Stained Glass Window Project

Students must choose a window mandala to decorate, using permanent markers complete the mandala with a minimum of three colors of their choice, create a frame for the project and write a paper about the project.  The point break down is as follows :

• Stained glass portion – 15 points (is it crisp and clear? Is it pleasing to the eye?)
• Frame – 10 points (is it clean and well thought out – is the math correct or is it crooked or off center?)
• Paper – 15 points (did you answer the questions*? Did you clearly identify the math in the project?)

*The paper must answer the following essential questions: What would you title your piece and why? One paragraph minimum.  This paragraph sets the tone for your essay.  The title may be based on shapes found in the piece or colors use… go into depth in the body of the essay. What geometry is found within the project and it’s frame? Remember this can include shapes, symmetry, tesselation, measurement, angles, etc.  This section must be a minimum of two paragraphs. Why did you choose the colors you did?  The handout on color provides a glimpse into both the positive and negative attitudes surrounding color, but personal preference plays a part in the combinations used and their placement.  I DO NOT simply want a restatement  of the handout!!!  Think and reflect…  one paragraph minimum.

Math Unit : Fractions (to be used with Bits & Pieces I)

(Grade Level : Six)

Duration/ Length :  Three weeks minimum, four weeks preferred

Brief Overview :  This unit will cover fractions as parts of a whole, as measures or quantities, as indicated division, as decimals and as percentages. The goal of Bits & Pieces is to help the student come up with their own ideas about rational numbers, not to provide them with specific algorithms.  This unit does provide supplements to Bits &  Pieces to allow for additional practice and deepening of concepts as needed.

NCTM Standards Addressed :

Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand meanings of operations and how they relate to one another.

Compute fluently and make reasonable estimates

Algebra Understand patterns, relations and functions.

Geometry Use visualization, spatial reasoning, and geometric modeling to solve problems.

Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement.

Apply appropriate techniques and tools to determine measurements.

Problem Solving Build new mathematical knowledge through problem solving. Solve problems that arise in mathematics and in other contexts.

Apply and adapt a variety of appropriate strategies to solve problems.

Monitor and reflect on the process of mathematical problem solving.

Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics.

Make and investigate mathematical conjectures.

Develop and evaluate mathematical arguments and proofs.

Select and use various types of reasoning and methods of proof.

Communication Organize and consolidate their mathematical thinking through communication.

Communicate their mathematical thinking, coherently and clearly to peers, teacher, and others.

Use the language of mathematics to express mathematical ideas precisely.

Connections Recognize and use connections among mathematical ideas.

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

Recognize and apply mathematics in contexts outside of mathematics.

Representation Create and use representations to organize, record, and communicate mathematical ideas.

Select, apply, and translate among mathematical representations to solve problems.

Prerequisite Knowledge : Students should know their multiplication facts and recall previous units on factoring and least common multiple in order to see equivalencies quickly. Students should understand the basic concepts surrounding fractions, although it is essential to review concepts during the first week.

Materials/Resources:

Bits & Pieces I Teacher’s Manual, Workbooks and Skills Intervention Correlation

Fraction Strip Sets for each student

Fraction Circles Set for each student

Student Worksheets/Workbooks

Possible Problem Sets and answer keys

Overhead transparencies and manipulatives

Games that have fractions, factors, decimals and percentages

Candy pieces may be required for some lessons

Student Objectives :  Students will be able to:

demonstrate an understanding of fractions by using manipulatives such as fraction strips, fraction circles, counters, decimal squares, money and games.

compare fractions, decimals and percents.

identify equivalent fractions.

Complete problem sets that incorporate their understanding of the symbolic concepts that relate to fractions, decimals and percents.

The objectives will be met by using an interactive approach that reinforces student understanding of the symbolic concepts as it moves them toward more concrete operations.  Skill sets will require a 66 % (2 out of 3) pass rate in order to avoid further practice.  Tests (except the pretest) and quizzes will require an 80% score or better to demonstrate functional knowledge of the subject.

Assessments :  There will be a pretest to focus instructor attention on areas of greatest need.  Daily seatwork will be done along with minimal homework, these will be practice sets of three or four problems that are corrected daily (these sets will merely be a +/- or complete/incomplete).  Students will also participate in group activities and place fractional values on a number line as needed ( a participation rubric may be used here).  A final assessment test will be completed with 80% proficiency as the goal.

Adaptations:  Depending on pretest scoring and available staff, like ability grouping may be an option.  If it is not feasible, this unit is flexible in style.  Group activities are intermingled with individual ones and smaller cooperative groups.  The lessons are fun and attractive to children with multiple intelligences.

