This week: math

Decide whether you agree or disagree with these statements:

6 is the hardest number to throw on a dice.
A game is fair if you play it properly.

It's easier to get heads than tails when you flip a coin. If you buy lots of raffle tickets, you're sure to win a prize.

Discussion about these statements started our unit about probability.

Then we proceeded to test three of the situations. We learned about theoretical and experimental probability. We discovered how fractions help us to show the likelihood of something happening. We practiced recording our results with tally marks and presenting the final information on simple graphs.

 

To see whether lots of raffle tickets help you to win we put different colored cubes in a paper bag. More than half of the cubes were purple. There was one black cube. We tried several times. Black came out once even though it had the smallest chance. Purple came out only twice even though it had the largest chance. We figured that even if you buy almost all of the raffle tickets and have a big chance to win, it may not happen.

When flipping a coin there is 1/2 of a chance to get a head and 1/2 of a chance to get a tail. We tried. Above you can see the results of experiments by two different students.

When experimenting with one die the chance of getting any number is 1 out of 6. Results of two experiments are visible above.

When we started a racing game (roll two dice and the sum will move the horse) the students were sure it was a fair game and each number had the same chance to win. When they had rolled few times, several discovered that number one has no chance because it is impossible to roll one with two dice. Even when they finished they still thought that the other numbers had an equal chance to win. Only after they had looked for all the different ways to combine the dice, they discovered that there were 36 combinations and 7 came up the most, meaning that the horse number 7 had the biggest chance to win. Did it win? No.

Fraction - fun or fright

For the past two weeks we have been playing with fractions.  Fractions can be a lot of fun when you get to play with materials and you feel you master them. For some fractions may look frightening. Fraction concept is probably one of the hardest ones to truly understand. Even though children see pizzas and cookies shared, and are able to find a half or a quarter of a rectangle already in reception, the full understanding of part-whole-relationship idea, and what the numbers in written form of a fraction mean, may stay hazy for years. I am a firm believer in strong foundations, therefore I'd rather spend longer time building the conceptual understanding than quickly introducing new terms and galloping through curriculum. We use lots of hands-on materials in class instead of memorizing procedures and formulas. One of the assessments showed that the pie model is the easiest to understand. The set model is the hardest. This week we spent time finding fractions of a line and a set and finding the whole when only a fraction was given.

The two important ideas to understand:
A whole can be shared in fair shares - that is the fractional part and can be named.
The parts can be counted.
 
For example:

This is a whole. It has six fair shares. We can call them sixths. We can count the sixths.

This is one sixth

This is four sixths

This is ten sixths

Or

This is a whole. It has four fair shares. We can call them fourths or quarters. We can count the fourths.

This is one fourth.

This is three fourths

This is ten fourths

Making it even trickier is to figure out the whole when fractional parts are shown.


For example:

If this is four sixths then...

..... this fractional part is a sixth and ....

...we need six sixths to make the whole

or

If this is four thirds then....

...the fractional part is called a third and...

.... we need three thirds to make the whole

It is always easier to find a fraction when the whole is known. Only when the concept of fraction is firmly in place is it possible to find the whole when the fraction is given.






As I said earlier, the more practice there is with models the stronger the concept becomes.

Measuring excitement

Math is exciting! The students had a blast using different scales to measure objects in classroom. With each lesson they got a bit better at estimating and then accurately measuring mass of objects. 

Measuring continued

We will continue with measuring this week.

Today's lesson included some review of measuring perimeter and area.

The new concept from today was: Volume.

We measured the volume of some boxes. We looked how even when the volume of the shape remains, the units affect the answer.

Using inch cubes we measured the length 9 inches, the width 5 inches and the height 6 inches and got the volume of 4x9x6=270 cube inches.

Then we took centimeter cubes and measured length 17 centimeters, width 10 centimeters and height 11 centimeters, and got volume 17x10x11=1870 cube centimeters.

The students wanted to check whether this was true and filled the box with centimeter cubes. The box fit 1 thousands block, 8 hundred flats and 7 ten sticks = 1870 centimeter cubes altogether. Yay!

Then we looked at some smaller shapes and figured out their volume by counting. Can you say how many cubic units in this shape?

