2-Step Equation HW Answers and Solving Problems

Here are the answers to yesterday's homework. We went over the answers for 1-3. Students were told that they may complete 4-6 on their own -- check and see if they understand the steps - or - save to practice before the test. Their choice, but I will not check unless a student sees me for help.

This is a copy of today's problems.  The homework assignment is to make sure that the work is copied for problem #1 AND do any 3problems on the remaining pages.

2-Step Equations

Here are the notes and homework assignment for today.

 

Homework: Do the first 3.

Immersion Day

Here is a sampling of students working during Immersion Day #2 (for 2014-15 school year):

 

 

 

Unfortunately, I will be out tomorrow. I have given plans to Dren on 2-step equations for tomorrow. We will go over the homework at the start of Wednesday class and continue with solving problems and 2-step equations.  I WILL post a blog tomorrow with the planned notes and homework assignment.

Test 5 Review

Today, we reviewed Test 5.  Afterwards, tests were returned and students were allowed an opportunity to check their own work and make any necessary corrections.

This abbreviated test retake/corrections takes into consideration of the upcoming vacation week and avoiding the delay for corrections till after vacation.

Warren Advisory Group

Sample Design and Reflection Sheets

Team Vista participated in a different schedule.  This allowed the time for partner groups to build their designs from the Blizzard Bag Days.

Test 5

Students completed math test 5 -- fractions, prime factorization and divisibility. MTN's were also collected and will be returned on Thursday.

Update on NEML Contest:  Correction from yesterday's blog post:  June is when students will receive recognition at our all school assembly for the 5 highest scoring 7th graders and the 5 highest scoring 8th graders (usually scoring 20+).  According to test developers, students who receive a score of at least 14 points should be commended. Five students from the Vista Team scored 14 and higher: Alex A., Korbin T., James G., James H., and Derek ME. In communicating with other math teachers in the building, all were in agreement that this year's test was much more difficult than in the past. Congratulations goes to all students in participating in this test.

Prep for Test 5

New England Mathematics League conducts a Contest every year. It is administered on two dates throughout New England (Tuesday, Feb 17 or Tuesday, Feb 24). This is to accommodate for the different vacation weeks in our states.Students are allowed scrap paper and the use of calculators. All students are given 30 minutes to complete as many questions as possible. Recognitions will take place in June after all results are examined.

Afterwards, we reviewed for Test 5. This will be substantially shorter than those in the past. The topics are computing with fractions, prime factorization, determining divisibility, and simplifying fractions.

Notes on how to use Prime Factorization to determine GCF and simplify fractions to lowest term.

More with Divisibility at Work

Here are today's notes:

Test 5 will take place on Wednesday (Add/subtract unlike fractions, and prime factorization and divisibility to simplify fractions).

FRIDAY the 13th -- February

Typically, I do not post on Fridays. However, since today is Friday the 13th, some students took part in an activity during basecamp time (some basecamps had other plans). Here is the activity. If you are not in Chimborazo and did not complete thisworksheet, challenge yourself to give it a go.  Have a safe weekend.

Divisibility at Work

We finalized writing the conditions onto the divisibility chart. Students were also handed a clean, typed copy of the coordinated student solutions to the conditions. These were taped into MTN's. See the copy below.

Then -- we began applying the work from the divisibility chart.

Some additional notes to help:

Divisibility - Day 2

Students continued working in partner groups on divisibility charts. Working on this chart required students to employ several problem solving plans (from the start of the year), such as looking for patterns, working backward, and logical deduction. Then as a whole class, we discussed possible statements for conditions/rules and other examples.

By tomorrow, ALL students will be given a clean and typed copy of the divisibility conditions to add to their own draft copies.

Homework for tonight: The two-sided worksheet on divisibility.

Divisibility Chart

Understanding divisibility makes prime factorization and working with fractions easier. It speeds up the processes in fractions allowing one to being more efficient. In partner groupings, students were given sets of tested examples showing when divisibility of a given number occurred and when it did not. From those examples, partners needed to devise their own condition or rule. Then they decided on two examples in order to apply their rule.

Below is a photo copy of the charts in students' MTN's and the first two items that were completed in class together. The remaining were worked on in partner groups and will be completed in class tomorrow. A divisibility worksheet was given; due in class on Thursday, 2/12.

Answers to Word Problems

Here are the answers to last night's word problems:

As I am out sick for today, students will be reviewing skills on prime factorization, LCD, and adding/subtracting unlike fractions (with and without word problems) on IXL: Level I: A.2, F.1, G.1 and G.2.

Adding & Subtracting Unlike Fractions

Prior to adding fractions with unlike denominators, one must make equivalent fractions. Here are today's notes:

 Here is tonight's homework:

Finding LCD/LCM -- Method 2

Homework completion via IXL was much better from last night. We shared a few glitches, offered possible solutions, and I explained some alterations for another homework assignment for the future with IXL. (No homework tonight, except make-up for anyone who did not complete IXL last night.)

Then we shared some observations and strategies for how to tackle difficult problems.

Students took notes on a second method to try with determining the LCM or LCD:

Have a great weekend and stay safe.

Continuing with LCM/LCD

On Monday, Tsuga received the following notes, but Betula did not. Today Tsuga reviewed these notes, while Betula copied and practiced with the notes.

In both classes we discussed the advantage of IXL. The most important, when a student makes an error on IXL, there is a "teaching" page that automatically pops-up to explain the correct answer and why the student's submitted answer is incorrect. It is important to read this page before continuing to the next item. It helps with the learning of the skill.

A student asked a good question about the IXL assignment: "What do you do when there are 3 denominators instead of 2?"

