What Make a Good Math CFA? 4 Qualities Every Assessment Should Have

When I talk with teachers about math CFAs (common formative assessments), two questions always come up: 

1. How do I know if an assessment is really worth my time? 
2. Will I actually be able to quickly use the data?

I was working with a 5th-grade team at the end of the school year, and they realized they had 5 math assessments to give before school was out. Five.

Why would they need 5 different math assessments at the end of the school year??

Well, each assessment measured something slightly different. And all of them, of course, were district and/or state-mandated. 

Now to be clear-I’m not saying there isn’t any value in those assessments. But here’s what I’ve noticed over the years: if you give an assessment and never do anything with the data, it’s a waste of time. 

Let's dive into what actually makes a CFA valuable.

1. It is aligned to a specific standard-the major work of the grade.

You don’t want to start with any random standard. You want to make sure that you are focusing on standards that are going to give you the biggest bang for your buck. That means that if I’m teaching 4th grade, I’m teaching and intervening on equivalent fractions, rather than spending time making sure my students know how to use protractors.

If you’re not sure what the major work of your grade level is, I highly recommend checking out the Coherence Map at Achieve the Core. It’s a great tool that will give you valuable insight into your essential standards.

CFAs should be aligned with one to two priority standards. The more standards you try to assess, the muddier your data can become.

2. It provides more than just a right or wrong answer.

One reason people love math is because there appears to always be one right answer. However, when we are actually diving into student work, we care less about the answer and more about the students’ processes when solving the problems. We are focusing on assessing thinking, not computation.

One way I love to do this is by using a rubric. Rubrics allow us to see how close students are to mastery. They also help determine gaps in a student’s learning. Check out these rubrics for 4th grade math CFAs.  

Notice how there are different areas? That means if a student understands the basic procedure of the addition algorithm, but still needs help with their facts, they still get points for what they understand!

Using rubrics really helps guide your intervention blocks.

3. It actually gives you action steps, instead of just being another thing to grade.

Just because you can grade something doesn’t mean you should. Spending time grading something that you'll never use is a waste of your time-and your time is precious. If you're not sure if something is a good CFA candidate, check out the list below. 

Good CFAs should:

• Be put together or agreed upon by your team (hence the “C” for “common” in CFA)
• Take 10-15 minutes
• Have 3-6 targeted problems
• Be easy to analyze 
• Provide insights into further interventions

If the assessment you're looking at checks all the boxes, you've got a good CFA on your hands!

Want an example of a CFA you could give with your team tomorrow? Check out this one!

(And yes, I know I’m not on your school team. But I’ve always found it easier to start from something instead of having to start from scratch.)

4. We Have Data. Now What?

Let’s be real. CFAs are only worth your time if you use the data. After looking at the data, you can then use it to determine how to adjust instruction and provide intervention. It can really guide your PLC conversations, too. 

This honestly deserves its own post (and it will get it too!). Make sure to check back to see how to do a data dive with your team that will yield powerful results for your students.

Want to Try a Done-For-You Math CFA? 

Want to see what a great CFA looks like in action? Grab this free Addition & Subtraction CFA toolkit with all 4 forms and data trackers. It’s the perfect starting point for you and your team to begin assessing one of the first major standards of the year. And the best thing? It’s ready for you to use tomorrow. 

Math CFAs don’t need to be complicated, but they need to be intentional. And if you're looking for a done-for-your-team PLC/CFA toolkit and you teach 4th grade, I've got you covered. Click here to see more!

You've got this!

Happy Teaching!

Jamie

4 Ways to Increase Fact Fluency (Without Memorization!)

During my last year teaching in 4th grade, I focused on increasing multiplication fact fluency with my students. I gave my students a baseline test and then had a series of lessons and activities designed to help them become more fluent. 

One student did very well on her baseline test. She was able to get all of the answers correct in a short amount of time, and could easily answer everything up to 10 x 10. This is great, I thought, because she'll really be able to help other students as we work throughout this unit! 

Well, we started our unit, and I could tell she would need an extension, as she already was very fluent with her facts. I started giving her harder problems to work on, like 12 x 3, or 13 x 4. 

