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Project GLADMatanuska-Susitna Borough School District

Algebra- Grade K-5By Bettina Mileur

Idea Pages

I. UNIT THEME-The National Council of Teachers of Mathematics (NCTM) tells us that Algebra helps us be better at solving equations. NCTM standards for algebra are to 1) understand patterns, relations, and functions; 2) represent and analyze mathematical situations and structures using algebraic symbols; 3) use mathematical models to represent and understand quantitative relationships; 4) analyze changes in various contexts. Sometimes Algebra simplifies problems by using letters to represent numbers. It is a basis for math expression of many scientific formulas. Here are some examples of algebra: 1) How many cups of flour does it take to make two batches of holiday cookies? 2) Find the weight of how many students are in a classroom 3) Estimate the number of cups of milk students drink in one month, one year, or one lifetime. When we use algebra in our daily life we would be able to find and describe patterns in numbers, charts, operations, geometric figures, and graphs.

Algebra and the history of math has spanned thousands of time! Math started with early man counting by 1’s and making marks on a wall. It has really changed from 30,000 years ago! Mathematicians from around the world and over history added to the complexity of numbers and now, we see simple marks changed to different groupings, patterns, and expressions using lines on graphs, data streams, and more. “Mathematics is a science of pattern and order” (National Research Council, Mathematical Sciences Education board 1989, p.31) People investigate problems that can be shown and described in algebraic equations and in the real world around us. Their expressions are used to explain lots of different studies in our world. Science, technology, music, and entertainment use algebra.

Algebra can be found in man-made and natural patterns such as Fibonacci swirls and amazing architecture, number patterns such as the Erostothenes’ patterns, graphs and charts like the growth of a tiger kitten, reading data streams as you grow. There are other fun and interesting skills with math such as compass work with geocaching, map references, knowing coordinates, and measuring area.

Games such as letters and numbers, function machine, SET, cribbage, chess, and checkers, compass direction, and many computer puzzles are used in learning algebra! When I study algebra I become a better problem solver, science expert, musician, and computer nerd! Algebra is for me…..

II. FOCUS/MOTIVATION

Superkid MATH Award Inquiry Chart: Algebra Important Book about Algebra Observation Charts Picture File Cards Video Clips from www.NLVM.com

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CCD with Signal word Algebra “ALL AROUND US” hike: 1) looking at patterns and graphs in our school building, finding

the area of our room, researching how algebra is used in science, technology, and many other fields of expertise for my future.

III. CLOSURE

Process all charts Portfolios: 3 pieces of writing –expository, narrative, poetry Teacher and student made quizzes and test Personal exploration with rubrics Team/Class Big Books Insect Journals Group Presentation of all team tasks

National Council of Teaching Mathematics ALGEBRA STANDARDS for GRADES 3-5

Algebra understands patterns, relations, and functions. Algebra is representing and analyzing mathematical situations and structures using algebraic

symbols. Algebra uses mathematical models to represent and understand quantitative relationships. Algebra analyzes change in various contexts.

StrandStandardsReference

*Assessed Locally

Grade 5: MATH Grade Level ExpectationsSBA

Emphasis

NumerationM 1.2

UnderstandingNumbers

The student understands WHOLE NUMBERS, POSITIVE FRACTIONS, MIXED NUMBERS, & BENCHMARK PERCENTS. Student can:

22-26%

[5] N-1 Read, write, order, and [count*] numbers to millions.

[5] N-2 Identify place value positions from tenths to millions.

[5] N-3Convert between whole numbers expressed in expanded notation and standard form.

[5] N-4Model, identify, describe with explanations, or illustrate equal parts of a whole, a region, or a set.

[5] N-5

Model, identify, describe with explanations, or illustrate equivalent fractions or mixed numbers of positive fractions with denominators 1 through 12 and 100 with proper and mixed numbers and benchmark percents (10%, 25%, 50%, 75%, 100%).

Understanding The student understands MATHEMATICAL OPERATIONS. Student

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Operations can:

[5] N-6[Use models, explanations, number lines, or real life situations*], describe, or illustrate the processes of division and its relationship to subtraction or to multiplication.

[5] N-7[Use models, explanations, number lines, or real life situations*], describe, or illustrate the process of adding and subtracting proper fractions or mixed numbers (like denominators).

[5] N-8[Use models, explanations, number lines, or real life situations*], describe, or illustrate the process of adding or subtracting decimals that represent money.

Number TheoryThe student understands NUMBER THEORY. Using manipulatives or models, student can:

[5] N-9Describe or illustrate commutative or identity properties of addition or multiplication using models or explanations.

