Wednesday, April 12, 2017

Geography Game

This is a very straight forward way to study countries of the world. All of the kids enjoyed playing the game when they were about six years old.

Internet and printer or Blank outline country map
Crayons or colored pencils
Letter dice
Object counters such as dried beans

Set up
  • The first step is to decide on a continent to study and then print out a Blank Outline Map.
  • Next color each country a different color.
  • When you are ready to play, each player chooses two dice.
  • Then decide on a winning number. This is the number of beans a play must collect to win the game. 30 would be a good place to start.
  •  The first player rolls the two letter dice and then finds all the countries that begin with the letters rolled. A bean is placed on each country.
  • When the player is finished placing beans, other players have a chance to place beans on any missed countries.
  • The player removes and keeps the beans and play proceeds to the next player. 
  • When a player collects 30 beans, or then number agreed upon at the start, the game is over.

Wednesday, April 5, 2017

Area of a Triangle: Hands-on Math

We did a simple hands-on activity to prove the area of any triangle is 1/2 the area of a rectangle.

This activity came from the Murderous Maths book Savage Shapes. (Great series, bad title.) In the UK math is maths. This British series discusses pre-algebra level math concepts in story format. The books feel more like comic books than text books. They are quirky and entertaining, yet educational. I highly recommend you check them out.

To begin this activity sketch three parallel lines. Then measure four draw marks the same distance on the center line to serve as the base for the shapes. Perhaps 1.5 inches. Next draw two perpendiculars extending from the first base to create a rectangle. Connect the base lines for the second base to a point in the center of the base above the line (and below the line) to create two isosceles triangles. The third base should be connected to a point above one endpoint to create a right triangle. The final base should be connected to a point outside the base to create an obtuse triangle.

Cut out the shapes. 2 rectangles, 6 triangles. (Only 1 rectangle is needed)

Place each pair of triangles on top of the rectangle to fully cover the area. This shows that the area of one triangle is equal to the area of 1/2 of the rectangle.

Note: It will be necessary to cut some of the triangles in order for them to fit onto the rectangle.

Wednesday, March 29, 2017

Math with Mandalas: Perpendicular Bisector

We learned about bisecting angles and perpendicular bisectors through creating Mandalas.

Creating Mandalas with children is a fun way to teach math concepts that doesn't feel like work. Kids can learn about degrees, angles, bisecting, radius, diameter, circumference, perpendicular, parallel among other geometry concepts.

To begin, all that's needed is a good quality compass, paper and a straight edge (like a ruler). There is an endless possibility of mandalas that can be created. We have a book of simple geometric mandalas and find it very educational to try to recreate them. Interestingly enough, there usually ends up being more than one way each mandala can be created. In other words, sometimes steps can proceed in different orders, or alternative steps can be used which arrive at the same result. After walking kids step-by-step through the creation of several mandalas, I like to give them a challenge mandala and see if they can create one on their own.

Each mandala created requires some construction lines which end up being erased in the final version. Therefore, it's best to draw them lightly. Here are the steps we used to create the above mandala.

1. Draw a horizontal line on your paper with a straight edge. The line should be approximately the diameter of the outside circle. Set the compass radius to slightly greater than on half of the line. Place the pointer on the end of the line and create an arc above the line. Create another arc below the line. Repeat placing the compass point on the other end of the line.

2. Create a perpendicular bisector by using a straight edge to connect the two crossing arc points.

3. Set the compass radius to the desired radius for the center circle. Draw the center circle placing the compass point on the point where the two lines cross.

4. Bisect the perpendicular angles. Place the compass point on one point where the circle and straight line cross. Create an arc just outside the center circle. Repeat the process placing the compass point on the adjacent point where the circle and other straight line cross. The two small arcs should cross.

5. Bisect the angle connecting the center point of the circle and the crossing arc point with a straight edge.

6. Repeat the process to bisect the other 90 degree angle.

7. Find the center point for one of the eight surrounding circles. Referring back to the first picture, you can see that the center is difficult to locate, but a tangent point on the edge of each of the eight surrounding circles lies on the point where the 45 degree angle line and center circle cross. Therefore, set the compass radius to the same radius as the center circle. Place the compass point on the point where the 45 degree line and center circle cross. Create an arc to mark the center of the circle crossing the vertical line.

