Good Group Work and Painted Cube

THIS POST IS FOR WEDNESDAY, 9/28 AND THURSDAY, 9/29!

In order to allow sufficient time to complete a field study in science, math and science classes are double blocked for today and tomorrow. Thus, anyone in math today or tomorrow, had a lot of work to complete both individually and in groups.

FIRST:
Good Group Work Project -- Now you are to organize the patterns that you can view among all the posters. Click onto your class Padlet to add post-its, rearrange, sequence in order, etc. until we have a class poster. (This was for in-class only --- not at home. All Padlet pages will be turned to "Read Only" at 2:30).

Roberts Group

Bayle Group

Shaw Group

(As of 2:30 on 9/29, all Padlets will be in "Read Only" mode.)

SECOND:
Students were shown a sample 3x3x3 cube with manipulatives and  projection. In their MTN's students needed to answer the following independently:

If we took a 3x3x3 cube and dipped it into paint, so the paint completely
 covered the cube, how many small cubes would have
three sides painted? Two sides painted? 

One side painted? No sides painted?

Then student groups were given centimeter cubes to make their own 3x3x3 cube to investigate. Students were provided with chart paper to record their findings. They were then instructed to predict the same for 4x4x4 cube, 5x5x5 cube, and beyond. It was recommended to students devise a plan to best organize their data for presentation. Group assignments were as follows: 1. Project Manager, 2. Encourage & Strategies Checker, 3. Block Builder & Materials Caretaker, and 4. Recorder.

HOMEWORK:  None for tonight.

Hailstone Sequence Share

Students had an opportunity to show their trials with Hailstone Sequences.  All expressed the fun that was had with math!  Students were also able to share a variety of information learned from last night's links and added to their notes.

We then discovered conditions that led to fewer steps and examined whether or not negative integers work and why.

Here is a calculator link that reveals the number of steps necessary to reach "1" from any positive integer.
Hailstone Sequence Calculator



HOMEWORK: 

• Play with MIT Hailstone Calculator and jot down observations.

Conjectures

First, class began with a new vocabulary word: conjectures. Students were given a process for math vocabulary words using word origin (which will be covered more in depth in SSEnglish classes). After the individual parts to the word was given, students brainstormed possible definitions. Then I shared a math definition and synonym. This process has a page dedicated in students' MTN's and will be followed throughout the year.

Then students were given the following handout with additional information:

Tonight, students will calculate their own hailstone sequence and check out additional information on the provided links about Hailstone Sequences.

HERE ARE THE 3 LINKS FROM WHICH TO CHOOSE:
1.  Wolfram
2.  NASA Hailstorm
3. Wikipedia


HOMEWORK: 

• 1. Begin with a number between 50 and 100. Following the Hailstone Sequence String rules, complete the calculations till you arrive to 1 (one).
• 2. Go to my Blog and check out any one of the three links. Write two things you learned.

Overnight Prep

Due to shortened Delayed Opening Schedule, an unexpected -- although pleasant surprise -- guest speaker, and the last chance to complete: final-gear-checks-nature-journal-preview-water-bottle-filling-pack-labeling . . . . we did not have core classes today.

We will see you on Friday around 2:00ish and the next post will be on Monday, 9/26.

HW: None for tonight.

Squares to Stairs -- Part 2

After checking completed homework, students were instructed to draw a line across the page under their work. As an individual student shared her/his thinking and work, the remaining students copied the ideas in their MTN with a different colored writing utensil. At the end of each class, I collected all MTN's in order to determine "Practices improved skills," one of the Work Ethic Process Grades. While I have students' MTN's I will also be evaluating another process grade: "Demonstrates perseverance to meet task requirements, AND two Math Practice Grades: "Makes sense of problems & persevere in solving them." AND "Model math by applying math to solve problems."  The final component that I will be examining is students' understanding of "squared" and "square root".

I also had each student create an account for Desmos Graphing Calculator. We were able to enter one expression and I suggested to students to "play" with other possibilities.    Desmos Screenshot

HW:  There is not homework tonight (and will not be any assigned work till we return on Monday, 9/26).

Squares to Stairs

We began class with a table mates sharing of individuals' growth patterns from last Thursday's work. Then all shared in a whole class discussion. It was interesting to watch the color designs along with the verbal explanations to how students interpreted the growth patterns.

Students were shown how to express the stairs growth pattern in a table. . . . .:

. . . .and from there, we were able to write an algebraic expression.


Some students claimed to understand HOW this works while others were still uncomfortable with WHY and HOW this expression works -- and that is okay. Everyone "gets it" at a different pace.

Here is a link that can further your understanding (or maybe not):
Techniques for Adding the Numbers 1 to 100


HW: Answer the following in your MTN: Can you use 190 squares to make a stair-like structure? Justify you thinking with different representations -- visually, numerically, and algebraically.  WORK ON THIS FOR AT LEAST 20 MINUTES.

Graph Process & Squares to Stairs

Most students came to class with a variety of topics for their homework graphs.  A number of students took the extra time and to include elaborate and creative representations on their graphs. Students were also able to express their understanding of graphs and interpret the data in order to draw conclusions. The errors that were made led to good processing discussions.

Our classes were slightly shorter in order to allow time tent set ups. We began the activity titled, Squares to Stairs. We will complete the remainder of the discussion and writing an algebraic expression on Monday.

Students do not have any homework --- BUT --- can always play with more growth patterns in their MTN.

THE NEXT POST WILL BE ON MONDAY.

Graphing Activities

We began our class time with reviewing student ideas and solutions from last night's homework, Fewest Squares. Share with your family the results we discussed in class.

A short video clip from Dr. Jo Boaler was shown to students about the making mistakes and making corrections versus making irresponsible decisions.

A graph without numbers was given to table mates and students needed to interpret the information. After the whole group processed the graph, students were assigned to create their own graph.  They are allowed to choose any topic and must include 2 dimensions.

Dot Card & Good Group Work

Today's lesson was in three parts: 1) Dot Card, 2) Good Group Work, and 3) Fewest Squares.

Students were allowed to look at a card for 1 second, and were then asked how they saw the dots arranged to arrive at 6. Here are the results from three classes.

We then processed the objective of this activity.

Students discussed "Good Group Work" actions -- what it looks like -- what it sounds like to observers.  Students wrote these ideas in their MTN's. We also discussed what might detract good group work and how to solve those situations.

Finally, I described the expectation for tonight's homework . . . "Work  on Fewest Squares for at least 20 minutes.

Problem Solving & Math

We began our year with setting up our math composition books, which will be referred to as MTN's (Math Thinking Notebooks). Table of Contents (TOC) pages were set aside and labeled. Each day, I begin class with the date and title of the day's activity. Then, students were given Polya's Problem Solving Strategies that you can reference as a page tab near the top of this blog. Students were also given a list of possible plan ideas for math problem solving. Both sheets have been taped on the inside cover of their MTN's for easy reference. We spent a good deal of time processing how to use these strategies.

Then I introduced Week of Inspirational Math -- Year 2 from Dr. Jo Boaler of Stanford University. Over the next 5 days, students will be involved in problem solving situations in order for them to understand that math can be seen in many different and creative ways. Students who took part in these activities last year spoke highly of that time, and I also observed how students referred to these days as the basis for persevering some difficult problems during the entire school year. At the end of the five days, students will complete a survey and I will invite parents to complete the survey, if so desired.