Boy, is it HOT out there!!! If the temperature outside is 100 but air conditioning keeps the atmosphere inside at 85 degrees, what is the percent change when you come in from the heat? (100-85)/100........(the original amount minus the new amount) divided by the original amount).......the amount of change divided by the original amount.....The air inside is 15% cooler than the air outside.
In times of extremes, like in the weather, even the kids are aware of numbers. What a great opportunity to demonstrate a few math concepts like percent change.
Here's another one. The days are getting shorter. Yesterday the sun rose at 5:14 and set at 8:24.....that's 15 hours and 10 minutes......910 minutes (multiplication).......tomorrow the sun will rise at 5:16 and set at 8:21.....that's 15 hours and 5 minutes. [These are simple arithmetic problems and the times are only samples and not accurate.] Students can look up sunrise and sunset on the computer and do the math on the calculator. Now, calculate the percent change. For what portion of the day is the sun up? (tomorrow: 905/1440) Can you use ratios to predict the number of minutes of sunshine the day after tomorrow? next week?
Interested in health? Take your temperature orally or in the ear. One reading when you're outside in the heat and another when you're inside an air conditioned space. Is there a difference? What about your temperature when you're sitting in the sun versus sitting in the shade? Do you have one of those forehead temperature readers? Is there a difference in your skin temperature inside? outside? in the sun? in the shade? Doe sitting in the pool lower your body temperature? Will pouring water over your head lower the body temperature? How could these observations apply if you're an athlete working out on the football field or soccer field in this heat?
You may feel more comfortable sitting in front of a fan, but is there a difference in your body temperature just because of the moving air? Take your temperature with and without the fan.
Is there a candy thermometer in the kitchen? How hot will a bowl of water get if you set it in the sun? Will a smaller container get hotter? more quickly? glass versus metal?
Will warm water heat up faster than ice water if identical containers are set out in the sun? Will boiling water cool off at the same rate that warm water heats up if both are put in the sun?
These are teachable moments because even the youngest students are aware of the extreme heat. Whatever the student's age, there are math and science questions that can be related to today's extraordinary weather. What questions can your kids come up with? And how can an answer be found?.....The Teachable Moment for The Normal Genius in each of our kids!!
Showing posts with label arithmetic. Show all posts
Showing posts with label arithmetic. Show all posts
Monday, July 2, 2012
Monday, August 9, 2010
NUMERACY: A FIRST STEP TOWARD PRESCHOOL MATHEMATICS
This is a special article on the blog, just for parents of all those youngsters I met at Northbrook Days and who I hope will become Tutoring Resources students in 8 years or so from now. Usually I’m totally focused on the preteen to adult ages. I like working with kids old enough to question a teacher, even challenge the teacher’s knowledge.
But Math education starts long before Middle School and parents are the first and most influential teachers that every child can have. So here are a few things to do before students get into Preschool.
NUMERACY: This is the internal understanding of numbers. It involves number order, recognition of number symbols, and the one-to-one relationship of counting. Using the Tutoring Resources Math Cards distributed at our booth, select a few of the positive numbers, say 1 through 5 for the youngest kids and up to 10 as a child progresses. Lay them out on the table in numeric order.
Activity #1: (for ages as young as 2) Point to each number in order and say it’s name. Show the child how to point to the letters as you say their names. Ask the child to repeat the numbers after you’ve said them, starting with one at a time and progressing to the whole list at once. Eventually, have the student name the cards without help.
Activity #2: Using the same numbers that have been practiced in Activity #1, ask the child to point out a certain number, first with numbers laid out in order and then with cards randomly spread on the table.
Activity #3: Using manipulatives (navy beans, candy pieces, dots....something large enough that the child can pick it up without much discomfort), demonstrate the concept of each number by laying one item on the #1 card, 2 items on the #2 card, etc. As a second step, put the manipulatives in one central location (like a dish) and demonstrate that each number is the previous number with one more added. Help the child “count” with you, identify the number verbally and pick out the card with that number on it. Evenutally, have the child lay out the right amount of manipulatives to correspond with a random number that you pick from your deck.