Here is the response to that question via an example:

Tonight's Homework:  IXL  Level: I  Skill: F.4  Goal: 85% or higher

One-step Wrap-up AND LCM

Here is the key to Thursday in-class assignment. As a whole we reviewed the writing of an equation, the steps to solving the equation, labeling the answer, and the steps to checking work. At this time, we're taking a bit of a break from this concept and return in a few weeks.

Our next focus for the upcoming weeks will be LCM (lowest common multiple), LCD (lowest common denominator), divisibility, and adding/subtracting fractions.

TSUGA Notes:
What are the multiples of 3 and 4?
3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . .
4:  4, 8, 12, 16, 20, 24, 28, 32, 36, . . .

What are the common multiples of 3 and 4?
  12, 24, . . .

What is the least or lowest common multiple of 3 and 4?
  12

BETULA Notes:
What are the multiples of 2 and 5?
2:  2, 4, 6, 8, 10, 12, 14, 16, 18, 20, . . .
5:  5, 10, 15, 20, 25, 30, 35, 40, . . .

What are the common multiples of 2 and 5?
  10, 20, 30, 40, . . .

What is the least or lowest common multiple of 2 and 5?
  10

HOMEWORK:     IXL;   Level: I;    Skill: F.4

Where Are We At?

After answering questions, students completed these three problems independently. This is not an assessment, but a chance for me to check as to what each student can solve without help. Students will receive a process grade on powerschool.

MORE PRACTICE WITH SOLVING EQUATIONS

1. Mrs. Souza kept 16 of the cookies that Nathan baked. That was 2/3 of all of them! How many did Nathan keep?

Equation:

Answer:

Check:

2. If 9/10 of the weight of a package is 21.6 pounds, find the weight of the package.

Equation:

Answer:

Check:

3. Izzy gave Bailey $8.91 with which to pay the bill at the restaurant. This covered 5/6 of the cost. How much was the total bill?

Equation:

Answer:

Check:

IF YOU WERE ABSENT -- please see me first thing tomorrow morning. Thanks!

Answers to Thursday HW

Here are the answers to the word problems assigned last Thursday, 1/15:

The plans for tomorrow include a bit more practice with one-step equations, examining "friendly fractions" over "messy decimals," and a review of adding/subtracting fractions.

Test 5 Update

At this writing, Test 5 will be postponed until next week.  For the remainder of this week, our focus will be spent on solving one-step equations and working with fractions.

Table of Contents

Here's a photo of the items we have added to our MTN's over the past two weeks. Make sure these are also entered into your TOC. Have a good long weekend.

Solving Multiplication/Division Equations

Answers to last night's homework.

Review/practice -- in class.

Today's Notes

Homework page 1, due 1/20

Homework page 2, due 1/20

Solving One-Step +/- Equations

Notes for today involved practicing with solving one-step equations using addition and subtraction. Homework is solving 3 word problems which require students to apply writing expressions and solving the equation.  I am requiring students to check their work (insert their solution for the variable) and must always LABEL the solution for a word problem.

Homework for tonight (along with read over notes for 1/7, 1/8, 1/12, 1/13, and 1/14): 

1. Joe ran 17 miles less than Alison last week. Joe ran 11 miles. How many miles did Alison run?

    Expression:

Answer:

2. Last week Ted ran 30 miles more than Julio. Ted ran 41 miles. How many miles did Julio run?

   Expression:

Answer:

3. Mark paid $8.54 for a pizza. He now has $17.75. How much money did he have before buying the pizza?

   Expression:

Answer:

 

Writing Expressions

After a review of last night's homework assignment, we practiced the skills of PEMDAS and critical reading to write number expressions (not inequalities). Some practice items included:
a plus 7 (a + 7)
x decreased by 4 (x - 4)
5 less than s (s - 5)
The product of 8 and c (8c)

Then students, with partners, played a "Bingo" game with given word expressions and matched them with the correct number expressions. Here is a sample of some examples that students worked on:

The product of 5 and t                                                                       

The product of 8, m,and n

The product of 3 and the quantity of  p plus q                                    

Twice the sum of  x and y

The product of m and 3 less than m                                      

x  divided by 5

Homework for tonight: read over notes 1/7, 1/8, 1/12, and 1/13.

Practice with Polynomials

Two loose ends were tied up today: 1. returned US History Population Chart and Questions (90.2% of the students finished this homework assignment - ask your child about this) and 2. returned Test 4 Retake.  All grades have been updated on Powerschool.

Then we continued with notes from Thursday and moved into Examples of Simplifying Polynomials. See the photos below.

 

Homework for tonight is simplify these 5 examples:

More Polynomials

First, we reviewed and tried more examples to test our written expressions from yesterday (Calendar Trick).

Then, we moved into notes of polynomials and using the new knowledge from yesterday to define the terms to polynomials. Student notes should look "something like" mine. Examples will vary from class to class because different students offered different examples. (The blanks to my notes refer to the parts we have not yet finished.)

Calendar Trick

We are beginning a new calendar year.  This activity is a way to review distributive property and working with fractions, and to introduce polynomials (an expression that consists of a coefficient and variable, and involves operations - add,subtract,multiply,divide). There is more to the definition, but we are working with just one piece at this time.

Students were shown a calendar and a volunteer was asked to secretly pick three numbers and then give me the sum. I then gave them the three numbers that the student had chosen. Then we went through a series of steps as to how to figure it out and how to write an expression.

 

Betula Notes from class.

Tsuga Notes from class.

Immersion Day

As you are aware, our entire core time was spent with immersing ourselves in a self-guided learning experience. Teachers modeled the behavior by immersing our time into our own topic of study. My time was spent with reading the book, The Power of Habit by Charles Duhigg.

Here is a link to Charles Duhigg's website for resources, if you are curious.  The Power of Habit
(The "Resources and Teaching Guides" page is interesting.)