[5] N-10Identify or list factors and multiples common to a pair or set of numbers.

MeasurementM 2.2

MeasurableAttributes The student understands MEASURABLE ATTRIBUTES. Student can:

12-16%

[5] MEA-1* Estimate length to the nearest one-fourth inch or centimeter.

[5] MEA-2*Estimate temperature (degree Celsius or Fahrenheit, plus or minus 5 degrees) or weight (half-pound or kilograms) to the nearest unit.

[5] MEA-3Identify or use equivalent measures for weight/mass (16 oz. = 1 pound or 1000 grams =1 kilogram), length (1000 millimeters = 1 meter), or time.

MeasurementTechniques

The student understands MEASUREMENT TECHNIQUES. Student can:

[5] MEA-4* Measure temperature or weight using appropriate tools.

[5] MEA-5Tell time using analog clock to the nearest minute and using AM or PM.

[5] MEA-6Determine possible combinations of coins and bills equal to given amounts.

[5] MEA-7*Simulate multiple purchases and calculate the amount of change from a given bills up to $100.00.

[5] MEA-8 Measure length to the nearest ¼ inch or centimeter.

Estimation & Estimation The student understands ESTIMATION. Student can: 18-22%

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ComputationM 3.2

[5] E&C-1

Identify or use [a variety of*] strategies (e.g., rounding to appropriate place value, multiplying by powers of ten, using front-end estimation) to estimate the results of addition or subtraction computations from tenths to 100,000, including money, or simple multiplication or division.

Computation The student understands COMPUTATION. Student can:

[5] E&C-2*Recall basic multiplication facts, products to 144, and corresponding division facts efficiently.

[5] E&C-3Add or subtract four-digit whole numbers, fractions with like denominators to 12, or decimals involving money.

[5] E&C-4Multiply two-digit numbers by two-digit numbers or divide three-digit whole numbers by single-digit numbers.

Functions &Relationships

M 4.2

Patterns &Functions

The student understands PATTERNS & FUNCTIONS. Student can:

12-16%

[5] F&R-1Extend patterns that use addition, subtraction, multiplication, division, or symbols, up to 10 terms, represented by models (function machines), tables, sequences, or in problem situations.

[5] F&R-2Use rules to express the generalization of a pattern using words, lists, or tables.

[5] F&R-3Identify or apply addition or subtraction patterns to find missing values in a function.

[5] F&R-4*Use manipulatives, including a calculator, as tools when describing, extending, or representing a number sequence.

Equations/Inequalities

The student understands EQUATIONS & INEQUALITIES. Student can:

[5] F&R-5

Use an open number sentence (addition, subtraction, multiplication, or division) to solve for an unknown represented by a box or circle

(e.g., 256 ÷ o = 8, o ÷ 8 = 56, 36 ÷ 3 = o).

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GeometryM 5.2

GeometricRelationships

The student understands GEOMETRIC RELATIONSHIPS. Student can:

12-16%

[5] G-1

Use the attributes and properties of angles and the number, length, and orientation of sides to identify or compare triangles (scalene, isosceles, or equilateral) or quadrilaterals (parallelograms, trapezoids, rhombi).

[5] G-2

Use the attributes and properties of solid figures (edges, vertices, or the number or shape of faces) to [model*], identify, compare, or describe solid figures (cubes, cylinders, cones, rectangular prisms, spheres, pyramids) (e.g., boxes, buildings, packages).

ShapesThe student understands SIMILARITY, CONGRUENCE, SYMMETRY, & TRANSFORMATION OF SHAPES. Student can:

[5] G-3Illustrate or identify the results of transformations (slides, turns, or flips of polygons) (e.g., pictures of cultural art, fabric designs, architecture, logos).

[5] G-4Identify, create, or draw geometric figures that are congruent, similar, or symmetrical.

[5] G-5*Model designs (e.g., tessellations) that contain a series of slides, flips, and/or turns.

Perimeter &Area

The student understands PERIMETER, AREA, VOLUME, & SURFACE AREA. Student can:

[5] G-6Estimate or determine area or perimeter of rectangles using a key, ruler, or given measures.

[5] G-7*Estimate or determine the area and circumference of a circle using a grid or manipulatives.

Position &Direction

The student understands POSITION & DIRECTION. Using manipulatives or models, student can:

[5] G-8*Locate points of given coordinates on a grid or identify coordinates for a given point (e.g., items on a treasure map).

ConstructionThe student understands GEOMETRIC DRAWINGS OR CONSTRUCTIONS. Student can:

[5] G-9* Identify or draw perpendicular line segments or midpoints.

