Brain Break: Sudoku and KenKen Puzzles

We have been working SO hard to finish third quarter in Math Workshop.  With CGA 3 behind us and FCAT ahead, who needs a little brain break?  In December, I taught the students how to do Sudoku puzzles (we started with "light and easy" 4x4 puzzles).  These puzzles are excellent for developing logic skills, which are essential for critical thinking in problem solving (and they are fun!).

Light and Easy 4x4 Sukoku puzzle

 

Traditional 9x9 Sudoku puzzle

These addictive puzzles are great for rainy days and long rides!

This weekend, I discovered KenKen puzzles, which are related to Sudoku puzzles.   

Today I showed the students how these puzzles work.  There are also free KenKen apps (I use Ken Ken II).

As a math teacher, KenKen puzzles interest me because they are a fun way to practice basic fact operations.  Be forewarned, they are very addictive (there's a timer you can turn on or off), especially if you are competitive like me!  My best time on a 3x3 KenKen puzzle was 14 seconds.  Can you beat my time?  :-)

Area & A Mathematical Milestone

This week, we started our first geometry unit, Area.

We've learned that area is the number of units needed to cover a shape.  Since square units are easiest to cover most shapes and count,  we usually use these to measure a shape's area.

Today we broke out the GeoBoards and learned how to use them as tools for modeling area and other two-dimensional shapes.

(First, we had 5 minutes to "explore" our new tools, be creative, and use them as toys.  Naturally, this lead to a nice review/discussion about symmetry!)

Next, we made a grid on the GeoBoards and found out each board has an area of 16 square units.

From their work with arrays in third and fourth grades, the students have realized they don't need to count squares for rectangles one by one. (Yes, a square is a rectangle!)  Instead, we can multiply the dimensions (number of rows times number of squares in each row).  Knowing this, the students learned their first mathematical formula:

Area of a rectangle = Length x Width

Then we practiced making shapes with a given area--2 square units, 3 square units, and 6 square units.

Some students remembered from third/fourth grade fractions that two triangles are equivalent to one square unit of area and used them in their designs.

I don't even think some of the students realized it was raining outside and recess time.  :-)

Math & Science

I love it when what we're studying in math and science overlap!  In math, we recently finished our unit on fractions and decimals, which included some time learning about percents.  Our students came up with some great examples of where they have seen percents--shopping (sales and sales tax), clothing (50% cotton), and food (2% milk, 100% juice).

In science, we've been studying minerals, and a few of our students brought up taking vitamins, which often contain minerals too.  What exactly is the difference between a vitamin and a mineral?  We've learned that minerals are formed in the earth and are non-living (have never been alive).  Vitamins, on the other hand, are produced by living things.  (Thanks, students, for challenging me to research this.  I learned something new too!  :-))  This being said, minerals such as calcium, potassium, iron, and zinc are extremely important for our bodies to grow, develop, and repair themselves.  Our bodies absorb minerals better from whole, natural foods than supplements such as vitamins (plus eating good, nutritious foods satisfies hunger and can be an enjoyable experience!)  Here is an article our students might enjoy to learn more about the importance of eating minerals every day.

 

 

 

All of these foods come from living things, but contain minerals, which are non-living and produced in the earth.  How do you think that happens?

It's Beginning to Look a Lot Like...

Both classes joined together for our Holiday Party on Tuesday.  We started the morning making a healthy holiday snack and decorating (brown paper grocery bag/yarn) stockings while watching The Polar Express.

Snowmen on a (Skewer) Stick

Then we spent some time working on loom knitting projects.

After that, Ms. Kirkham read aloud The Night Before Christmas Left Right Passing Game for our $1 gift exchange.

 

While this took place, our wonderful volunteers set up for lunch in the classroom.  We had clementines, cheese sticks, crock pot hotdogs, baby carrots, chips, Capri Suns, and a treat.

Several older siblings,

parents,

and grandparents

were able to join us for lunch!

After lunch, we split into two teams.  Everyone crumbled up six pieces of paper from the recycle bin, 

and we went over the rules for our Florida Snowball Fight on the tennis courts:

• Stay in the boundaries (outer white line) of your team's side of the court at all times.
• If snowballs go out of boundaries and you can reach them without stepping over the line, you may get them.  Otherwise, your teachers will throw them back in.  If you step out of boundaries, you sit out a round.
• Keep your hands off the net.  If you touch the net, you sit out a round.
• Your goal is to keep as many snowballs as possible off your team's side, so don't waste time trying to aim at specific people.
• There are three rounds, five minutes each round.  When the whistle blows, freeze.  Your teachers will make an official count of how many snowballs are on each side and declare a winner for the round.
• At the end, there will be a bonus (clean up) round to see which team can pile up the most snowballs on their side.

We wrapped up a fun day with a cute snowman craft (using Mentos gum containers and colorful socks) similar to these

discovered our stockings had been stuffed with goodies, participated in Minute to Win It mini marshmallow challenges,

and learned to play the card game Spoons.

