Math

10 Practices to Improve Students’ Mental Math

Mental math isn’t explicitly part of most curricula, but students who can’t answer relatively-simple equations in their heads with speed or automaticity will likely struggle with harder content.

For example, an oft-cited study of a 1st grade class found that students who quickly recall addition facts had more cognitive resources to learn other skills and concepts.

Thankfully, you’re already helping students build core mental math skills when you teach rounding, estimating and fact fluency — developing number sense, as well as how they remember and reproduce steps and solutions.

To improve how your students build and practice these mental math skills, try the 10 strategies below. Use the ones that best work for you, and keep the downloadable list at your desk for quick reference.

1. Introduce Mnemonic Devices

Students who struggle with basic fact fluency can improve by using mnemonic devices — cues such as rhymes and acronyms to help recall information.

Take this mnemonic device for a multiplication fact as an example: I need to be 16 years old to drive a 4×4 pickup truck.

Because they must be easy to remember, it helps if the cues involve:

• Rhymes
• Tangible objects or scenarios
• Quick stories that distill larger chunks of information

Although you can think of mnemonic devices yourself and share them with students, it’s beneficial if you run an activity that gets them to make their own.

They’ll likely find it easier to remember mnemonic devices they create.

2. Read Math Books

There are many math books that effectively contextualize the processes behind solving equations, helping students commit them to memory.

Depending on student age, consider:

• Each Orange Had 8 Slices — This book focuses on counting and addition, presenting problems in easy-to-process sentences. It sets a new scene, complete with questions, with each turn of the page.
• The Grapes of Math — Containing basic multiplication problems, this book is a series of illustrated riddles. Each riddle offers clues and secrets to solving a specific equation, helping students improve reading comprehension along with math skills.
• Sir Cumference — Set in medieval times, this book series focuses on measurement and geometry. With occasional help from his son and wife, Radius and Lady Di of Amater, the knight Sir Cumference must solve math-related challenges that pose threats to his family and kingdom.

As you read books out loud, your students can practice their mental math.

Just pause after identifying an equation, giving them time to work through the problems in their heads. After they share their responses, read on to discover the answer.

3. Provide Relevant Word Problems

Many students will be more receptive to math drills and practice if the material is engaging.

A straightforward, yet effective, way of enlivening content is by creating math word problems. This is because you can tailor questions to students.

For example, you can:

• Reference Student Interests — By framing your word problems with student interests, you should grab attention. If most of your class loves baseball, a measurement problem could involve the throwing distance of a famous outfielder.
• Make Questions Topical — Word problems based on current events or issues can engage students by providing clear, tangible ways to apply knowledge.
• Include Student Names — Naming a question’s characters after your students is an easy way make it relatable, motivating your class to tackle the problem.

By capturing interest, student motivation should increase when practicing skills important for mental math.

4. Play Estimation Games in Class

Estimation games encourage students to develop skills and techniques they can use to simplify equations in their heads.

Easy to run but challenging to play, a popular estimation game in many classrooms involves only two dice and a sheet of paper that’s divided into two columns. One column lists the values on each dice face, whereas the other contains numbers of your choosing.

For example:

To play, pair students together. Taking turns rolling the dice, they must add the corresponding numbers together in their heads. For example, if a student rolls five and six, the equation is 878 + 777. Without pencil, paper or calculator, the student must solve the equation. If he or she is within a range of five numbers — verifying the solution with a calculator — the answer is considered correct.

The first student to answer five questions right wins.

For more advanced classes, you can simplify the numbers but require multiplication instead of addition.

5. Play Fact Fluency Games in Class

A fun alternative to flashcards, fact fluency games allow students to build recall and reproduction skills important for mental math.

Engaging options for 1st to 8th grade classes include:

• Math Facts Bingo — Create bingo cards that contain answers to different equations. Then, hand them out to students. Instead of calling numbers, state equations such as 8 x 7. After determining the product is 56, they can check off the number if it’s on their cards.
• Stand Up, Sit Down — Pick a number and share it with students. Then, read equations out loud. Sitting in a circle, students must stand if the answer matches the number you picked. If they incorrectly stand or remain seated, eliminate them until one student remains.
• 101 and Out — As the name implies, the goal is to score as close to 101 points as possible without going over. Start by dividing your class into groups, giving each a die along with paper and a pencil. Groups take turns rolling the die, deciding if it’s best to count the number at face value or multiply it by 10. After each roll, the number is added to the group’s total. The game ends when a group hits 101 points or goes over — whichever comes first.