Statistics/Probability

M 6.2

Data DisplayThe student understands ORGANIZATION & CLASSIFICATION OF DATA. Student can:

12-16%

[5] S&P-1 [Design an investigation and collect*], organize, or display, using appropriate scale, data in real-world problems (e.g., social studies, friends, or school), using bar graphs, tables, charts, diagrams, or line

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graphs with whole numbers up to 50.

Analysis &Central Tend.

The student understands ANALYSIS & CENTRAL TENDANCY. Student can:

[5] S&P-2Use information from a variety of displays (tables, bar graphs, line graphs, or Venn diagrams).

[5] S&P-3Use mode, median, or range with up to 10 pieces of data with a value of 10 or less each.

Probability The student understands PROBABILITY. Student can:

[5] S&P-4Predict or explain the probability of all possible outcomes in an experiment using ratios or fractions to describe the probability.

[5] S&P-5Solve or identify solutions to problems involving money combinations (e.g., how many ways can you make 25 cents using nickels, dimes, or quarters?).

ProblemSolvingM 7.2

ProblemsSolvingThe student understands PROBLEM SOLVING STRATEGIES. Student can:

Assessedbut notseparatelyreported

[5] PS-1Select & apply an appropriate strategy (e.g., tables, charts, lists, or graphs; guess & check, extended patterns, make a model) to solve a problem and verify results.

[5] PS-2Explain and verify results of an original problem and apply what was learned to new situations.

CommunicationM 8.2

CommunicationThe student COMMUNICATES MATHEMATICAL THINKING. Student can:

[5] PS-3

Represent problems using mathematical language including concrete, pictorial, and/or symbolic representation; or organize and communicate mathematical problem-solving strategies and solutions using mathematical language.

ReasoningM 9.2

ReasoningThe student uses LOGIC & REASONING to solve mathematical problems. Student can:

[5] PS-4Draw logical conclusions about mathematical situations (given a rule or generalization, determining whether the example fits) or justify answers and mathematical strategies as reasonable.

ConnectionsM 10.2

ConnectionsThe student CONNECTS & APPLIES MATHEMATICAL CONCEPTS. Student can:

[5] PS-5Understand & apply mathematical skills & processes in real-world contexts such as social studies, friends, and school

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ReadingStrand

PerformanceStandardReference

*Assessed Locally

GRADE 5: READING Grade Level ExpectationsSBA

Emphasis

WordIdentification

Skills

PS R2.1The student USES STRATEGIES TO DECODE & COMPREHEND MEANING OF WORDS IN TEXT. Student can:

20-26%

[5] 2.1.1Demonstrate knowledge of word structure (root words, prefixes, suffixes, abbreviations) and language structure through reading words in text (word order, grammar).

[5] 2.1.2Use knowledge of word families, phonetics, context/visual cues and structural elements to determine meaning of unfamiliar words.

[5] 2.1.3Use textual cues/clues to gain information (e.g., bold/italicized text, headings, pictures, illustrations, graphs, charts).

[5] 2.1.4Identify relationships between words by categorizing (e.g., synonyms, antonyms, homophones, homographs), and [identifying shades of meaning].

[5] 2.1.5*Self-monitor & self-correct while reading (e.g., sound out words, adjust pace, re-read difficult or relevant material).

Forming aGeneral

Understanding

PS R2.2 The student COMPREHENDS LITERAL OR INFERRED MEANING in text. Student can:

44-48%(PS R2.2,

R1.4 - R1.6)

[5] 2.2.1Locate information explicitly stated in narrative & informational text and use it to answer literal comprehension questions.

[5] 2.2.2*Self-monitor comprehension while reading (e.g., predict outcomes, formulate questions, reread for clarification, confirmation, correction).

[5] 2.2.3Make inferences (e.g., predict logical outcomes, deduce missing outcome or information).

[5] 2.2.4Draw conclusions based on information presented in text (e.g., character motivation, cause & effect).

Fluency

PS R2.3 The student READS TEXT ALOUD. Student can:

0%

[5] 2.3.1*Read aloud with rhythm, flow, expression, attention to punctuation and other conventions of print.

Forming aGeneral

Understanding

PS R2.4 The student accurately RESTATES & SUMMARIZES information. Student can: 44-48%(PS R2.2,

R1.4 - R1.6)[5] 2.4.1 Restate/summarize main idea or events in correct sequence (e.g., paraphrase, construct a topic outline, use graphic organizers) or identify accurate restatements and summaries

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of main ideas/events/generalizations of a text.

