## Friday, July 14, 2017

### Speed! - New Font

Skip-counting is a key ingredient in teaching upper level elementary math concepts. Once kids have a good handle on the numbers 1-100 and can count backwards from 20 to 0 they are ready to learn skip-counting. This usually happens between the ages of 4 and 8 years old and around the same time as kids are learning addition. Numerous math skills are based on skip-counting such as multiplication, division, adding and reducing fractions. With a good understanding of skip-counting, children are able to progress much more rapidly through these upper elementary math concepts.

Songs, the card game Speed! and hands-on practice work well together to cement the fundamentals of skip-counting. When playing Speed! kids learn to skip-count beginning on any number. For example, if they are skip-counting by 3's, they may begin at 18 and progress to 21. They also learn to skip-count backwards. The rhythm and rhyme of song helps engage memory and the colored decks of cards in the game Speed! help kids create a visual association with numbers.

The card game Speed! has just been given a facelift. The exterior of the container was lightened from a dark blue to a light blue and the numbers on the cards are now a more common font which is easier to rapidly read. The original version is shown above on the left, and the updated version is on the right.

If you haven't purchased this game yet, now's the time. After all, it's fun and a great way to keep kids learning over the summer! Kids play because they want to win, not to learn to skip-count. The beauty of the game is that in order to win, they have to have the skip-counting numbers memorized and they do so enthusiastically. The big secret, is that the numbers are all the answers to the times tables. After playing Speed!, kids can quickly apply what they've learned to multiplication, division, factoring, and fractions. How can you beat an educational game kids actually want to play.

## Friday, July 7, 2017

### Bridge Unit Study - Lesson 8: Maintenance

Our bridge unit study ended with a discussion on maintenance.

Too often the cost of maintenance is not considered as part of the cost of a project. Whether you are building your home, a building or a bridge, maintenance should be a huge consideration. After all, if the structure breaks down, we will have to do without or start over from scratch.

Therefore, I was pleased that the book we chose to follow for our bridge unit study Bridges: Amazing Structures to Design Build and Test addressed the issue of maintenance. Painting, erosion, weather, corrosion, and traffic load are a few issues that determine how long the structure will last. The book does a good job of summarizing maintenance considerations.

To gain a better understanding of weather effects, my son explored corrosion with a science experiment. Putting steel wool into different types of water, he watched it over a 24 hour period to see how much it rusted. It was a very simple experiment and a great way to wrap up our bridge unit study.

Now where ever we go we take a good look at the different bridges around us.

Honfleur Cable Stay Bridge (Normandie, France)

London Bridge

Tower Bridge

Charles Bridge, Prague

## Wednesday, June 28, 2017

### Bridge Unit Study - Lesson 7: Bridge Design

My son designed several bridges.

What type of bridge would you build across a busy shipping waterway? How about over a deep ravine?

The book Bridges: Amazing Structures to Design Build and Test discussed advantages and disadvantages of many types of bridges including beam, arch, suspension, cantilever, draw, and hanging. It also addressed how the loads are carried, options for materials and brief changes throughout history.

What I really liked was the challenges the author posed to readers. Several times, kids were given a set of requirements and asked to design a bridge to meet those requirements. Each time my son was eager to design a bridge. Well he is far from an expert bridge designer, these questions enabled him to think about what he would do.

## Wednesday, June 21, 2017

### Bridge Unit Study - Lesson 6: Hanging Bridge Model

My son built a hanging bridge.

Although hanging bridges are rarely used today for transportation, they can make wonderful play structures. The one shown below is at a high ropes course. The hanging bridge is mounted on a pulley to a cable. The bridge is controlled with the rope to pull it near, and by gravity when traveling to the other end.

A similar bridge can be constructed over a calm waterway by attaching a floating raft to a cable spanning the waterway.

The book Bridges: Amazing Structures to Design Build and Test was the inspiration for this activity as it has been for most of our other bridge modeling projects.

This time, two straws were attached to a piece of cardboard to run on the main cables of the bridge.

Again, my son used two chairs as the main supports for his bridge.

A basket was hung from the cardboard pulley system to transport traffic across the bridge.

Please visit each of the pages on Highhill Education for more hands-on activity ideas. Math, Science, History

## Wednesday, June 14, 2017

### Programming for Kids

My son is learning to program using Javascript.

After many years learning the basics of computer programming with Scratch, my son is learning his first programming language. Javascript. His last project on Scratch was a Mrs. PacMan game. After working many weeks on his design, which included downloading and reading the code of a similar game, he was ready to move on. Well, actually he wasn't. He wanted to make his game perfect which is a common trait of a computer programmer and engineer, but we told he he was ready to level up, or graduate if you will, to bigger and better things.

We found the key in the book Javascript for Kids. After reading the first chapter I was hooked. The author explained that in reality, computers were actually very dumb. They can after all, do only what humans have told them to do. It made perfect sense and made me laugh.

Then we moved on. This book is perfect because it starts with the very basics and builds from there.  In discussing variables, the first main topic, the difference between numbers, strings and booleans is explained. Short program examples are given and the kids can type them right into the browser to see how it works. Chapters also contain challenge questions designed to get kids creating their own programs using the tools they learned.

We covered about a chapter per week and by the end my son was on a roll.