As skill-building as they are engaging, your students’ improvement in fact fluency should be clear after playing a few rounds of these math games.

6. Encourage the Use of Math Apps and Websites

An alternative or supplement to drills and worksheets, consider using a digital program that features a range of problems aligned with different skills.

Such math apps and websites prompt students to continuously answer questions in an often-engaging environment, building a range of skills important for mental math.

Popular options include:

• Prodigy Game — Free and aligned with curricula across the English-speaking world, Prodigy automatically differentiates content and gives adaptive feedback tailored to each student. Teachers can also make in-game assignments to deliver custom content, making it a favourite of more than 700,000 educators.
• NRICH — An ongoing project by the University of Cambridge, this website features math games, articles and problems. It divides resources by United Kingdom key stages and United States grade levels, allowing your students to easily access the right content.
• Math Is Fun — This website contains content suitable for younger students, using concise sentences and cartoon characters. On top of exercises that cover essential math skills, there are games and puzzles.

Because all students need is a computer or mobile device to use these programs, it’s likely some will voluntarily practice at home.

7. Round Up when Multiplying by 9

There are simple ways to alter difficult equations, making them easier to solve with mental math.

Students can use existing rounding and fact fluency skills when multiplying by 9, 99, 999 and any number that follows this pattern.

First, tell students to round up the 9 to 10. Second, after solving the new equation, teach them to subtract the number they just multiplied by 10 from the answer.

For example, 67 x 9 will lead to the same answer as 67 x 10 – 67. Following the order of operations will give a result of 603. Similarly, 67 x 99 is the same as 67 x 100 – 67.

Despite more steps, altering the equation this way is usually faster and allows students complete it in their heads.

8. Double and Halve

When mastering multiplication beyond basics, students can quickly use mental math skills to multiply two integers when one is an even number.

They just need to halve the even number and double the other number. They stop this process when the even integer cannot be halved, or when the equation becomes manageable.

Using 33 x 48 as an example, here’s the process:

• 33 x 48
• 66 x 24
• 132 x 12
• 264 x 6
• 528 x 3
• 1,584

The only prerequisite to this mental math trick is understanding the 2-times table.

9. Cover-Copy-Compare

Normally used as an intervention tactic, Cover-Copy-Compare can have a place in most fact fluency lessons.

There are three steps to this mental math practice, which are:

• Creating a Math Fact Sheet — Divide a sheet into two columns, writing about 10 math facts pertaining the same skill in the left column. Include number-sentences and answers. In the right column, write “Responses.” Distribute copies of the sheet to students.
• Running the Exercise — The goal for students is to study the math facts in the left column, correctly reproducing them in the “Responses” column. To do so, give them time to study the facts. After, they fold the paper to cover the left column while writing — from memory — the first fact in the “Responses” column. If correct, the student can move onto the next fact. If incorrect, the student tries again until he or she has properly reproduced the math fact.
• Recording Mastered Skills — Once a student has completed a certain number of sheets related to a common skill, you can award him or her a badge that denotes skill mastery. This gamification strategy can make the exercise more engaging.

To go beyond basic fact fluency, you can make sheets that focus on rounding, memorizing steps to complex equations and more.

10. Use the Taped-Problem Approach

The taped-problem approach is one of the most effective ways for students to build fact fluency, indicates a 2004 study that pioneered the strategy.

First, obtain or make an audio recording of basic math problems that has short pauses between stating the problem and revealing the answer. Second, provide each student with a pencil and paper.

As you play the recording, students must write out each equation and try to solve it before the answer is revealed. If the student cannot solve the question, he or she writes down the correct answer. If the student reaches an incorrect answer, he or she crosses it out and writes the right response.

You can lengthen the pauses so students don’t depend on hearing the answers, whereas you can shorten them to encourage automaticity.

Downloadable List of the Mental Math Practices

Click here to download and print a simplified list of the 10 mental math practices to keep at your desk.

Wrapping Up

Using these mental math practices should help your students build rounding, estimating and fact fluency skills — allowing them to solve many equations with ease and automaticity, preparing them to tackle tougher content.

Armed with increased confidence, you may notice an uptick in student engagement and motivation.

These benefits, in of themselves, make a strong case for practicing mental math.