Activity #4: Start “counting” stuff.....lots of stuff. Count the number of chairs at the dinner table, the number of plates or forks while setting the table, the number of shoes in daddy’s closet, the number of winter coats in the front hall, the number of toy cars or stuffed animals or Barbie doll dresses. Count, count, count until it becomes “natural to count” 1-2-3... These are the “natural counting numbers” that the student will use in kindergarten and first grade and which are the first group of “Real Numbers” as described in Pre-algebra. Imagine! Your 3 year old is already learning one of the Pre-algebra concepts!!
OTHER RESOURCES: The library has numerous number books with themes that may be stimulating to your child -- animals, characters, etc. There are puzzles that reinforce the shapes of numbers; I just found one at the one-dollar store.
Repetition and exposure are the keys to teaching NUMERACY, the vitally important first step in the understanding and love of math. It is my goal that your child have FUN with numbers and develop a sense of accomplishment and competence that will spur him or her to success in Math class. To receive a packet containing the Tutoring Resources Math Cards, dice, dots, and sample games for first grade through sixth, contact your local Tutoring Resources center in Barrington or Northbrook. Visit the website at
www.tutoring-resources.com for contact information.
But Math education starts long before Middle School and parents are the first and most influential teachers that every child can have. So here are a few things to do before students get into Preschool.
NUMERACY: This is the internal understanding of numbers. It involves number order, recognition of number symbols, and the one-to-one relationship of counting. Using the Tutoring Resources Math Cards distributed at our booth, select a few of the positive numbers, say 1 through 5 for the youngest kids and up to 10 as a child progresses. Lay them out on the table in numeric order.
Activity #1: (for ages as young as 2) Point to each number in order and say it’s name. Show the child how to point to the letters as you say their names. Ask the child to repeat the numbers after you’ve said them, starting with one at a time and progressing to the whole list at once. Eventually, have the student name the cards without help.
Activity #2: Using the same numbers that have been practiced in Activity #1, ask the child to point out a certain number, first with numbers laid out in order and then with cards randomly spread on the table.
Activity #3: Using manipulatives (navy beans, candy pieces, dots....something large enough that the child can pick it up without much discomfort), demonstrate the concept of each number by laying one item on the #1 card, 2 items on the #2 card, etc. As a second step, put the manipulatives in one central location (like a dish) and demonstrate that each number is the previous number with one more added. Help the child “count” with you, identify the number verbally and pick out the card with that number on it. Evenutally, have the child lay out the right amount of manipulatives to correspond with a random number that you pick from your deck.
Activity #4: Start “counting” stuff.....lots of stuff. Count the number of chairs at the dinner table, the number of plates or forks while setting the table, the number of shoes in daddy’s closet, the number of winter coats in the front hall, the number of toy cars or stuffed animals or Barbie doll dresses. Count, count, count until it becomes “natural to count” 1-2-3... These are the “natural counting numbers” that the student will use in kindergarten and first grade and which are the first group of “Real Numbers” as described in Pre-algebra. Imagine! Your 3 year old is already learning one of the Pre-algebra concepts!!
OTHER RESOURCES: The library has numerous number books with themes that may be stimulating to your child -- animals, characters, etc. There are puzzles that reinforce the shapes of numbers; I just found one at the one-dollar store.
Repetition and exposure are the keys to teaching NUMERACY, the vitally important first step in the understanding and love of math. It is my goal that your child have FUN with numbers and develop a sense of accomplishment and competence that will spur him or her to success in Math class. To receive a packet containing the Tutoring Resources Math Cards, dice, dots, and sample games for first grade through sixth, contact your local Tutoring Resources center in Barrington or Northbrook. Visit the website at
www.tutoring-resources.com for contact information.
Sunday, August 8, 2010
GET READY FOR THE NEXT LEVEL OF MATH
With the Fall semester right around the corner, conscientious students are starting to recognize that familiar “butterfly” feeling. What will my classes be like? What will I be expected to learn? to do? to know already?
It’s that last question that you can control. Be prepared to move forward in your next math class by reviewing what you already know. Here’s a handy list of concepts for the most frequently required math classes.
