Here is a collection of articles written for the weekly Math Corner by Raina Fishbane and Merry Adelfio.
Table of Contents
Reading Lists are Everywhere - What about Math Over the Summer?
Da Vinci Code Math
Family Math Activities
How to Help Your Children Be Great Mathematicians
Multiple Ways to Multiply
Can You Subtract Multi-digit Numbers from Left to Right?
Sports and Math
Why Teach So Many Different Strategies?
More Wonderful Math Literature
Math at Home
Computation and Arithmetic - Is there really more to math than that?
Family Math Activities of the Week
READING LISTS ARE EVERYWHERE --WHAT ABOUT MATH OVER THE SUMMER??
It seems that the end of every school year is the same – students get to bring home all of their work from the year, as well as a wonderful reading list to make sure that they keep reading throughout the summer. But where are the summer math lists?
Just like continued reading is important, children should absolutely keep exploring numbers and thinking about math throughout the summer. But to do effective math work is a little more complicated than simply providing a list of exciting books to read.
Instead, parents need to be involved in their child’s summer math work. Here are the goals that we think would be ideal for the summer:
· Children should maintain their number flexibility. Talk to your kids about numbers. Are they able to take them apart and put them back together? For example, can they find 7 different ways to make the number 6? For older students, can they come up with mental strategies for a multi-digit multiplication problem? The more they do it, the easier it becomes!
· If your children have already memorized their “math facts,” they should continue to practice them over the summer so they don’t forget them. But practice should be fun! If your child is working on addition or subtraction facts, play blackjack (21) or cribbage. Does your child love the computer? Have him or her play Math Blaster or another quality program that will help reinforce their math fact knowledge. (Second graders should know their addition and subtraction facts to 20, third graders should also know their multiplication facts, and fourth graders need to keep practicing long division.)
· Play a math related game together every week – Uno, Top It, Othello, Mancala, etc. We have a large list on the Math Adventures website of wonderful games. Go with your child to a toy store together and pick out some new games to play this summer.
· Take out your old wooden blocks. Think your kids are too old? They are not! Dig them out and watch your kids discover again the joy of building with blocks while developing their visual discrimination and geometry skills.
· Try to incorporate “math talk” in your day to day conversations. Count your steps when you are going for a walk, determine in advance the change you’ll get at a store, estimate the number of people in a group, or notice or find shapes and angles on one of your summer outings.
We will be creating a new Summer Math page on the Math Adventures website. Look for it in June and we hope it will be a good resource for math ideas for your summer.
Have a great summer and please let us know if you have any questions or would like any other recommendations!
Merry and Raina.
Back to Table of Contents
DA VINCI CODE MATH!!
The best selling novel the Da Vinci Code is about to be released as a movie. Have you read the book? There was lots of math throughout the book – it is filled with secret codes and even talks about the Fibonacci sequence and describes the properties of the Golden Ratio! But was it all true?
The Da Vinci Code describes the secrets of the Golden Ratio – and claims that its mysterious properties are found throughout nature, as well as ancient art and architecture.
But what is the Golden Ratio? The Golden Ratio is an irrational number – a number that cannot be derived by dividing one whole number by another (i.e., a/b).
The Golden Ratio can be found in many different ways, including by dividing any two consecutive numbers in the Fibonacci sequence. The Fibonacci sequence is the following series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. Can you figure out the pattern?
Each subsequent term is the sum of the two terms before it (e.g., 1+1=2, 1+2=3, 8+13=21, etc.).
As you divide progressively larger numbers in the Fibonacci sequence, you get progressively closer to the Golden Ratio, which starts as 1.61803…., and is often represented by the greek letter Phi. Like the number pi, Phi goes on infinitely and never repeats.
To get the Golden Ratio exactly, take any line segment and divide it into two more line segments such that the ratio of the whole segment to the longer of the two pieces is equal to the ratio between the longer piece and the shorter piece.
On many plants, the petals on the plant’s flowers is a Fibonacci number: 3 petals on a lily or iris, 5 petals on a buttercup, 8 on many delphiniums, and many daisies have 34, 55, or even 89 petals!
Sunflower petals grow in two spirals – one almost always has 21 or 34 petals growing clockwise and the other spiral has 34 or 55 petals growing counterclockwise.
Looking at the arrangements of seeds on the heads of flowers, the seeds grow in circular patterns with the numbers of seed in each concentric ring also equal to a Fibonacci number!
Not convinced? Look at a pinecone. Pinecones clearly show the Fibonacci spirals!
In the DaVinci Code, author Dan Brown states that the proportion of anyone’s height divided by the distance from their belly button to the floor will equal Phi. Try it and see whether he was right!
Finally, what does the Golden Ratio have to do with Da Vinci? Look closely at The Mona Lisa and see whether you can figure it out!
Back to Table of Contents
Here are some fun ideas for activities to do with your kids.
For younger children:
Here’s a quick and easy game that incorporates art while teaching about symmetry and spatial reasoning.
Take a large piece of paper and fold it in half and then open it again so you see the crease in the middle.
Take out a bunch of buttons, different shapes of macaroni, beans, or cut out different shapes and different colors from paper.
· Have your child place one shape somewhere on his or her half of the page. Then you copy his or her move by placing an identical shape on the corresponding part of your half of the page. By you being the first one to “copy,” you can model behavior for your child’s turn.
· Now you go first. You place a shape and then your child copies you by placing an identical shape in the corresponding place on his or her half.
· Keep going until you have made an interesting pattern and have filled much of the page.
· When you are done, glue everything onto the page and then display your masterpiece!
· Talk about where else you can find symmetry (a butterfly, a pair of eye glasses, a flower).
For older elementary aged and middle school aged kids:
Here’s a game based on Euclidian principles that is fun to play while also giving kids extra practice with multiples, greatest common divisors, and strengthening logical reasoning.
· With two players, each player secretly chooses any number between 20 and 200. The players then reveal their numbers and then begin the game. (In order to illustrate, pretend the 2 numbers picked were 27 and 151).
· The first player subtracts any multiple of the smaller number from the larger number that produces a difference that is greater than or equal to 0. (If the first player takes 3 x 27 and gets 81 and subtracts that from 151, the difference will be 70).
· The second player does the same thing but using the original smaller number and the new number formed by determining the difference. (So the 2 numbers now are 27 and 70. Assume the second player takes 27 and multiplies it by 1 and then subtracts it from 70, the difference is 43 so the 2 remaining numbers for the next turn are 27 and 43).
· Play continues until one of the players produces a new pair of numbers where one of the numbers is 0. That player is the winner.
After playing a few times, think about whether it matters who goes first. Is there a strategy to the initial picks of numbers?
Euclid, who lived around 300 B.C., helped invent a way to determine the greatest common divisor of two numbers (the largest number that will evenly divide two given numbers). What is the connection of this game to greatest common divisors?
Are you interested in more math activities to do as a family? The above activities are all adapted from a wonderful series of books called Family Math, Family Math for Young Children, Family Math II: Achieving Success in Mathematics, and Family Math: The Middle School Years that provide great hands-on experiences for families interested in exploring mathematics together.
Back to Table of Contents
Some of you might remember learning “long” division and not
so fondly. We can assure you that your children will learn to divide at Lower
School; however, they will learn some strategies you might not recognize.
Our favorite way to introduce multi-digit division is by alerting kids to the fact that they merely need to know how to multiply (and subtract and add) in order to divide. We teach our students how to use the partial- quotients method, which is a most forgiving method for division. At each step, the student finds a partial answer and at the end, these partial answers are added to find the quotient.
Study the example below delineating how partial quotients can be used to find the answer to 94 ÷ 6.