Note to the Teacher

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Note to the Teacher

Some materials in each lesson plan in this Structured Curriculum Handbook arecopyrighted by THE WORKSHOP WAY, INC. Pilon WORKSHOP WAY® is a trade-marked system of Human Growth for Education.

If you decide to incorporate the WORKSHOP WAY activities in your daily lessonplans, you will want to begin using this book with the lesson plan for Day 001. Day 001 and 002are an introduction to the components of the WORKSHOP WAY and its related activities.

If you decide against including the WORKSHOP WAY activities, please start using thisbook with the lesson plan for Day 003; it will not be necessary to execute the lessons for Days001 and 002.

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General Information

The vast majority of the daily lesson plans in this program follow a specific pattern of activities.The pattern or format is as follows:

Educational Strategies/Instructional Procedures Warm-up Activity Lesson Ten Statements Free-Choice Lesson Six-Group Activity Math Workshop

The Warm-up Activity is intended to be a brief, five-minute exercise designed to focusstudents’ attention on mathematics. These exercises can be review of previously -taughtconcepts or problem-solving exercises.

The Lesson is the segment of the day’s math activities in which new concepts are presented,previously introduced concepts are practiced and/or reinforced, and quizzes or unit tests areadministered. This is the most important activity of the day’s mathematics instruction.

The Ten Statements activity provides a means by which both teacher and student canmonitor students’ ability to retain what was taught during the day’s lesson. Each day, studentswill be presented with Ten Statements, either orally or in written format. The students are toreview each of the Ten Statements, then respond with one of the two following responses:

yes, indicating that they heard the statements in that particular day’s lesson, or,no, indicating that they did not hear the statement in that particular day’s lesson.

The teacher should respond with The statement is true, but it was not heard in today’s lesson foreach no responses.

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The Free-Choice Lesson consists of daily mathematics activities taken directly from themathematics textbook. They are written in a grid format of five vertical squares and fivehorizontal squares; there are 25 Free-Choice Lessons on each Free-Choice Lesson sheet. The25 boxes are numbered from 1 to 25 and each box contains a lesson different from all the othersin the grid.

Ex.1)P. __________# __________Study p. _____

2)P. __________# __________Study p. _____

3)P. __________# __________Study p. _____

4)P. __________# __________Study p. _____

5)P. __________# __________Study p. _____

6) 7) 8) 9) 10)

11) 12) 13) 14) 15)

16) 17) 18) 19) 20)

21) 22) 23) 24) 25)

Each of the 25 lessons includes problems taken from the mathematics text.

Have students randomly select one of the 25 squares from his/her Free-Choice Lesson sheeteach day, complete the exercises listed in that square, then cross out the square when the workhas been completed.

Because of the variety of textbooks in use, it will be necessary for the teacher to choose thelessons he/she would like to include in the Free-Choice Lesson sheet grid every 25 days. (Newsheets containing new exercises will need to be created every 25 days.)

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Six-Group Activity is an activity designed to provide remediation/reteaching or enrichmentexercises for students in a small-group setting. There should be two to six students involved inany teacher-directed Six-Group Activity session. It is important to note that the students whoparticipate in the Six-Group Activity sessions are designated by the teacher and that the studentmembers in each session change daily. Group membership and participation never remains thesame because each student has his/her own set of needs, skills, and abilities. In other words,each Six-Group Activity session will be provided for a different set of two to six studentsdetermined by the teacher’s perception of students’ understanding of a specific concept or groupof concepts. There is no prescribed number of minutes for the Six-Group Activities; timeexpenditures will also vary each day.

