Math Mansions Decimals - tenths, hundredths, and thousandths

Math Mansions Episode 22

Maths Mansion is a British educational TV series.  It covers many mathematical concepts.

This videostreaming clip is on decimals (tenths, hundredths and thousandths)

Math Mansions - Decimals tenths and hundredths

Math Mansions Episode 3

Maths Mansion is a British educational TV series.  It covers many mathematical concepts.

This videostreaming clip is on decimals (tenths and hundredths)



Decimal Squares

Our first unit of study is place value and understanding decimals.  Students will be working on this unit over the next few weeks.  There is a great decimal website called www.decimalsquares.com .  This site has interactive games that provide extra practice on the concepts covered in class.  It is a great way for students to practice their skills and expand their decimal knowledge. 

Origami

http://www.origami-instructions.com/origami-flowers.html

Origami is a great hands-on activity that improves students' spatial visualization skills.  There are lots of great sites on the Internet.  This is one we used today in class. 

Internet Resources

http://www.khanacademy.org/math/arithmetic/#negative-numbers

This is a link to the Khan Academy page where students can watch a series of mini-lessons to help them better understand negative numbers.  This is a new skill which I've only begun to teach this week.  At this point, several students are finding it challenging - as I would expect.  I'm sure this will be helpful.

Quite often, after I've taught a math lesson and we practice a new skill together in class, students feel that they "get it."  When they have to do some additional practice independently for homework, they get stuck and there's no one available to answer their questions or to offer some help. 

Khanacademy.org is a wonderful site full of brief video lessons on a wide variety of math topics. Students should explore this site so that when they need it, they can navigate it efficiently. In addition, students can turn to Google in order to find math tutorials. I will demonstrate this for them in class.

As the end of the school year approaches, I'm asking myself what more I need to teach my students before they leave elementary school.  Since I can't possibly teach and review everything that every student will need to know going forward - and ensure that they will remember everything - the single most important thing I need to teach them is how to answer their own math questions. 

Decimals on a Number Line

This is a review skill that I went over in class today.  Students in homeroom 152 have to do this for tonight's homework, so I thought it would be helpful if they had a video to refer to.

April is National Financial Literacy Month

This post isn't directly related to what we're teaching in the red pod this week, but I recently read about an interesting website that I want to pass along.  It's called KidWorth and it enables parents to set up a (non-interest earning) bank account for their child into which their allowance and monetary gifts can be deposited.  Kids can then set goals for saving, charitable giving, or future spending on something they must save up for.  At the same time, they are learning about saving, budgeting, and the rewards of delayed gratification.

I Googled KidWorth reviews and found that several mommy-bloggers endorse this site, but at the bottom of their blog posts they disclose that they are paid for their endorsement, so I looked further and I found the Living in Digital Times blog.  The post entitled Reimagining Kids' Birthday Gifts gives a more objective (and overall positive) review of KidWorth, along with links to other websites that are designed to teach kids money-management skills.  Here's a Wall Street Journal article entitled How I Spent My Allowance about a 10-year-old's experience using a site like KidWorth. 

Since my own kids are grown, I have no firsthand experience with sites like this.  However, my 28-year-old daughter uses a site called Mint.com to keep track of all things financial in her life.  After becoming keenly aware of their spending habits and redirecting that money, she and her husband saved for a downpayment on their first home.  I asked if she wasn't concerned about having all her financial information stored in cyberspace and she responded, "Mom, your information is stored in cyberspace whether you choose to access it there or not." 

So this is the world our children live in, or will live in.  The more cashless our society becomes, the more mindful we need to be about our money. 

Do you use KidWorth or a site like it?  Leave a commnt to share your firsthand experience.

