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Author Archives: Sue Wachter

About Sue Wachter

Sue is a Consultative Sales Representative at Demme Learning. Sue has been consulting homeschool parents in regards to best curriculum choices for over 30 years. She is a wife, mother and grandmother. She enjoys spending time with her family and teaches art classes. Her goal, whether in art or curriculum support, is to provide tools and inspiration for each individual's next step.

Addition Facts Strategies for Parents


Read Sue's addition facts strategies that she has acquired during time spent in the trenches with parents that she's worked with.

In 2016 I wrote a blog post similar to this: How to Teach a Child Math Facts. However, because I have the privilege of consulting with parents weekly–even daily– and addressing fact mastery strategies, I have learned more. I want to share this additional information I have acquired during time spent in the trenches with you, the parent.

Fact mastery is a hot topic with parents of students of all ages. If nothing else, after reading this post I hope you remember two things: 1) Regardless of your student’s age, you are not alone, and 2) We do have solutions.

Is Fact Mastery Really Necessary?

Often I am asked whether fact mastery is really necessary. To be honest, I have no doubt there are adult mathematicians out there who do not know all of their math facts and may even need to count on their fingers. However, when consulting day to day, I have talked to many parents who admit that they still count on their fingers. They are often even more committed to finding a better way for their students because they tell me “I have always struggled in math because of it.”

I like the way Mary from our customer service team says it:

Fact mastery will give the student confidence. When they are solving complex problems they do not have to stop to think what is 5 + 6 or 7 x 9. When they must stop and think about these facts, it makes them think “If I can’t do something simple, how can I do something like Algebra?

So yes, while your student might become confident in math and be set up for success in upper level concepts without having facts mastered, chances are that it will affect their ability to efficiently process more complex concepts. It is possible that you would be sending an otherwise successful future math student to try to master higher level concepts with a math deficiency.

Let’s Inventory What You’ve Likely Tried

1) Flashcards

For some students flash cards will work. If you are making progress using flashcards I recommend that you read this blog post written by Gretchen to even find more success.

2) Speed Drills

Speed drills can be an effective tool for some. However, if you find your student panics or seems to forget everything you thought they knew once you start drilling, the drilling activity may need to either cease or be modified.

It is rare that speed drills teach. However, they can be a tool that helps a student become faster with their fact recall. It is recommended that you drill only math facts the student already knows. As an adult, I can’t think of any new information I have learned by just going faster. The Math-U-See website offers a worksheet generator to help with this. You will find addition/subtraction drills under Alpha, multiplication drills under Gamma, and division drills under Delta.

3) Math Games

Games are another commonly used tool that can result in supplementing success. Amanda has some great ideas in her blog post.

Breaking the Habit

When a student has been finding the answer by finger counting for several years, the key is to assist them in breaking the habit. For them the only place to look for the answer is on their fingers. When instructed to stop counting and memorize they are being asked to develop a new tool to help them see the answer. The Math-U-See curriculum focuses on giving them effective and alternative strategies which intentionally pave the path to memorization so they can store the needed information in their long-term visual memory.

Subitizing

The key to no longer needing to count to add is subitizing. Subitizing is the ability to see a small group of objects and know the amount without counting each singular object. A common example of this is dice. By regularly playing games involving dice we are able to roll a 4 or a 5 and, without counting, quickly know the numbers that are represented. Another example of subitizing would be Legos. If your student often builds with Legos you will notice while they do not count the knobs, they are able to quickly fill in spaces with the correct block or two without counting.

Math Manipulatives: The Secret Sauce

With the Math-U-See program, the blocks are more than just an option: they are an integral part of the mathematical learning process. Through intentional use they become a tool not only for understanding but to be able to see facts and remember concepts. The blocks and the strategies combined provide the important bridge to committing math facts and other formulas into long-term visual memory.

Intentional Order of Mastery

The order in which math facts are presented is another key to escalating fact success. Once the zeros, ones and twos are memorized along with the Commutative property, the student is ready to find success with eights and nines, because of the way the Math-U-See program connects them to the mastered ones and twos. Once the eights and nines are mastered, there are only a few addition facts that remain. Taking the time to solidify the addition facts along with what makes ten and the introduction of algebraic thinking with solving for the unknown, the student will find a higher level of success when they spend the second half of Alpha mastering subtraction.

Here at Demme Learning we get excited when supporting parents, especially those with older students who have been striving for success and need the tool of fact mastery to achieve that success.

So let’s take first things first. It is important to pause and evaluate exactly which of the addition and subtraction facts your student knows without counting or long pauses. With that clarity it is easier to put together a plan which will replace the need to count with a strategy intentionally designed to strengthen your student’s fact mastery in the most time and cost effective way.
Due to knowledge of the materials and years of learning from the parents we talk to, we have designed support strategies which we are privileged to share with you to assist you in building a plan to fit you and your student’s specific learning needs.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!


Is Counting on Fingers Ok?


One of the most common “go to” math manipulatives students use to learn their math facts are their fingers. Is counting on fingers ok?

We all know the importance of math fact memorization as a part of the framework that underlies success in all math concepts. One of the most common “go to” math manipulatives students use to learn their math facts are their fingers.

Some students are able to transition from finger counting to rote memorization. However, many become more reliant on finger counting and do not transition. I have no doubt there are mathematicians out there who, as adults, have figured out how to be successful without mastering facts.

Most of the parents I speak to regarding their struggling math student report that the student is still counting to solve single-digit math facts. Many parents who themselves struggled in math know the limitations of finger counting.

Long-Term Effects of Counting on Fingers

Often the finger counter can “get by” for a few years. However, the wheels often fall off when they encounter long division. With all the steps involved in long division, even when the student understands the concept, the process becomes cumbersome due to working memory over load. The bottom line is that there is only so much room in the brain’s working memory to process the growing complexity of more advanced math concepts. Finger counting requires the use of working memory. There just is not enough room, or as my colleague told me recently, “Finger counting drains the battery.” That “shut down” you may have observed in your student is not intentional or a lack of intellect; it is how the brain is designed.

The Role of Subitizing

For the student who has learned to add, subtract, multiply. or divide by counting fingers, there is no other place for them to look for the answer. The answer is not in their mind (unless they envision the counting there.) It is important to replace the physical action of counting with a better, more effective tool. The most effective tool will be some form of subitizing.

My favorite way to describe subitizing is, “To suddenly see without counting.”

Think about what you experience when you roll dice and you see a four and a five. Through repetitive exposure of the same pattern combination, you eventually do not need to count the individual dots and know immediately the combination is nine. Another example is building with LEGO® blocks. As a child repeatedly plays with these blocks, they no longer need to count the nubs on the top to distinguish between the pieces. If they run out of a specific size block they quickly learn that they can substitute smaller blocks to replace the larger missing block. This is what subitizing or using visual memory “looks like.” Research shows that rectangular and dot arrangements are the easiest to retain in long-term visual memory.

Students of all ages are unfairly judging themselves as “just not good in math” because of the missing tool of fact automaticity. It is important to think of fact memorization recall as a vital tool for math success. For many students, their reliance on finger counting is preventing this tool from developing.

Story of Success

In closing, I tried to think of a specific story to share with you to personalize this topic and provide an example of hope.

The “story” has been shared with me hundreds of times over the past 25+ years collaborating with Math-U-See parents. It is more important to me to speak to the heart of you, the parent who has tried everything to encourage your student to no longer count on their fingers to solve math facts. I hear your concern every day in my phone conversations that you have tried everything. You may be just discovering the effect it is having on your student’s ability to find success as math concepts become more complex. Your student could be anywhere from 6-16 years old. Some of you are homeschooling for the first time; others have always homeschooled. You have not failed your child.

Many curricula teach counting as a pathway to learn math facts, and for some it does work. Most students, whether they have it modeled to them or not, will discover the option of finger counting if counting is presented as a process. You did not know it would become an ingrained habit instead of a temporary method. If you personally still use counting to solve math facts yourself and consequently do not feel confident in math, think of it is a bonus, not a limitation. To model to them your willingness to seek solutions to set them up for academic success and learn alongside them will one of the most important lesson you ever teach them.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!


Are We Ready for Algebra 1?


Algebra 1 is an opportunity for many students to pause and personally learn what they need when facing a subject that does not come easily.

There is a reason I have the word WE in the title. So often, this is where many parents assume they will not be able to support or continue as their student’s math teacher.

However, I suggest this is the best opportunity to hang in there. Modeling to your student how to approach material you feel is challenging might be the best instruction you ever present. In fact, if you find there are times your student ends up teaching you, consider that a bonus! When a student is required to have to figure out how to explain a concept to someone who does not quite “get it”, they understand it more deeply.

Regardless of you and your student’s math confidence, pausing before heading into Algebra 1 will have great benefit.

5 Tips for Algebra 1 Success

1) Evaluate

Success in Algebra 1 requires not only a solid understanding of Pre-Algebra but basic math concepts as well. More than once, while offering Algebra 1 support the student will indicate they thought they were done with fractions and struggled with them previously. This is a perfect time to assess if you or your student need extra support with concepts such as fractions or decimal. You might find our Algebra 1 Readiness Test helpful to pinpoint any gaps.

>> Download the Algebra 1 Readiness Test [PDF]

2) Encourage Showing Work

While mental math is important, you will want to see the process being used. This will also help you identify if there is an area of struggle that needs to be reviewed or if an incorrect answer was merely a careless error. Additionally, if you contact us for a post-evaluation consult, we will be able to more effectively assist you.

3) Assess

Take note of any areas on the assessment where the student either struggled or needed to be reminded of how to complete a problem.

4) Shore Things Up

In any areas you or your student showed lack of immediate recall on the assessment, take the time to lock these concepts in. Take the time to solidify even the most basic concepts. There is no shame in having some missing pieces. The shame would be if you and your student are actually ready for Algebra 1 but struggle due to not having efficient, strong, basic tools for success. Most of the Algebra 1 calls I support are not about Algebra 1, but rather the inability to be able to look at the equations and simplify by applying basic math concepts.

You will find the solutions and corresponding levels/lessons for the previous levels of Math-U-See here. You may find that you only need to use our worksheet generator for practice and review. Print off the relevant sheets and complete just a few problems a day (e.g. no more than 3-4 problems) until they can be solved confidently. If you feel that you or your student need a more in-depth review, contact us for a consultation. We have solutions that are timely and cost effective for these situations.

5) Review

One of my favorite support experiences was with an 18-year-old customer I will call Alice. When she called for support, it was obvious she needed to go back and review some basic skills. She indicated she was just “not good in math” but needed to complete Algebra 1 as soon as possible because her focus was on graduating. I suggested that it was more important to become solid in Algebra 1 to prepare her for success in the next required levels and beyond. I knew without this, that I would likely not be able to offer her much support. She was willing to slow down and work toward mastery of the material. When she couldn’t wrestle it to the ground herself, she would call for support. Math was a challenge for Alice, but she was able to successfully complete Algebra 1 by the end of the school year.

It was a privilege to see Alice develop into a confident Algebra 1 student. Had she not been willing to slow down, review, and set herself up for success it could have ended much differently.

To me it seems as if Algebra 1 is often the transition into the adult world of math and life. It is an opportunity for many students to pause and learn personally what they need when facing a subject that does not come easy.

Also, remember if the two of you can’t figure a lesson out together we are here to support you.

You’ve got this!

Get a free consultation from a Math-U-See expert.


Keep Math Skills Sharp Over the Summer


As the school year winds down, parents are faced with the question of what to do in regards to keeping math thinking alive during the summer.

As the school year winds down, parents are faced with the question of what to do to keep math thinking alive during the summer. A creative bridge between your accomplishments of this year to the beginning of the next provides opportunity for a successful transition in those early back-to-school weeks.

4 Tips for Summer Math

Be Honest with Yourself

Create a strategy that you will be able to follow through with. Remember that you are on a school break as well.

Keep formal academic practice brief. For example, if your student spent the end of the school year learning multi-digit multiplication, put one problem up on a wipe off board daily to keep the process fresh.

Evaluate What You Worked on Last Year

What might still be a little fuzzy? You many find that consistently spending five minutes on practice a few times a week will serve your student well and keep them from needing to totally relearn the same concepts in the fall.

A fast track of math fact mastery is a great summer project. I have discussions daily with parents whose students from 7-16 are struggling to memorize basic math facts. One of my past blogs, How to Teach a Child Math Facts, focuses on effective strategies that work well with brief consistent sessions.

Add Puzzles to the Mix

If I could re-school my children, I would include more puzzle solving in their lives. These could be anything from formal puzzles to life situations that invoke moments of pausing and gathering what we know to solve what we do not know. As they move into higher mathematical thinking, confidence in this kind of reasoning will be of great benefit. Math and puzzles go hand in hand. As you enjoy your vacation, be on the lookout for opportunities to solve situations that naturally arise with a simple problem-solving conversation that starts, “Ok, what DO we know?”