And this was where she shocked me. She stared at me like I had just asked her to build a rocket to the moon. She had no idea how to mentally come up with an answer for these problems.

It didn't take me long to realize that all she had done was memorize the answers to each multiplication problem. She excelled at memorization, but she hadn't developed the number sense to apply what she had learned to other situations. 

We want our students to be fluent. But what does fluency mean? According to Math Fact Fluency by Jennifer Bay-Williams and Gina Kling, there are 4 components to fluency:

• Accuracy: The ability to produce mathematically precise answers
• Efficiency: The ability to produce answers relatively quickly and easily
• Appropriate Strategy Use: The ability to select and apply a strategy that is appropriate for solving the given problem efficiently
• Flexibility: The ability to think about a problem in more than one way and to adapt or adjust thinking if necessary (Bay-Williams & Kling, 2019).

My student was accurate and efficient, but she was not flexible, nor could she select a strategy to help her solve the more complex problems I gave her.

Now you might be thinking, "But Jamie-why does this even matter? She had her facts memorized! Most of my students are still figuring out 3 x 7!"

Here's why. Her main strategy is memorization. She doesn't have an underlying conceptual understanding of how numbers work. 

We don't ask students to memorize how to say words. We teach them phonics, increase their phonemic awareness, and work with them until they can sound out unfamiliar words independently. We need to be doing the same in math. 

So how do we do this? Going back to Math Fact Fluency, here are 4 suggestions on how to increase fact fluency without drills, flashcards, or timed tests.

1. Get a Baseline

Figure out where your students are at using a quick interview. Show students a variety of facts and ask them to tell you the answer, and, more importantly, explain how they figured them out. If they skip count, we know they haven't mastered them yet. If they can recall it automatically, we can check that off as mastered. 

Once you have a baseline, you can determine which facts your students need to work on. Bay-Williams and Kling recommend starting with 2s, 10s, 5s, 1s, 0s, and squared facts in that order. If students have mastered those facts you can move on to strategies like doubling, adding a group, subtracting a group, decomposing facts, and using known facts to derive the answer.

2. Use Pictoral Representations

One strategy they recommend is called "Quick Looks." This is where you show students a visual of the math fact or strategy you are trying to teach. For example, let's say you are working on 2 x 7. You would show them a picture that has 2 groups of 7. The trick with this though, is that you would only show it to them for about 3 seconds before hiding the picture.

Then you'd ask them to recall what they saw. You can discuss that there were 7 circles on top and 7 circles on bottom. Two groups of 7 is 14. Could they do it without having to count the individual circles? 

The goal is to help students get to a point where they don't have to count each circle but can use what they already know to determine the represented number.

3. Use Story Problems

We're not giving up on word problems at all here. In fact, in the "real world," students are never going to come across random math problems without any context. Every time I've had to use math, it's in the context of something, whether that's food, gas, money, time, etc. 

So we ask students to visualize and comprehend what is happening in word problems. If I'm working with a group of students on their 2 multiplication facts, the story problem might be something as simple as "Tamarita has 2 baskets with 8 apples in each one. How many apples are in each basket?" 

I'd ask the students to draw a quick representation of what is happening in the story, and then write an equation to match their drawing. Some students might write 8 + 8. That's okay! That is a great way to lead into a discussion about how 8 + 8 = 2 x 8. 

4. Play Games! 

Games are so much fun to play, and kids enjoy them much more than timed tests. If I'm helping students with their 5s facts, I might have them play Trios, where they'll get practice multiplying by 5.

Just as important as playing the game, however, is the discussion after the game is done. For example, after playing this game you could ask students "What number would I need to roll to get a 35?" or "How could I use 5 x 5 to help me figure out 5 x 6?" 

Debriefing the game will help students solidify their thinking, learn from others, and gain strategies that can help them in the future.

If you want to learn more about improving multiplication fact fluency with your students, I highly recommend that you check out Math Fact Fluency. There are so many good ideas there! 

Grandma's Famous Coffee Cake

 Okay, I know this isn't a recipe blog. It never has been and never will be. 

But I just couldn't let this holiday season pass by without sharing a piece of my childhood.