ELEMENTARY ARITHMETIC:
-- Start practicing adding, subtracting, multiplying, and dividing.
-- Practice multiplication tables and number families.
PRE-ALGEBRA:
-- Practice those computation skills so adding, subtracting, multiplying, and dividing are quick and easy for you. This will give you the mental space to learn the first concepts that will take you from arithmetic to mathematics.
ALGEBRA I:
-- Review last year’s work in Pre-Algebra if you still have it.
-- Ask the local library if there is a copy of the Algebra textbook on the shelf. It would probably be a reference copy, so you won’t be able to check it out. Make a photocopy of the Table of Contents and leaf through the first chapter which is frequently a review of past material.
-- Be prepared for these concepts:
COLLECT LIKE TERMS
SOLVE EQUATIONS WITH ONE VARIABLE
PROPERTIES OF REAL NUMBERS (Commutative, Associative, Distributive, Identify, Inverse, Reflexive, Transitive, Substitution)
GEOMETRY:
Do you want the good news first or the bad news? The good news is that there is very little in the average Geometry curriculum that you don’t already know. You’ve been learning a little Geometry every year since Kindergarten, which is the bad news. Some of the concepts you learned maybe 9 years ago and they may be buried under a lot of other stuff that you’ve learned in the interim. Start digging!
-- SHAPES -- square, rectangle, rhombus, parallelogram, trapezoid, circle, triangle. Know how to tell what each shape is (properties) and the equation for finding the area.
-- AREAS -- yes, I know I’ve mentioned that already, but it is a basic concept that causes trouble for many students. Know how to calculate areas and perimeters, too.
-- VOCABULARY -- The names of shapes is an example of vocabulary that you will be expected to already know. Add point-line-plane to the list, as well as diagonal, radius, diameter, arc, area, perimeter, volume (and related equations), Pythagorean Theorem, isosceles, equilateral, equiangular, skew, obtuse, acute, complementary, and supplementary. There may be more terms that you’ve already learned. Can you add to the list?
-- ALGEBRA -- “WHAT? I have to know last year’s Algebra in order to succeed in this year’s Geometry?” Yes. You’ll be asked to solve Geometry problems by using one-variable equations (like area) and systems of equations too. There may even be a few quadratic equations, so review factoring.
The biggest hint for success in your Geometry class is to learn the postulates and theorems well and as they are introduced.
ALGEBRA II:
-- Review your Algebra I notes from 2 years ago. If you haven’t developed the practice of filing notes from each class, resolve NOW to archive old class material now that you see how helpful it can be in future years.
-- Be prepared to factor quadratic equations and FOIL binomials.
-- Review the real number properties that allow you to solve equations.
TRIGONOMETRY:
Triangles are paramount shapes in Trig, so review everything you've learned about them. Pythagorean Theorem will have new applications and SohCahToa with be the basis for learning 3 more side relationships. A little review of circles will be helpful in the first couple of weeks when you're introduced to the Unit Circle.
A huge hint for success in Trig is to learn the Unit Circle when told to do so. You can expect to be tested on it in a stringent, timed format. After enough time to forget what you've memorized, you'll be expected to actually USE the information, so try to find patterns in the angles and the sine, cosine, and tangent values. This strategy will help you access the information in later problems.
PRECALCULUS:
Factoring is a stumbling block for even some high ability students. Practice it until you could "factor in your sleep." Review graphs of second and third degree equations, square roots, absolute value, and rational equations. A quick review of your old Algebra II work can help you to recall concepts you learned previously. Much of Precalc will be an exercise in deeper analysis of these same concepts.
IN GENERAL:
Check out older blogs for more detailed tips for each class.
GOOD LUCK! Not everyone is as excited about the beginning of a new semester as I am, but I know for sure that success in the first few weeks of school can lay the groundwork for a productive course and a good grade. My goal is for YOU to be the first student in the class to answer a question correctly. I want the teacher to go home that night believing that YOU are the best student ever. My experience shows that this can become a self-fulfilling prophesy that can enhance your classroom and exam performance.
It’s that last question that you can control. Be prepared to move forward in your next math class by reviewing what you already know. Here’s a handy list of concepts for the most frequently required math classes.
