## Memorization Supports Mental Math & Struggling Students

Many mental math strategies emphasize efficiency and flexibility by finding friendly or compatible numbers, such as those constructed of twos, fives or tens . Given this, developing automatic recall of certain math facts benefits students ability to engage with mental math. For example, the ability to;compose;and decompose;tens, doubling and halving,;as well as;multiplying and dividing by 10.;

; Figure 2. Mental math strategies, along with corresponding supporting math facts

## Students Who Were Fluent With Doubles And 0s/1s Facts Solved Other Facts Faster

The students who were fluent with doubles facts produced correct answers to other facts significantly more quickly than students who were not fluent with doubles. Additionally, the quicker students answered doubles facts, the quicker they answered other facts. That is, students who could answer doubles facts within 6 seconds answered other facts faster than students who could answer doubles facts within 15 seconds. A similar pattern was true for fluency with 0s/1s facts, although these facts had a weaker association to speed on other facts than did doubles facts. Still, the association between fluency with each helper fact group and speed in solving other facts is consistent with the idea that students were using the helper facts to help them solve other facts.

Although we cannot make any definitive conclusions based on our study, we believe the results strongly suggest that teaching basic facts through a helper-fact approach can be beneficial for students.

## Index By Activity: Basic Facts Worksheets Available On This Site

Having a good understanding of basic facts is critical to help make learningmore difficult math problems easier for the student. Students that arequick and confident with their basic facts will learn difficult processes likelong division more quickly because they won’t get distracted with counting ontheir fingers or in their heads to figure out ‘basic facts’ at each step of theprocess.

The worksheets below are to help your student become confident with basic facts:

1. Addition Basic Facts: Questions up to 12 + 12

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## Students Seem To Become Fluent With Doubles And 0s/1s Facts Earlier Than They Become Fluent With Other Facts

About 32% of the students in our study were fluent with doubles facts, 0s/1s facts, or both without also being fluent with all facts. By contrast, less than 2% of students were fluent with mixed facts without also being fluent with doubles or 0s/1s. This suggests that it is much more common for students to develop fluency with doubles and 0s/1s early in their fluency development, further supporting the use of doubles and 0s/1s as helper facts.

## Tools For Reinforcing Math Skills

**Flashcards** are a great no-fuss way to learn math facts. Shuffling a deck makes it easy to mix up the order in which students practice, a learner can study them together with a tutor, a peer, or on their own, and flashcards provide both visual stimuli and a chance for kinesthetic learning. Students can flip the cards over, stack them, or sort them into piles.;

There are also a number of **apps** designed to help students learn math facts. Many of them use gamified approaches which may include drills that motivate students to practice, or actual games based around providing math fact answers and solving simple equations.

**Touch-type Read and Spell** is both a computer program and an app that teaches touch-typing. Originally designed to help learners with dyslexia, it uses an Orton-Gillingham phonics-based approach to learning in which students see words on the screen, hear them read aloud and type the corresponding keys.

Multi-sensory practice helps reinforce learning and short modules build knowledge and memory for math facts in a gradual and gentle way. TTRS also has a series of lessons on math subject skills that help students build confidence and reinforce classroom math education.;

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## Why Are We Concerned About Attention To Math Facts During The Pandemic

Our students benefit from lots of discussions about, and practice with, basic math facts. Daily lessons in K-5 classrooms frequently focus on the development of mental math strategies associated with different fact sets, but even when lessons focus on other math skills, fact fluency tasks appear each day at centers, in mini-lessons, or as practice tasks. With class time reduced due to online learning or briefer in-class periods, this daily exposure to math facts, and daily practice time, has been reduced or, in some cases, eliminated.

## Computers And Mobile Devices

To supplement practice, try some of the fun and engaging computer games and math apps for mobile devices that focus on fact practice. Many of them are free or very low cost. Work them into your weekly routine for short periods of time for extra practice. You child may also enjoy using Skype or Facetime with long-distance family members to practice facts.

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## More Students Were Fluent With Doubles Facts And 0s/1s Facts Than With Other Facts

More than 32% of the students in our study were able to consistently answer doubles facts correctly in less than 6 seconds. Over 25% were able to consistently answer 0s/1s facts correctly in less than 6 seconds. By comparison, only 12% of students were able to consistently answer all facts correctly in the same amount of time. This suggests that doubles facts and 0s/1s facts are easier for students to learn, on average, than other facts. Doubles and 0s/1s therefore seem good candidates for use as helper facts.

