Positive and Negative Integers

First, we finished correcting all work on integer worksheets. Then students had just a little time to try the game variations "Enter with Integers". We will finish all variations tomorrow along with answering all reflection questions in class. Here are the directions and game board copies. Photos of students engaged in the activity are below.

Review

Time was spent reviewing 1. PEMDAS and 2. started Adding with Positive and Negative Integers. Tomorrow we will be engaged in a game "Enter with Integers".

Orleans-Hanna

Today, students took part in the administration of the Orleans-Hanna Test. For 7th graders, the results are  one measure to help determine the readiness for pre-algebra/entended thinking curriculum. For 8th graders, the results are one measure to help determine high school math placement recommendations.

Tomorrow -- we will continue with positive and negative integers.

November will be spent with fractions, properties of math, and Pythagorean Theorem.

Adding Integers

Planned lesson included the following notes:

Students would have had lots of class time to complete both blue practice sheets. 

Have a safe and spooky Halloween weekend. Remember that Sunday morning at 2:00 am, Daylight Savings Time ends; turn your clocks back 1 hour (and change your smoke detector/carbon monoxide detector batteries). See you on Monday, Mrs. Warren

More PEMDAS

Here are the notes from today's class.

Students have two short yellow worksheets in their MTN that is due on Monday.

I will be absent for the next two days at a Math Conference in Portland, ME. Students will be working with "Adding Integers."

Order of Operation

Today, we began taking notes and completed some practice items using PEMDAS.

HOMEWORK: Complete the yellow sheet for Tuesday, 10/27:

I will be absent on Monday, 10/26. The team will be administering the NWEA tests (Reading and Math) on Monday during core class time. The next Blog Post will be on Tuesday, 10/27.

The Next Billion -- Part 2

After reviewing the required components to a proper line graph, students edited their rough drafts and completed a final draft (homework tonight if not completed in class).

Then, I showed the students a cool website that calculates U.S. Population and World Population in the moment. Take a look by clicking onto the link.  Population Clock Link

The Next Billion

The short story, One Grain of Rice by Demi was read to students to demonstrate the enormity of one billion and the power of exponential growth.

Then students followed a series of steps to help predict when we will reach 8 billion people on Earth. We also discussed why these steps were taken as given on the data collection table.

HOMEWORK: Complete a ROUGH DRAFT of the line graph of the above data.

Scientific Notation - Part 2

Here is a copy of today's notes and work that students completed in class. (If you were absent -- see me BEFORE advisory tomorrow morning.)

 

Tomorrow, students will hear a short story (which they will review Elements of Fiction and theme) that is related to exponential growth. Then partners will follow a given series of steps that involve exponents and scientific notation to help answer the question: When will the world population reach 8 billion? Afterwards, each student will complete a line graph with their collected data.  THIS WILL BE AN ASSESSMENT GRADE.

Scientific Notation

After reviewing last night's homework and then taking a quick mini-evaluation, students moved on to scientific notations. We had a discussion about when used, the types of numbers that are represented with scientific notations, and the rules to follow when writing or converting standard numbers and numbers written with scientific notation. On Monday, we will be involved in a math lab where students will investigate ("dig deeper") with the concept of scientific notation.

Here are the notes for homework review and today's notes:

 

HOMEWORK: Complete the above page by Monday.

Properties of Exponents

Here is the homework review answers from last night:

 Today's notes:

Exponents

Students took notes as we discussed and solved situations with exponents. After the notes, students were allowed to work with partners to answer the given tasks. Homework is to finish the yellow sheet. Here are the notes and the items:

 

Processing

Today was a day that we reviewed the activities and the main purposes of this week's activities. We began the discussions of the bulletin board display photos, but were not able to finish. This will be finished on Tuesday. The students, for the most part, were enthusiastic about their research and discoveries. My goal for the BB Display activity is to help students recognize that math is all around us.

Have a safe and relaxing long weekend.  