The Math Workshop is an optional activity that teachers may or may not choose to includein their daily mathematics lessons. The 14 different activities that students perform while in theMath Workshop are intended to provide activities that combine and/or bridge mathematics withother. Core curriculum areas. Creative teachers may wish to include additional activities in theMath Workshop. A more detailed explanation of the Math Workshop is as follows:

Math Workshop

The Math Workshop is a series of tasks or jobs which students are to complete independentlyor in small groups throughout each day while teachers conduct learning sessions (Six-GroupActivity). Instruct students to work on the various Workshop tasks when they complete the Free-Choice Lesson. All students are to begin with the Task #1 everyday, then proceed at their ownrates of speed through the Workshop tasks. Students do not have to finish all of the tasks eachday; no one has to remember where he/she left off the day before.

It is important that each Workshop task be taught and /or explained thoroughly before its signis displayed in the Math Workshop.

Prepare weekly task assignments for the various Math Workshop activities before/afterschool or whenever students are not present; this reduces delays during math instruction.

A shoe organizer with nine compartments or stackable trays are two suggested structures thatcould be used as the “Finished Box”, the place where students will turn in their completed workfor each task in the Workshop.

The Finished Box should be located in a place in the classroom which is accessible to allstudents. Each compartment in the Finished Box should be clearly labeled so students knowwhere to place each of the completed task assignments

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A brief explanation of the Math Workshop tasks is listed below. Refer to the Appendix at theback of this book to find where in the Pilon Workshop Way® book you can find more detailedinformation about each task.

5-Across:

The purpose of the 5-Across activity is to develop students’ concentration and consciousness.Students are to work independently at their desks. Each day students refer to a starting number.They use the starting number as the first number to be written on their papers; they then proceedto write the next four consecutive numbers spaced evenly across their papers. Students continuethe task by skipping a line, then writing the next five consecutive numbers across the followingline. Students continue this pattern to the bottom of the page. An example of students’ work isas follows.

511 512 513 514 515516 517 518 519 520521 522 523 524 525

Students are expected to complete a minimum of ten rows. With that many rows completedstudents should notice the pattern that develops in the ones column of vertical rows of numbers.

Rounding Off:

The purpose of the Rounding Off activity is to provide students with practice of the skill ofrounding numbers to specific place values. Student are to work independently at their desks tocomplete this activity. Each day students refer to a given number and directions. (Ex: 1268;round to the nearest ten, round to the nearest hundred and round to the nearest thousand)Students’ responses, written on a half-sheet of notebook paper, should look like this:

1268

Round to the nearest ten 1270Round to the nearest hundred 1300Round to the nearest thousand 1000

Precision Cards:

The purpose of the Precision Cards activity to help students develop critical thinking andprecision thinking skills. Students are to work independently at their desks or any other alternatework station. Students are to choose one Precision Card which shows a picture or newspaper adand ten related questions. Students are to refer to the article, picture, menu, advertisement, etc.,to respond to the questions.

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An example would be a Precision Card which displays a menu and prices from a fast-foodrestaurant where hamburgers, hot dogs, potato chips, cookies, soda, and ice cream are sold.Sample questions would include questions similar to the following: Which item is the leastexpensive on the menu? Which two items could you purchase for $1.75? Do any of the itemscost the same amount of money?, etc.

Three In A Group:

The purpose of the Three In A Group activity is to promote students’ belief in theircapabilities to learn and to reduce students’ fear of the textbooks and mathematics. Students areto work in groups of three on the floor or at a table. Students refer to a card posted in the ThreeIn A Group station which contains a page number and problem numbers; the page numberrepresents a page in the students’ mathematics text which has word problems on it and theproblem numbers represent the problems the students are to work together to complete. Anexample Three In A Group Task Card would look like this:

p. 41#21, 22, 23

Although students are expected to work in groups or three, each student is responsible forsupplying his/her own mathematics text, paper, pencil and other needed supplies (ruler,protractor, etc.) and for putting his/her own completed work in the correct slot in the FinishedBox.

Daily Dozen:

The purpose of the Daily Dozen activity is to provide a review of the previous day’s lesson.Students are to work independently at their desks or at alternate work stations of their choice.

