Have a Mathy Summer!

    By Dawn Lamping

Summer is always welcome in the Rockies, and it beckons us to have fun. Why leave math out of that?

Here are some great outdoor math games and projects that are guaranteed to hold the interests of all your crew and keep everyone’s skills sharp until the days get shorter again. Not only will your kids enjoy them, but they’re adult-tested for fun, too!

purple Columbine[1]For the youngest set, counting is the name of the game. There are so many beautiful plants to count in summer! Some have three petals, many sport six. The rose (an edible math treat as long as it’s safe from pesticides) is built on the principle of 5, as is our state flower, the columbine. Older siblings can help younger ones press flowers, and these can be used to make math cards! Let an older child glue specimens to index cards and laminate or cover with Contac paper. If you have three cards that each have a three-petaled flower on them, count how many petals in all. Children like to make up their own games with such cards. You can choose to follow up the activity with writing multiplication equations if you like. For pre-algebra-with kids as young as kindergarten and as old as teens-add and subtract things your children gather in their romps by writing the first letter of the object along with the amount. Although you can’t add leaves and pinecones, you could do something like this by writing “p” for pinecones and “l” for leaves: 2 p + 3 p + 4 l + 7 l – 2 l = 5p + 9l.

Little ones also love motion. Sidewalk chalk can be used for a number line to play addition and subtraction games. For the older set, make jumps of a certain number to skip count, or skip count backwards to divide. Make “four square” with numbers in each cell, and toss a pebble in turns to see which numbers to add. Expand the square or add fractions and decimals for greater challenge.

Ball games help with skip counting. Even very young children can learn to count by twos, fives, and tens just playing catch and counting aloud each turn. Older kids will enjoy skip counting. For a larger group at the park, it can help children reorganize their energy to get in a circle and toss a ball to anyone in the circle while skip counting. Let the ball bounce once without saying that number to work through all the “every other” patterns: fours are every other two; eights are every other four. Sixes are every other three; twelves are every other six.

Use a duck-duck-goose format in a circle for the “every third” sets. Choose a target “goose” number on the times table you will practice before you begin, and when that number is reached, then the chase ensues. Nines are every third three; twelves are every third four. Sixes are every third two. Let “it” run around the circle of friends who are sitting down and touch everyone’s head. Each person in the circle must be silently skip counting to keep up. Only every third person says their number aloud. If you are counting by threes, the first person would be three, the second six, the third nine. Only the third person says “nine.” If the target number-such as 36-is reached without errors, then the target person gets up to chase “it” around the circle and if they catch “it” before “it” can run around once to sit in the target’s place, then “it” has to stay “it” for another round.

Sunny DayUse sunny days to your math advantage. Chart sunrise and sunset times to watch the coming and waning of the solstice on the longest day of the year, June 21. Students can chart these on a graph and determine the rate of change daylight and find the average rate of change in a week’s time or across the whole summer. Temperature charts lend themselves to this activity also. A next step is to combine temperature and day length for comparisons.

Shadows can be used to measure the height of a tall building or tree. Just measure the shadows of yourself and the tall object. Then measure your own height and figure out the height of the tall object through setting up a ratio by imagining right triangles. The right angle will create comparable proportions. If you are five feet tall, and your shadow is seven feet long, and the tall object’s shadow is fifteen feet long, set up the following proportion: 5 : 7 as h : 15. Solve for the unknown height h. This method is called “shadow reckoning” and was used by the ancient Greek mathematician Thales to measure the height of the Great Pyramid using only shadows.

Above all, stay outdoors as long as you can and enjoy learning together. With a bit of creativity, you and your children will have fun without even realizing how “mathy” the summer has been!

What are you most looking forward to this summer?

    ___________________

    Dawn Lamping didn’t see much of fifth grade recess because she was held in to try to “catch up” in fractions. That experience cooled any interest she had in mathematics until she started her family in 1994. Through the journey of homeschooling two children, Dawn discovered the “blueprints of Creation” within mathematics. She feels blessed to share the joy of math and enjoys exploring and mastering numeracy in the classroom through hands-on experiments, fun drill games, geometry, and art. She holds an Honors Degree in Psychology from the University of Missouri and completed teacher training at Arizona State University.

