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## Math PD this Summer! Moving Math Forward

Math teachers want quality and affordable math professional development that will impact their students. A new virtual conference this summer brings together a team of math educators sharing strategies for the middle school math classroom. I am excited to be a part of the Moving Math Forward Conference and to learn from the variety of sessions.

**You can find all the details and register here! **

The Moving Math Forward Conference is happening virtually on June 22 and 23 (but you can watch at your own pace for 3 months if needed). Topics include:

- Deconstructing Standards and Intentional Teaching
- Geometry Through Discovery
- Building Number Sense with Mental Math Strategies
- Virtual Teaching
- Math Workshop
- How & Why to Incorporate Creativity in Math
- Ways to use Algebra Tiles
- Small Groups Simplified
- Making Intervention Work in the Middle School Math Classroom

I am excited to talk about 2 of my favorite topics during the conference: Geometry through Discovery and Building Number Sense with Mental Math Strategies. Both are topics that I know have a great impact on student learning. In these sessions, participants will get ideas for activities to use in class with their own students.

I hope you will join us and learn ideas for a successful upcoming year!

Learn all about the Moving Math Forward Conference here.

*Thanks for reading,*

*Rachael*

## 3 Valentine Math Activities for Middle and High School

Engage students with these low-prep Valentine’s Day math activities! They are fun, but they will have students thinking and calculating to complete each one.

With these Valentine Math Stations, students visit 8 math problems. On their answer recording sheets, they show their work and write things they love, corresponding to the solution.

For example, the “D” station has a solution of 3, so they write down 3 places they love.

Five versions of math problems are included for grades 5th – 9th, or you can edit the math problems to fit your students.

__Practice adding and subtracting integers with this fun Valentine’s Day coordinate graph picture.__

Students add and subtract positive and negative numbers. Each solution creates an ordered pair that students graph to reveal an image of a heart emoji.

If you’re looking for a first quadrant only activity, check out this cupcake mystery graph that challenges students to use LCM and GCF of numbers.

Practice solving multi-step equations with this Valentine activity!

Each equation reveals a fun fact about Valentine’s Day. Equations are appropriate for 9th-12th grade students who are familiar with exponents, roots, brackets, and solving multi-step equations.

Need a simpler version? I also have a one-step equation version and a two-step equation version.

*Happy Valentine’s Day! (Hopefully yours involves some math!)*

*-Rachael*

## Low Prep Winter Math Activities

Themed activities can add a little excitement to otherwise ordinary practice. I love these resources that up the engagement with little to no prep work!

This Wintery Personality Test is sure to get students excited to practice graphing ordered pairs. First, students take a personality test. The results are revealed in different colored snowflakes on a coordinate grid.

Students practice converting fractions to decimals in this Build a Snowman Activity. Each correct answer gives them a detail to add to the snowman. It is a fun and easy way to check for understanding of rational numbers.

Challenge students to use order of operations to simplify expressions with this winter math activity. Each answer reveals an interesting cold weather fact.

Practice several skills with this fun mystery graph. Students must translate written words into mathematical expressions, operate with integers, and graph ordered pairs to reveal the image of football. Perfect during football season!

See if students can work with roots, exponents, and scientific notation with this hidden picture puzzle. Each correct solution gives them a piece of the picture to draw.

These snowflake angle puzzles are fun but tricky! Different versions are included to practice vertical angles, supplementary angles, mixed angles, and equations.

Engage students in solving multi-step equations with this Candy Cane Math Activity. Each correct answer reveals a world record made with candy canes! (Students may even want to try to break some of the records.)

Transformations are incredibly exciting when they turn into emojis! Students practice all types of transformations to create these winter emojis on the coordinate plane. Some are very challenging!

Want to create your own winter activity for any topic? Use this “Build a Snowman” template to make creating simple!

## 4 Questions to Ask when Planning an Inquiry Lesson

Incorporating inquiry into a math lesson has many benefits (as outlined here), but creating a quality inquiry-based lesson can be a challenge. Below are 4 questions that can spark planning and lesson ideas for discovery lessons.

**Is this a hands-on concept?**

When a concept can be taught with physical objects or models, use those to guide your lesson planning. Many geometry topics fit in this category. Plan for students to explore and think about models. An inquiry-based lesson can begin with students playing with physical objects, then answering questions, and then proving a concept. Many formulas can be discovered by students when given the opportunity and guidance.

Examples of Hands-On Inquiry-Based Learning:

- Volume of Rectangular Prisms
- Area of Parallelograms, Triangles, and Circles
- Circumference
- Angle Relationships
- Pythagorean Theorem
- Transformations on the Coordinate Plane

**Is there a pattern?**

We’ve been trained to find patterns since we were young. If a standard is based on extending a pattern in math (and many are), we can let students figure out the pattern and discover the rule. To build a lesson, let students examine patterns, prompt them with questions, and lead them to figuring out how the pattern continues.

