets:

Instagram

Facebook

Day 3: Using Models and Manipulatives to Make Addition and Subtraction Word Problems Visual

Models are very well-suited to addition and subtraction problems. They not only make the problem easier to understand, but reinforce the inverse relationships between addition and subtraction. This video shows two different problems and how bar models can be used.

**Note** I neglected to make the parts of the bar different sizes in the second problem. This is my mistake, and I will be re-creating this video soon. In the meantime, please note that the pieces should be more to scale to show the differences in the magnitude of the numbers.**

View this video below or on these social media outlets:

Instagram

Day 4: Using Models and Manipulatives to Build Multiplicative Reasoning

Models are a must-use tool to develop multiplicative reasoning. They beautifully illustrate the relationship between multiplication and repeated addition, and can take complex multiplication problems from difficult to easy-to-imagine.

View this video on these social media outlets:

Instagram

Facebook

Day 5: Using Models to Make Division Problems Visual

Bar models for division are pretty straightforward, and we might neglect to use them because they don’t feel necessary. However, remember that modeling simple problems is important so that students feel comfortable with models as a tool for more complex problems. Additionally, I love how division models effectively connect multiplication and division, as well as build a foundation for fraction concepts.