8. Create one of the eight surrounding circles. Place the compass point on the point where the vertical line and arc meet. Draw the circle.

9. Repeat the process creating three more circles.

10.  Using the same method, repeat the process to create the four arcs which are not quite complete circles.

11. Draw the outer circle. Open the compass so the radius is set for the size of the outer circle measuring the point with the sketched geometry.

12. Erase all construction and undesired lines.

13. Use a sharpie or black marker to define the desired lines.

14. Color the mandala any way you choose.

Wednesday, March 22, 2017

The Tuttle Twins

The Tuttle Twins is a new series of books to help children learn about complex political and economic concepts.

There are currently five books in the series targeted at children ages 6-13. Each 50 page book focuses on a government policy or concept that has real life consequences for all citizens.

The Tuttle Twins and the Creature from Jekyll Island
The Tuttle Twins Learn about the Law
The Tuttle Twins and the Miraculous Pencil
The Tuttle Twins and the Food Truck Fiasco
The Tuttle Twins and the Road to Surfdom

For example, the Food Truck Fiasco explores protectionist laws designed to prevent competition when the owner of a restaurant convinces the city to pass laws that make it difficult for food truck vendors to continue to compete. Eminent Domain, Free Market, and concepts of liberty are among those introduced.

Because these books are targeted at young children, they are brief and the language is simple. The story line does a good job of introducing complex topics but doesn't go into a lot of detail, and does little to address opposing view points. Overall, they are a descent introduction especially if the parents encourage further discussion.

An unrelated follow on series that continues to explore similar complex topics is Richard Maybury Uncle Eric Books. The Uncle Eric books are better for children a little older. (Ages 12-18)

* I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
 ** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.

Wednesday, March 15, 2017

The Importance of Skip-Counting

Skip-counting is a fundamental math skill which is often not covered by math curriculums.

What is skip-counting? Quite simply, skip-counting is counting by multiples of a number. The following list shows skip-counting by the numbers 2 through 9. In each example, the list could continue on indefinitely.

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

If kids begin elementary math with a strong foundation in number sense, which involves skip-counting, it enables them to rapidly absorb higher level math concepts. It is not unreasonable to cover math that is typically taught in grades 3-6 in less than a year. This is because there are lots of math concepts with roots in skip-counting. It takes the majority of math time in grades 3-6 to cover these concepts. Once kids understand and can rapidly skip-count, they can fly through these numerous math concepts.

Not only does skip-counting have benefit because it enables children to rapidly progress through math curriculum. Skip-counting has value on its own. I often use skip-counting when knitting and crafting. Instead of counting stitches by 1's, counting by 3's or 4's is much more efficient. Many people use skip-counting during their work day. A store owner uses skip-counting to take inventory of products. It comes in handy when playing games and in estimating. Since skip-counting is so valuable and can be fun to learn, it shouldn't be skipped.


Math Concepts Based on Skip-Counting 

Lowest Common Factor
Greatest Common Factor
Adding and Subtracting Fractions
Reducing Fractions
Prime and Composite Numbers
Recognizing Number Patterns and Sequences

Multiplication and Division

Numerous math concepts are based on skip-counting. Multiplication, for example, is directly related to skip-counting. The numbers in the list above are the answers to the multiplication tables.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Skip-counting by 4's, referring to the above list, 4x1=4, 4x2=8, 4x3=12, 4x4=16 and so on. The answers are the same as the list of skip-counting numbers. Therefore, if kids learn to skip-count, they have already memorized the answers to the multiplication tables, before being asked to multiply. In other words, if children understand what skip-counting is and how to do it, multiplication becomes second nature.

The concept works equally well with division. Again, referring to 4's as an example: 4÷4=1, 8÷4=2, 12÷4=3, 16÷4=4. In this case, they have memorized the problems, but can count up to the correct answer.

