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

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

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!

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.