Review, PEMDAS, & Exponents

Today was used to review the notes from last Wednesday and practice PEMDAS with the expression derived from Painted Cube project. The Mini-Eval will be given tomorrow.

Here are 3 posters from last week's group work. They demonstrate how groups were able to visualize and work out the problem to a solution to the given question. Ask your child about the question.

HOMEWORK: Mini-Eval #1 is tomorrow.

NWEA Testing

Math classes were not held due to NWEA Testing.

HOMEWORK: Read over Painted Cube and Square/Cube Notes for Mini-Eval #1 on Wednesday.

Quick Review for Mini'Eval #1

Here is a copy of teacher notes from today:

 


***SPECIAL NOTE:  Mini-Eval #1 has been changed from tomorrow to Wednesday, 10/12/16.

HOMEWORK:  Read over Painted Cube and Square/Cube Notes for Mini-Eval #1 on Wednesday.

PC Presentations & Square/Cube Notes

Students were given 20 - 25 minutes to polish their group poster and prepare their shared presentation to class.  Groups were given 2-3 minutes to present their findings.

Tomorrow, students will participate in a YouCubed Survey about the math problems which we have tackled over the past couple weeks. Then square/cube number notes will be given to students.


HOMEWORK:  Look over Painted Cube and Notes in MTN for Mini-Eval #1 on Thursday.

Painted Cube Group Share

Today, students continued working in groups.  The groups must design a method that best demonstrates their understanding of given questions for cubes that measure 3x3x3, 4x4x4, 5x5x5, and relate to the growth pattern for cubes with larger measurements.

Below are photos of students working:

HOMEWORK:  Be prepared to present with your group tomorrow.

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.

Final Post

This will be the last post for this academic year. Students finished their pentagon folding directions and answering the questions.

I have enjoyed being the math teacher to Team Vista students. I know I learned much and all of the students have advanced their thinking in math. Have a safe and restful summer. I know I will be enjoying some off time with my two sons. Good luck at the high school!

Paper Folding -- Regular Pentagon

Partner groups were given a set of directions and needed to work together to construct a regular pentagon. There are 5 questions that must be answered about the constructed pentagon in class tomorrow.

HOMEWORK:   None for tonight.

Paper Folding -- Equilateral Triangle

Partner groups were given a set of directions and needed to work together to construct an equilateral triangle. There are 5 questions that must be answered about the constructed triangle.

HOMEWORK:  Complete Equilateral Triangle Folding Questions in your MTN.

Congruence

Homework review from last night:

Today's Notes:

HOMEWORK:   Complete Congruent papers in MTN for Monday, 6/6.

Triangle Theorems

Notes from today's class:

HOMEWORK:  Complete Triangle Theorem papers in MTN.