For students that are struggling, have manipulatives available to practice and even to use on the tests.  Bits & Pieces does allow calculator use once the students have a grasp on the concepts.  Most of the problems and practice will not require a calculator as long as the students know their multiplication tables, factors and multiples.  I suggest the use of a multiple chart and counters to help those who need it.  It is also fascinating to note the patterns in the chart.

This classroom has one autistic child that excels in Math as long as procedures stay concrete.  This student has a difficult time in groups, so his group needs to be created carefully.  He may prefer to work on his own doing practice problems, so it is important to have worksheets ready for him. 

Possible Time Line:  Each day do number line practice and

Week One :

Day One:  Pretest
Day Two: What is a fraction?  Vocabulary…Numerator, Denominator, Equivalency.  Make sure to cover unit fractions and fractions with like numerator/denominator.  Also cover zero as a denominator to get that out of the way.  Practice writing fractions by doing the secret fraction game.
Day Three: Fraction strips lesson from Bits & Pieces(“Fund Raising Fractions”).  Look at the worksheet and mix the lesson, some work together on the overhead, some in groups. Day Four: This lesson can lead into discussion about equivalency.  Play with equivalent fractions.  Analyze greater than/ less than/same as by using the number line.  This is the ACE lesson for Investigation Two in Bits & Pieces I. 
Day Five: Vocabulary  review.  Review the concepts by playing games about fractions.

Week Two:

Day Six: Review.  Add / subtract fractions with like denominators. Give them at least six problems of practice a day but do not exceed 9.
Day Seven: Hand out the fraction circles of different colors and have the students cut up the pieces. Make fractions figures to be used on day eight.  Make sure that students label all pieces before they place them.
Day Eight : Have the students write an addition problem that covers their fraction figure. Start to add/subtract different denominators after practicing conversions to like denominators.  Explain and define mixed numbers to finish fraction figures.
Day Nine: Multiply fractions.  Bring up the concept of reciprocal and how multiplying by them will yield ‘one’. 
Day Ten: Try division by reiterating the concept of reciprocal.

Week Three:

Day Eleven; Review and continue week two work until satisfied that most students are up to speed.
Day Twelve:  Highlight the concept that the line in a fraction is also a division sign. “The World As 100 People” can yield practice in writing fractions with a 100 denominator and then translating them into decimals. Investigation 5 “Moving Between Fractions and Decimals” in Bits & Pieces I.
Day Thirteen:  Equivalency  of fractions, decimals and percents and interchanging them.  Work through a worksheet that has equivalencies.  Investigation 4 “From Fractions To Decimals”.
Day Fourteen:  Look at the percentages from “The World…” worksheet and translate the percentages into fractions.  Look at percentages in their lives.  Have students translate their scores on worksheets from before this unit.
Day Fifteen: Memory game with the equivalencies.

Week Four:

Day Sixteen:  Review. Decimal computations.
Day Seventeen:  Word problems
Day Eighteen: Game day review.
Day Nineteen:  Final Assessment.

Lesson Plan :  The Seven Triangles

Name:Paula Wiederhold
Date: 11/14/01
Type of Lesson: Hands-on Geometry

Objectives: SWBAT: Identify the three types of angles, the three types of triangles and by doing so, identifying the seven kinds of triangles.

Motivation/Prerequisites: How many different triangles are there? To answer this question by categorizing previously learned concepts we will learn there are only seven types of triangles.    Used with third grade students.

Resources:  pencil, seven triangles manips, 14x16 paper or paper large enough to be folded into twelve sections – each section capable of holding a triangle manipulative.  

Procedure/Activities:   Fold a large sheet of paper into twelve sections in front of the students. Make sure you have the seven triangles ready for use.  Ask the students to identify a type of triangle.  The types (scalene, isosceles and equilateral) are written down the left -hand column.  Ask the students to define each type and write the definition on the master that you are working on.  Add a thin line across the top labeled angle types.  Ask the students to list the angles (right, acute and obtuse).  Now have the kids choose the appropriate triangle for each of the nine squares.  The group will notice that there are only seven triangles and nine squares…they must determine the two impossible combinations. Now, break the group into small groups and have them repeat the process of folding the paper.  Have the students then ID and define the terms as you did as a group, then fill the squares with appropriate drawings.  Have the seven triangles available for reference.        

Assessment: The completed grid is worth ten points.

Reflections/Changes: