ATN Study Guides and Review Packet

Your Unit Assessment will be on Tuesday, December 20th.

Here is the Study Packet

Click here to access

Here are the answers to the study packet.

Click here to access.

Have fun reviewing!

Inv 4 - Distributive Property

Expanded Form and Factored Form.

Here is a good link to a Maine Public Video on Distributive Property

Click here to access

Hour of Code Links

Hour of Code is here!

We live in a world surrounded by technology. And we know that whatever field our students choose to go into as adults, their ability to succeed will increasingly depend on understanding how technology works.

But only a tiny fraction of us are learning how technology works. Fewer than half of all schools teach computer science.

That’s why our entire school is joining in on the largest learning event in history: The Hour of Code, during Computer Science Education Week (December 5-11). More than 100 million students worldwide have already tried an Hour of Code.

Article - "A Plan to Teach Every Child Computer Science"

Click Here to Access

Click here for Hour of Code.

Investigation 3.3 and 3.4 Multiplication and Division of Integers.

Problem 3.3

Focus Questions: What algorithm can you use for dividing integers?How are multiplication and division of integers related?

Problem 3.4 -

Focus Question: What pattern do you notice on the game board for the Integer Product Game that can help you win?

Click here to access the online Integer Product Game.

Brain Rush

Click here to access a multiplication game

Click here to access a positive/negative game with integers

multiply with negatives

multiply with positive and negative

Inv 3.1 and 3.2 Multiplying Integers

Problem 3.1 -

Focus Question: How is multiplication of two integers represented on a number line and a chip board?

Problem 3.2

Focus Question: What algorithm can you use for multiplying integers?

Click here to access the online Integer Product Game.

Brainrush

Try out this math facts card game. If you are still grappling with the algorithms for adding and subtracting rational numbers, try these links (sign in using your school google account):

Add and Subtract w/ Integers Practice

Practice: Subtracting to Yield a Negative

There are many more great topics to try that can help with our unit work or with skills sheets. Check out the 7th Grade Math Library here:

Brainrush 7th Grade Math

ATN - Inv 2.1 -2.3 Focus Questions and Help Videos.

Focus Question: How can you predict whether the result of an addition of two numbers will be positive, negative, or zero?

Adding Integers

Online Help Math is Fun Site:

Adding and Subtracting Negative Numbers

Click here to access

Decimals and Fractions

Problem 2.2

Focus Question: How is a chip model or number line useful in determining an algorithm for subtraction?

Problem 2.3

Focus Question: How are the algorithms for addition and subtraction of integers related?

Math Team Challenge

Math Team Challenge

11/14/2016

1. Classic Riddle: What is the maximum value of change that you can have in U.S. coins (pennies, nickels, dimes, and quarters) without being able to give someone exact change for a one-dollar bill?

2. How many triangles are in a fully connected pentagon?

Practice for the Skills Quiz #2

In preparation for tomorrow's Skill's Quiz, please review your skills sheets, pay special attention to problems you had trouble with.

Try them again and check your answers. You can review the answers here.

If you'd like additional practice on specific problems, try these sheets:

Order of Operations

Percents

Multiplying and Dividing Mixed Numbers

Subtracting Mixed Numbers

Dividing Decimals

Interactive Games for Adding and Subtracting Integers

Walk the Plank - Click here to access

Orbit Race - Click here to access

Fruit Shoot - Click here to access

Spider Match- Challenging!  Click here to access

Investigation 1.1 and 1.2 Notes and Information

Click here to access the class notes on Inv 1.1 and 1.2

Problem 1.1

Focus Question: How can you find the total value of a combination of positive and negative numbers?

Problem 1.2

Focus Question: How can you use the number line to compare two numbers?

Comparing Integers

Accentuate the Negative Unit 2

Link to our Accentuate the Negative Page and Parent Letter
Click here to access

Unit Goals:

In this unit, the focus is on 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.


Important concepts outlined below.

Math Team Challenge #2

Math Team Challenge #2 10/17/16

1. John took a picture to a copy machine and had a copy made, not realizing that someone had left the machine set for a reduction to 80 percent of the original size.  What percent setting will John have to use on the copy machine to obtain from his reduced copy a picture with the original dimensions?

2. Mr. Corey is wrapping a gift for Mr. Warshaw.  He wants to cover the 8 inch x 10 inch x 5 inch box with wrapping paper.   How many square inches of of paper will he need if the paper fits perfectly over the box?  How much ribbon will he need if the bow itself adds 15 inches?  

3. At this time of year many postal workers have to work overtime, so a supervisor at one large post office planned a late-night snack for the employees.  She ordered 1 extra-large pizza for every two workers, 1 large bag of potato chips for every 3 workers and 1 two-liter bottle of cola for every four workers.  When the order arrived, 26 items were delivered.  How many employees were working that evening?

Investigation 3.2- Designing Triangles

Focus Question: What's the smallest number of side and angle measurements that will tell you how to draw an exact copy of any given triangle?

We started this investigation on Friday looking at the idea of recreating an exact triangle from specific directions. Some of these included: side-angle-side, angle-side-angle...

Shapes and Design Unit Test Review

We are finishing up our first math unit, Shapes and Designs. 

The Unit Test is scheduled for Friday 10/21.

Start studying now to make sure you're ready!