When my dad was growing up, his mom would make a stellar coffee cake. He and his 4 older brothers would look at the cake after it came out of the oven and thought it looked like lava. They nicknamed it Lava Cake, and that's what we've called it in my family ever since!

Don't be fooled though: this is nothing like the molten lava cakes (also delicious, just not this recipe)!

So I'm sharing this recipe with you today!

Ingredients

• 3/4 cup shortening
• 1 1/8 cup sugar
• 1 1/2 teaspoon vanilla
• 5 eggs
• 3 cups flour
• 1 1/2 teaspoon baking powder
• 1 1/2 teaspoon baking soda
• 1/2 teaspoon salt
• 1 1/2 cup sour cream
• 6 tablespoons butter
• 1 cup packed brown sugar
• 2 teaspoons cinnamon
• 1 cup pecans

Directions

1. Cream shortening, sugar & vanilla together.
2. Add eggs one at a time, beating well after each addition.
3. Sift flour, baking powder, and baking soda together.
4. Alternate adding sour cream and flour mixture to the creamed mixture.
5. Spread half of the batter in a greased 10" tube pan (or angel food cake pan).
6. Cream butter, brown sugar, and cinnamon together.
7. Add the nuts and mix well. 
8. Dot the batter in the pan evenly with half of the nut mixture.
9. Put the rest of the batter in the pan.
10. Cut thru the batter with a butter knife to create a swirl.
11. Put the rest of the nut mixture on the top of the cake.
12. Bake at 350 degrees for 60-65 minutes.
13. Cool for 10 minutes then remove from the pan.

Enjoy!!

6 Reasons You Should Be Playing Math Bingo Games in Class

You know that sound when you tell your kids to take out their math books and turn to page 394? (I know you can hear it in your head right now.)

We all know that math is an essential subject that builds critical thinking, problem-solving, and logical reasoning skills in young learners. However, for many 4th-grade students, math can sometimes feel dry and intimidating. One way to combat this is through playing math bingo games! Check out 6 reasons to play math bingo games with your 4th graders below!

1. Reinforce Mathematical Thinking

Bingo games provide an excellent platform to engage and entice students! When students are engaged in what they are doing, they are more likely to develop their skills and increase their productivity. Want your students to revisit past skills? Pull out a bingo game!

2. 2. Use Math Bingo Games to Improve Mental Math Skills

One of the most significant benefits of incorporating bingo games in math lessons is their ability to improve mental math skills. In traditional math exercises, students might use paper and pencil to solve problems, but bingo encourages them to perform calculations mentally and quickly. The thrill of trying to be the first one to mark off a number on their bingo card motivates students to think on their feet, leading to improved mental agility in mathematics.

3. 3. Enhancing Problem-Solving Abilities

Bingo games often involve a bit of strategy. Students must think strategically about which numbers they need to complete a pattern or win the game. This problem-solving aspect adds an extra layer of excitement to the activity and cultivates critical thinking skills among students.

4. 4. Fostering a Positive Learning Environment

Math anxiety is a common issue among students, which can hinder their learning progress. Bingo games offer a low-pressure and enjoyable environment for practicing math skills. As students participate and engage in the game, they become more comfortable with the subject matter. This positive learning experience can significantly impact their overall perception of math, helping them develop a more positive attitude toward the subject.

5. 5. Encouraging Collaboration and Communication

Bingo games can be adapted to encourage teamwork and collaboration in the classroom. You can organize group bingo games where students work together to complete their cards. Students also have to use appropriate social skills to play the game with peers. This fosters a sense of camaraderie among students and promotes healthy communication skills as they discuss and solve problems collectively.

6. 6. Easily Assess Students

Traditional assessments can sometimes feel stressful for students. Introducing bingo games as a form of assessment can alleviate some of this stress and create a more enjoyable evaluation experience. Teachers can use bingo games as review sessions before quizzes or tests, allowing students to review concepts in a relaxed and fun manner.

As teachers, it's essential to create a well-rounded and enjoyable learning experience for our students, and bingo games provide a fantastic tool to achieve that goal. Now you're probably thinking "But Jamie. I just don't have time to create math bingo games for my 4th graders." Don't worry. I've got your back. I've created bingo games for almost each skill in 4th grade math. Want to check it out to see how it will help your kids? Click here!