Greatest Common Factor and Lowest Common Multiple

Greatest common factor (GCF), Lowest common multiple (LCM) and factoring are concepts taught in conjunction with fractions. Likewise with multiplication and division, having a good handle on skip-counting eases understanding of these concepts.

For example, the greatest common factor of the numbers 12 and 16 is 4. Why? Because both 12 and 16 are part of skip-counting by 4's. They are also both part of skip-counting by 2's, but the "greatest" word in the question requires the greater of the possible numbers. This answer of 4 can be visually seen by scanning the above list of skip-counting numbers and finding the biggest number that contains both 12 and 16 in its list.

Lowest common multiple is related to the greatest common factor in a similar way that division is related to multiplication. For example, 21 is the lowest common multiple of 3 and 7 because when referring to the list of numbers above, 21 is the lowest number in both the list for 3's and 7's.

When to Begin Skip-Counting?

If a math curriculum does cover skip-counting, the lessons usually begin around 2nd or 3rd grade. In general, this makes sense because kids should have a good handle on counting the numbers up to 100, counting backwards, and have a basic understanding of addition and subtraction. Although counting to 100 should really be second nature before beginning skip-counting, the other concepts could be mastered in conjunction with skip-counting. So for many kids, 2nd or 3rd grade works just fine, but kids as young as 4 or 5 years old can begin to master skip-counting.

Skip-counting by the numbers 2 and 5 usually comes first, because they are the easiest. Next it's best to work the way through the numbers concentrating on one until it is mastered as kids can become confused by advancing too quickly.

What's Next?

Once the child can skip-count well with all the numbers, or with any one number, the concepts of multiplication and division can be introduced. By placing effort on skip-counting, and making it fun, the pain parents often feel when teaching multiplication can be greatly reduced.

When my oldest daughter was about 4 years old a neighbor and friend of mine asked me, "Do you know how important skip-counting is in learning to multiply?" No was my answer that day, but I quickly learned how right she was. I followed her advice and used this method with all three of my own children who each learn very differently. Despite their differences, they all had fun learning to skip-count and rapidly learned follow-on math concepts. If you have a young child who has not begun learning math, are struggling to teach multiplication, factors, or fractions, or have an older child that could use some review, I highly advocate for a little skip-counting practice.

Thursday, March 9, 2017

Best International Historical Fiction

By reading my daughter and I have studied many historical topics. Although we often read historical fiction in connection with our history studies, it happens to be a favorite genre of both my daughter and myself. These books are great reads for upper elementary and middle school students, and are excellent for sparking interest in historical topics.

Snow Treasure tells the story of school children in the north who save the town's treasure from Nazi's during World War II occupation.

The Well of Sacrifice
Red Sand Blue Sky (Girls First!)

The Endless Steppe: Growing Up in Siberia
During World War II a family is set to Siberia. This is the story of how they adjust to this harsh land during hostile times.

Viking Adventure
The Vikings discovered America long before Columbus. In this story, a young Viking boy leaves home seeking adventure. Trained for a life of exploration, he is part of a voyage to Vineland.

The Apprentice

The Children of the New Forest
During the time the British kicked out the king, a family of soldier's children are orphaned and go into hiding. Their lives change dramatically as they learn to hunt, cook and care for themselves.

Trapped by the Ice!: Shackleton's Amazing Antarctic Adventure - Shackleton, an explorer, lead an expedition to the South Pole. During his journey the crew suffered many hardships but were able to overcome due to the outstanding leadership of Shackleton.

* I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.

Thursday, March 2, 2017


We are trying something new with science. With our microscope the kids are inspired to explore bugs, pond water, fish scales, hair, foods and more. The first time we got it out my son couldn't wait to look at his hair. Following the book The Ultimate Guide to Your Microscope by Shar Levine is helping us learn the basics of how to use the mircoscope and create different types of slides by doing actual activities.

I'm going to encourage the kids to get the microscope out at least once per week. How do you use your microscope?

