Have a great summer!

Enjoy your summer.
Remember to keep up with you math work if you need some extra practice.
Here is the link to the Spectrum 7 Workbook.

http://www.amazon.com/Spectrum-Math-Grade-Thomas-Richards/dp/0769636977

Monday and Tuesday June 3rd and 4th

We completed Investigation 4 today and are starting our review for the Final Unit Assessment.  

Essential Learnings:

• Translates information about linear relationships given a table, a graph, or an equation to one of the other forms.
• Solves problems and make decisions about linear relationships using information given in tables, graphs, and symbolic expressions.

Areas of Focus:

• Constructs tables, graphs and symbolic equations.

• Recognizes linear relationships

• Solve and equation for an unknown.

• Find x or y when you substitute in the other value in an equation.

• Understands the rate change, slope and y-intercept.

• Finds the slope of a line given 2 points on a line or given an equation.

• Finds point of intersection of two lines given a graph or a table.

• Find y-intercept when given an equation.

Here is the study packet for students to complete.  These were handed out in class today.

Click here to access.

Friday May 24th - Inv 3.3 and 3.4

Today we continued the work in looking at two step equalities.

Here are the notes from today.
Click here to access.

To continue our work on these type of problems, please complete 10 of the following 15.

Investigation 3.2 - Tuesday May 21st

Investigation 3.2 - Exploring Equalities

Mathematical Goals:

• Develop an understanding of equalities
• Begin to use the properties of equalities to solve equations that are represented in pictures (word problems).  

Here are the notes from today's class- Click Here to Access

Practice Problems for Skills Test

Order of Operations Practice Problems- Click Here

Answers to OOO Practice Problems

Tuesday May14 - Study Sheets for Investigation 2 Quiz

In Moving Straight Ahead, students will study some basic ideas of algebra and some ways to use those ideas to solve problems involving linear relationships and linear functions. In particular, they will be assessed on:

• Recognize problem situations in which two variables have a linear relationship to each other;
• Describe the patterns of change between the independent and dependent variables for linear relationships that are represented in tables, graphs or equations;
• Construct tables, graphs, and symbolic equations that express linear relationships;
• Translate information about linear relations given in a table, a graph, or an equation to one of the other forms.
  
  
  
  
  Here are the answers the the Skill and Additional Practice Study Sheets

May 10th - Investigation 2.3 and 2.4 Notes Slope- intercept form.

Here are the notes from today's class.
Slope- intercept form.

Click here to access notes.

Here is a helpful video on slop-intercept form.
Watch the Concept video and Problems 1 and 4.

Investigation 2 - Exploring linear functions

The goals for Investigation #2 are:

• Find solutions to a problem using a table or graph
• Understand the connections between linear equations and patterns in tables and graphs.
• Translate information about linear relations into tables, graphs and equations.
• Understand how the y-intercept appears in tables and equations.

Here are the notes from todays class on how linear relations are seen in tables, graphs and equations.

May 1st - Investigation 1 - Moving Straight Ahead

Today we reviewed and completed an additional practice worksheet in class.

Goals for today:

• Understand positive and negative rates of change and how they are represented in tables, graphs and equations.
• Continue to explore y-intercepts.
• Describe the information the variables and numbers in the equation represent.

Here is the Additional Practice and the answers to check your work.

Thursday April 25th- Pledge Plans

We just covered looking at linear equations in terms of walking rates (distance and time variables).  Today we will focus on pledge plans using the variables of distance (x) and money raised(y).

Our goals for today's lesson were:

• construct graphs and tables to model problem situations.
• translate information about linear relations given a table, graph, or equation.
• explore what a y-intercept means in an equation.

Here is the graph for Investigation 1.3 Problems A-C.

Wednesday April 24th - Investigation 1.2

Today we started with the following entry slip.
Those needing more practice with the vocabulary should look to the last post.

We also looked at walking rates and the following formulas:

Speed = distance/ time

Distance = speed x time

Time = distance / speed

Continue working with Google Graphing Calculator.

Monday and Tuesday April 22nd and 23rd

We started a new unit- Moving Straight Ahead today.

The Units first Investigation focuses on:

• Understanding patterns of change between independent and dependent variables for linear relationships.

Here are the notes from today.  These terms are all review from previous units.

Linear relationship or function: “A relationship in which there is a constant rate of change between the two variables.”

 Ex: y= 4x + 10 

Independent variable (x-value): “A variable that isn’t effected by the other variables. Stands alone.” 

Ex: (4,10) (6,2) 

Dependent variable (y-value): “A variable that depends on the independent variable.” 

Ex: “For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.”

y - Intercept: “Location where the line crosses the y axis.”