PS R2.5 The student understands the concept of MAIN IDEA. Student can:

[5] 2.5.1 Identify main idea/concept in various types of text.

[5] 2.5.2Locate information in narrative & informational text to answer questions related to main ideas and key details.

[5] 2.5.3*Identify/describe related experiences and events to support understanding of main idea (e.g., what event in history is similar to this one).

PS R2.6 The student FOLLOWS WRITTEN DIRECTIONS. Student can:

[5] 2.6.1* Follow written, multi-step directions to complete a task (e.g., origami).

[5] 2.6.2 Identify sequence of steps in multi-step directions.

Analysis ofContent andStructure

PS R2.7 The student analyzes content and structures of GENRE. Student can: 28-32%

[5] 2.7.1*Identify or explain characteristics of the four major genres of fiction: short story, drama (plays), novel, and poetry.

[5] 2.7.2 Identify or explain the characteristics of fiction and nonfiction.

[5] 2.7.3Identify/explain use of literary elements and devices (i.e., dialogue, rhyme, alliteration, simile, metaphor).

[5] 2.7.4* Identify characteristics of prose and poetry.

PS R2.8 The student ANALYZES LITERARY ELEMENTS & DEVICES. Student can:

[5] 2.8.1Identify or describe in fiction: plot (e.g., main conflict/problem, sequence of events, resolution), settings (e.g., how they affect characters or plot), characters (e.g., physical characteristics, personality traits, motivation), point of view (who is telling the story).

[5] 2.8.2 Compare/contrast plots, settings, & characters in various texts.

PS R2.9 The student differentiates between FACT & OPINION in text. Student can:

[5] 2.9.1 Distinguish fact from opinion.

[5] 2.9.2 Express opinions related to text and support opinions with evidence from text.

PS R2.10 The student CONNECTS THEMES. Student can:

[5] 2.10.1 Identify author’s stated or implied message, theme, or purpose (e.g., helping others brings great rewards).

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[5] 2.10.2Identify themes in texts and make relevant connections to [personal experiences, experiences of others*], or other texts.

PS R2.11 The student makes CONNECTIONS BETWEEN TEXT AND CULTURE. Student can:

[5] 2.11.1* Identify cultural influences in text (e.g., dialects, customs, traditions, geography).

[5] 2.11.2*Identify common ideas, events, and situations in multicultural readings (e.g., trickster tales about Africa, American Southwest).

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WritingStrand

PerformanceStandardReference

*Assessed Locally

Six-TraitReference

GRADE 5: WRITING Grade Level ExpectationsSBA

Emphasis

Write Usinga Varietyof Forms

PS W2.1 The student WRITES ABOUT A TOPIC. Student can:

50-57%

[5] 2.1.1 O, I/CWrite more than one paragraph stating and maintaining a focused idea and including details that support the main idea of each paragraph.

[5] 2.1.2* O Use paragraph form: indent or use paragraph breaks.

[5] 2.1.3* O, I/COrganize ideas logically to establish clear relationships within and between paragraphs (e.g., use transition words or phrases that reveal order or chronology).

[5] 2.1.4 O Write a concluding statement.

PS W2.2 The student WRITES FOR A VARIETY OF AUDIENCES. Student can:

[5] 2.2.1 O, I/C Write an understandable story that incorporates setting, character, and basic plot.

[5] 2.2.2 AllWrite in a variety of non-fiction forms using appropriate information & structure (i.e., step-by-step directions, descriptions, observations, report writing).

[5] 2.2.3* VUse expressive language when responding to literature or producing text (e.g., writer’s notebook, memoirs, poetry, plays, lyrics).

Structuresand

Conventions

PS W2.3The student uses CONVENTIONS OF STANDARD ENGLISH to write and edit. Student can:

22-27%

[5] 2.3.1* SFVary the beginnings, lengths, and patterns of sentences to improve flow and to enhance meaning of writing.

[5] 2.3.2 CIdentify/correct mistakes in spelling (e.g., grade-appropriate, high frequency words, homophones, contractions).

[5] 2.3.3 CIdentify/correct errors in punctuation (i.e., end of sentence, commas in dates, salutations & closings in letters, commas in a series) and capitalization.

[5] 2.3.4* SF, CIdentify/correct mistakes in usage (i.e., subject/verb agreement, verb tense, sentence fragments and run-on sentences, possessives).

Revise PS W2.4 The student REVISES WRITING. Student can: 22-26%

[5] 2.4.1 I/C, O Rearrange and/or add details to improve focus, to support main ideas, and to make sequence clear.

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[5] 2.4.2* AllGive/receive appropriate feedback and use established criteria to review own and others’ written work (e.g., peer conferences, checklists, scoring guides, or rubrics).

