Just like the scientific method, math modeling has specific steps and goals to check off as you go. There are seven steps to the math modeling process.

1. Establish a real-world problem

   The point of mathematical modeling is to create an equation that helps you understand and solve practical problems. So, the first step in the process is to figure out what real problem you want to try solving.

   Math modeling is used in countless areas of life, such as determining the optimal manufacturing process for a company, calculating flight paths, estimating car value, or managing a bank account.

   So, choose a problem or question you want to answer, big or small. This will be the focus of your math model.

2. Identify the variables

   Every problem has variables.

   Want to figure out what your pet’s favorite food is? You’ll need to think about a) the food type, b) the speed at which your pet eats their food, and c) other visual signs of enjoyment in your pet.

   What about trying to predict tomorrow’s weather? You’ll need to consider a) barometer readings, b) the current weather state, c) wind patterns, d) the types of clouds you can observe, etc.

   Whatever the problem is, think about the specific variables or data points you need to collect in order to find a solution.

3. Research

   After establishing your problem and defining variables, it’s time to gather some data. You can collect data through many methods, including observation, surveys, experiments, or information found online.

   For instance, if you want to estimate the value of your house in 5 years, you’ll need to research the values of houses like yours. What do other, similar houses sell for? What do houses in my area sell for? How have house values changed in the last 5 years? What do economists predict will happen to the country’s economy in the near future?

   Finding an answer to your big question requires asking a lot of little questions! But the more questions you ask and the more research you do, the more accurate your math model will be.

4. Make assumptions

   This step may seem contradictory, but it’s essential to the modeling process! After completing your research, you’ll probably have a better idea of what the solution to your problem may be—in other words, an assumption.

   What trends are you noticing in your research?

   Questions like that can help you build the foundation of your math model. But don’t worry if your assumption is wrong. It’s not about right or wrong; it’s about having a foundation to work from.

5. Make your model

   At this stage, you’re ready to come up with your math model—your equation(s).

   The type of math you use here fully depends on the problem you’re trying to solve. If your problem is especially complex, don’t be afraid to ask a teacher for help.

6. Analysis

   Now that you’ve created your model, it’s time to test it out! This is the fun part, when you can use trial and error to tweak your model until it’s perfect.

   Try to solve your problem using your model, and if something doesn’t seem to be working, this is your chance to go back to the drawing board and create something that works. Most models don’t work perfectly on the first try, so don’t feel discouraged.

   Keep going until you’re happy with it.

7. Report your results

   The most satisfactory part of mathematical modeling is being able to report your results. Turn your results into a data table, a short paper, a chart, a video, or any other method that you think would work best.

   If your results aren’t 100% accurate, don’t beat yourself up. Just go back to step 2 and try again!

1. Advertise Family Game Night On the Right Avenues

Family game night can’t be a hit if nobody shows up. That’s why advertising the event is so important.

Put up posters, banners, and flyers around the school to make students aware of the upcoming event. Have teachers announce the event in class. Send out event information in family newsletters. And talk about the event during PTA meetings.

Whatever you do, make sure parents are informed, and students are excited!

2. Get Parents Involved

Most parents value the feeling of community within their children’s school. They like being involved in their child’s education, getting together with other parents, and enjoying educational activities as a family.

So, when advertising your family game night, let parents know that they can come early to help set up, bring their own math activities and games, make event decorations, or bring snacks to share!

More opportunities for involvement mean more engagement.

3. Get Students Involved

Some students may want to avoid doing math outside of regular school hours and, therefore, avoid the event. That is, unless they know how fun it will be. Don’t just tell students about the upcoming event—get them involved in setting up the event space or even creating the math games and activities themselves!

Students can also be put in charge of different event stations, giving them a sense of responsibility over the event and making them more likely to come and have fun.

4. Have a Snack Table

If your math night takes place after school or in the evening, you’re definitely going to be dealing with hungry kids. And who can focus on math with a grumbling stomach?

To keep your guests focused and happy, set out snacks, drinks, and finger food. Pizza is an easy option, and who doesn’t love pizza?

5. Create a Family Math Night Store

One of the most common uses of math in the real world is through the use of money. So, why not bring that real-world experience to your guests with an event store?

Guests can use real or fake money to purchase game and activity supplies, little toys, or candy. And, if enough students are available, you can put them in charge of running the store, giving them the chance to take money from “customers” and calculate change.

6. Set Up Hands-On Activities

Hands-on activities can be fun for both kids and their parents, and they don’t have to be complicated! Set out geometric blocks or mosaic tiles for participants to create their own artwork. Leave paper out for a paper airplane contest, or put together a collection of popsicle sticks and host a tower or bridge-building competition.

7. Create Estimation Challenges

Estimation challenges are some of the oldest math activities out there. Whether you fill a glass jar with jelly beans, a milk jug with quarters, or a bucket with pebbles, you can give your guests the chance to estimate the quantity of items within the container.

Activities like these are easy to set up, great tools for improving students’ visualization skills, and can be a lot of fun for people of all ages.

8. Offer a Variety of Engaging Stations

Not every child or parent will be excited by the same activity. To keep everyone entertained and engaged throughout the event, you need variety!

Set up board games, card games, hands-on STEM activities, math-related art projects, and estimation challenges. A good variety of activities not only keeps people engaged but activates different parts of the brain, leading to more fun and better learning.

9. Create a Math Scavenger Hunt

This activity may take some time to set up, but it could end up being the highlight of the night!

Set up a scavenger hunt around the room or school with clues featuring numbers, word problems, or equations. For instance, one clue could be: “The next clue to seek can be found in Room 5 + 2 × 3!”