 * I did not receive any compensation for this recommendation. I'm just a homeschooling mom who has found many products that I like. If you're interested in the products I recommend on this blog I want to make it easy for you to find them. 
 ** I am an Amazon associate and receive a small portion of the sales on orders made after clicking in from this site, which I promptly spend on homeschooling books and supplies for my children.

Thursday, February 23, 2017

Triominos for Family Fun

The kids love playing Triominos.

This game is a spin on the traditional game of dominoes which involves math and strategy. Players try to be the first to play all of their tiles by matching two or three numbers on the tile to existing numbers on the board. Each time a tile is played the player receives points equal to the numbers on the tile. Bonus points are awarded for a few special circumstances such as when all three numbers are matched to place a tile. Play continues in this fashion until 400 points are scored and a winner is determined.

After completing several games, players begin to develop strategy and notice that the numbers always increase in a clockwise fashion. With this knowledge, players understand which plays can allow or prevent players the ability to complete a hexagon. The more the game is played, the more strategy becomes understood. 

We enjoy this game as its fun and builds thinking skills.

Thursday, February 16, 2017

The Story of Electronic Speed!

My husband is the brains behind the electronic version of Speed! He is a computer programmer and really likes to write code.

Speed! is a skip-counting card game that helps kids learn multiplication.

Physical Cards
iPad app Lite version - free, Two Speed only
iPad app Full version 
iPhone app.

When the physical version of Speed! went up for sale at in September 2011, he began working on an electronic version. Although he is a computer engineer, he wasn't familiar with X-Code. So he not only needed to create the program, but also needed to understand and learn X-Code, which is the language Apple Apps are written in.

Pretty much all of his weekends and free time between September 2011 and January 2013 were spent on this project. He was on track to have it in the iStore at the end of the summer, before Jemma was diagnosed with Leukemia. After the diagnosis instead of working on Speed! he spent much more time cleaning, caring for our kids and handling all of the insurance paperwork.

In between his new added responsibilities he still found some time to play with the kids and finish the code for Speed! I think he did an awesome job! I knew he could do it, but had no idea it would look so good and play so smooth.

Here is a picture of him the day Speed! was available in the iStore for the first time...... You are Smrt dear! I love you!

 To find Speed! in the App Store switch the category to education and then search on

  • Speed, math
  • Speed, highhill
  • Speed, multiplication
or click the links below.

Physical version
Lite version - free,Two Speed only 
Full version 
iPhone app

Thursday, February 2, 2017

Knitting - Interested Based Education

We constantly shift our daily routines between various degrees of interest based education and loosely structured basic requirements. During our last adventure moving toward interest based education I constantly worked to ensure my children were growing in their knowledge of their areas of interest.

A few years ago my youngest learned to knit around the age of five years old with a peg loom. She went on to both crochet and knit herself hats. After she made a second knit hat identical to her first I was hoping she would be interested in another knitting project which was slightly more difficult.

I was in luck. All I had to do was suggest she search the internet for fancy hats. She giggled as she looked, but then chose a very appropriate hat to increase her knowledge and continue her knitting.

After finding the hat she wanted to make she chose her yarn.

While she was selecting yarn, I worked to write down a pattern for her to follow. We talked about the Fibonacci numbers as they are useful in designing stripes. In addition, we counted the number of rows in her hat and how many rows of each color were to be knitted, which involved lots of addition and subtraction.

This project was perfect because she worked on it several days in a row while sick with a fever, was able to read the directions on her own, and able to see how math is involved in pattern creation. It is always interesting to see where kids go when they are given the freedom to explore.

For more great educational activities check out these blog hops.

Thursday, January 26, 2017

Preparing for the CLEP or AP Government Exam

I am reading the book Collins College Outlines: Introduction to American Government.

My daughter has passed several CLEP exams which grant college credit. Soon she will be taking the American Government CLEP exam.  This year has been a very different school year in that it is the first time I feel like I am teaching to the test.

Over the past six years my daughter has learned a lot about many history, art, government and economics topics through reading engaging books and hands-on activities. This year, she is documenting her knowledge by passing CLEP exams. In preparation for each for each exam she has spent approximately six weeks reviewing material and filling in gaps.