ELEMENTARY ARITHMETIC:
-- Start practicing adding, subtracting, multiplying, and dividing.
-- Practice multiplication tables and number families.
PRE-ALGEBRA:
-- Practice those computation skills so adding, subtracting, multiplying, and dividing are quick and easy for you. This will give you the mental space to learn the first concepts that will take you from arithmetic to mathematics.
ALGEBRA I:
-- Review last year’s work in Pre-Algebra if you still have it.
-- Ask the local library if there is a copy of the Algebra textbook on the shelf. It would probably be a reference copy, so you won’t be able to check it out. Make a photocopy of the Table of Contents and leaf through the first chapter which is frequently a review of past material.
-- Be prepared for these concepts:
COLLECT LIKE TERMS
SOLVE EQUATIONS WITH ONE VARIABLE
PROPERTIES OF REAL NUMBERS (Commutative, Associative, Distributive, Identify, Inverse, Reflexive, Transitive, Substitution)
GEOMETRY:
Do you want the good news first or the bad news? The good news is that there is very little in the average Geometry curriculum that you don’t already know. You’ve been learning a little Geometry every year since Kindergarten, which is the bad news. Some of the concepts you learned maybe 9 years ago and they may be buried under a lot of other stuff that you’ve learned in the interim. Start digging!
-- SHAPES -- square, rectangle, rhombus, parallelogram, trapezoid, circle, triangle. Know how to tell what each shape is (properties) and the equation for finding the area.
-- AREAS -- yes, I know I’ve mentioned that already, but it is a basic concept that causes trouble for many students. Know how to calculate areas and perimeters, too.
-- VOCABULARY -- The names of shapes is an example of vocabulary that you will be expected to already know. Add point-line-plane to the list, as well as diagonal, radius, diameter, arc, area, perimeter, volume (and related equations), Pythagorean Theorem, isosceles, equilateral, equiangular, skew, obtuse, acute, complementary, and supplementary. There may be more terms that you’ve already learned. Can you add to the list?
-- ALGEBRA -- “WHAT? I have to know last year’s Algebra in order to succeed in this year’s Geometry?” Yes. You’ll be asked to solve Geometry problems by using one-variable equations (like area) and systems of equations too. There may even be a few quadratic equations, so review factoring.
The biggest hint for success in your Geometry class is to learn the postulates and theorems well and as they are introduced.
ALGEBRA II:
-- Review your Algebra I notes from 2 years ago. If you haven’t developed the practice of filing notes from each class, resolve NOW to archive old class material now that you see how helpful it can be in future years.
-- Be prepared to factor quadratic equations and FOIL binomials.
-- Review the real number properties that allow you to solve equations.
TRIGONOMETRY:
Triangles are paramount shapes in Trig, so review everything you've learned about them. Pythagorean Theorem will have new applications and SohCahToa with be the basis for learning 3 more side relationships. A little review of circles will be helpful in the first couple of weeks when you're introduced to the Unit Circle.
A huge hint for success in Trig is to learn the Unit Circle when told to do so. You can expect to be tested on it in a stringent, timed format. After enough time to forget what you've memorized, you'll be expected to actually USE the information, so try to find patterns in the angles and the sine, cosine, and tangent values. This strategy will help you access the information in later problems.
PRECALCULUS:
Factoring is a stumbling block for even some high ability students. Practice it until you could "factor in your sleep." Review graphs of second and third degree equations, square roots, absolute value, and rational equations. A quick review of your old Algebra II work can help you to recall concepts you learned previously. Much of Precalc will be an exercise in deeper analysis of these same concepts.
IN GENERAL:
Check out older blogs for more detailed tips for each class.
GOOD LUCK! Not everyone is as excited about the beginning of a new semester as I am, but I know for sure that success in the first few weeks of school can lay the groundwork for a productive course and a good grade. My goal is for YOU to be the first student in the class to answer a question correctly. I want the teacher to go home that night believing that YOU are the best student ever. My experience shows that this can become a self-fulfilling prophesy that can enhance your classroom and exam performance.
Subscribe to:
Posts (Atom)