For homeroom 152

Hi Room 152!  For homework this week, I want you to practice multiplying multi-digit numbers.  Here are the directions from the homework board:

Lattice is optional, but please practice the other two methods.  If you forgot to bring your notebook home and don't remember how to do the area model, watch the video in the previous blog.  I'll check in with you in class on Wednesday to see if we can schedule a quiz for Thursday or Friday.  Let me know before then if you need my help.  Remember - On a quiz, you may use whichever method of multiplication you like best.  :)

Multi-digit Multiplication Methods

Last week, students practiced multi-digit multiplication using the traditional method.  Today, Mrs. Banspach brought us her middle school perspective on this topic.  The traditional method is the one most commonly used here at school and at home when students ask their parents for help.  It's great when taking a timed quiz (which our district requires,) and it's efficient when students are working on multi-step word problems.

The second method we looked at today is sometimes referred to as partial products and sometimes it's called the area model.  It's easier to show you this method than to explain it in words, so take a look at the following short video.

We'll continue to practice this next week.  Mrs. Banspach showed us how middle school math teachers use this method when teaching algebra.  They report that students who learned this in elementary school have an easier time understanding the structure of algebraic equations.

Production note:  Thanks to Jake, my cameraman today.  He got it in one take.  :)

More Pi

If the diameter of your bicycle tire is 23 inches, and you move your bike so that the tire makes 3 complete revolutions, about how far have you moved your bike?

definition:  Revolution means one complete turn.

Hint:  d * pi  = c  (d = diameter and c = circumference)

And for fun, try this:

Write 3.14 on a piece of paper and hold it up to a mirror.  (Go light on the decimal point.)  Thanks Daelynn  :)

Fifth Grade Celebrates Pi Day!

Ordinarily, I don't encourage children to play with their food, but working with their food...now that's something else.  Yesterday was Pi Day and 5th graders in the red pod celebrated by measuring the diameter and circumference of their round snacks.  They learned that circumference divided by diameter equals 3.14159... and of course the inverse is also true.  (We learned those fact families in the second grade for a reason.)  Although this was a break from our unit in fractions, Pi Day offered us an opportunity to review decimals and variables within an algebraic equation. 

During the activity, students traced their round snack, then placed a piece of string around that circle and cut it to size.  They measured their string in centimeters in order to do their calculations.  Then, they placed their string across the diameter of their circe and cut it to size.  This yielded 3 pieces of string, and a small piece left over which gave them a visual represenation of 3.14.

Mrs. Banspach, our district math coach, joined us during this celebration and she reminded students that Pi isn't the decimal 3.14159...  Rather, Pi refers to the relationship of a circle's diameter to its circumference. 

I'd like to thank Mrs. Banspach and Mr. Main for all their help and mathematical insights, not just yesterday but always. 

Unit 5

The major focus of Unit 5 is understanding fractions. The website www.visualfractions.com is a great site that allows students to explore their conceptual understanding of fractions. This website is a tutorial that models fractions with circles and number lines. It provides practice with working with fractions and has detailed explanations to help teach many different skills. There are also some games that students can use to check their understanding. Check out this helpful website whose motto is "Fractions are better understood when seen!"

A Visit From Biomes

This is off topic but last Thursday, 5th graders enjoyed a visit from Biomes Marine Biology Center.  This kicks off our next science unit where students will learn about and observe a variety of marine life. Take a look at some of the samples that Shelby (our Biomes presenter) brought to the red pod.

Students were given a free pass to Biomes, which is open to the public.  Visit their website for directions, their hours of operation, and the cost of admission.  They are moving to a new location soon so check on that before going. 

Hope everyone is enjoying the weekend.

Mental Multiplication of Multi-Digit Numbers Ending in Zero

Here's more video of the mental math strategies we're working on this month.  Here, you'll see my helpers putting a box around the zeros so they can focus on the basic fact. I refer to this as putting the zeros in your pocket.  After solving the basic fact, they take the zeros out of their pocket and put them in their answer. 

I apologize that the numbers in the video are a bit difficult to see.  The problems that are being solved are 200 x 40, 500 x 40, 60 x 80, 300 x 800, and 70 x 30.

As I said in the previous post, some students will jot down the numbers in order to give an answer.  With enough practice, some students will be able to look at the problem on a flashcard and give the answer without writing anything down.  Students may use whatever process works for them, in class as well as on quizzs and tests. 