And if you want to check it out first before purchasing, I totally get that! That's why I've created my area & perimeter game available for you to download for FREE! All I need is your email and I'll send it straight to your inbox!

4 Ways to Help Students Master Equivalent Fractions

Error analysis for the win!

I'll send you a free set of error analysis task cards that focus on adding and subtracting fractions.

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One of my favorite parts of math instruction is teaching fractions. I know several people who when they hear the word fractions shrivel up like a grape left in the hot Sahara sun. Not me though! Fractions are so intuitive and can be taught in a way that really helps students grasp and understand the concepts. Here are 3 things that I used to help my students solidify their understanding of equivalent fractions.

1. Ditch the Pictures!

It may seem counterintuitive to begin teaching about equivalent fractions by not showing students a picture of 1/2 and 2/4. Instead, to introduce fractions, I begin with equal-sharing word problems. I do this because students are so familiar with this example in their real life. 

These problems often involve splitting up some type of food item between a certain number of people. You can use these to help students understand equivalent fractions. Here is a question that I like to use to see if my students can make the connection of equivalent fractions on their own.

"There are two groups of kids sharing pizza. In one group, three children share one pizza equally. In another group, six children share two pizzas equally. Who will get more pizza? A child in the first group or the second group?"

After examining the problem, we can see that each child is going to get 1/3 of a pizza regardless of which group they are in. We can talk about how in one group the students might just get 1/3. In the other group, the students can get 2/6 a pizza. Having these discussions with your students can really help them conceptualize the same amount, just different sizes of pieces.

(And, just because you don't provide students with a picture doesn't mean students can't draw a picture. In fact, it's preferred! That way, students are sharing their model, instead of just doing what the teacher tells them.)

2. Use Manipulatives to Find Equivalent Fractions

Okay, I know I just told you to ditch pictures, but once students have worked through a significant number of equal sharing problems, then I will introduce manipulatives. I don’t like to use manipulatives to start with because I really think that fractions can be intuitive if presented correctly. Manipulatives, however, are a great way to show equivalent fractions after students have 1) already identified what they are, and 2) are familiar with various ways to find them. 

I will do something similar to what I did in the pizza problem. I will have the students pull out 1/2 and 2/4. They will then determine if they are equivalent or if one is greater than the other. The danger with this is that some fractions can look really close to being equivalent well just being slightly off. Take a look at this example.

Here you can see that 3/5 and 7/12 look really close. They are *almost* equivalent. And to students who are still trying to figure out how to be precise, this can be an issue if this is the only way that students are taught to find equivalent fractions.

3. Use Multiplication & Division to Find Equivalent Fractions

After using manipulatives, we talk about how we can find equivalent fractions without using fraction bars. This is when teaching students about multiplying and dividing comes in. It is not enough however to just teach the students how to find the equivalent fraction. It must be accompanied by an understanding in order for students to really internalize it. 

I like to draw models with my students that then show why I multiply by two over two or three over three. We discuss why I can divide a fraction by two or by three in order to find an equivalent fraction.

4. Practice Finding Equivalent Fractions

After students know how and why finding equivalent fractions works, they are ready to practice. My favorite way I have to practice is by using games and other activities in the classroom. Some of my favorite activities to do with my students are games like bingo or a board game set up similar to Candyland. I’ve also used coloring pages to help my students find equivalent fractions as well. Want to check out some of my equivalent fraction activities? Click here to see some of the activities you can use with your students in your classroom.

Teaching equivalent fractions doesn’t have to be the bane of your existence. By introducing equivalent fractions through word problems, manipulatives, having students discover how to find equivalent fractions, and fun and engaging repeated practice, your students are sure to become masters of fractions.

Want a free fraction activity to do with your students? Check out this FREE set of addition and subtraction fraction task cards that focus on error analysis! These are perfect for helping your students find and fix mistakes in their work too!

6 Ways to Help Your Students to Celebrate Mistakes in Math

Error analysis for the win!

I'll send you a free set of error analysis task cards that focus on adding and subtracting fractions.

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Simply print it off and use it with your class today!

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I always loved Ms. Frizzle’s motto of “Get messy, make mistakes!” As educators, we want our students to be successful, which somehow translates to “don’t make mistakes.” I know that I’ve been guilty of thinking “Man! I’ve taught this concept over and over again! You would think they would have it down perfectly by now.” This is especially true when it comes to my students making mistakes in math.

As I’ve shifted away from this mindset, I’ve come up with 6 ways that I’ve been able to help my students not only identify and fix mistakes in their own work but celebrate them and recognize that they are learning.

Here are 6 ways to help your students identify and fix their mistakes in math:

1. Make Mistakes On Purpose

Each day, my students complete a spiral review with 4 questions. As they are working, I walk around, observing their work. Oftentimes, I will notice that some students are making the same mistake. When we go over the spiral review as a class, I will make the same mistake they have made on purpose. When I get the incorrect answer, I will often have a student say "That's not right!" They then get to explain where my mistake was.

One word of caution with this method: Once you are finished making the incorrect mistake, you want to make it very clear where the mistake was, and how to fix it. With the attention span of a goldfish, some students might just catch the "mistake" part, and not the "how-to-fix-the-mistake" part, and continue to solve it incorrectly. 

Sometimes, I will tell my students before I solve it that I am going to make a mistake and that they need to find what I did incorrectly. This helps my students focus on the work I am doing because they are hunting for the mistake.

2. Have Students Share Out Their Mistakes

After we do our spiral review, I give the students a chance to explain mistakes that they made in their work. They get to come up to the front of the room and tell us what mistake they made and how they fixed it. My students love doing this. If I ever forget to ask "Did anyone make any mistakes they want to share?" one of my students will remind me.

I love this because it allows other students to hear where common mistakes are. They also learn that their peers make mistakes, just like they do. It really helps to build a culture of making mistakes in our classroom (which I talk more about below).

3. Use Error Analysis Activities

I love giving my students the opportunity to find mistakes. It helps them to develop critical thinking skills that they can use to solve their own math work. One of my favorite ways to do this is to grab a set of error analysis task cards that focuses on the math skill that we are working on. 

There is a math problem that needs to be solved on each card. Then, someone has gone through and solved the entire problem. However, there is always some simple mistake in the work that has been done. When we do these task cards, I give my students the chance to go through the work and find the mistake. When they find the mistake, they write down what the mistake was, and then they solve it correctly.

Making error analysis task cards can be a little time-consuming though, so I’ve got a free set for you if you want to check them out. CLICK HERE to grab a FREE set of error analysis task cards for adding and subtracting fractions with like denominators. 

4. Create a List of Common Mistakes Students Make

Another thing I like to do to help my students identify mistakes is to create a list together of common mistakes that students make. For example, when we are talking about multi-digit subtraction, one common mistake is that students forget to ungroup when it is necessary. We give specific examples, like trying to subtract from 0.  Another mistake is that students will make is adding instead of subtracting. We create this list and post it in the classroom, so my students have something to refer back to when they are doing their math work in the future.

5. Create a Culture of Making Mistakes

I believe the most important thing that you can do to help your students find and fix their mistakes is to build a culture of having a growth mindset in your classroom. I love it when my students make mistakes because that is how they learn and grow. I tell them that each day. I praise them for making mistakes. I want them to feel like making mistakes is okay. I want them to feel like when they make mistakes they are learning. 

Making mistakes easier for some students than others. I have had my fair share of students who are such perfectionists that they do not even want to try for fear of being wrong. As we build a culture of making mistakes in our classrooms, our students will feel safer in trying new things, and their confidence in their math skills will grow.

6. Change the Problem to Make the Mistake Correct

Let’s say you are reviewing multiplication facts with your class, and you come to 7 x 8 (a trickier math fact for some kids). One student says the answer is 54. Rather than stating that the answer is 56 and moving on, ask the student if they can come up with a problem where 54 would be the correct answer. This could be a good practice to do with the whole class, or in a small group. By coaching students to see that there is a context in which their answer could be correct, we are empowering them to become more flexible mathematicians in the future. 

Having your students find and fix their mistakes in math can be a challenge. It takes time to build up that culture, but it is well worth it as your students can really find and identify mistakes in their work.