Rational VS. Irrational Numbers

Prior to taking notes on rational and irrational numbers, students determined how to say and write ratios with numerous items that I had set up around the room. Then students took notes as we discussed extending points.

HOMEWORK: Today, students chose a photo from the bulletin board display. Tonight, students will research one photo (see the "BB Display" tab page for viewing) to determine "what or where is the math" in that photo.

Exponents and Squares

Approximately one third of the team did not finish last night's homework. This causes us to hold back the ability for us to conclude with the ideas from the activity. It is important that everyone finishes the homework tonight in order to have a productive discussion.

In the mean time, we moved on to exponents and squares. A copy of the notes is as follows:

Maze Board & What's Happening Here?

This was part one of working with numbers during class time:

Students attempted to acquire the largest Finish number. Mark S. from the Aquila group acquired the largest team number: 6332.738. Can you find his path? Can you surpass his final answer?

For homework tonight, students must work with a partner from home. The paper is in their MTN and the directions are at the top of the paper. Students MUST generate their own list of numbers first. Student and partner work out the number for and who will complete the work for the slightly smaller than one multiplier and the slightly larger than one multiplier. USE A CALCULATOR.  STUDENTS must answer the 3 questions at the bottom, but are encouraged to discuss with their partner. (Also make sure that all questions are answered on the white sheet -- "Maze Board Record Sheet.")

I have included a couple of student Table of Contents samples:

Problem Solving Methods -- part 3

Here are the problems that the students have been working in partner groupings, then table groupings, and finally as a whole class.

After all the solutions were revealed, students discussed the positive aspects of participating in this type of activity. One observation mentioned by students is the importance of finding patterns in math. Another observation is that there are more than one method to solving a problem. And a third observation was that when something is hard, skip it and try again -- don't give up. These statements indicate skills that the students will be able to apply throughout the school year.  NICELY DONE!!!

Problems Solving Methods -- part 2

We continued work with choosing effective methods to solving problems. This will be completed by tomorrow.

Practice with Problem Solving Methods

We began with reviewing Polya's Step 2: Devise a Plan. Students were given a handout to tape into the inside back cover of their MTN's with a list possible suggestions. Then in partner groups, students worked on a set of 10 challenging problems. Students needed to identify the method that would help them solve the question, then attempt to apply the plan while following Polya's Strategies.  Work will continue tomorrow to complete these tasks.

Polya:   Devise a Plan (Solving Methods)

Polya mentioned that there are many reasonable ways to solve problems. Your ability with choosing the appropriate method improves with practice. Here is a partial list of methods:

·          Guess and check (Trial & error)              

·          Look for a pattern

·          Make an orderly list

·          Draw a picture or use a model

·          Eliminate possibilities

·          Solve a simpler problem

·          Work backwards

·          Use direct reasoning (Logical deduction)

·          Use a formula

·          Solve an equation

·          Be ingenious

 

HOMEWORK: No new homework tonight (only make up for those who did not complete last night's hw).

Problem Solving -- Growing Shapes, part 2

Today, students were able to share their examples of how the block towers grew in size. There was some drawing, but large wooden blocks also became useful. Then we took a look at the growth pattern in a table and suddenly, students became aware of the number pattern and could solve solutions for a nth.

HOMEWORK: Answer the reflection question in MTN.

Problem Solving -- Growing Shapes

In this problem solving activity, students were instructed to look at the growing cases and describe how they saw the shapes growing. After some struggle and brainstorming, students shared some of their idea(s) and gave the growth a name. A little more time will be given on Monday to complete this lab. We will then use this concrete example to investigate both the number pattern and constructing a table which then leads to writing algebraic expressions.

Students were given 10 minutes to answer 3 review questions about the four previous math labs.

There is no homework for tonight.

Organization of MTN's

Due to shorter classes that resulted from the delayed opening, we spent time updating and organizing papers in individual MTN's.