CiteSources

PS W2.5 The student DOCUMENTS SOURCES. Student can:

0%

[5] 2.5.1* I/CGive credit for other’s ideas, images, and information by citing title and source (e.g., author, storyteller, translator, songwriter, or artist).

UsesResources

PS W2.6 The student USES RESOURCES. Student can:

0%[5] 2.6.1* C, P

Use dictionary to look up spelling or definitions of words or use software programs to correct misspellings.

[5] 2.6.2* WC Use thesaurus to find synonyms for common words.

[5] 2.6.3* P Write using a word processor.

Six-Trait Reference: I/C=Ideas & Content; O=Organization; V=Voice; SF=Sentence Fluency; WC=Word Choice; C=Conventions; P=Presentation

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Alaska State Communication Standards

1.1 Uses listening and observation skills and strategies to focus attention and interpret information.

1.2 Understands, analyzes, synthesizes, or evaluates information from a variety of sources.

2.1 Uses language to interact effectively and responsibly in a multicultural context.

2.2 Uses interpersonal skills and strategies in a multicultural context to work collaboratively, solve problems, and perform tasks.

2.3 Uses sills and strategies to communicate interculturally.

3.1 Uses knowledge of topic/theme, audience, and purpose to plan presentations.

3.2 Uses media and other resources to support presentations.

3.3 Uses effective delivery.

4.1 Assesses effectiveness of one’s own and others’ communication.

4.2 Sets goals for improvement.

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V. VOCABULARY

numbers measuring constant X,Y,Zobjects relationships change logicorder algebra operations directionpatterns equations comparisons persistencerepeating coordinates vertical hintssets graphs functions understandingsorting charts variables axissymbols tables horizontal plotting

“Kid Friendly” Vocabulary Definitions

Algebra- the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations.

Axis-central line that bisects a two-dimensional body or figure. A line which a three-dimensional body or figure is symmetrical. Change- to transform

Chart- a graphic representation

Comparison- the considering of two things

Constant- not changing or varying;

Coordinates- to define the position of a point, line, or the like

Direction- the line along which anything lies, faces, moves, etc., with reference to the point or region toward which it is directed

Equation- Mathematics. an expression or a proposition, often algebraic, asserting the equality of two quantities.

Function - a factor related to or dependent upon

Graph- a series of points, discrete or continuous, as in forming a curve or surface, each of which represents a value of a given function.

Hints- an indirect, covert, or helpful suggestion

Horizontal- at right angles to the vertical; parallel to level ground. Measuring - a unit or standard of measurement

Numbers- numeral or group of numerals.

Objects- thing, person, or matter to which thought or action is directed

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Order- things following one after another

Operations- A process or action, such as addition, substitution, transposition, or differentiation, performed in a specified sequence and in accordance with specific rules.

Pattern- a combination of qualities, acts, tendencies, etc., forming a consistent or characteristic arrangement

Relationship- state of being connected or related

Repeating-to do, make, or perform again

Sets-a collection, each member of which is adapted for a special use in a particular operation

Sorting -to arrange according to sort, kind, or class; separate into sorts; classify

Symbols letter, figure, or other character or mark or a combination of letters or the like used to designate something

Tables-a concise list or guide: a table of contents.

VI. Resources and Materials

Non-fiction

Burns, About Teaching Mathematics K-8

King, Math for Fun Projects

Holtzman, Susholtz, Object Lessons

Nagda, Bitzel, Tiger Math Learning to Graph from a Baby Tiger

National Council of Teachers of Mathematics, Principles and Standards for School Mathematics

National Council of Teachers of Mathematics, Navigating through Algebra

Parker and Baldridge, Elementary Mathematics for Teachers

VanDeWalle, Karp, and Bay Williams, Elementary and Middle School Mathematics

Vorderman, How Math Works

Fiction

Kroll, Equal Schmequal

Hong, Two of Everything

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McCallum, Rabbits Rabbits, Everwhere

Birch, The King’s Chessboard

Glass, The Fly on the Ceiling

Franco, Mathematickles

Hulme, Sea Squares

Poetry

www.matsuk12.us

Technology

www.coolmath4kids.com

www.calculationnation.nctm.org

www.shodor.org/interactivate /activities

www.mathplayground.com/thinking blocks.htm

www.brightstorm.com

www.Aaplusmath.com

http://nlvm.com

www.ixl.com

www.aaamath.com

www.ppst.com

www.brainpop.com

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Project GLAD

Matanuska-Sustina Borough School District

Algebra-Grade K-5

By Bettina Mileur

Planning Pages for ALGEBRA THEME

I. FOCUS/MOTIVATION

Superkid Math Award 3 Personal Standards- Respect, Make good decisions, Be a Problem Solver CCD (Cognitive Content Dictionary) with TPR (Total Physical Response) signal award,

ONGOING! Inquiry Charts Big Book about Algebra Observation Charts Preview/Review Direct Experiences Realia Picture File Cards Read aloud-variety of Languages Video Clips Algebra “Walk About” – Looking for Math in our World

II. INPUT

Graphic Organizers- Timeline of Mathematics and Algebra 30,000 B.C.-2012AD and Comparative Chart of pictures of ALGEBRA/pictures of GEOMETRY.

Read aloud/ Shared Book Experience-“The Fly on the Ceiling” Pictorial Input- “Tiger Math” Comparative Input-Patterns, Charts and Graphs, and Input and Output Machine Read Aloud with 10/2 lecture

III. GUIDED PRACTICE

T-Graph for Social Skills/Team Points: Cooperation Picture File Cards of Algebra- observe, categorize, classify, label Exploration Report Found Poetry Poetry/songs/chant Sentence Patterning Chart-noun: Algebra

o Read & Trade Gameo Flip Chant

Personal Interactions 10/2 Lecture/ Numbered Heads Together Expert Groups-(History of mathematics, Patterns, Charts and Graphs, Realia) Mind Maps Process Grid Flexible Groups-ELD review Daily review and processing charts

IV. Reading/Writing

1. Whole Class

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Cooperative Strip Paragraph

Poetry Frames

Found Poetry

Timeline on Math History with an emphasis on ALGEBRAIC discovery

Listen & Sketch

Strip book

Process Grid on ALGEBRA

Mind Map

Big Book

2. Flexible Groups

Team Tasks

Ear-to-ear reading “Equal Schmequal”

Guided READING

Group Game for ELD student generated text:

Flexible groupings: leveled and heterogeneous

Clunkers & Links with SQ3R

Coop Strip Paragraph-Emergent/Struggling

Expert Groups

Reader’s Theater- BADWOLFPRESS.com-Mastering Math-“Sherlock Holme’s Problem Solving Play in Musical Form for grades 2-7. 30 minutes.

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3. Individual

Individual tasks

Interactive journals

Home/School connection-Share the importance of math in our world today and the need for math related activities with the family. Examples are geocaching, puzzle solving, game nights including cribbage, checkers, and chess!

Learning Log

Narrative Writing, expository, writing, poetry writing

Reading /writing choices: picture file cards, add to charts, make word cards, highlight poetry booklets, flip chant

4. Writer’s Workshop

Mini Lesson

Write

Author’s Chair

Conference

Publish

V. EXTENDED ACTIVITIES

Create your own make believe story about a famous math discovery or story problem. Illustrate your own narrative story about math Re-visit Inquiry chart Student made Big Book Team Task Presentations Portfolios Group Frames and Learning Logs Team Exploration Teacher /Student Made Rubrics Personal Exploration Team Action Plan Teacher and Student made quizzes

I. FOCUS AND MOTIVATION-

Zero Noise Class Rational/ Why do it?- Get attention without vocals

FOCUS AND MOTIVATION-

Three Standards: Show respect, make good decisions, solve problems

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Research: Brechtal/ Haley/Johnson

Rational: Brain Imprint

Management Tool (Scouts)

FOCUS AND MOTIVATION- Metacognition is thinking about thinking and they include:

Three Standards

Cognitive Content Dictionary with Signal Word-“Algebra”

Big Book about Algebra- “What is Algebra?”

Observation Charts

Inquiry charts

Preview/Review

Realia Photos

Superkid Math Awards

Read aloud- Ear to Ear-“Sea Squares” by Joy Hulme

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Come with me to the side of the sea,

Where the ocean meets the shore

We’ll count some creatures that crawl and creep

Or grow on the ocean floor.

Some flop, some dive, some swim, and swish

Some fly where the breakers roar

One ton-ton whale with one water spout,

And one strong tail to push him about

Can you count 1 spout, 1 whale and 1 strong tail? Continued….

II. INPUT

Three Standards with Scouts-use scout awards

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Realia pictures

Graphic Organizer- Algebra and the History of Mathematics! (5-10 min.)

Math Timeline and Realia Pictures

70,000-30,000 BC- Numbers have been known for thousands of year now. When man first used numbers it was for counting. Over the course of history, mathematicians have manipulated numbers to gain new information! Did you know that math didn’t even look like the math we see today? It was marks on a slab of rock. (picture of prehistoric math) Mathematicians could see that single things could be grouped, then grouped in many ways, then these groups could be described in patterns.

3,000 BC- Egyptians use fractions!

2,000 BC- Babylonians used numbers and place value

600 BC- Greek mathematicians Aristotle, Euclid, Plato, Pythagoras start to make great strides in math because this kind of work becomes highly regarded.

240 BC- Eratosthenes uses a sieve algorithm to find prime numbers.

50 BC- Algebra is important because it makes numbers easier to work with. Numbers are now used in expressions like 10^5 to describe 5x5x5x5x5!

600AD- India makes the numbers that we recognize today where everything is based on 10 symbols: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 together with hundreds, tens , and ones.

600-400AD- Greek mathematicians, Plato and Thales help traders and soldiers with business sense and logistics.

600AD- Chinese invent the abacus, the first type of hands on computer. The Arabs make a system called “multiplication and division!”

1591 AD- Francois Viete creates an entirely symbolic system of Algebra

1631 AD Descartes and Leibnitz- Letters X, Y,Z are used to represent variables. This created real excitement because symbols other than numbers were used to express groups or a certain condition. When we want to figure out real world situations we might use these algebraic symbols. Some examples are the lift of the wings of an airplane, current of electricity, or a ball falling into earth.

2012- Mathematics and its expressions are used in science, technology, and economics. Music, philosophy, and entertainment are math related too! The more math you know the better you can figure out the world around you!

INPUT-

Narrative Story “Tiger Math” by Ann Nagda and Cindy Bickel

Imbed the concept of one of the ways algebra is used and how it applied to a little tiger growing up.

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By Ann Nagda & Cindy Bickel

T.J is a Siberian tiger cub born at the Denver Zoo. When he is ten-weeks old, his mother dies and he is taken to the zoo hospital to be hand-raised. At first he won't eat. The zoo staff tries to tempt him with treats, but he refuses them all. The staff doesn't give up and persistence pays off. T.J. grows up to be a huge, healthy tiger. The delightful pictures of T.J. and the heartwarming story of his life will charm young readers as they learn the basics of graphing.

Cindy Bickel has worked at the Denver Zoo for over thirty years. During her career, she has hand raised hundreds of babies for the zoo, using math every day in her job as a veterinary assistant.

Publisher: Henry Holt & Co, 2000

Reviews

"A true story of a baby tiger's brush with death from starvation is an opportunity for learning about graphs. . . Different kinds of graphs track a variety of data. A bar graph measures how much meat T.J. ate every day. A line graph shows T.J.'s weight loss. A picture graph compares tigers in the wild, and a circle graph show the information in another form. Interesting photographs taken at the Denver Zoo detail every aspect of the story. . . A delightful way to learn math."

--Kirkus Reviews.

III. GUIDED ORAL PRACTICE

GLAD ALGEBRA POETRY-

Is this MATH?

By Jeannie Johnson

Is this math? Yes, ma’am!Is this math? Yes, ma’am!Where is it found? Everywhere!

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Where is it found? Everywhere!Does it include numbers? Yes, ma’am!Can you tell me all? Yes, ma’am!0,1,2,3,4,5 0,1,2,3,4,56,7,8, and 9! 6,7,8, and 9!

Are there other numbers? Yes, other numbers!Made of these? Are made of these!What about 42? Yes, ma’am!How about 100? Yes, ma’am!What about 23? Yes, ma’am!How about 89? Yes, ma’am!Oh, WOW! Oh, WOW!Oh, YAH! Oh, YAH!

All other numbers! All other numbers!Are made of these!

GLAD POETRY ALGEBRA

Integer Bugaloo

By, Mr. Beig, Ms, Gonzalez, Miss Weiss, Ms. Afzal, & Ms. Camey

VERSE 1

I’m a mathematician and here to say,

I can add and subtract integers all day.

Sometimes I use positives, sometimes I use negatives,

Most of all, best of all, I keep the signs true

Chorus:

Positive to negative

Negative to positive too

Doing the integer Bugaloo!

VERSE 2

A positive added to a positive, results in something new,

It results in a larger positive, positive just like you.

A positive subtracted by a positive, depends on the size,

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The bigger number’s sign, always takes the prize!

Chorus:

Positive to negative

Negative to positive too

Doing the integer Bugaloo!

VERSE 3

A negative added to a negative, is always the same,

Resulting in larger negative numbers, is the game.

A negative subtracted by a negative, changes one sign,

Makes the answer larger in size.

Chorus:

Positive to negative

Negative to positive too

Doing the integer Bugaloo!