Coordinate Pair: “A pair of numbers in the form of (x,y) that gives the location of a point on a coordinate graph.”

Ex: (4,6)

Coordinate Grid: “A grid in which you can plot coordinate pairs, on the axis of (x,y).”

Monday April 8th and Tuesday April 9th - Test Prep Answers

Unit Assessment- Accentuate the Negative-  Wednesday and Thursday Part I and II!

Here is the link to the Test Prep Answers for Accentuate the Negative.

Friday April 5th - Study Guide for Unit Test

Here is the link for the Unit Test Study Guide - Accentuate the Negative.

Please rework and work through these problems in the next few days and be ready for the Unit Test Tuesday and Wednesday of next week.  Please come and discuss any areas you are confused with.

Hi All,

Today we continued our work on Investigation 4.3 about the Distributive Property.  We worked with multiplication over both addition and subtraction.  The students also did well to take their knowledge of the order of operations and positive and negative numbers to help expand expressions.

To help drive the property home, I thought I would share a helpful link from cool math.com:

COOL MATH --DISTRIBUTIVE PROPERTY


Remember, Skills #17 is due tomorrow! :)

Wednesday, April 3, 2013

4.3 The Distributive Property and Subtraction

Hi All,

We continued our work with the Distributive Property today and began to shift our focus from working with multiplication and division to working with multiplication and subtraction.

Our Goals for the Day:

1. Develop and use the Distributive Property of multiplication over subtraction.
2. Use the Distributive Property to solve problems.

Here is a look at the notes we took today.  Be sure to take the time to review these notes and your own so that you are confident and ready to continue our work on 4.3 tomorrow!

**Also be sure to keep working on Skills #17 and reworking any problems you had incorrect on the Skills #1-16 Quiz last week.

4.2 Notes

Hi All,

Here is a sample of the notes we took in class from Investigation 4.2 Distributing Operations:

Be sure to check out the Homework Calendar to see what your class has assigned.  The Devils and Tweeties will be back on the same page tomorrow!

Monday-Tuesday, April 1-2, 2013

This week we are focusing on honing our SKILLS!

The Devils jumped right into Distributing Operations on Monday:

Our goals were to:

1. Model the Distributive Property with areas and rectangles that have edges subdivided.
2. Develop and use the Distributive Property of multiplication over division.

The Tweeties took time to practice the Order of Operations with some ACE Questions and work on their Skills Quiz from last Friday.

Tomorrow, we will flip roles and the Devils will work on the Order of Operations/Skills while the Tweeties will tackle Distributing Operations

Wed and Thursday 27th and 28th - Study Guide for Skills Test and Class Notes

Investigation 4.1  Goals:
This investigation focuses on the order of operations.
Students will explore the use of the order of operations to order computations in provided problems.

Link to notes from class.

SKILLS TEST PRACTICE PROBLEMS
Here is the study guide sheet for the Skills Test 1-16 (this Friday).
Page 1
Page 2

Tuesday 26th - Study Guide for Investigation #3

Accentuate the Negative - Check-in Investigation 3
Study Guide Essential Learning: 
• Demonstrate an understanding of arithmetic operations for integers (positive and negative numbers)
• Understand commutative property, distributive property and order of operations

Content covered:
1. Solve word problems involving positive and negative numbers Examples: Skill Sheet: Multiplying Integers
2. Solve problems involving addition, subtraction, multiplication, or division of positive and negative numbers Examples: Skill sheets (the papers with the circled problems)

 Study:
*Look over the first quiz from this unit. Make sure you can do any of the problems, especially any that were incorrect.
*Check the problems that you’ve marked wrong from your homework- redo them, if you can’t get the right answer, ask questions.
*Do some of the problems from the handouts and then check to see if they are right using a calculator. 

Vocabulary use be specific, use the terms we have learned – see the list in your vocabulary notebook and vocabulary crossword puzzle.

Tuesday, March 26, 2013

Quiz on Investigation 3 Tomorrow

Greetings all, 

Today we worked on a Check-In review packet about what we have learned in Investigation 3 about multiplying and dividing positive and negative integers.

Use the packet wisely tonight to help you practice and stay fresh for the quiz.  I have even attached the answers here.

Monday, March 25th 2013

Introducing Division of Integers

Today in math class we explored the division of integers using what we have learned about the relationship between division in multiplication found in fact families.  This allowed us to create algorithms for dividing integers.

We worked through 3.3 and collaborated as a class to explore various fact families with both positive and negative numbers.  During this process we found that multiplication is commutative (3x2=2x3) and that division is not commutative (3/2 is not equal to 2/3).

Here is a link to the notes from class today: Problem 3.3 Notes <-- For those of you who did not get a chance to finish in class I have put the answers on the notes for you.