Homework for tonight is to read over all pages in MTN from 9/9/15 to 9/21/15. Tomorrow, you will be given a 1/2 sheet of paper to answer questions about the four math labs.

This is also a good time to go to the BB Display page of this blog.

Problem Solving -- Pascal's Part 2

After reviewing last night's homework, students were given time to finish up their investigations and answering the questions about Pascal's Triangle. Then partners presented their findings to the rest of the class.

I urge students to use their new knowledge to tackle some investigations from the photos on the BB Display (see the page tab).

There is no homework tonight.

Problem Solving -- Pascal's Triangle

After viewing a short video about patterns, students were introduced to Pascal's Triangle. By observing the patterns, they first filled in the missing numbers in partner groups and then answered some additional questions. Partners will share their observations with classmates tomorrow.

****Students do have a homework assignment tonight! It is located in their MTN.

Here is a copy of TOC thus far:

Problem Solving -- Paper Folding

The first part of today's lesson required partners to share two roles ("convincer" and "skeptic") and at the same time were required to follow a set of specified directions. The construction activities required students to review and verify some mathematics terms such as: area and congruent.

Half way through the Paper Folding activity, students were instructed to stop their constructions while I conducted a "Dot Card" activity. This interruption allowed students to think of something else for a while their subconscious was still tinkering with the first problem. The Dot Card activity demonstrated to students as to how interesting and important it is for people to "see" things differently.

Number Visuals -- Part 2

Today was a follow-up from Monday's Number Visuals. Here is a copy of the two worksheets given to each partner:

Students were given 20 minutes and again, each pair shared one observation with the rest of the class.

Papers were collected and students were given a copy of the class's Four-4's results and "tested" as to whether or not all expressions matched the value.

See you tomorrow.

Problem Solving -- Number Visuals

The second problem solving task took place today. Students first watched a two minute video about the advantage to thinking visually. Then partners were given a sheet with visual representations and a second sheet with guiding questions. Students were encouraged to identify the number to the representations, investigate interesting aspects of the representations, look for interesting patterns, and highlight or color code the patterns. Finally, partners had 1 minute to share their findings to the rest of the class.

***Tomorrow I will be absent from school. Students will work on a follow-up activity to today's work. In addition to the follow-up activity, students will be given a portrait copy of the class' Four 4's final solution work from last week. The table groups will verify as to whether or not the expressions truly match the desired solution (from 1-20).       All plans were shared with students in classes today.  A blog is "scheduled" to show after 8AM tomorrow for your review.

These are today's worksheets:

Problem Solving -- Four 4's

In today's problem solving activity, students wrote expressions for the values of 1 to 20 using only four 4's -- all four of them needed to be used each time. First, a list of possible operations were created in class. I gave students a head start by giving an example. Students worked in groups of four (interestingly, we have four groups of four). As groups discovered possible solutions, a member from each group would go up to the board and write their group's solution. This continued until all numbers 1 - 20 were filled.  If students noticed any errors -- they were not allowed to erase another group's response. All will be used as discussion points at our next meeting.

Here are some notes from the board prior to group work:

Responses from individual classes:

Aquila

Perseus 

Andromeda

Welcome Back!

Today, was our opening day to 7th and 8th grade math on Team Vista.  The students and I were engaged in a number of activities:
1. The introduction to an interactive bulletin board display titled, "What's/Where's the Math?" Ask the students about this.
2. We set up MTN's (Math Thinking Notebook) with the Table of Contents.

3. Taped Polya's Strategies to problem solving on the inside cover to MTN's (interestingly can be used for more than math).
4. Introduction to Week of Inspirational Math; a 5-day problem solving series that focuses on ". . . inspiring students through open, beautiful and creative math.   [The staff at Stamford University, under the direction of Professor JoBoaler have] . . chosen the different tasks so that students see math as a broad, interesting and visual subject that involves deep thinking."
5. The first lesson, Honoring Ideas:  Wanted: Everyone’s! will take place tomorrow.