## Wednesday, June 7, 2017

### How to Teach Math Without a Curriculum

Math is everywhere; games, art, and life and it's possible to teach kids lots of math with little to no curriculum. What's more, it's easy to do. However, as skills increase beyond addition, subtraction, multiplication, division, fractions and geometry curriculum makes teaching math much easier.

All three of my children learned fundamental math skills through play. Kids learning math this way don't fall behind, or miss steps. On the contrary, they build a solid foundation of skills that enables them to understand higher level math much easier. Many concepts can be taught and absorbed rapidly enabling them to fly through more advanced math curriculum. Because my children were playing, they were motivated to learn. At age 15, my oldest daughter passed the calculus CLEP exam and at age 10 my youngest daughter tested at a 9th grade math level.

Learning math still takes time. The difference here is the way math is being learned. Note that each of these skills should be mastered before moving onto higher level math and it is necessary to master some skills before beginning others. For example, kids should be able to recognize their numbers and count before moving onto any of the other games or activities. However, there are many skills which can be learned at the same time. For example, when kids are busy playing Black Jack 21 to learn to add, they can play Cribbage which reinforces adding skills and introduces strategy and skip-counting. Speed! teaches skip-counting of numbers one through nine. Kids can begin playing the game learning to count by 2's and 5's while mastering their addition facts.

If you want to teach math this way, here is a list of progressively more difficult activities to try and master. This list covers the core skills of elementary math. We covered this list, added in other activities to introduce time, money, shapes and patterns, and also added a workbook or two each year so the kids could see math as written symbolically. Only the core activities are listed, supporting activities such as weaving potholders, drawing symmetric monsters, and additional games which involve a variety of math skills can be found on my Math Page. It is typical to move through the list of games and activities with some overlap concentrating on one game, but mixing in other games and activities for fun.

#### Number Recognition

UNO is one of the best games to begin with when introducing kids to math.

#### Counting

Chutes and Ladders is a classic game that kids enjoy playing. I like it because it helps with number recognition and they count from 1-100.

#### Writing Numbers

Make a homemade calendar. Doing this activity with each of my children, they were able to practice writing their numbers, learned about months, and again counted numbers from 1-31.

#### Number Value

War is the single best way to teach greater than less than. After flipping a card from a standard deck, the person who flipped the card with the greatest value gets to keep both cards. The game ends when one person holds all the cards.

Black Jack 21 is a gambling game played with a standard deck of cards. We didn't play Black Jack to gamble. We played it to learn to add. The dealer gives each player one card face down and one card face up. After peeking at their secret card, kids decide whether or not they would like an additional card to bring the sum of their numbers as close to 21 as possible. They can ask for as many additional cards as they would like receiving and deciding one-at-a-time. If they go over 21, they loose. If they stay under 21, the dealer gets a chance to get a higher total than the child. This game teaches prediction, statistics, strategy and most important - ADDING.

Similar to War, players win a game of Adding War by getting all the cards. The only difference is that two cards are flipped over instead of one and the player with the greater sum of cards gets all four cards.

#### Skip-Counting

Speed! teaches skip-counting by 2's through 9's. Mastering this fundamental skill makes learning multiplication, division, factoring and fractions much easier.

Cribbage is a much more complicated game than Black Jack or War, where players try to get points by getting numbers in a row, pairs and cards that total 15. It reinforces skip-counting by 2's and is wonderful for practice with addition. Since the game is more complicated, I would recommend playing after kids have a good handle of the above games, so around age 8 and up.

#### Fractions

Every homeschool mom knows that cooking is fraction application. We incorporated food into history and geography as well. Here are some fun dishes to make with kids.

#### Geometry

Geometry can be introduced by creating art with a compass and a straight edge. The geometric designs, shapes in circles found on my Math Page can be completed with kids around age 8 after they can draw a circle with a compass. The activities increase in difficulty when exploring math art with mandalas. The mandala activities are great for kids around age 10 or when they have completed the shapes in circles activities.

Please see my Math Page for additional activities to learn and practice math skills without a curriculum.

## Wednesday, May 31, 2017

### Speed! on the iPad and iPhone

Are you looking for educational apps? Speed! is a fast-paced card game that teaches skip-counting. Two players compete against each other to be the first to get rid of their cards, but they must watch-out...... if the number in the middle is the same they must be the first to shout Speed!, otherwise they will get all the played cards added to their stack. Skip-counting is a fundamental math skill that leads right into multiplication. Kids love to play this game because it's fun, but parents like it because it's educational.

Speed! is available as physical cards, an iPad app or an iPhone app.

On the iPad players begin as a Trainee and can advance through the levels to become a Legend. With five levels to pick from and eight numbers to skip-count this game will keep kids entertained for hours. They don't realize how much they are learning because they are busy trying to win. The Lite version is free and contains the Two Speed deck of cards at all levels while the Full version costs only 99 cents and contains card decks Two Speed through Nine Speed.

To find Speed! in the App Store switch the category to education and then search on
• Speed, math
• Speed, highhill
• Speed, multiplication

Then download it and have fun playing! (Be sure to let the kids have a turn.)

## 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
1:30-3:00 - Errands (Optional if dad is home)
3:00-5:00 - Swimming
5:00-6:00 - Dinner
Bedtime

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.

## 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.

Materials:
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.
Play
•  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.