This week: in the words of the students

In the world of math, area has taken over our math unit. Since Monday our carpet has been covered in squares. Everyone has been enthusiastic in this unit. We have all understood and learned a lot.

Poetry has been ruling  over our writing/reading unit. After reading tons of poetry books we have tons of poetry knowledge. Jack Prelutsky, Shel Silverstein and Judith Viorst are poets. Poets use interesting words. They think and carefully use words to make fantabulastic poems. Whenever we read them, some of us feel like writing them when we grow up, and it gives us inner happiness.

In the wonderful world of UOI we have learned, about inventions. Since our topic is Technology and Inventions. We have learned that inventing is a process. You might fail a few times but it wil maybe turn into a invention.

Measuring perimeter and area

Estimate and measure - has been our motto in Math lessons this week. We have measured length of lines, and perimeter and area of simple rectangles. When you peek into our classroom, you will see several large rectangles made from masking tape on our floor. It has been a pleasure to see kids working together to measure the different squares and rectangles.

In addition to this we have continued practicing multiplication facts. The students have various strategies for finding the answers. Now we aim to achieve automaticity of recalling the basic facts. It means it should not take any more than three seconds to tell the answer.

This week: in the words of the students

 This is what the students say about learning this week:


Assessment:

This week we had our three MAP tests. First we had reading, then we had math, then language. When we have our MAP tests we have to sit quietly and take our time. When we are done, we raise our hand and the teacher takes our score, then we take our books and read until everyone has finished. The MAP tests make your brain ache. The challenge on a MAP test is that it asks you questions you haven't learned because the test doesn't know you. The test helps teachers to know how good you are, and how easy or hard things to give you.

We write reflections for the portfolio. Writing reflections is challenging because some things you have to write about are difficult like: who are you as a reader and why do you like to read...

There is not only one answer. Writing reflections makes you think harder. It is good because it helps you tell parents what you are good about. It's good for us, so we can see what we are capable of.

UOI:

Inside UOI we are making projects. Some people have partners and some people don't. Since our topic is energy, we picked a form of energy, so now we are working on the texts When we are done, we will share it with the lower school.

Reading:

This week  Ms.Terje  is reading The Tale of Despereaux for  snack/read aloud and we do work, like for example we tell the feelings of the main character. We learn how to write about reading. We think along when the teacher reads. You get to listen to a story.  This story is about bravery, about being different, and it tells you how some might feel when you treat them badly because they are different.

In independent reading people choose what they want to read, and read.

Independent reading

In Literature Circles we discuss about a book. The main idea is to be cooperative, work with a team. You need notes to make a good discussion, so you remember your ideas.

Math:

In math we learn to multiply. We practice on paper or apps on iPad. The important thing with practicing times table is that when you practice a lot, it will be in your head. Learning is about practicing and being enthusiastic.

We love the doubles!

This week we learn different strategies that help us to remember multiplication facts.

We use patterns and connections whenever possible.

Last Friday we looked at multiplying with one and zero:

This week we started with doubles. If you know doubles, you know many more facts.

Yesterday we built towers of 2-s, 4-s and 8-s

 two times three is double three- double three is six
four times three is double that - double six is twelve
eight times thee is double of four times three - double twelve is twenty-four

Anything two times means to double the number

Anything four times means to double the double 

Today we used the same double to connect to three times facts

3X6, 

Think: double six is twelve, six more is eighteen

If you know your doubles and three times table, you can use it to find six times a number, because six is double three.

Three times six is eighteen, double eighteen is thirty-six

We can't go without fun in a lesson, so we finished the lesson with a game:

Roll two dice and show thier product as an area model. Fill as much of the gameboard as you can. 

The one who covers more area is the winner.

Beauty and patterns of multiplication

Take a look at this Stephen Von Worley's animated visualization of numbers.

Factorization on higher level is not third grade math, but the beauty and patterns of this animation made a perfect hook for a math lesson inquiring into patterns, models and vocabulary of multiplication. It also allows extension into primes and composites for students ready for challenges.

I showed the animation from my I-Pad. "Look" and "Wow" and "Cool" cheered with bright eyes made me smile. After watching numbers all the way to 300 (the animation seems to continue forever) the students worked in groups with different numbers to design their own patterns, realizing that some numbers can be arranged only in one way and some others in more than one way.