Mental math strategies are tested periodically, but are not timed.

Special thanks to my helpers for demonstrating their math skills on camera.  You know who you are.  :)   

Computational skills in Unit 4 include mentally multiplying 2-digit numbers by 1- digit numbers.  Students begin by taking the 2-digit number and breaking it down into its tens and its ones. 

Watch my helper demonstrate this process.

You may wonder why this is called mental math when you just watched my helper writing numbers down.  The goal is that with enough practice, less and less writing of the numbers will be necessary.  As you saw, some students will eventually be able to arrive at the correct answer without writing anything down.  Some students will only need to jot some of the numbers as they think it through, and other students will continue to write out the entire thought process.  All of these variations on the process are valid and may be used during class work as well as on quizzes and tests. 

Special thanks to my student helper for participating in this video.  (You know who you are.)  Thanks also to everyone at home for taking the time to read this blog.  Stay tuned.  There's more video to come.

Student-Written Word Problems

1.  Aspen had 80 dog toys.  She chewed some of them.  How many toys are left?

    Solution:  (80 - n)                                          written by   T. O.

2.  Andy and some friends bought 20 pieces of bubble gum each.  Each piece of gum costs 5 cents.  How much money was spent in all?
   
    Solution:  (20 * .05) b                                    written by B. B.

3.  Mrs. Schart had 30 math papers.  Her students threw away half of them.  She copied some more.  How many papers does
     she have now?

    Solution:  (30-15) + m                                    written by R. B.

4.  There is 1 Zack.  Ten more Zacks come in and some Zacks leave.  How many Zacks are left?

    Solution:  (1 + 10) - z                                      written by Z. A.

5.  Bob and his brothers went to buy a bag of chips each.  Each bag costs $3.00.  How much money did they spend?

    Solution:  (1 + w)3                                          written by T. N.

6.  Four people went to the store.  Each bought a bag of apples.  There are p apples in each bag.  How many apples in all?

    Solution:  4p                                                    written by K. W.

My thanks to all the students who shared their work in front of the class today.  Well done!

Unit 4

Happy New Year everyone!  We've settled back into our routine here at school and have begun Unit 4.  It breaks down like this:

Review Skills

• Coordinate graphing (like playing the game Battleship)
• Divisibility - This was introduced in Unit 1 and students have a list of divisibility rules in their math folder.  They may refer to it as needed.  This skill will be helpful and important when we study fractions.

Computational Skills

• Long division with remainders
• Mental math strategies using multiplication and division

New Material

• Division word problems where students must interpret the remainders 
• Algebraic word problems
• The commutative property of addition (a + b = b + a) and multiplication (a x b = b x a)

Here is a sample of a problem where students must interpret the remainder:

There are 123 guests attending a wedding.  They will be seated 10 to a table.  How many tables are needed?
Solution: 123/10 = 12 r 3    There will be 12 full tables and 3 people without a seat.  13 tables will be needed.


A basic algebraic problem looks something like this:

Kevin has 10 marbles in his collection.  He wins some more marbles during a game at recess.  When he goes home that afternoon, he gives 5 of his marbles to his younger brother.  Write an expression to show how many marbles Kevin has now.
Solution:  (10 + m) -5

The trickiest thing for students to understand is that the algebraic expression is their answer.  The word problem doesn't provide enough information to lead them to a final numerical answer.  As we progress through this unit, sometimes students will be given a value for the variable such as If m=7, how many marbles does Kevin have now?

We will practice this extensively in class and eventually, students will be ready to tackle more complex word problems.  They will also think this through in reverse by taking an algebraic expression and writing a word problem that fits it.

As always, if students find this material difficult and so are unable to complete homework, we trust that they will do their best to find something there (no matter how small) that they can attempt.  Each day, we will go over the previous night's homework aloud and answer questions.  Students may then complete the work as we are discussing it, or ask to see something they struggled with done on the board.  Our cooperative groups earn bonus points when someone is brave enough to raise their hand and ask a question or ask for help understanding something in class.