Engaging Math Activities to Reinforce Learning and Boost Retention

 

Math practice is essential for mastery, but let’s be honest — worksheets can get repetitive. If you’re looking for fresh ways to engage students while reinforcing foundational skills, incorporating activities can make a significant impact by encouraging deeper understanding and fostering meaningful mathematical discussions among students.

Why Interactive Activities Work:

1. Builds Confidence: Struggling students get guidance from peers in a non-intimidating setting.

2. Encourages Discussions: Students must verbalize their reasoning, which deepens understanding.

3. Frees Up the Teacher: With students working collaboratively, you can circulate and provide targeted support.

Matching Activities: Extra Practice

Matching activities provide a hands-on way for students to strengthen their math skills while actively engaging with the material. Rather than solving problems on a worksheet, students must analyze and connect different representations of mathematical concepts.

Some examples include:

1. Graphing Linear Equations Matching: Students match linear equations in slope-intercept form to their corresponding graphs. By identifying key features such as slope and y-intercept, they build a stronger conceptual understanding of linear functions.

2. Exponent Rules Matching: Students apply the exponent rules to simplify expressions and match them to their simplified equivalent forms.

3. Equation Form Matching: Students match different representations of equations—standard, slope-intercept, and point-slope form—helping them see the connections between them.

Peer Coaching: Encouraging Mathematical Discussions

Another powerful way to increase student engagement and retention is through peer coaching. When students explain their reasoning to each other, the peer coach's understanding is reinforced while simultaneously helping classmates.

How Peer Coaching Works

In a peer coaching activity:

1. Students are paired strategically (without telling them) as Partner A and Partner B.

2. Partner A solves a problem first, explaining their thought process aloud while Partner B listens. Then, Partner B solves a related problem, applying what they learned from Partner A’s explanation.

3. The cycle continues, with students alternating roles, discussing their solutions, and correcting misunderstandings together.

This method is especially effective for foundational concepts, like simplifying expressions or solving systems of equations, where students can coach each other through procedural steps.

Seamlessly Integrating These Activities into Your Classroom

Incorporating these activities into your classroom does not require an overhaul of your lesson plans. Here’s how you can weave them into your existing structure:

• Use them as Bell Ringers or Exit Tickets to check for understanding in a quick, interactive way.

•  Warm-Up: A quick exercise at the start of class gets students thinking mathematically right away, while reinforcing concepts from the previous lesson.

•  Exit Ticket: A few problems (matching or peer coaching) at the end of class can serve as a low-stakes formative assessment.

• Pair students intentionally to maximize learning potential during partner activities.

•  Partner Work: Encourage collaboration by having students work in partners or small groups to discuss their reasoning for solving a problem.

• Encourage discussion and justification of answers to reinforce conceptual understanding.

•  Stations or Centers: A few problems at a station foster mathematical discussions while increasing the number of practice problems students complete.

These strategies not only make math practice more engaging but also empower students to take ownership of their learning. Give them a try and see how they boost student engagement and comprehension!

Ready to Use Resources

If you’re looking for ready-to-use matching and peer coaching activities, I’ve created resources that seamlessly integrate into any Algebra classroom. Click on the links for matching activities or peer coaching activities to find resources.

Engage Students with Math Labs

Are you craving new ways to engage students in math? Consider Math Labs! Much like science labs, Math Labs involve hands-on experiments, but with a focus on mathematical concepts. They are an exciting way to make math fun, interactive, and realistic!

My Introduction to Math Labs

I first encountered Math Labs during a professional development session hosted by the Math Science Innovation Center in Virginia. The session, designed for middle school math teachers, emphasized incorporating activities that make math enjoyable and relatable.

One memorable activity was called "Get Your Bearings." In this experiment, we measured water displacement caused by ball bearings dropped into a test tube of water. The collected data was used to create tables, graphs, and predictions. We extended the activity by combining data from two groups to form a system of equations. It was an enlightening experience, showing how hands-on activities could transform math learning.

Adapting Math Labs for High School

While the original activity was tailored for middle school students, I wanted to adapt it for my high school Algebra 1 students. These students needed to prepare for standardized state tests, so I couldn’t dedicate a day to an activity without clear relevance to their curriculum.

