Wednesday, May 17, 2017

Speed! Skip-Counting to Multiplication

This video explains how the card game Speed! works to help kids boost their math skills.

From skip-counting to multiplication, division and fractions, this game is excellent for kids ages 4-12, or anyone learning addition through multiplication.

Speed! is a fast-paced card game that helps kids learn how to multiply. What it does is teaches skip-counting which is a fundamental skill that leads right into multiplication. Continuing to build on math skills, Speed! helps kids with division, factoring, reducing fractions, and the many math skills that build upon skip-counting. I want to show you how this works.

The game contains eight decks of cards, 2-9’s. Each deck is color coded and based on a different number. For example, the three—speed deck contains the numbers 3, 6, 9, 12, 15, all the way up to 30. So playing 3-speed, kids learn to count by 3’s. Each deck is played the same way, only the numbers change. After kids master one deck, such as 3’s, they can move onto another deck, counting by 4’s or any number 2-9. Throughout this video, I will give examples referring to the 3-speed deck, but please keep in mind that the same principles apply to all decks. There is a video showing the game being played and I highly recommend viewing it if you haven’t yet.

A unique aspect of this game is that in order to win, kids not only need to know how to count higher by 3’s beginning with 3, but they need to be able to count higher by three starting with any multiple. That means they may start on 18 and count to 21, then 24.  They also need to be able to count backwards by 3’s starting on any multiple of three. In other words, they may start on 15, and count to 12, then 9. Kids play to win, not to memorize, but regardless of their reason, they are learning a critical skill.

After kids have played 3-Speed for a week or a month, or however long it takes them to get really fast they have memorized the answers to the 3 multiplication tables, but don’t necessarily understand the link between skip-counting and multiplication.

At this point, it’s a good idea to lay the cards out in order like this, and explain this is 3x1, 3x2, 3x3, 3x4, 3x5, all the way up to 30. Then after asking the child “what’s 3x6?”, they can point and say 18. “What is 3x8?” Well it’s 24.

Now the kids will begin to understand the link between skip-counting and multiplication, and it’s a good time to go back to playing the game. After all, the game is the drill work of multiplication and it’s the fun part. Kids are playing to win, and not to learn, but they are learning and that’s why it works.

Some kids will understand immediately and not need any flash card work to make the transition into multiplication. Others will still need some time with flash cards, but since they are already familiar with the answers to the multiplication tables, the time spent with flash cards should be greatly reduced. Sticking with one deck and mastering the corresponding set of multiplication tables before moving on to another deck will result in a greater reduction of time spent with flash cards since there are less numbers in their head from which to select an answer.

Learning division works the same way. Again, with the cards laid out in order, if the child is asked “what’s 24 divided by 3?”, they can count, 1,2,3,… it’s 8. What’s 12 divided by 3, It’s 4.

It’s best to begin with the 2’s or the 5’s because they are easiest, and concentrate on one deck of cards until it is mastered. Concentrating on one deck of cards reduces the number of options for answers and helps kids to create number associations.

In addition to building recognition within number families, kids that play a lot of Speed begin to  recognize patterns between the decks. When playing 3-Speed, they might say, well wait a minute, a lot of these numbers are in 6-Speed!, Six-Speed has a 6, 12, 18, 24, and 30. Those numbers are in both 3 and 6 Speed…. and wow! A bunch of these numbers are in 9-speed too. Nine-Speed has a 9, 18, 27. It’s unconsciously making number associations between different decks that can really help kids to boost their math skills.

Now when they get into higher level math such as reducing fractions, they might have to reduce the fraction 6/21. So then they think, wait a minute, both of those numbers were in 3-speed. There is a relationship between those numbers, and the common number is 3. The fraction 6/21 can be reduced to 1,2…..7ths.

When my own kids were around the age of 7 or 8, we played Speed! every day for about 4-6 months straight. It was our math curriculum. Each day, I would lay the cards out in order and quiz them orally on multiplication for about 1 minute. Then we would play Speed! for about 15 minutes concentrating on one deck until it was mastered. This emphasis on skip-counting and number association allowed all three of my very different children to fly through many math concepts.

I recommend this game for kids ages 4 through 12 or for anyone learning addition up through multiplication. As soon as kids have an attention span, a desire to play games, and can count they are ready. The 2’s and 5’s are easiest, so they are the best decks to start with. When kids are learning addition, they are ready to begin counting by 2’s.

We used this game as our primary method for teaching multiplication. Other families have used Speed! on family game night, to improve or review multiplication, to gain a good number sense, or as a fun way to work on math over the summer. Since there are 8 decks of cards in the set, 16 kids can play at one time making the game a great option for co-ops and schools.

Remember, kids play because it’s fun and they want to win. Not because they want to boost their math skills, not to learn multiplication, but they do. So have fun with it. Thanks for watching.

Wednesday, May 10, 2017

Our Summer Flow

Last summer, the kids got lots of exercise, had some fun, worked a little and got to sew.

We are a homeschooling family that looks forward to a relaxing summer off from school. Over the summer our priorities switched from schoolwork to exercise, reading, yard work, sewing and free time. Although exercise is something we do year round, we tend to spend even more time exercising during the summer months. The kids like to run races, we take family bike rides and we live in a beach town where there are lots of opportunities for swimming. We take full advantage of those opportunities.

In addition to exercise we tried to create a balance of other activities. Before the summer began, my nine year old was a very resistant reader. She could read, but didn't like it. Therefore, I wanted to emphasize reading in a positive way that would hopefully result in a willing reader.

Just under a year ago we moved into a new house with a lot of yard and yard work. Since there were many things I wanted to improve the yard work was the perfect opportunity for the kids to help out and earn some extra money. Each day I planned to work outdoors, but that was a lot for children. Therefore, I made yard work an option.

Our new house is very close to my parents house and my mom has a love of sewing. The girls and I, being quite crafty ourselves, wanted to learn from grandma. Thankfully she was willing to sew with us one morning a week.

With these goals in mind we put together a daily routine.

Wake-up-9:30 am - Eat breakfast and exercise
9:30 am - Listen to mom read (30 minutes) - Younger kids only
10:00-12:00 - Yard work for mom - kids can help and get paid (optional)
12:00-1:00 - Lunch
1:00-1:30 - Silent Reading
1:30-3:00 - Errands (Optional if dad is home)
3:00-5:00 - Swimming
5:00-6:00 - Dinner
7:30-8:00 - Reading Together

Wednesday Mornings Only 9:00-12:00 - Sew with grandma

This schedule was followed quite loosely which is why we called it a flow. Obviously rain changed many plans, as did orthodontist appointments, play dates and special events. Overall, it was successful as it helped us to make time for reading, sewing and yard work which would have been easily skipped without the plan.

Because the reading was spread throughout the day, we almost always fit in one reading session and usually completed two or three each day. At the end of the summer I was surprised at how many books were read. Sometime during the summer, my reluctant reader found the Magic Tree House series. From that time on, I found her reading at times not on the flow. I can't express how excited I am about this change.

 The yard still has a long way to go, but the kids pockets are full of money. They didn't help every day, but helped enough to make an impact. Once school started, they continued to help with yard work many times throughout the fall.

Sewing with grandma was a hit. I loved it! We continued to sew one morning per week throughout the school year, completed numerous projects, and learned a vast array of sewing techniques including applique, piping, putting in zippers, basic crazy quilting, and so much more.

Wednesday, May 3, 2017

Bridge Unit Study - Lesson 5: Suspension Bridge Model

My son made a model of a suspension bridge.

Throughout history humans have built three main types of bridges: beam, arch and suspension.

The book Bridges: Amazing Structures to Design Build and Test explains each type in detail including how the loads are carried, steps in design, installation issues to consider, well-known examples of each type and suggestions for hands-on activities. After reading the section on suspension bridges, we watched the video Bridges of New York.

With the East River and Hudson River surrounding the island of Manhattan, New York City is full of bridges. This video details unique aspects of many of the New York bridges as well as the people who designed and built them.

After learning about suspension bridges, my son built a model.

First he secured to main lines raised on chair back supports to two books serving as anchors.

Then he placed a cardboard road deck on top of the books with a heavier book on top of each end to hold it in place.

 Next he added thread lines connecting them from the deck to the main support cables.

Voila! What a cool project. I highly recommend this book The book Bridges: Amazing Structures to Design Build and Test.

Wednesday, April 26, 2017

Bridge Unit Study - Lesson 4: Cofferdam Model

My son built a cofferdam.

Have you ever wondered how construction engineers build structures underwater? Well they don't. They remove the water from the area they want to build with a structure called a cofferdam or a caisson. One method of building a cofferdam is to drive large metal structures into the soil in rings.  Then the water inside the ring is pumped out so the construction can be completed.

Cofferdams were used as many as 2000 years ago by the Romans who developed a unique type of concrete. Roman concrete incorporated ash material from nearby Mt. Vesuvius which made it very similar to modern concrete, but most importantly, the ash made the concrete waterproof. Since the Romans weren't building with steel, their cofferdams were constructed by driving two rings of wooden posts into the soil. The space between the rings was then filled with a watertight material such as clay to prevent water coming into the inner ring. They also did not have pumps, so the water was removed with buckets. Nonetheless, this method for removing water from an area allowed them to build support structures for bridges in the water.

While learning about cofferdams, we watches the video Engineering an Empire Rome as it was a very educational video which linked our bridge study to history.

The book Bridges: Amazing Structures to Design Build and Test is a fantastic resource for learning everything about bridges. It has been the foundation for our bridge study, and is packed with both information as well as activity ideas to help solidify concepts.

My son followed the instructions in the book for building his cofferdam. First he put sand into the bottom of a bowl and added water covering the sand. Next he put craft sticks into the sand in the water in a ring. The Romans would have used tree trunks for this step.

Then he put tape around the craft sticks to hold them in a circle and added a second ring of craft sticks.

The Romans filled the gap between the rings with waterproof material such as clay. Plastic wrap worked well for my son.

Finally, he used a turkey baster to remove the water from inside the cofferdam.

Please visit our Science Page for more interesting hands-on learning ideas.

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.
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