Also, a friendly reminder that the homework for tonight is ACE #7-8 on pg. 69 and #33 on pg. 77.

Help Video on Subtracting Integers

March 20th and 21st - Investigation 3.1 and 3.2

Investigation 3.1 - Introducing Multiplication of Integers

The goals of today's lesson:

• Use a number line and motion model to develop the relationship between repeated addition and multiplication with integers
• Develop and use algorithms for multiplying integers.

Some of the algorithms uncovered by our students were:

• When two factors have the same sign then the product is positive.
• When two factors have opposite signs the product is a negative number.

Investigation 3.2 

Here is a video showing a different method of understanding the multiplication of integers using a pattern method.

March 18th - Investigation 2.5 coordinate graphing

Today we reviewed coordinate graphing in all 4 quadrants.
Here is an image to remind you of the 4 quadrants.


Students need to complete Investigation 2.5 A-E on p. 36-37.

Here is a video on graphing coordinate points.

March 12th - Investigation 2.4 Fact Families

Today we completed the Investigation 2.4 Lesson discussing fact families.

Here is a word bank for the crossword puzzle:

• algorithm
• addend
• minuend
• integer
• rational number
• commutative property
• absolute value
• negative number
• positive number
• opposites
• subtrahend

Good luck!

March 11th - Investigation 2.2 and 2.3

Today we continued to look at integers and specifically subtracting integers.

We worked with the following number sets:

-8 - -3 =

8 -3 =

8 - -3 =

-8 - 3 =

-3 - -8 =

The following were the rules/ algorithms we came up with.

1. You will get a positive number if the number you start with is greater than the number you subtract it from.

2. If the first number is less than the second number then the difference will be negative.

Another student then said:
3. If the first number is greater than the second then the difference will be positive.

We had good discussions and a good use of the chip model today.

Here is an interactive link to chip models. 
Open in Safari

March 7th - Investigation 2.1

Goals for the day:
- Students will be developing algorithms for adding integers.
- Students will model addition of integers using distance/ direction on a number line and chip model.

The main algorithms discussed today were the following:

When adding integers:

1. If the addends have the same sign, combine and use the same sign.

2. If the addends have opposite signs, cancel and take the sign of the number furthest from zero (largest absolute value).

Complete the Check-in Inv 2.1

March 6th - Happy World Math Day!!!

The World Education Games is an annual global online challenge to get all students (4-18 years of age) excited about learning, and to give the top students in all schools an opportunity to see how they measure up against the best in the world. Last year, over 5 million students were a part of what is now the world’s largest online education event. 

Here is the link to the competition - Click here

Students from our math classes are competing against other students around the world on their math fluency.

Tuesday March 5th - Investigation 2.1

Goals for the day:

• Students will be developing algorithms for adding integers.
• Students wil model addition of integers using distance/ direction on a number line and chip model.

The main algorithms discussed today were the following:

When adding integers:

1. If the addends have the same sign, combine and use the same sign.

2. If the addends have opposite signs, cancel and take the sign of the number furthest from zero (largest absolute value).

Math this Week - 27th, 28th, and 1st of March

We worked through Investigation 1.  Students were aquatinted with number lines, read thermometers and how to use the chip model to work with adding and subtracting positive and negative integers.

Here is a cool interactive link working with the chip model.
Click here to access.  You will need to open this in Safari!

Here is a good link to Math is Fun on Number Lines.

Starting Accentuate the Negative - Feb 25th and 26th

Welcome Back!

Coming back from Break we are also moving into a new Unit called Accentuate the Negative.
The focus is on this Unit is understanding and developing systematic ways to add, subtract, multiply, and divide positive and negative numbers.  Students will develop algorithms for computations and will use the order of operations, the Commutative Property, and the Distributive Property to solve problems.

Worksheets to Complete in class or homework:
Accentuate the Negative- Prior Skills and Concepts

Working with Integers Document Link
If you can not answer a question circle it and place a question mark next to it.  Do not worry about not being able to answer every question, this is a baseline.

Skills Sheet due Friday March 1st:
Skills #13 Document Link

We started Investigation 1 by going over vocabulary and completing the reading on p. 5-7.
The vocabulary words are:

• Rational Number
• Positive Number
• Negative Number
• Integer
• Opposite

Be sure to review these and understand their meaning based on the worksheet and today's reading.

Wednesday Feb 13th

Here are the answers to the Skills Practice Assessment.

Be sure to fill out the reflection and focus on your areas of weakness.

Tuesday February 12th - Skills Assessment Review

With the #1-12 Skill Assessment coming up Thursday we will focus some class time on practice assessments and self-reflection to identify areas of focus.