Can you guess what numbers are represented?

Concepts and memorizing facts

I know that many students in the class already know multiplication facts. Knowing the facts is important and useful. Knowing the concepts is vital for further learning.

This Monday I asked the students to model what multiplication means. We have modeled addition and subtraction earlier. I asked them to use colored pencils to draw models of what they know.

Majority of the papers looked colorful like this:

There is clear evidence of knowing multiplication facts. These however are not models.

The next math lesson I modeled various multiplication problems. The students had to find what each model represented and figure out what types of models ( not materials) there were.

After this lesson the students began creating pictures like these:

Knowing these different models and meaning of multiplication will help the students later when they learn multiplication of larger numbers or division.

Practice makes perfect

Even though dance has filled most of our days, we made sure we were still working toward our goal to master multi-digit subtraction. Every day the students solved some problems, thinking through whether they needed or didn't need to regroup when subtracting. As soon as they had done their problems, they checked their answers and figured out why they had made a mistake. Was it because they still didn't exactly understand how to subtract or did they make a careless computation error. 

The students are at different levels.

Some still need the blocks to help them understand what they are doing.

Some can talk the problems through and mark the changes that happen after regrouping.

Some can figure answers out without marking the changes, but need more practice to avoid careless mistakes.

On Friday I gave a small quiz (similar to the one I gave on Monday) to see how the students learning had grown and whether they had achieved the goal.

The Friday usual and unusual

On every Friday we have a wordstudy test, a mental math test, and Five Minute Friday writing. This week's word was "Dog." This word was chosen by one student. In mental math students have 3 minute basic fact test and multi-digit untimed test on a computer.

This Friday was unusual because after the students were gone, our classroom hosted 23 Estonian teachers from Estonian Reading Association. Ms. Sirje and I talked about our school's reading and writing programme. I am very thankful to the students who had helped me to clean and organize the room. Working together and with a bit of music the job was done fast and joyfully. It may happen that Ms. Sirje and I will use grade 3 classroom for some reading workshops in spring.

Math/Dance/Music

When I was gathering ideas and resources for our UOI "Dance" I found a very interesting website called Math in Your Feet. On the very first page I viewed two videos of workshops where dance and math are combined. Oh, how I wished to invite Malke Rosenfeld, the workshop leader, to my class. Unfortunately she was too far from Estonia. Using her videos as inspiration, we still decided to try out the idea of combining dance and math.

First we looked at the vocabulary.

The first assignment was to create 4 beat pattern and to dance it in unison with a partner.

congruent (danced in unison)

Not in unison/ not congruent

The second assignment was to create a four beat pattern and dance it in reflection.

The third assignment was to create a 8 beat pattern with reflection and perform it to others.

first part of one 8 beat pattern

Ms. Rosenfeld has created a list of criteria to determine success.

Students thought of steps, created a pattern, practiced it, analyzed it, changed if necessary, and practiced some more.
On the fourth day we showed our patterns to our music teacher Ms. Karolina.

You can try these assignments. I was a partner to one student. Coming up with the steps was probably the easiest part, to get to the dance into unison and then reflect it. That took practice. Try. You can let your child teach you.

Today the students used some of the patterns in thinking about the dance we plan to create as a class performance.
 

Project: Let's Dance

Goal:

·      With a group create a dance.

Role:

·      Find some inspiration for your dance eg. a piece of music, a rhythm, a picture, a story etc.

·      The dance must be accompanied by something eg. music, narrative, poem, rhythm, percussion instrument etc.

·      Choreograph the dance

·      Perform the dance for assessment

Audience:

·      Perform your dance for your peers and parents.

Situation:

·      Use the things you have seen, heard and thought about during the unit about dance to help you to choreograph your dance.

Product:

·      The dance should be at least 1.5 minutes long if you are working alone or 2 minutes long if you working in a group.

·      The dance should not be longer than 5 minutes .

·      You need to think about what you will wear for your dance.  Your costume does not need to be fancy or made especially for the performance but think about what you might wear in order to illustrate your/the groups thinking during the creating process.