Look at Art

As an artist, I have found math concepts connected to art are what have not only improve my art but also given me a love of math. Perspective, ratio, angle, line, balance, graphing are just a few of the obvious. An example would be to visit a farm or gardens, which consist of rows. This could be a single discovery day or make it a multi-day/summer project. While there, pause and observe what you see and know. Gather clues. What size are the plants right in front of you? How about 20 feet away? They look smaller, but are they? Is there a point where all the rows seem to come together and become one or vanish? See if you can find the natural horizon line. Really look at what color(s) are there. One of my favorite arts instructors always said, “Trees are not just green!!” … and it is true! What actual colors are in the sky? Enjoy some time taking photos from different angles.

You will find additional ideas for math art, game and apps in Scottie Altland’s blog post Outdoor Summer Math Games & Apps.

The most important thing is to enjoy your time together this summer. As all grandmothers will tell you, the time passes.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!


How to Teach a Child Math Facts


You can teach math facts to your child; learn some of our strategies in this blog post.

You can teach math facts to your child; learn some of our strategies in this blog post.

Let’s say you and a friend are each making a cake. You both know how to make it and understand the recipe. However, your friend gets to use the fancy mixer which sits on the counter, while you use that old hand beater that is hard to crank. You both have the possibility of ending up with a yummy cake; however, one of you experiences more frustration along the way. In fact, if you knew that was the only tool you were ever going to be able to use, you might find cake-making a lot less interesting or even something you avoid.

The math student who does not have the tool of knowing math facts without counting or long pauses is likely to lose interest as well.

The Struggle with Math Facts

If you are a parent who is feeling the pain of watching your child struggle in math, knowing the problem might be that they have not memorized single-digit math facts, you are not alone. In my 25 years of supporting parents, with at least one parent with this exact issue each day.

For some, flash cards, drill sheets, promises, and incentives seem to work. The results reveal, however, that many of the learned math facts slip away from short-term memory after a break from school.

Flash card abuse is a problem for me as I try to encourage my children’s math fact memorization: “I just showed you this one two minutes ago!” are words I wish had never slipped from my mouth; I think that may be why I am so passionate about this subject.

Flash cards and drill sheets do not teach, and for most students. the sheer willpower needed to get those facts into rote memory will not make them stick.

While timed drill sheets are another method that might work for some, for others this creates anxiety attacks. Think about it; what if you as an adult wanted to learn something and the instructor said, “Just do it faster, and I will time you”?

BONUS DOWNLOAD: Download free addition facts songs, coloring pages, and activities.

Teach Math Facts with F.I.G.

You might be thinking this is all fine and good for an elementary student, but what about the fifth grade student or higher? It’s the same effective plan which we call F.I.G. (fill in the gap).

A few of the basic F.I.G. ideas are:

• Before starting actual fact practice, make sure the student has mastered block to integer correlation. Making the instant connection between the block and the integer while building facts will assist in escalating the memorization process.

• Master the facts in a sequential order that builds. For example in Alpha the 9’s and 8’s are mastered directly after 1’s, 2’s, commutative property and solving for the unknown as all of those concepts are connected and build on each other.

• Hang in there with the Build, Write and Say method keeping session’s brief, maximizing attention span.

• Celebrate both knowing and not knowing the fact. “Yeah! We know we don’t know that one!” I have found when the student begins to acknowledge this rather than hide the fact they don’t know progress escalates.

Many years ago one of my customers called regarding a 16-year-old who needed to go back to Alpha. He didn’t know single-digit addition and subtraction facts, which consequently was causing tremendous angst in math. Now THAT is a hard conversation to have!

Years later I receive a call from the mother of this young man.

She proceeded to tell me how he mastered his facts in just a few months using the strategy we discussed along with the Alpha level. Additionally, over the next few years he reviewed several other lower levels. Ultimately, he attended college on schedule, proudly heading straight into college math. She called wanting to refer to me to a friend in a similar situation for another one of those hard conversations. In retrospect, I don’t want to think what would have happened had they not had the courage and fortitude to know what they needed and did what was required to get there. How sad that would have been for her son to continue considering himself a failure in math because he did not have the basic tools! Opportunities like this to make little differences in big ways keep the sales and customer service teams at Math-U-See showing up for work and putting on the headset each day.

Free Math Facts Music & Activities

Songs, music, and rhyme are all helpful tools to aid students with math facts. Download some math songs to sing while you’re outside! There are also activities for when the weather doesn’t lend itself to outside math.

Download free addition facts songs, coloring pages, and activities.

Download free songs, activities, coloring pages, and more to help your students learn math facts!