Yesterday, in Math Workshop, we did several activities to help us develop logic, which helps us to be better mathematicians/problem solvers:

• Brain Teasers/Logic Problems
• Sudoku Puzzles
• 12 Days of Christmas Tangram Puzzles

Happy Holidays from Team Kirkham-Remley!

We hope our students enjoyed the s'mores trail mix we made yesterday and look forward to spending s'more time with everyone in 2014!

Celebrating (Winter in) Florida

Anyone else feel like songs about snow are out of place here on a day that was nearly 80 degrees?  Today Ms. Kirkham read

to introduce our Florida Christmas Tree holiday project.  Your student is bringing home a letter with more details today, so make sure you see it.

Ornaments are due Tuesday, December 10.  We can't wait to see our students' creations!

Fractions: Area Models

Over the past two weeks, we've been reviewing how fractions can represent part of a whole.

We've been representing unit fractions (fractions with a numerator of 1) and benchmark fractions (commonly used/familiar fractions such as 1/2, 1/4, 3/4) using 4x6 arrays as an area model.

In class, we've been looking at these models and having discussions to prove whether or not they are the fraction we're looking for (ex: 1/3 or NOT 1/3?).  Often, students think fractions have to "look" a certain way, but we've seen that fractions can be the same size (area), but different shapes.  Some students are even starting to make connections to division/multiplication as inverse to help them decide a fraction's area.  We'll continue to build on this strategy after Thanksgiving Break as we investigate fractions of sets and whether or not a fraction of one whole (or set) is always the same size as the fraction of another whole (or set).

If you've ever been asked to share something with a sibling (or friend), then you know how important it is to be able to compare fractions!

This year, I've shared a few stories about my brother, Andrew, and myself when we were kids.  Like most siblings, we argued, occasionally got in trouble together, and tried to trick each other.

(Coincidentally, my brother picture-mailed me this recently.  Notice how he chose to send a cute picture of himself and his big brown eyes that always make our mom, who also has brown eyes and is the youngest child like he is,  forget all about whatever he did and a picture of me on the verge of a tattle!)

Keeping peace in families and friendships...just one reason why being able to compare fractions is important in real life outside of school!

Multi-Digit Multiplication Strategy: Expanded Form Algorithm

Today I introduced our first multiplication algorithm.  Using an algorithm to perform a math operation simply means that so long as you follow certain steps correctly, the right answer will always result.  When using algorithms for some operations (subtraction, division), the order of the steps that are followed matters.  However, when adding and multiplying, the order of combining numbers does not affect the final answer (Commutative Property).  One of our students, Nick, proved this today when he "accidentally" found the the partial products in a different order than I modeled, but still came up with the same final product.  I chose to model the same order as the traditional multiplication algorithm, for the sake of easing the transition into using it.  That's one great thing about how different math instruction is these days--students going beyond a "one size fits all" strategy and truly understanding what they're doing and why it works.

The expanded form algorithm is closely related to last week's strategy, Partial Products.  Since our students were very successful last week with breaking apart both factors by place value and finding partial products, this week I've given our students the choice to use (or choose not to use) an array to model what's happening.

This week, we started writing problems vertically to prepare for using the traditional multiplication algorithm.  It's VERY IMPORTANT to make sure the digits are neatly-written, straight above each other (just like when adding and subtracting vertically, you might get the wrong answer if your digits aren't properly lined up, starting with the ones place).

I used color-coding to familiarize students with the order of the traditional multiplication algorithm:

First, find the ones place of the second factor (1).
Find the ones place of the first factor (4).
Find the partial product (1 x 4 = 4); record under problem.

Second, look back at the ones place of the second factor (1).
Find the tens place of the first factor (3). (It's very important for your student recognize and verbalize that this is not just 3, but 3 tens, or 30!)
Find the partial product (1 x 30 = 30); record under problem.

Third, find the tens place of the second factor (5, remember this is 5 tens, or 50!).
Look back at the ones place of the first factor (4).
Find the partial product (50 x 4 = 200); record under problem.

Last, find the tens place of the second factor (5, remember this is 5 tens, or 50!).
Look back at the tens place of the first factor (3, remember this is 3 tens, or 30!).
Find the partial product (50 x 30 = 1500); record under problem.

Are your partial products neatly lined up by place value?  Now combine the partial products by adding!  Draw a box around your final product.  Students may also use a calculator to check their final products.  In class, we indicate this by putting a check mark next to the final product after confirming this is the correct answer using a calculator.

I'm also making color-coding optional on Home Learning.  For many visual learners, this will help them see and remember the steps.  I also used to color to help students understand what they're doing (combining the red parts of a factor with the yellow parts of another factor to make the orange parts, the partial products.  I did the same having students combine the red parts of a factor and blue parts of another factor to make the purple parts, partial products). 

Verbalizing the steps using expanded form (telling the value of each digit) and using color as a visual will help the students develop greater number sense, which is the foundation for all math!

This will also lead to a much deeper understanding of the traditional multiplication algorithm.