Fool me twice, shame on me

I made the mistake of looking at a visual pattern number talk and thinking that I knew the ways that students would see it.  Yesterday we did a number talk with the following visual pattern:

    

I made the mistake of thinking that they would all simply see it as the pattern just adds an additional column of three red blocks.  Boy was I wrong.  The Lab Class students came up with all kinds of different and creative ways that they saw the pattern growing.  

One student saw it like a movie theater with the front (blue blocks) being the handicapped section and the rest as rows of seats that were growing.  Another student saw it as a growing family.  There was also the "Frozen" method that say it as ice crystals coming up from the ground like the movie Frozen.  We had another Tetris method (like in the WIM activity).  There was the building method where the blue section would be completed and turn red. Then another blue section would be built and completed and so on.  And one student actually saw it in a diagonal pattern (pictured below). 

Then on the next day, I gave them a problem from a new website that was shared with my called Which One Doesn't Belong.  The site give numbers, shapes, and graphs & equations in groups of fours.  Students are to choose which one doesn't belong and tell why.  I used the following problem:

This time I was sure that I knew what the class would come up with.  I chose this one because I wanted to do a quick number talk.  Ha!  Once again the students were incredibly creative with their thinking.  

I saw that there was only one even number and only one number that was a single digit.  I figured those were the two answers that all students would come up with.  I personally felt that 43 would was the "right" answer because it's the only one that not a square.  If figured a couple students would come up with that as well.  

The first answer that was shared was that was that 9 didn't belong because it was a single digit.  Ok.  But then students amazed me.  They said that 43 didn't belong because its tens didn't follow the pattern (0, 1, 2...).  Nice!  Then 43 was given but because it wasn't part of the family of 25-16=9 or 16+9=25.  Great!  There was also the answer that 9 didn't below because the sum of its digits isn't 7.  Excellent!

I will never underestimate what students can come up with in a number talk (or anywhere for that matter) again.

Student-Centered Centers

Today in the Lab Class we tried doing student-centered stations (or centers) where students rotated around the room doing various activities.  One station had students working independently on a Gooru collection on brain science.  Students looks at the various parts of the brain and what they do, how the brain works as it relates to learning, and at how having a growth mindset can improve your learning.

At another station students created a ThingLink using a picture of themselves where they added tags to pictures of themselves to show what they learned about their brains and how they learn.  They first took pictures of themselves on their netbooks and then added information to the images with ThingLink.  This became known as the "selfie station".

The final station had the students playing the Factor Game.  Player A chooses a number (1-30) and Player B circles all of its factors.  Then vice versa.  The game continues until all of the numbers are circled.  The players score points for the value of each number circled.  A lot of strategy is involved and it's a great way to practice with factors.  Students were highly engaged and having fun while learning...what a great idea!

Number Talk, Talk, Talk

An activity we did this week in the Lab Class was representative of the shift that we're making in our classroom.  We did a number talk where students were asked to come up with all of the different ways that they could represent 3 within a given time period.  They first worked individually and then in groups.  In their groups they were to share what they came up with, and then decide on one that they thought no other group would have come up with.  They all came up with unique answers, but for the most part used fairly traditional equations.  We challenged them to try to come up with some more creative answers as a part of their homework.

They all came in with their new, more creative answers.  They were encouraged not to just use traditional whole numbers.  They shared them with their groups and came up with another answer that they thought no other group would have.  A couple of the groups shared their answers.  One answer used the whole number 81 inside parenthesis.  The class didn't want there to be any whole numbers.  One student threw out the suggestion of turning 81 into a fraction.  He had a great idea but then kind of got lost in his idea.  So we turned to the rest of the class to find how we can make 81 into a fraction.  This turned into a 20 minute conversation.

Almost immediately a student suggested 81 over 1.  We then looked for another way to get 81 with a fraction.    Shortly later a student came up with 162 over 2 and explained his reasoning.  This became known as the "Luke method".  Other students came up with other equivalent fractions using the "Luke method".  We then had students share their learning about equivalent fractions and their relationship to division.

All-in-all our number talk (designed to take about 15 minutes) took over an hour spanning over two days.  We got a lot of rich discussion about various parts of number sense and many students developed a deeper understanding of division and fractions (among other things).  This is what math looks like in the Lab Class.

Students reflecting on their learning.

A Powerful Story...

During the Week of Inspirational Math by Jo Boaler and YouCubed, the topic of math and speed came up.  The idea was shared that there is no correlation between speed and being strong in math.  In fact, many top mathematicians are not quick with their math because they focus on looking more deeply into a math problem.  Also discussed was the idea that the timed math tests that many students are given can be damaging.  They can cause anxiety in students and have lasting implications.

One Rio Lab Class student shared a personal story about his experience with timed math tests.  He talked about how his second grade class did a timed math sheet with 70 problem.  He could never complete these (or anywhere close to it) in the time allotted.  This made him feel as if he was not very good at math.  His words tell a powerful story...

Fortunately this student now understands that math is not about speed, and he is currently one of the top math students at his grade level in his school.

Week of Inspirational Math

The Lab Class is taking part in a program from a Stanford University math professor named Jo Boaler.  She created a website called YouCubed that offers many math related resources and videos.  The Week of Inspirational Math, or iMath, offers fun math problems and puzzles for students to work on and solve in groups.  It is designed to get students thinking about math differently and to have fun playing with the numbers and patterns.  Here is our experience with iMath.

Day 1

We first began with an activity on group work.  Students were to discuss what they like and what they don't like about group work.  They created posters with their groups.  We then came together to create a class list of the dos and don'ts of group work.

Four 4s

After watching a short video, we then did the Four 4s activity.  Students are to use four 4s with any operation to find the numbers 1-20.  We first brainstormed what operations we could use (+, -, x, ÷) and then the students came up with some other ideas like fractions, square roots, negative numbers, etc.  Students were a little slow to jump in to the activity.  Once they got a hang of it, they began to enjoy playing around with the numbers and finding new answers.  We still haven't found all of the solutions so we will come back to it throughout the week...

Day 2

Day 2 of iMath has students explore visual patterns using a sheet made up of circles in various shapes and patterns.  Students are to look at it and find any patterns that they can.  Watch as they discover patterns and make connections...

 Now listen to one student explain his color-coding system for the visual patterns he found...

And another student sharing her ideas on prime numbers (which don't have any "friends")...

Day 3

Paper Folding Activity

Today the students did the paper folding activity.  The students are given a standard 8.5 x 11 sheet of paper.  They are asked to fold it into a square.  They must be able to defend and explain how they know it's a square.  They are then given 5 challenges: 1. Construct a square with exactly ¼ the area of the original square, 2. Construct a triangle with exactly ¼ the area of the original square, 3. Construct another triangle, also with ¼ the area, that is not congruent to the first one you constructed, 4.Construct a square with exactly ½ the area of the original square, and 5. Construct another square, also with ½ the area, that is oriented differently from the one you constructed in 4.

This activity proved to be challenging.  Most groups were able to complete three of the tasks.  Some thought that they completed all five but weren't able to successfully explain that their shapes were the correct dimensions.  If you think you can do it, give this activity a try!!


Day 4

Number Dot Talk

For this activity, a group of dots were flashed on the screen for about 1 second.  Students were to tell how many dots they saw and describe the way in which they saw the dots grouped.  There were several patterns shared.  This activity is designed to show that we can come to the same answer, but often we see numbers and patterns in different ways.

Pascal's Triangle

This activity is again looking at numbers and patterns.  Students worked in groups to find the missing numbers in Pascal's triangle.  They were then given questions to help them to find more patterns that emerge when you look deeper into the triangle.

Day 5

Seeing Shapes Grow

On the last day of the Week of Inspirational Math, students were asked to explain how they saw the shapes growing from one figure to another.  The idea was for students to see that we don't all see things the same way.  There is more than one way of looking at things mathematically.   The students were asked to share and name the different ways that they see it.  They were very creative in their visions...and their naming.

A student sharing his "push-up" method.

The "rainbow", "Tetris", and "crane" methods.