Here is the link to the Practice Assessment Skills #1-12.

After you complete the practice assessment correct it with your teacher and then start the self-reflection. This focuses on the last skill sheets you have completed #8-12 as well as the skills review #1-12 and the skills practice #1-12 you just completed.  Read the directions and fill it out.  Have your parents sign this as well showing they have discussed your skill progress with you and have seen the areas you have identified as your areas of focus.  We will work on these areas tomorrow, prior to the assessment.

Here is the link to the self-reflection.

February 7th - Final Question Bank Answers

Here are the answers to the final question bank.

Comparing and Scaling Unit Test:

• Thursday is the multiple choice portion.
• Friday is the written task portion 

Thursday January 31st -

Looking Back Looking Ahead p. 81 - Answer Key

Wednesday January 30th -

Here is the answer key to the Additional Practice.

Here is the answer key to the Babysitting/ Texting Problem.

Thursday January 24th - Investigation 3.3

In this next Investigation 3.3 students are comparing and scaling unit rates.
Specifically they were faced with two different cd deals.
The students were tasked with scaling down the deals to a unit rate and then creating an equation out of that unit rate (this is review from Variables and Patterns our first Unit).

Here is a helpful video if you want to watch more on Unit Rates.
Video 1 - Unit Rates
Video 2 - Comparing Unit Rates

Wednesday January 23rd - Investigation 3.2

Investigation 3.2 p. 42

Today we discussed unit rates in terms of time, distance and speed.
Students had to :

• Further develop an understanding of unit trates and how to compute and interpret them.
• Work with the important application of rates to miles/ hour (speed).
• Apply the understanding of average speed or rate of progress.

Wednesday January 16th - Scaling Ratios

Hi kids - for class today here are some related videos:

Review how to write proportions

Finding and unknown in a proportion

Finding an unknown ratio value using equivalent proportions.

Monday January 14th - Investigation 2.2

Today we completed Investigation 2.2 together.
We will continue to work through ratio comparisons in the this example using campers and pizzas.

Here are the notes from today's class.
Click here to access notes.

Thursday/ Friday January10th/ 11th

Investigation 2.1 p. 22-23 in the text.

The mathematical goal for the next two days is for students to become comfortable with writing ratios and related forms of comparisons to solve problems.

The following is the provided note sheet we completed together in class for the investigation.

Students had two days in class and the weekend to complete ACE Problems # 1, 2, 3, and 9, 10, 11, 12, 13.  These will be due Monday along with a binder organization check.

Wednesday January 9th - Check-in Investigation 1

Today students took the Investigation 1 Check-in for Comparing and Scaling.

Here is the Math Teacher Survey from Today's Class.

Tuesday January 8th

We completed the End of Investigation Reflection on p. 21 in the text giving examples and telling what each of the following comparisons mean:
   - ratio
   - fraction
   - percent
   - difference

The students then started the Additional Practice Sheet for Investigation 1.
Here is the link to the worksheet and the answers.

Friday January 4th - Investigation 1.1

Today we covered investigation 1.1 -  Making Comparison Statements.

We focused on two goals today:
1. Explore strategies to compare information
2. Use the language of ratios

Thursday January 3rd

Today we started Investigation 1.1 in the new Comparing and Scaling Book.
We focused on the ability to make comparisons of quantitative data.
We focused on making comparisons through:
1. ratios
2. differences
3. percents
4. simplified ratios

Here are the notes from today.

Comparing and Scaling the Next Unit

Dear Students and Parents,

The next unit in your child’s mathematics class this year is Comparing and
Scaling: Ratio, Proportion, and Percent. Students look at problems involving
many situations and learn to make comparisons using ratios, fractions, percents,
and rates.

UNIT GOALS

One goal of this unit is to develop students’ abilities to make useful comparisons
of quantitative information using ratios, fractions, decimals, rates, unit rates, and
percents. A second goal is to have students learn to use quantitative comparison
information to make larger or smaller scale models.  Students should also learn different ways to reason in proportional situations and to recognize when such reasoning is appropriate.

Wednesday January 3rd

Hello everyone and Happy New Year!

I wanted to share some good practice sites for order of operations in case you wanted to practice on your own - we will talk more about these in class, but I have noticed that some of you need a little more work in this area so try some of these:

https://www.khanacademy.org/math/arithmetic/multiplication-division/order_of_operations/v/introduction-to-order-of-operations?topic=order-of-operations

https://www.khanacademy.org/math/arithmetic/multiplication-division/order_of_operations/v/more-complicated-order-of-operations-example?topic=order-of-operations

http://www.basic-mathematics.com/order-of-operations-game.html

and this one - but run it in chrome or safari - http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/

Have fun practicing!