## Math Fact Fluency Is Possible

Should problem-solving be a major focus in math?

Absolutely. Higher-level math builds upon multi-step word problems and elementary students need to have exposure to these types of problems as they work toward middle school and beyond.

However, we need to find a balance between skill-building and application if we want to give students the best chance for long-term success.

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## Address Basic Facts When Should Students Be Expected To Know Their Facts

Helping children learn the basic facts is an important goal in the Everyday Mathematics curriculum. Most children should have developed an automatic recall of the basic addition and subtraction facts by the end of the second grade. They should also know most of their 1, 2, 5, and 10 multiplication facts by this time. By the end of the fourth grade most students should have an automatic recall of all the basic multiplication facts and be familiar with the basic division facts. Multiplication and division facts are reinforced at the beginning of fifth grade.

The Everyday Mathematics curriculum employs a variety of techniques to help children develop their “fact power”, or basic number-fact reflexes. These include:

## How To Teach Math Facts

For our purposes, math facts are the basic number combinations for the different operators. from 0 + 0 to 10 + 10, from 0 – 0 up to 20 – 10, 0 x 0 up to 10 x 10 or 12 x 12, and 0 Ã· 0 up to 100 Ã· 10 or 144 Ã· 12.

Why is it important to memorize, to become fluent, or to achieve automaticity in the basic math facts? Lets make an analogy to reading. In reading, phonics are the basics, and knowing what sounds the phonemes, or basic letter combinations make, is key. A student who is weak in them takes so long to get to the end of a sentence, that by the time they do, theyve forgotten what the sentence was about in the first place. The same thing holds for math facts. If a student is not fluent in them, when a teacher is explaining a math sentence, if the student has to figure out the answer to each basic math fact, they will get so far behind that they will forget the purpose and steps of what they are doing. Math facts are the phonics of math. Except instead of only 44 phonemes from 26 letters, there are 121 facts for addition, another 121 for subtraction, etc. A total of 580 facts if you go up to 144 Ã· 12! No wonder it takes so much practice!

Now some advice:

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## How To Drill The Math Facts

Our resident math expert, Kate Snow, helps you drill Math facts.

Imagine trying to make spaghetti sauce if you didnt know how to chop an onion, brown ground beef, or measure spices. Even with a recipe, you would find yourself puzzling over every single step: Do I need to take the skin off the onion first? How high should the heat be when I cook the meat? Whats the difference between a teaspoon and a tablespoon?

This is how math feels for kids who never master the basic facts: painstaking and hard. Whether theyre learning how to divide decimals, subtract fractions, or multiply polynomials, they spend so much of their working memory on simple calculations that they have no brain space left for understanding new concepts.

Thats why its so important that children master the math facts during the elementary years. Once theyve learned these basic number relationships, theyre much better prepared to tackle challenging topics in their middle school and high school math courses.;

**What are the math facts?**

The math facts are the sums and products of the numbers from 1 to 9, as well as the related subtraction and division problems:

- Addition from 1 + 1 to 9 + 9
- Subtraction from 1 1 to 18 9
- Multiplication from 1 × 1 to 9 × 9
- Division from 1 ÷ 1 to 81 ÷ 9

**3 steps to mastering the math facts**

**Step 1: Teach your child the mental strategy with hands-on manipulatives and visuals. **

2 × 8 is 2 groups of 8. 2 × 8 is 16.

#### ABOUT THE AUTHOR

## Why Are Math Facts So Important

Knowledge of basic math facts provides a foundation for multi-digit addition, subtraction, multiplication, and division, but the importance of these facts goes far beyond the foundation for more complex computations. Through a careful study of math facts, students gain a deeper understanding of operations, greater skill at applying mental math strategies, and a stronger understanding of numbers. Their experiences with math facts shape their understanding of properties. How can 5 + 2 and 2 + 5 have the same sum ? If you forget the product of 6 × 7, can you find it by knowing 6 × 5 and 6 × 2 ? How do you find the quotient of 24 ÷ 4 by knowing 4 × 6 = 24 ? As students explore addition, subtraction, multiplication, and division math facts, they make sense of many of the core principles of mathematics and develop deep number sense.