Examples of Pattern Inquiry-Based Learning:

- Integer Exponents
- Operating in Scientific Notation
- Quadratic Functions in Vertex Form
- Absolute Value Functions
- Central and Inscribed Angles
- Trigonometry Ratios

**Does this concept build on a previous topic?**

Some concepts seem brand new to students, but many lessons we teach are building on previous learning. Even when students are familiar with a topic, inquiry learning can still be applicable. If students already know the basics, we can push them into deeper understanding with questioning. Begin with what they know how to do and guide them to go further.

Examples of Inquiry-Based Learning Building on Previous Learning:

- Reflecting over an Axis on the Coordinate Plane
- Slope Intercept Form
- Graphing Systems of Equations
- Finding Midpoints

**Is there a real world application?**

Most math concepts can be applied to real world situations, but we often wait until after students understand the concept to do so. Sometimes, the real world connection can help students discover and understand the concept. We can use real world questions to get students thinking and problem solving. Through this process, they can figure out solutions and discover new learning.

Examples of Inquiry-Based Learning through Real World Application:

*I hope these ideas help with your inquiry-based lesson planning. Thanks for reading!*

*-Rachael*

## 5 Reasons to Use Inquiry-Based Learning in Math Class

Inquiry learning is an approach where students explore, try their own methods, make mistakes, get creative, and hopefully discovery a new concept. It is my favorite way to teach math. In this post, I will share why.

**Inquiry learning is engaging. **

The puzzle-like quality of an inquiry lesson grabs students’ interest. The challenge to figure something out is exciting. And the satisfaction of discovering a concept is hard to beat.

**Inquiry learning makes the concept stick.**

Math is full of procedures and steps. When students find solutions by following steps, they may get the answer correct that day. However, students forget steps and procedures. With inquiry learning, students make sense of the math and the steps they use. This process helps the learning to stick with them.

**Inquiry is the heart of math.**

When we think about how mathematicians learn math, inquiry is key. Mathematicians explore ideas for themselves in hopes of discovering something new or understanding a concept better. When students partake in inquiry learning, they are learning like mathematicians.

**Inquiry learning teaches students to think on their own.**

We want students to learn to think, problem solve, and draw conclusions, but how will they learn to do these things? Inquiry learning can teach students to think for themselves. It helps them build confidence in their own math abilities.

**Inquiry learning makes procedures meaningful. **

In a inquiry-based classroom, teaching mathematical procedures still happens. When the procedures follow the inquiry, they are more meaningful. Instead of following a list of steps, students understand why the steps are necessary. They may even discover the procedure through the inquiry process.

Inquiry-based learning completely changed my teaching approach for the better. The more I allowed students to discover concepts for themselves, they more I saw students learning, retaining, and enjoying math. Additionally, inquiry learning encourages students to use Common Core’s Standards for Mathematical Practice:

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

My next post will include ways to make inquiry a part of math class. Check back soon!

*Thanks for reading.*

*-Rachael*

## 3 Last Minute Ideas for Math Class on Halloween

I love Halloween, and I love math… but math class on Halloween is a tricky combination. I haven’t always planned something special for the day. However, it is the perfect opportunity to do something fun and channel that enthusiasm (or candy high) towards some math.

**Here are some last-minute, low-prep ideas for Halloween in math class:**

**Candy Container Challenge**

Materials:

- Paper
- Scissors
- Tape
- Rulers
- Large bag of small candy

Give all students the same amount of paper (half a sheet is plenty). Challenge them to create the container that holds the most candy using only the paper given. Students measure and calculate the volumes of their containers to predict who will win. Test the containers by seeing which one holds the most candy.

**Area of Jack-o-Lanterns (or Composite Shapes)**

Materials:

- Graph Paper
- Markers/Pencils

Students draw jack-o-lanterns and calculate the areas. Depending on how creative they get with the designs, these composite areas can be pretty challenging! This activity can be accomplished with graph paper, or here is a premade template with example figures ready to go!

**Haunted House Calculations**

This last option is perfect if you want to fill an entire class length (or maybe more) with engaging math. This Haunted House Math Activity is ready to print and easy to use. Each student gets a floor plan of a haunted house. Seven task cards relate to 6th, 7th, and 8th grade math topics. Choose the tasks best for your students, or have students try all seven!

Thanks for reading, and Happy Halloween!

Looking for more Halloween Math Ideas? Check this post for more!

## Ideas to Make Scientific Notation Fun and Meaningful!

Scientific notation was once a topic I dreaded, but now I like it! Maybe it isn’t a topic we use in everyday life, but **scientific notation can deepen students’ understanding of many important everyday concepts**, such as…

- Measurement
- Place Value
- Powers of ten
- Exponents
- Understanding word problems

Over the years, I have found ways to make scientific notation fun and meaningful!

I like to start by showing a short, engaging video to hook students. Here’s a great one showing sizes of planets and stars: https://www.youtube.com/watch?v=HEheh1BH34Q

Seeing the size comparisons of these planets and stars is engaging, and it gets students thinking. It leads nicely to why we need scientific notation.

Next I write the number “2000000000000000000000000000000” on the board and tell students that is the mass of the sun in kilograms. I ask if anyone knows that number. We discuss how difficult it is to communicate this number. What if you type it and forget a zero, how does that change the value? How do you even say this number? **That is why we need scientific notation! **

Reviewing exponents, powers of ten, and evaluating some expressions written in scientific notation (even before students know what it is) comes next. I like this guided notes set. We use those notes to learn how to **properly write in scientific notation**. Then we return to the sun’s mass and write that number in scientific notation.

Next we explore **operating in scientific notation**. I like for students to discover the rules and any shortcuts on their own. The last page of the guided notes set helps us do this.

Students can practice operating with numbers in scientific notation with this fun group challenge. Students work in groups of 4, each completing their own page. Together all 4 pages make a picture.

**Word problems** can be a challenge, so I have a variety of practice activities. Scientific notation word problems can overwhelm students. Therefore, I like to start with a simple word problem comparison. Students see a word problem with whole numbers so they can think about the meaning and operations needed. Then, they solve the same problem with scientific notation problems.

Next, students can get creative with word problems. I give them information and an answer; they write the question. This “backwards” activity really makes students think.

Last, I give them a story with numbers missing. They have to think about all the information given in order to correctly fill in what is missing. Altogether, these different approaches to scientific notation word problems require a lot of critical thinking!

If students need an **extra challenge** (early finishers or extra credit), I give them this graphing with scientific notation task. They have to think about distance, rate, and time while using scientific notation.

I hope you will find some of these ideas useful for teaching your students scientific notation!

*Thanks for reading,*

*Rachael*

## What is Number Fluency? (and how to build it!)

Number fluency is a critical key to student success in math. Let’s break it down, so we know what we are trying to help students develop.

Earlier this year, I spoke about this topic on Instagram. You can see the replay below.

Number fluency begins with **number sense**. Number sense starts early. It is a person’s understanding of numbers. It is the ability to imagine 5 objects when you see the number 5. It is also the ability to actually see 5 objects and know there are 5 without counting them one by one. It is an understanding of the value of numbers. Number sense is developed by counting and becoming familiar with numbers at an early age.

Number sense should increase as students get older. By middle school, students should have the number sense to compare numbers and know how numbers will be affected by operations. Number sense does not involve following procedures and steps. Number sense is the understanding and reasoning students need to make **sense** of math.

As students learn more and more math, that number sense develops into **number fluency**. Being fluent in math means a student can mentally use operations, apply procedures appropriately, problem solve, manipulate numbers, estimate, and think creatively with numbers.

Although procedures are often noted as an indicator of number fluency, simply following procedures is not what is important. The understanding of concepts and reasoning behind those procedures should be emphasized to truly build number fluency.

Helping students learn strategies as they build number fluency will help students retain **math facts**. Without number sense and fluency, math facts are difficult to learn. Memorization without meaning does not result in long term memory of math facts.

Math facts are not a succinct list. Math facts could go on forever, and depending on whom you ask, you may be told different math facts are the most important. In elementary school, we expect students to add, subtract, and multiply some numbers mentally. Those are math facts. In middle school, we expect them to know factors, multiples, integer operations, and division. If we made a list of all the “math facts” a student should know, the list would be overwhelming.

Many middle and high school students do not know their math facts, which makes learning upper level math extremely difficult and frustrating. As much as many teachers would like to have a growth mindset, it seems hopeless for these students. Strategies to help these students often involve memorization and redundant drills (often with poor results).

Let’s try a better approach. First of all, we cannot write these middle and high schoolers off as just “not math people.” People who lack number fluency (in my experience), simply have not been given the time and strategies to develop it. Not knowing math facts is a symptom of this problem.

When secondary students develop number sense and number fluency, math begins to make sense and become enjoyable.

One way to develop fluency is to teach students mental math strategies. When students get creative and flexible with numbers, their understanding and comfort with numbers increases. Just 5-10 minutes a day can make a big impact.

Try these mental math lessons with your students for free!

Or, find the whole year of powerpoints with visuals here:

## 3 Math Activities for the First Day of School

What should we do on the first day of school? Teach? Get to know students? Go over procedures?

Planning the first day can be stressful. I’ve always been told the first day sets the tone, so I always try to incorporate some math. Below are some activities that work perfectly that first day.

I love this activity, and so do students. They get a list of statements and determine which ones are true about themselves. Each true statement gives an ordered pair to graph, which creates a unique image for every student.

Set the expectations for group work with this fun activity. Students work together to find examples of geometry terms in the classroom.

Simplifying Expressions Coloring Activity

This fun activity is a great way to see what students remember about order of operations, exponents, and absolute value. Students will think it’s fun, but they’ll have to think and work carefully to get it right.

**I love first day activities that involve a little math and are engaging too. Set the tone that we do math in this class, and it’s enjoyable. 🙂**

I often have gotten one or two classes much longer than any other classes the first day or first week of school. The extra time may be intended for turning in paperwork, but I like to have one of these activities for that time as well.

*Thanks for reading!*

*-Rachael*