Writing in Math Class

These past few weeks, students in Division 5 have continued to develop their understanding of multiplication and division through hands-on activities, problem solving, playing games, and last week through reading and writing.

Over the course of the week, we watched One Hundred Hungry Ants, written by Elinor J. Pinces on YouTube...

And then I read aloud A Remainder of One, also written by Elinor J. Pinces.

We did a hands on problem solving task.   The students were asked to demonstrate all the ways 36 ants could march in equal groups.  The sequins were added for a little fun - although some of my mathematicians chose to use markers as they could show their thinking quicker!

After reading the Remainder of One together, we talked through all of the scenarios presented and added mathematical symbols/equations to each page with sticky notes.  Next, I asked the students if they could create their own mathematical stories.   Below are some examples of a few...

I think what I love best about open ended activities like this one, is how they allow for diversity.   Some children wrote about division stories that worked out evenly, others had remainders and one went beyond the task to discuss prime numbers (see the last two pictures).  This led to the student and I entering into a discussion about the properties of prime and composite numbers.  I wondered how he chose this number and when asked he replied "that he chose the number from our class number line".  Running across the front of the classroom is a number line with numbers from 1- 100.  Above most of the numbers are coloured circlular dot stickers (a Kim Sutton resource) that show multiples of numbers and as my friend discovered, factors too!

Making teams

Hello Division 5 students,

Once again I need your help!   Matthew's birthday party is fast approaching.   We sent out 12 invitations and all 12 friends have confirmed that they are able to attend the party.   Matthew would like to arrange for a hockey game and needs to make 2 teams.  

Some notes:
- Matthew also wants to play on a team.
- Scott will be the refereee and I cannot play as I will be busy making lunch and taking pictures.
- Megan will not be playing as she plans to go to a friends house.

How many players will each team have?   Please do NOT just give me an answer.   I LOVE to know how you arrived at your answer... what did you do?  Why?

Thanks for helping me out,

Mrs. Barker

I have a question for you!

Hello Division 5 students,

I am beginning to plan my son's Matthew's birthday party.   He is inviting 12 children to his party and I need to figure out how many pizzas I need to order.   A large pizza has 8 slices.   I would like to buy enough large pizzas so that each child can have 3 slices.   How many pizzas do I need to order to have enough slices for all the children?

Can you help me?   Please write your answers in the comment section.

Thanks for your help,   Mrs. Barker :)

Hershey's Chocolates = Multiplication FUN

Last week I told the children that the Hershey's President was interested in having students help him with figuring out how to package his chocolates.   Instantly after mentioning the word "chocolate" the students were completely engaged.

I began by reading the Hershey's Milk Chocolate Multiplication Book and followed this up with a Marilyn Burns lesson that I finessed to meet the needs of Division 5.


Next, each student was given four 1 x 1 cm brown squares.   They were to pretend that each square represented an individual chocolate.   I asked the students to explore how many different ways they could package their chocolates.   Since we have already learned about 2-D shapes, the students understood when I told them that they could only make regular shaped polygons, such as a square or rectangle.

Quickly the students were volunteering their answers...

It could be a 1 x 4 - which lead me to explaining that this was called an array.  I always remind the students that when we are doing mathematics, we speak the language of mathematicians.   We added the word "array" to our Math Word Wall.

Another student then offered that the chocolates could also be packaged as 2 x 2.

Then we had a real "ah-ha" moment when a student asked whether or not a 4 x 1 array would count as a third option, or was it the same as a 1 x 4.

Instead of answering this student, I asked the class if anyone had any thoughts.   Someone suggested that since this shape was "congruent" (YES, that was the term used - I did a happy dance!) that it would not count as a third option.

Another student put his fist up in the hang-loose hand signal (which I have used with a clicking sound to teach the commutative principle) and told us that it was true for addition and multiplication.   Then together the whole class did the hang-loose motion together.   The commutative principle, simply put, states that any factors in a multiplication statement can be switched place, and the product (answer) will remain the same.

Following the class example, the students were put into cooperative groups and given 6, 12, 18, 24, and  36 squares of pretend chocolates and challenged to discover how many different ways they could be packaged.  The students were very creative in explaining why they felt the 'President' should chose one array over another.   We concluded the lesson eating mini-Hershey's chocolate 2-square bars!

At the suggestion of my class, I have sent an email to the Hershey's Company detailing this lesson and how much fun the students had.   I think they are hoping for some free samples! ~ as am I.

Classroom Easter Egg Fun

Thursday Division 5 spent doing "Egg-sellent" activities!   Together the students worked cooperatively in groups to discover how to determine whether an egg was hard-boiled or not.

Smelling

Spinning/Observing

Shaking/Listening

Next, we took our eggs outside and played with the strength of an oval.   I instructed the students to use one hand only, and squeeze the egg as hard as they could ~ but they had to apply equal pressure all around (example: don't just press hard with your thumb).   The students were shocked that they could not break the eggs, as we all know eggshells are pretty fragile little things.   But when you squeeze an egg in your hand (all rings must be off), its' strength is amazing.   The strength of an egg lies in its shape.   If you took a sharp object to the side of an egg, it puts pressure on the thin shell and easily breaks it.  But squeezing it directs pressure into the egg, so that it compresses along, not across the shell.

In our structures unit last term, we learned that architects and engineers have used smooth curves, known as arches, to support the weight of structures for centuries.   An arch directs pressure so that it compresses (squeezes) the building material.  An egg is really and amazing piece of natural engineering.

We ended the day, celebrating Easter with jellybeans.   I decided to let the students demonstrate their understanding of a "fair share" or "fractions of a group".  I gave each small group a handful of jellybeans and asked them to figure out how to share them equally amongst each other.   When the task was completed we discussed how the lesson was related to both fractions and division.  Math with food is always full of enthusiasm!

The Doorbell Rang

Last week I read Pat Hutchins book The Doorbell Rang to my class.   The students enjoyed figuring out the mental math in their heads.   It is a story about a mother who makes twelve cookies and asks her children to share them fairly.   After figuring out how many each child will get, the doorbells rings and more kiddies arrive.   As the number of children grows, the students need to re-think how the cookies can be distributed fairly.  The pattern continues throughout the book until their are 12 kids and 12 cookies and then the doorbell rings... and it is Granny bringing more cookies.

Then I taught another wonderful lesson from Marilyn Burns... (although the worksheets were self created).  I explained to the students that they were going to need to work cooperatively in groups to share paper cookies.   We talked about what cooperation looks like and sounds like.   I had 4 groups of four students and 1 group of six students.  

Once the students solved the problem of sharing a specific number of cookies, they brought me their evidence (the worksheet with cut up cookies shared equally) and I would assign them a new challenge to share a different number of cookies.

In the second block of the lesson we met back together as a class and the students shared their answers.  What was wonderful was the connection the students made to equivalent fractions.   Through looking at the multiple ways the students divided up the cookies we could see visually and symbolically equivalent fractions!

The Four Triangle Problem

Last week my students worked hard to solve a Marilyn Burns (a highly respected Mathematical Educator)  lesson called The Four Triangle Problem.

In groups, the students had to find all the possible arrangements using four triangles, two of each colour, and tape together the four-triangle shapes they made.   In each arrangement, each triangle must touch the side of at least one other triangle and follow the rule that the sides that touch must be the same length and match exactly.

In my many years of teaching, no one group has ever discovered all 14 non-congruent shapes... that is, until this year.   One groups did discover all 14 shapes.

Many of you know I love math but this lesson is one of my favourites.   It elicits mathematical language and introduces regular and irregular polygons.   As well, students learn the term "congruent" when they see that shapes that can be flipped or rotated to fit exactly onto another shape are actually the same shape or in mathematical language, "congruent".

After the students have had a full block to make the shapes, I ask the groups to volunteer to bring up the shapes.   I glue them onto a blank piece of chart paper.   As I glue them I am classifying the shapes but do not share my sorting rule with the class until the end of the lesson.   Usually at that point one of the students has caught onto to what I am doing and volunteers to tell the class.   The above chart was the one the students constructed this year.

Structures

Fridays can sometimes be a hard day to keep students motivated.   Often they are tired from the busy week and excited for the weekend, which can lead to a lot of chatter.   So these are the days I like to plan hands-on, collaborative activities.

I have been following the Schwakida School Of Thought blog (excellent place for ideas - see the link on the side) and THIS post from December caught my eye and since we are studying structures, I decided to give it a try.

I challenged the students to either work in a groups of 2 or 3 or by themselves, if they preferred, to create the tallest structure using only cards, straws, and paper clips.

This open ended activity drew upon their knowledge of structures, imagination, and problem solving skills.   It took a long time for some groups to develop a plan.   Many groups experienced frustration as their structures sometimes fell over.   Overall, it was a great exercise that encouraged the students to "Think Outside The Box", as the Schwakida team proposes.