After some reflection, I decided to modify the lab:

* Increased Rigor: I incorporated higher-order thinking questions (beyond DOK 1) to challenge students.

* Enhanced Scientific Approach: Students made predictions, compared tables and graphs, and used calculations as evidence to support their claims.

These changes elevated the activity to an Algebra 1 level. To my delight, my students loved the "out-of-the-box" approach to practicing math.

Initially, I planned to use the Math Lab at the start of our Relations and Functions Unit to gauge prior knowledge. However, after co-planning with another Algebra 1 teacher, we decided to use it as a review activity. This timing allowed for richer discussions and encouraged students to apply relevant vocabulary.

Why Try Math Labs?

If you want to get students excited about math, try something new! Many Math Labs I’ve conducted or developed began as simple word problems from the curriculum.

Example: Probability
Consider those classic probability questions about marbles in a bag. Why not recreate this scenario in your classroom? Extend the lesson by discussing experimental versus theoretical probability or exploring the difference between probability and odds. These hands-on activities deepen understanding and make abstract concepts tangible.

Free and Editable Resource: Get Your Bearings Math Lab

If you’d like to try the "Get Your Bearings" Math Lab, click here for a free download of the resources I used.

Important Notes:
Math Labs require additional materials, which might involve purchases or borrowing from other departments.

While they require extra preparation, Math Labs are worth the time and effort for the engagement and learning they bring to your classroom.

8 Benefits of Content Posters in Math Classroom

 

Some people don’t see the educational benefit of having posters in the classroom. They see posters merely as decorations with inspirational quotes. What if I told you that having content posters in your classroom were vital for students’ learning? 

Content posters are learning aids that provide visual representations of mathematical concepts, which makes understanding and retaining information easier. Here are 15 reasons why you should have content posters in your math classroom.

Organization and Structure

Posters can help organize complex math topics into clear and structured visual displays, aiding comprehension and organization skills. Below you can see posters outlining how to solve multi-step equations. My students loved having these up when they were first learning to solve equations because they were a quick reference! 

Increased Independence

Well-designed posters can boost students' confidence by providing visual affirmation of their mathematical skills and achievements. You can see the same posters from above but printed to fit on students’ desks. Students became more independent rather than constantly asking me what they should do next. This strategy was also a tremendous tool for my introverted students who were not comfortable speaking with other students.

Reinforcement of Key Concepts

Posters serve as a constant reminder of essential math principles and formulas, reinforcing learning over time. I once had a student tell me they were stuck on a problem, but remembered a poster I had in the room that helped them solve the question. I’ll take that as a win!

Reference Guides

Anchor charts act as handy reference tools, allowing students to quickly access important information during class or while working independently. The anchor charts below were a wonderful reminder to my students at the beginning of Algebra 1. We were able to quickly review these concepts while mainly teaching procedures because students could reference these posters daily. Also having these previous courses’ content posted, my co-teacher and I have been able to scaffold instruction to our students who struggle with math.

Memory Aids

Visual cues on posters can trigger memory recall, helping students remember mathematical concepts. During and after COVID, I noticed my students had huge gaps in their knowledge of basic math principles. The Hidden Math posters below have constantly been referenced by my co-teacher or myself over the past few years. Seriously, a life saver!

Problem-Solving Support

Posters can display problem-solving strategies, tips, and techniques that students can refer to when tackling math challenges.

Vocabulary Expansion

Math posters often include relevant mathematical vocabulary, expanding students' understanding of mathematical language and terminology. We all know students cannot answer a question if they do not know what the question is saying or asking! Building vocabulary is a monumental task that is overlooked in math classes. My co-teacher bought the vocabulary posters below to help our “return from COVID closures” students. I could not be more thankful for his purchase because we also had several English Language Learners (ELLs) that year. These Posters with the visuals exponentially increased our efforts with our students!

Collaboration

Posters can serve as focal points for teacher-student as well as student-student discussions. They act as conversation starters which can lead to mathematical concepts and applications of problem-solving activities. Ultimately, this creates a collaborative learning environment in the classroom.

These benefits collectively contribute to a more engaging and effective math learning experience for students. And don’t forget the added bonuses of increased independence and helping at-risk students like ELLs!