After she decides to take an exam she first takes a practice exam from the CLEP Study Guide. Next, we work together to identify any weak areas. Then she reviews previously read materials and we work to find new materials that help with the review.

In helping her find resources to study for the Government exam I came across the book Collins College Outlines: Introduction to American Government and I am really enjoying reading it. The book is part of a series that is marketed as helping students to prepare for AP exams. In general, AP exams and CLEP exams cover the same material, but the university decides which one, if any, or both, to accept. CLEP exams can be taken at any time of year, by anyone, but AP exams are only open to high school students. My daughter is in the unique position to be eligible for both exams.

Getting back to the book, since it is written for the general audience as a review for exam preparation it is mostly unbiased, a little dry, but very informative. It covers the creation of American government, federalism, mass media, interest groups, elections, congress, bureaucracy, civil liberties among other topics. My daughter and I are both familiar with many of the topics in the book but like they way it defines basic terms and explains the roles and interactions between groups. The book is meant for reviewing. It doesn't go too in depth into any topic, but gives enough information that can lead to further research by an interested reader.

Before reading this book we read the Uncle Eric Series by Richard J Maybury, The Five Thousand Year Leap, The Freedom Answer Book and others that can be found on the History Page. This book expands on that knowledge and we are drawing many connections between the book and current events.

I'm confident that after reading this book she will be prepared for yet another CLEP exam. Although this year has been a little less mind expanding than years past, it is really exciting to see how much she has learned by reading interesting books and hands-on activities. Homeschooling really does work!

For more great educational activities check out these blog hops.

Saturday, January 21, 2017

New Nation Crafts: Quilting, Felting and Embroidery

My daughter quilted, felted and embroidered like the Americans of the mid to late 1800's.

Although quilting, felting and embroidery were known in Early American times, they were not the handicrafts which kept most women busy. Opposite to popular belief, most Early American women were kept busy sewing, spinning and knitting as these handicrafts were more essential to their survival. It was only the wealthiest of early Americans who could afford to spend time quilting, embroidering and felting. However, by the mid to late 1800's industrial producers of cloth changed the availability of materials. It was during these later times when American quilting gained popularity.

Since we are a family who loves fiber and fabric based handicrafts, my daughter did all three.


Once industrial produced fabric became available in America, the popularity of quilting increased. Contrary to popular belief, most quilts were created from new fabric. Patchwork is actually the word for cutting out and piecing together different fabrics. Quilting refers to the decorative stitching which holds the patchwork together. Regardless, my daughter spent time working on the quilting/patchwork process.

First she created a design and used a protractor to help her create the pieces for her design.

Next she cut out pieces of fabric.

Then she stitched them together.

Finally she ironed the seams of the stitched pieces. Currently, she is no where near completing the quilt she designed as she is a child who much prefers short-term projects. I'm not sure if she will ever finish this project, but am happy she has a good understanding for the effort involved.


There are several different methods for felting. Fibers from sheep and other animals will shrink and cling together after agitation. This can be accomplished with long sharp needles, or with soap and water. Many of us have accidentally felted wool sweaters in the washing machine and are surprised how dramatically small large sweaters can become. My daughter chose to create a purse by first knitting yarn with very large needles and then shrinking the knitted purse down to size.

 Following a pattern from the book Pursenality Plus, she created her purse.

 Next she squeezed warm soap and water through the purse for several hours until it shrank down to size.

Finally she stuffed her purse with treasures and carries it around town.


Today machines are used to make dynamic embroidery designs like this hedgehog created on my mother's machine. After the 30 minutes or so required to line up the design, program the machine, and place the fabric into a hoop with proper stabilizing papers above and below, the machine only takes about 30 minutes to whip out a finished product.

In the past simple embroidery designs took much longer. My daughter spent about 10 hours working on her embroidery sign for her room.

Like hand knitting a sweater, creating a full sampler must have taken weeks to months. Maybe I should invest in a knitting machine?

To see more American History lessons for kids please visit our archives on our History Page.

For more great educational activities check out these blog hops.
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