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## What Specific Features Of The Mtbmf Books Are Most Helpful

These books take a simple approach to math fact fluency that begins with setting a context for a fact set through a piece of childrens literature, exploring the number patterns and mental strategies related to the set through models and math talk, and engaging students in fun practice to provide repeated exposure to each fact set. One book focuses on addition and subtraction facts, while the other focuses on multiplication and division facts. The following features have been built into the books and related online resources:

- lots of short, engaging lessons that focus on number patterns and mental strategies specific to each math fact set
- hundreds of online resources and game templates that are perfect tools for home practice
- online resources and games that are available in both English and Spanish, so they can be sent home with directions that are understandable to parents
- parent letters to help parents better understand how to support fact fluency at home

## Make Learning Math Facts Fun

There are many ways to make learning math facts fun. In the classroom, there are math games such as Concentration, Old Maid and Go Fish.; At home, there are books and online games such as Greg Tangs Web Bonds and Reflex Math.; There are numerous ways to make math games out of household items such as cards, dominoes, marbles, clothes pins, bobby pins, pennies, etc.; Place these items into a ten slot egg crate and simply ask questions such as, If I have 4 marbles, how many more do I need in order to have 10?; If I give you 5 marbles and give her 5 marbles how many do we have?; What if I give you 6 and her 3.; How many more do I need to give one of you in order to have 10?; Or move to real life events such as an upcoming vacation.; Ask, If our vacation is in 2 weeks, how many days is that?

The questions and options are endless.; Like with most things, the more we practice the better we get, right?; Soon, children will move from their counting strategies to more advanced reasoning strategies Like solving in their heads.; Problem Solved!

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## Playful Math Fact Memorization

Traditionally,;helping students build math fact automaticity has been approached through rote memorization techniques such as flashcard drilling and testing. Unfortunately, these methods also frequently result in increased math anxiety iv. This can interfere with students ability to process math and negatively impact both their learning and performance;v. Thankfully, the goal of building automaticity can be furthered through more playful means. In fact, research suggests games present an ideal method of supporting math fact memorization. Games not only tend to increase engagement and interest, but also support students with gradual memorization, allowing them to come to the answer through counting and reasoning before moving toward memorization;vi. This gradual process supports greater conceptual understanding of numbers and math facts, which in turn allows them to apply their understanding more flexibly;vii.;

## Stage : Fluency Building

Once students have a strong foundation and conceptually understand the computation process for basic facts, they can begin to transition from toward fluency building.

At this stage, students should begin to memorize their facts as a result of repeated practice. For some students, this begins to naturally occur through their exposure during the early phases of learning.

**The goal at this stage is accurate, rapid recall of basic facts.**

For other students, this requires a concerted effort and possibly some tricks or mnemonics. At this stage, it can be helpful to spend 5-10 minutes practicing facts. There are lots of ways teachers can build math fact fluency practice into their schedule. I’ve shared a few of my favorites here: 5 Simple Ways to Build Math Fact Fluency

As students work to build fluency, they may continue to rely on ineffective means like counting on their fingers when tackling more difficult facts. This is totally normal and should not be discouraged unless it is consistently causing the student to get incorrect answers. The fluency building stage is a process that occurs gradually across time.

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## Assessing Math Fact Fluency And Reasoning Strategies

If done well, the assessment of basic math fact fluency can provide a teacher with invaluable information about what a student knows, doesnt know, as well as any misconceptions the student may possess. These assessments do not need to be lengthy or complicated; its actually the use of a few well-constructed questions that can yield an abundance of information about student progress and next steps for instruction.

According to the article Assessing Basic Fact Fluency by Gina Kling and Jennifer Bay-Williams, there are three important ways to glean important data about students understanding.

**Interviews**- Engaging in a brief discussion with a student provides a window into their thinking and reasoning. Also, as students talk through how they are solving problems, there is an increased likelihood that they begin to check the reasonableness of their answers and self- correct when it is necessary. Listed below are some sample questions that can be used when interviewing individual students:
- Write a problem on an index card. Ask the student the answer to the question, as well as how they found the answer and if they know of another way to solve the problem.
- Ask students how they can use the answers to facts they know to solve facts they dont know. For example, as questions like How can 5 + 5 help you to solve 7 + 5? or How can 3 x 3 help you to solve 4 x 3?

## How To Study Basic Mathematics Algebra And Geometry

The following tips are just my advice; They are not absolute. Choose those that will best fit you.

- Plan a regular time to study

- Choose a quiet place where you will not be distracted.

- When you study, try to study an entire lesson, or an entire chapter.

- When you finish a whole lesson or a whole chapter, it may leave you with a great feeling of accomplishment

- When you feel sleepy, take a short break; you will not learn much,;if anything if you are not alert.

- You are now ready to experience the most rewarding endeavor right here in this website.

Learn to solve a system of equations with three variables with one solution using substitution

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