ATN - Study Guide and Packet

Your Unit Assessment will be on Thursday, December 21st.

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 3 - Multiplying and Dividing Integers

Problem 3.1 -

Focus Question: How is the 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?

Problem 3.3

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

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

Hour of Code is here!

Hour of Code links

Click here to access coding resources

Inv 2.1

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

Inv 1.4 - The Chip Model

Problem 1.4

Focus Question: How can you use a chip model to represent addition and subtraction?

In this investigation, we will be using chips to represent positive and negative integers. 

You may have heard the terms, "In the red" (meaning you owe or have a negative amount of money) and "In the black"(meaning have a positive amount of money)

In the image above, there are black positive chips and red negative chips on the board. Some red and black chips have already been put together in "zero pairs" that cancel each other out. Is this image "in the black" or "In the red"? How do you know?

Now try for yourself: 

CLICK HERE TO ACCESS THE ONLINE CHIP MODEL

Inv 1.3- Number lines

Problem 1.3 -

Focus Question: How can you write a number sentence to represent a change on a number line, and how can you use a number line to represent a number sentence?

Help Link to a site on number sentences and number lines.

In a number sentence, it is very important to have the following

• A starting value
• A change in value
• An ending value.

Example:                      112˚ F + n = 40˚ F

                                                               start            change    ending

Inv 1.2 - Plotting Inequaltiies

EQ: How can you use a number line to compare two numbers?

Help Video
Plotting Inequalities

Symbols

Practice ONLINE!
Link to Practicing Plotting Inequalities

Inv 1.1 and 1.2

Helpful Links
Great site on adding and subtracting positive and negative numbers.

Great Site on Understanding the Number Line

Helpful link from Math Plant on Rational Numbers

GUIDED NOTES
Click here to access the guided notes to Inv 1.1 and 1.2


ESSENTIAL QUESTIONS

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 -Operations with Integers

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 Mob Challenge Games

1010!

KENKEN

Bloxorz

Hex Blocks

Shapes and Designs Study Guide for Assessment

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

The Unit Test is scheduled for Thursday/Friday 10/26 and 27th.

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.

Random Number Generator - Link

Helpful Links:

Click here to access the virtual polystrips

Link to Math Warehouse Triangles sides and angles.

Students working with Polystrips today to find out what combinations of side lengths will create triangles.

Investigation 2.3 and 2.4

Focus Question: What is the exterior angle of a polygon, and what do you know about the measures of exterior angles?

Notes from Class

Helpful site:

Math is Fun - Polygon angles

Helpful Video to Watch

Inv 2.2 - Angle Sums of any Polygons, Inv 2.3 - Tiling and Tesselating

Another cool Tesselation
Thanks Joshua


Tessellation Link- 

Click here to access

Or 

Pattern Blocks - 

Click here

Beautiful Shape Art by Ben S.

Investigtion 2.1

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

Check-ins we completed after Inv 1.5 along with the Inv #1 Check-up.

Here is a Formative Check-in we completed and an Investigation #1 Reflection.

Check-in #1 - Click here to access

Reflection After Investigation #1 

Math Reflection Write-up adapted from p. 39  In Shapes and Designs

In your math notebook please answer the following questions with reference to the text, notes, or problems we have completed in class.

Possible Vocabulary to use: vertex, sides, regular polygon, irregular polygon, angles, acute, obtuse, supplementary angle, complementary angle, right angle, degree, rotation, straight angle, angle ruler, protractor.

1. What are common properties of all polygons?  Draw two polygons and two non-polygons to prove this.  

2. When a drawing shows two rays with a common endpoint, how many rotation angles are there?  Draw a model of this and explain.  How would you demonstrate how to measure an angle?

**Careful**  Three parts to this question!

3. What strategies can be used to estimate angle measure?  Explain and show in a sketch.

Here is a link to the Check-up #1.  You will see this come home Monday with a a reflection that your son/daughter completed on where they did well and where they still need to improve.

Helpful video on angles and measuring angles.

Interactive sites and practicing measuring angles

Visnos-interactive

Math Playground

Math is Fun - scroll down to find angles on polygons

If you want to review our work on angles you 

can watch this video.

Khan Academy how to use a protractor to measure angles

Inv 1.2 and 1.3 Notes

Here are our notes and key concepts for 

Investigation 1.2 and 1.3

Here is a copy of the Benchmark Angles we used in class.

Investigation 1.2 -

Essential Questions:
What are some common benchmark angles?
How do we estimate the measure of an angle?

A copy of some of our warm up review notes.

Another copy of the notes found here - Click to access

Investigation 1.1

Investigation 1.1

Essential Question: What properties do all polygons share?

Students working on the launch and explore during our math lesson. 

Today's essential notes!

Build a Tower Build a Team

Students working through the Marshmallow Activity

Team Work, Communication, Problem Solving

Welcome Back and First Unit

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.