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Finding the Music in Math

    By Dawn Lamping

      “Mathematics is the language with which God has written the universe.” -Galileo Galilei (1564-1642)

      Photo credit: Wikimedia Commons

      Photo credit: Wikimedia Commons

      Something very sad has happened to numeracy in our culture. Most of us were educated in a school system that isolates mathematics, teaching one single path to math: memorization of abstract facts and algorithms. Cut off from its context, its separation renders it dead, lost, decidedly “other”- easy to dismiss or feel antagonistic towards. Consequently, many of us have divorced ourselves from math.

      But as Galileo told us, math is important, a vital and fundamental part of this beautiful Creation we are gifted to live within. Creation is its context. Math is a blueprint from which we cannot separate ourselves: it is in music, in our bodies, in the structure of elements, in color and in dance. In some deep way, to separate ourselves from math separates us from God. Or alternately, when God is alive in our hearts, math comes alive in our minds.

      To give our children the gift of a Classical Christian math education is to open a door for them they will journey through all their lives. With the right viewpoint, drilling and memorizing numbers can be fun; it feeds confidence and builds a foundation for success. Even better, when beauty is found in numbers, it feeds the hungers of the soul and sets a foundation for truth in the heart.

      For the very young, finding numbers they know in nature and life is like a treasure hunt. Flowers exhibit petals in multiples of three and six (monocots), or multiples of four or five (dicots). There is one sun, one moon, seven continents, one mother, one father, two parents. Families come in many number combinations, and drawing a family tree will reveal patterns of the powers of two (aptly named!). It can be fun and revealing to keep a number journal with photos and drawings representing the numbers.

      For older students, the history of numbers is fascinating. A math timeline illustrates the relationship of man to number in a graphic way. The writing of numbers predates writing of literature! The earliest examples of writing we have show tallies of moon cycles and the trading of goods. The ancients saw numbers as having color and personality. Musical scales were an essential element of the study of geometry, and instruments were based on mathematical models of tone and form. The ratios of the lengths of strings were the basis for the discovery of harmonies in math, while the golden ratio (www.goldennumber.net) of 1: 1.618 was the basis for beauty in art and architecture. Even the dimensions of Solomon’s Temple and the Ark of the Covenant follow this pattern.

      A project the “tweens and teens” enjoy is one I call “Meet the Numbers.” We divvy up the list and research each number from 0 – 12 to “introduce” the number to the group as one would a new friend. Each number has its own configuration of factors, multiples, and shape. Sometimes amazing stories of the “lives” of numbers pop up, such as the strange battle over the number zero in the Middle Ages. Zero was a new number in Arabic culture (called the “sifr”), and the rulers of Western Europe actually outlawed its use until it was finally accepted in the 1500’s.

      One sequence of numbers-which adds each new term to the previous one-looks like this: 0 + 1 = 1; 1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8. It was discussed by Leonardo Fibonacci of Pisa, c. 1130. The “Fibonacci Sequence” can be found in the measurements of the human body (all ages love measuring themselves), in musical scales, in church architecture, in natural spirals of leaf growth in plants and sunflower seeds, in the cycles of the solar system, and many more.

      We are quite lucky, we who get to explore this pattern with our children, because it also teaches us the things we never had the opportunity to learn about math. When children are young, they can find the numbers in nature. As they get older, they can draw things such as the golden spiral (see the “Nature by Numbers” video, below), or compare proportions through algebra.

      To step forth on this path as mothers and teachers asks us to let go of our assumptions about what math looks like and add another dimension to our work. This can seem strange at first until we form a new conception of what math means. Without shorting on memorization, adding space for math discovery will enrich and motivate both us and our kids.

      It’s time for us to relax and discover numbers afresh; resting in the truth that when numbers have meaning and depth, facts are just plain easier to memorize anyway!

      Let’s chat: How do you view math? Is it a blessing or a curse?

      (Readers: as an extra bonus, check out the “Freebies” tab at the top of this page for one last piece of advice from Dawn!)

      A few good resources:

      Living Math (www.livingmath.net)
      Math From a Biblical Worldview
      Nature by Numbers (www.youtube.com)
      The Golden Ratio (www.goldennumber.net)
      Donald in Mathemagic Land (Disney, 1959)

    _________________

    Dawn Lamping didn’t see much of fifth grade recess because she was held in to try to “catch up” in fractions. That experience cooled any interest she had in mathematics until she started her family in 1994. Through the journey of homeschooling two children, Dawn discovered the “blueprints of Creation” within mathematics. She feels blessed to share the joy of math and enjoys exploring and mastering numeracy in the classroom through hands-on experiments, fun drill games, geometry, and art. She holds an Honors Degree in Psychology from the University of Missouri and completed teacher training at Arizona State University.