VERSE 4

A positive added to a negative, is a tricky mix,

I look at the larger number sign, it does the trick.

The larger number sign has the power to keep its sign,

Positive three plus a negative six, the answer will be negative that’s devine.

Chorus:

Positive to negative

Negative to positive too

Doing the integer Bugaloo!

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Order of Operations Cadence

By Unknown Author

We just know what we’ve been told,

Evaluating expressions are ways of old.

There is a formula that flows left to right,

We now know Mrs. (insert teacher name here) by sight.

Sound off – Parentheses

Sound off – Exponents

Sound off – 1, 2, 3, 4

Left to right!

There is an order for all expressions,

If you follow the rules you’ll have no corrections.

First you solve all expressions in parentheses,

You shouldn’t have to wait for please.

Sound off – Left

Sound off – Right

Sound off – Par-en-the-sis

First of all!

After that you simplify your exponent

Take your time or else it could torment.

Next on the list is multiple or divide,

Left to right is how you decide.

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Sound off – Simplify

Sound off – Exponent

Sound off – To-the-pow-er

Multiply!

Follow that with add or subtract,

And your answer should be exact.

Now follow these orders perfectly,

Operations will go very smoothly.

Sound off – Left to right

Sound off – Parentheses

Sound off – 1, 2, 3, 4

Order of operations!

Solving Equations

Tune: Yankee Doodle

VERSE 1

My class and I began to solve an algebraic equation,

We looked to see the sign it used and find a good solution.

Chorus

Hey Miss (add teacher name) keep it up! (students read)

Hey class, don’t you worry. (teacher reads)

Mind the rules and the steps and it won’t be blurry.

VERSE 2

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There we were with this puzzle, we knew just what to do,

Isolate the variable and balance both sides too!

Chorus:

Hey Miss (add teacher name) keep it up!

Hey Class, don’t you worry.

Mind the rules and the steps and it won’t be blurry.

VERSE 3

What you do to one side, you do unto the other.

We get the variable by itself, and evaluate the answer!

Chorus:

Hey Miss (_________) keep it up!

Hey Class, don’t you worry!

Mind the rules and the steps and it won’t be blurry.

VERSE 4

I need to look at the symbol to figure out these lessons.

And then I can solve using inverse operations!

III. GUIDED ORAL PRACTICE

T-GRAPH for Social Skills and behavior management, academic discourse, processing meta cognition. Students work together and practice:

Tolerance

Cooperation

Responsibility

Helpfulness

Patience

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Consideration

GUIDED ORAL PRACTICE

ALGEBRA PROCESS GRID

ALGEBRA Where are “________” found? Fun and “ __________”Patterns Patterns can be seen all over the

world on buildings, on furniture, clothes, and even on bodies!

coolmath.comTangrams, cubes, and math manipulatives

Sets Simple number patterns are turned into shapes everywhere in Nature called “Fibonacci sequence” 1 1 2 3 5 8 13 21 34..There are many other patterns everywhere

Game SETTower of HanoiNLVM.comBrainpop.comGame cribbageGame checkersGame chess

Charts Charts make information clearer. Scientists use charts to keep their information organized and collected

Keep a chart on how many times you can jump rope without stopping! Mark your wall to see how tall you grow this year!

Graphs Graphs make information clearer and can be started from data lists.

Collect data! See how one thing relates with a time, place, or amount. Record one as horizontal info and one as vertical info.

In our math books Counting by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10’s.Making equal equationsLooking at fractionsLooking at math relationships

Jumping to the multiples with tarps!RapsChantsSongsInput/Output Math Machine

In the world around us Nature, architecture, furniture, computer language, clothing,

Go on a walk through different environments looking for patterns in nature, people, buildings, clothing and more.

IV. READING and WRITING Strategies

Team Tasks

Possibilities are:

CCD- Algebra

Picture file cards

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Narrative- Tiger Math

Graphic Organizer-Math timeline

Chants,

Inquiry chart-

Big Book

Reader’s Theatre- “Mastering Math”

Exploration Report as a group

Rational:

Notetaking, differentiating , rational use of information, t-chart attributes, working as a team, achieving a goal of interdependence, to practice something before they are assessed.

READING AND WRITING STRATEGIES

Story Map with “The Fly on the Ceiling” By Julie Glass

Choose the Character:

Setting:

Place:

Time:

The Problem:

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The Goal

Event #1

Event #2

Event #3

Model the writing skills of:

Sequencing

Comprehension

Scaffolding for the narrative

Retelling

Story planner for Writer’s Workshop

Team Collaboration.