10. Set Out Number Puzzles

Printouts of Sudoku, Ken-Ken, Kakuro, Hidato, brain teasers, and other number puzzles can be completed by students or parents individually.

Whether guests have downtime between activities, have already completed everything else, or just want quiet time to work independently, puzzle printouts are a great—and inexpensive—way to keep the fun going.

11. Have a Virtual Math Games Station

There are countless virtual solo and multiplayer math games and activities. A station with tablets or computers can be a great way to engage students—especially those who are not usually interested in working with numbers.

Popular platforms include Prodigy, Math Playground, and digital math programs like DreamBox.

12. Play Shut the Box

In this game, players take turns rolling dice and matching them with numbered levers on the game box.

Players can either knock down one lever matching the combined value of both dice or two levers that add up to the same number.

Each turn requires addition, and the rules can easily be tweaked to include multiplication and division as well.

13. Play Take It Easy

Like Bingo, this board game can be played with any number of participants and features one “caller” who reads out game pieces for players to place on their boards.

Players aim to create the highest-scoring board, with scores calculated through multiplication—making it a perfect game for practicing number combinations.

14. Play Set

This card game requires players to find patterns among cards featuring different shapes, quantities, colors, and shades.

Up to 20 people can play simultaneously, making it perfect for a family math night.

While no calculations are required, Set strengthens pattern recognition and focus—essential skills for mathematical thinking.

15. Give Out Take-Home Kits

Don’t let math night be a one-time thing! Families can continue the fun at home if you provide take-home games, materials, or other math activity resources.

Hand out goody bags with cards, simple games, or math challenges to keep students learning and excited about math long after the event ends.

Teachers all over the world have their own methods for improving their students’ math fact fluency. But no matter if you’re an elementary school teacher, a university professor, a student, or a stay-at-home parent trying to help their child succeed, there are eight techniques everyone can agree on.

1. Define your math facts

Different teachers expect students to know different ranges of math facts. For instance, some schools might ask students to memorize multiplication facts from 0 x 0 = 0 up to 20 x 20 = 400. Meanwhile, other schools may only teach up to 10 x 10 = 100 or 12 x 12 = 144.

That’s why, when setting study goals for students, it’s important to first clarify what exactly they’re expected to know.

2. Display math facts

Once the math facts have been defined, it’s best to display them where students can see them every day. You can purchase or make math fact posters and hang them up on the classroom wall, or you can make a math facts printout and ask your students to keep them in their folders.

The more students look at math facts, the faster they will notice patterns and make connections, making fact recall much easier.

3. Turn math facts into a song

Most people learn the ABCs and state capitals through fun, simple songs, and math facts are no different!

The most common math fact songs help students memorize multiples of single-digit numbers. For instance, multiples of 3 up to 30 can be sung to the tune of “I Love You” from Barney & Friends.

Multiples of 4 up to 40 can be sung to the tune of “Bingo.”
Multiples of 6 up to 60 fit well into the tune of “Twinkle, Twinkle, Little Star.”
And multiples of 7 up to 70 can be sung to the tune of “Baby Beluga.”

Memorizing just those four math fact songs can help students solve 40 multiplication facts and 40 division facts. That’s 80 facts from four nursery rhymes!

So, look up some catchy math fact songs or create your own to teach your students their addition, subtraction, multiplication, and division facts through music.

4. Understand number connections

There are dozens of number connections that make memorizing math facts easier. The most important are:

• Adding to 10

The combination of specific single-digit numbers will always equal 10: 1 + 9, 2 + 8, 3 + 7, 4 + 6, and 5 + 5.

• Doubles

The double of each single-digit number is always important to know, and helps with both addition and multiplication.

• Fact families

Any group of three single-digit numbers can create four different facts. For instance, the numbers 2, 8, and 6 create the fact family 2 + 6 = 8, 6 + 2 = 8, 8 – 6 = 2, and 8 – 2 = 6.

5. Use the derived facts strategy

Derived facts are math facts that can be derived, or figured out, based on their association with or proximity to other facts.

For example, if asked to solve 5 x 6, you may not know the answer off the top of your head. But if you already know that 5 x 5 = 25, then solving 5 x 6 is easy! Just add another 5 to 25 to get 30.

The derived facts strategy eliminates the need to memorize every math fact, making the mental load lighter for students.

6. Explain foundational rules and properties

Math exists because of specific properties and foundational rules of numbers that are always true. Luckily for us, many of those properties and rules can help students understand and memorize math facts.

One basic math rule is that a number plus or minus 0 will always equal the number. For instance, 5 + 0 = 5 and 5 – 0 = 5.

Also, a number multiplied by 0 will always equal 0—8 x 0 = 0—and a number multiplied or divided by 1 will always equal the number—3 x 1 = 3 and 3 ÷ 1 = 3.

On the topic of properties, it’s always important to know the commutative property, which states that the order of numbers being added or multiplied does not matter; the answer will always be the same. That means, 5 x 3 = 3 x 5 and 5 + 3 = 3 + 5.

These simple math rules may seem confusing to students at first, but they need to grasp these concepts before attempting to memorize math facts. After all, memorization without understanding is not the goal.

7. Practice skip counting

Skip counting is the first step students can take toward understanding multiplication. The ability to skip count every single-digit number up to a multiple of 10 will make memorizing multiplication and division math facts effortless.

8. Practice every day

A student can’t learn every math fact in a day, but they can learn them all over time with consistent, structured learning. Use worksheets, do classroom activities, have fun competitions, or play math games on websites or math apps to improve math fact fluency in a way that’s engaging and exciting.