Final Study Guide - Shapes and Designs

1. Draw, construct and describe geometrical figures and describe relationships between 
2. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Review - Investigation 1 

    1. Sorting and sketching of regular polygon (specific to parallelogram and triangle)
    2. Benchmark angles
    3. Measuring angles

Review - Investigation 2

    1. Formulas - sum of angles in a regular polygon (n = the number of sides in polygon)
        • S (sum of angles) = 180 (n-2)
        • A (individual angle in a polygon) = 180 (n-2) / n
    2. Finding exterior angles in a polygon.

Review - Investigation 3

    1. Sides lengths and forming triangles:
        • The sum of the two shorter sides must be greater then the longer side in a triangle
    2. How to create a unique triangle:
        • SAS (side-angle-side),
        • AAS (angle-angle-side),
        • SSS (side-side-side),
        • ASA (angle- side-angle)
    3. Finding angle measures when given parallel lines and transversals.
        • supplementary angles
        • complementary angles
        • isosceles/equilateral triangle properties
        • parallelogram/square/rectangle properties
        • angle sums for regular polygons

Specific work to review:

    • Warm-up problems (Do Nows)
    • Specific ACE Problems or Investigation Problems to review to review:
    •Inv 1 ACE: #10 page. 27, Check-in Quiz, Problem 1.4 C and D page .21
    •Inv 2 ACE: #1 page. 52, #12 page. 54,
    •Inv 3 Problem 3.2 A, ACE #9 page. 77, Problem 3.4 B and C page. 70
    • Check-in 1 and Partner Quiz Inv 2

Review Practice Sheet

Review Practice Sheet Answer Key

Inv 3.1

Focus Questions: What combinations of three side lengths can be used to make a triangle? How many different shapes are possible for such a combination of side lengths?

Additional questions:  

• Are there special conditions for the side lengths of a triangle?  
• Can a triangle be built with any three side lengths?  Explain.

Click here to access the virtual polystrips

Link to Math Warehouse Triangles sides and angles.

Here are some images of our kids using the polystrips.

Practice for the Skills Quiz

In preparation for tomorrow's Skill's Quiz, please review your skills sheets, pay special attention to problems you had trouble with.

Try them again and check your answers. You can review the answers here.

If you'd like additional practice on specific problems, try these sheets:

Order of Operations

Percents

Multiplying and Dividing Mixed Numbers

Subtracting Mixed Numbers

Dividing Decimals

Inv 2.3 - Tiling and Tessalations

Focus Question: Which regular polygons can be used to tile a surface without overlaps or gaps, and how do you know that your answer is correct?

Tessellation Link- 

Click here to access

Or 

Pattern Blocks - 

Click here

Inv 2.2 - Angle Sum of Any Polygon

Focus Questions: What is the angle sum of any polygon with n sides? How do you know that your formula is correct?

Students went over different methods of finding angle sums of any polygon from ripping corners to dividing shapes into triangles.

Here are some pictures of today's activity.

Helpful site:

Math is Fun - Polygon angles

2.1 Investigtion

Investigation 2.1

Focus Question: What are the size of each angle and the sum of all angles in a regular polygon with n sides?

The students will review what is important in a polygon and how regular and irregular polygons compare.  The goal is for students to develop formulas the sum of interior angles for a polygon of n sides.

S - Sum of all angles

S = 180 (n - 2)  

when n = any number of sides of a polygon

A - measure of one angle

A = 180 (n - 2)/ n

OR  

A = 180 - 360/n   

when n = any number of sides of a polygon

Link to Interactive Protractor

Inv 1.4 and 1.5

Investigation 1.4

Focus Questions: When a drawing shows two rays with a common endpoint how many rotation angles are there? How would you estimate the measure of each angle? How do you measure and angle with an angle ruler and a protractor?

Important vocabulary:

• supplementary angle - angles that add up to 180˚
• complementary angle- angles that add up to 90˚

Here are the notes from today's class and the 1.3 and 1.4 homework.

Click here to access the notes.

Here is a sheet to help with benchmark angles.  This was given as a hard copy to all the students.

Click here to access the worksheet.

Investigation 1.5 

Focus Question: In a triangle, what measures of side length and angles give enough information to draw a figure?

Notes from class- click here to access

(These notes cover the Investigation Questions A and B from class.)

Investigation 1.3- Estimating Angles

Estimating measures of an angle

Here is a helpful game estimating angles
Link to beehive game.

HINT:  Use your benchmark angles and estimate.

Skill Sheet #2

Skills Sheet #2 can be accessed here.

Click here to access.

Investigation 1.1 and 1.2

Access today's notes here.

Inv 1.1 and 1.2. 

Focus Questions:
1. What properties do all polygon's share?
2. What are some common benchmark angles?

The Four in a Row game is a great way to learn benchmark angles

Investigation 1.1

Focus Question: What properties do all polygons have?  

Diving into polygons!

In the first section of Shapes and Designs, students spent time defining the characteristics of polygons. Ask your student, "What makes a shape a polygon?" These shapes have some specific properties!

Next, everyone got some hands-on time, looking at a variety of shapes and categorizing them. Most groups categorized the shapes by the number of sides they had, but then many expanded those further into sub-categories. How many different categories can there be for quadrilaterals (four-sided polygons)?

Here is a picture of the students in action with the shape sets.

Weekly Skill Sheet Link

Here is a link to our weekly skills sheets and their answers.

Welcome back!

Our first Unit of Study will be:

We will cover the following Common Core Standards-

All Investigations - 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Investigation 2 - 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 

Investigation 2 -  7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 

Investigations 1, 2, and 3 -  7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.