Alternative Assessments in Algebra 1

Everywhere we turn in education, teachers are being asked to have students produce examples of their learning rather than just regurgitating facts.

Educational buzz words that have circulated over the years are authentic assessments and alternative assessments. The purpose of an alternative assessment is to showcase a student’s understanding of the concept beyond what traditional quizzes and tests show, which in turn promotes deeper learning and engagement for the student. Some teachers have students write letters to state senators, create portfolios of their artwork, or design an experiment. But the big question for math teachers is how can we incorporate alternative assessments into our classes for additional insights of our students’ learning?

One solution that has worked incredibly well in my classroom is a Gallery Walk. I allowed this assessment to take the place of a regular multiple choice, matching, or fill-in-the-blank quiz. For the explanation, I will focus on the Properties of Real Numbers Gallery Walk.

First, I wanted students to engage in a dialogue over the properties of real numbers, so I allowed students to work in groups of 2 or 3. Some years I assigned the groups and others I let students pick their groups. After using both ways, both group selection methods worked for me.

Next, I only provided 2 days in class for students to complete the assignment. I did not want students using class time as a social hour instead of learning and working, so I limited their time. At first, I was concerned that 2 days was not going to be enough time. Surprisingly, I received better final products with only providing 2 days versus 3 days. I did not ask my students, but I think the shorter time frame caused an urgency in my students to work rather than socialize.

Finally, I provided them with a loose structure of what to complete and a deadline. For example, on the first day, I told the students they needed to have a property picked out to focus on, an explanation of the property, and at least 4 examples of the property. 

The second day was participating in the gallery walk and then creating the finished product.

Some of you are wondering “what is a gallery walk?” Well, it is simple. In this alternative assessment, students walk around the room (either in their groups or individually) and fill out a quick questionnaire about other projects in the room. It’s very similar to walking through an art museum with a friend. You look at a piece of art and then discuss it with whomever is with you at the museum. 

After the gallery walk, groups are able to see what feedback might help them earn a higher grade. The students take that feedback and decide to use it (or not) when finishing up their final product.

A word of caution, I highly suggest going over what appropriate feedback looks like with your students before setting them loose in the gallery walk. I made a slide and projected it during the gallery walk with some examples for students to follow.

The final products for all my classes were displayed for a few weeks. Once, I had a student turn in a video of the reflexive property and he permitted me to show other classes his video. I loved hearing all the conversations that occurred because of the final products.

This simple gallery walk had students talking and thinking about the properties of real numbers more than a simple quiz. I truly believe students understood the properties more because I allowed them the opportunity to dive into the meanings of the properties rather than having them memorize facts.

Other topics you could easily use with a Gallery Walk are real-world word problems for equations, inequalities, systems of equations, and systems of inequalities.

If you want to see the exact alternative assessment I wrote about, you can click here.

Three Benefits of Spiral Reviews in the Classroom

There seems to always be an argument in the education community about the best way to help students retain information. Based on over a decade of teaching experience, I fully support using spiral reviews in the math classroom. 

I use spiral reviews as warm-ups for my students to complete while I take attendance before the start of the lesson. My students know the procedure for completing their 2 problems for the day: start working on your review as soon as the bell rings, you have 7 minutes to complete the 2 problems, and ask your neighbor for help before you ask me.

After several attempts over just as many years at other types of warm ups, I switched to spiraling the content as my bell ringer. I saw tremendous growth in my students' retention the first year I used spiral reviews, which also translated to higher end-of-course and state exam scores. 

So, let's dive into the benefits I think spiral reviews had on my students: reinforcement of previously learned concepts, continuous skill development, and increase in long-term retention.

Reinforcement of Previously Learned Concepts

I designed my spiral reviews for students regularly revisit and practice previous concepts, including the essential skills taught in previous grades. By consistently reviewing older material and learning new topics, students reinforce their understanding and retention of foundational concepts. This approach helps prevent knowledge gaps and promotes a deeper understanding of mathematical concepts over time. This strategy also provides students who struggled with previous concepts another opportunity for success.

Continuous Skill Development

Spiral reviews allow students to continuously develop and apply their skills as they encounter familiar topics in new contexts. By revisiting skills presented as new concepts and incorporating them into higher order thinking (HOT) questions, students gain a deeper understanding of how mathematical concepts connect. This approach fosters critical thinking, problem-solving skills, and the ability to apply mathematical knowledge to real-world situations. As I previously stated, I fully believe this is why my students showed improvement on their end-of-course and state exams.

Long-Term Retention

When my students regularly reviewed content in a spiral manner, their long-term retention improved. When students revisit previous material, they strengthen their memory and increase their ability to recall information when needed. This systematic approach to review helps transfer knowledge from short-term to long-term memory, supporting students' overall mastery of mathematical concepts.

The Best Method of Review to Increase Student Retention

Teachers are under so much pressure to have their students do well on standardized tests. So, the question is how do teachers even begin to help their students actually retain information? For me, the answer was reviewing my content in a cyclical manner.

I have been teaching for over a decade and I finally saw success when I implemented spiral reviews as warm ups in my classroom. I would like to put a disclaimer up front and center. Spiral reviews were not the answer for every one of my students, but these reviews did help a majority of my students.

Let’s start at the beginning. At my first teaching job, I was handed a 1-inch binder of the “curriculum” the previous teacher used. I opened the binder to find most of the pages were blank and the ones that weren’t were merely used as scratch paper with no context of the problems. I was shocked! Straight out of college, I was completely lost on how to help my students. Let’s just say I learned a ton in my first-year teaching.

My next few years were spent learning how students learn: what methods work, where mistakes and misunderstandings happened, what is the best way to explain this process, etc. I eventually realized my students were just learning the material for the chapter assessment and then they would forget it. I was literally watching the old adage “out of sight, out of mind” playing out before me.

About this time, my administration was pushing for teachers to implement the practice of bell ringers or warm ups. Most teachers, as well as myself, would use this time to review skills needed for the current lesson. I began to create weekly papers to hand to my students that had 2 questions per day for them to complete that pertained to that day’s lesson. I would then collect these at the end of the week. This worked as a quick reminder for my students how to do the prerequisite skills needed, but severely lacked increasing long-term recall.

Our school's next initiative was to incorporate higher order thinking (HOT) questions into our lessons. So, I revised my weekly warm up questions. I had Monday to Wednesday with the basic 2 question skill review, then Thursday and Friday were adjusted to the HOT questions. These questions were still related to the skills needed for the current lesson. This change did help students think more deeply about math, but long-term retention was still an issue.

I finally decided, after 3 years, to completely overhaul my thoughts on how to use warm up questions in my classroom. I decided to spiral the questions' content. Let me clarify what I mean by spiral. I would start with basic information students should know from previous classes. For example, in algebra 1, I would start with a rectangle and ask students to divide the shape into 7 parts and shade 3 of them. I know this seems elementary, but the first few spirals were used to teach the procedure of my warm ups as well as give students confidence in math class. Below is the first spiral review I use with my class.

After 2 or 3 weeks of basic review, I added the content that we had been learning about. Again, for algebra 1, this started to include order of operations, evaluating expressions, and combining like terms. So, in the 4 - 5 weeks of school, students were reviewing concepts from previous grades as well as content from the first weeks of school. I would continually add concepts about a week after students were first introduced to the material. At the same time, I would add questions from previous chapters and grades. By the end of the first quarter, students were not only reviewing previous grades’ content, but also content of the first 3 chapters WEEKLY. Below is the 4th spiral review I use with my students in the first quarter.

I continued the process of rewriting my warm ups with previous content for the rest of the year. I kept the same structure of some days practicing only skill recall and other days incorporating HOT questions. At the end of this first year, I finally started to see increases of students' scores on standardized tests as well as students’ long-term recall. Over the years I have continually adjusted the questions to fit with my school’s curriculum, the pace of my teaching, and the rate at which my students learn. 

Here is what my students are reviewing in the 7th week of the 3rd Quarter: dividing polynomials, function notation, slope, multiplying binomials, simplifying radicals. And those concepts are just in the first 3 days of the week!

Last year, I was blessed enough to have a remediation teacher help me once a week. Her job was to work with the lowest 3 - 4 students to help them with understanding our most recent content. At the end of the school year, she told me the reason my students were seeing so much success in Algebra 1 and on the end of the year state test was because of my spiral reviews.