Students are to refer to the task card entitled Daily Dozen which contains twelve problemsthat can be solved with adequate understanding of the previous days’ lesson. As with othertasks, students are to put their completed activity sheets in the appropriate slot in the FinishedBox.

Thinkers:

The purpose of the Thinkers activity is to develop all modes of thinking and allows studentsto concentrate on specific skills. Students are to work independently to complete the Thinkerstasks at their desks or at alternate work stations of their choice. Students are to record their ownprogress through the 100 Thinkers activities on their own individual.

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Progress Cards. (When a student has completed a specific Thinker activity, he or she is to circlethe number on the card to indicate that he/she has completed that particular activity card.)Students are to choose a Thinker activity card or envelope and work through the task. SeveralThinker activities are contained in envelopes because they require more than just one card orpiece. As each student completes his/her Thinker activity, he/she should place his/her progresscard on his/her work to signal the teacher to visit the student to check his/her work. (Whenstudents have worked through all of the 100 tasks, they may repeat the same tasks; this showsstudents the knowledge they have gained throughout the year).

Math-5:

The purpose of the Math 5 activity is to provide students with practice performing addition,subtraction, multiplication and division. Students are to work independently at their desks tocomplete this activity. Each day for four days students are to refer to the operational sign postedin the Math 5 area of the classroom: operational signs include +, -, × , ÷ . Students are also torefer to the two numbers posted on the chalkboard.

Ex: 2, 243; 5 (posted on the chalkboard) + (posted on the Math 5 card)

(Students are to add 2,243 + 5 and record their answer on a piece of paper which the studentsuse for a period of five days.) Each day for four consecutive days, students are to repeat thesame activity—refer to the numbers on the chalkboard and the operational sign posted on theMath 5 task card, compute, then record the answer. After four days, students should have foursets of numbers (the numbers that have been written on the chalkboard each day). On the fifthday, students are to add both columns of numbers.

Ex: Monday 2,243; 5 + 2243 + 5 = 2248 (M) Tuesday 1,611; 11 - 1611 – 11 = 1600 (T)

Wednesday 3,804; 2 × 3804 × 2 = 7608 (W) Thursday 6,090; 5 ÷ 6090 ÷ 5 = 1218 (Th) Friday (add both columns of numbers) 13,748 23 (F)

It is only necessary for students to place their Math 5 activity answers in the Finished Boxafter the fifth day.

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Five Sentences:

The purpose of the five sentences activity is to promote and foster students’ decision-makingand language arts skills. Students are to complete the Five Sentences activity independently attheir desks or other alternate work stations of their choice. Students are to take an envelope(from the Workshop area designated Five sentences) to their seats, empty the contents of theenvelopes, then work to construct five sentences using the word cards. (The word cards in eachenvelope are color-coded in five different colors, one color for each sentence. Each cardcontains only one word, but the first words in each of the five sentences begin with a capitalletter and the last words contain punctuation. These clues serve to help students as theydetermine how the word cards should be arranged in complete thoughts.) As students completeeach sentence, they are to have a classmate of their choice check their work.

Puzzles:

The purpose of the Puzzles activity is to promote concentration skills. Students are tocomplete this activity independently at their desks or tables. Students are to take one largeenvelope with a picture or printed article attached to it and matching puzzle pieces inside it totheir seats. Students are to study the picture or printed article then remove the puzzle pieces andput the puzzle pieces together to create the same picture or printed article as the one displayed onthe envelope. (All puzzle pieces should be squares identical in shape and size.) When studentshave completed the assembly of the puzzle pieces to match the whole picture or article, they areto have a peer check their work.

Tangos:

The purpose of the Tangos activity is to develop and enhance students’ concentration andvisual discrimination abilities. Students are to complete the Tangos activity independently or insmall groups. Students are to use Tangos pieces to match figures illustrated on the Tango cards.Tango cards are to be displayed and/or housed in the area of the room designated Tangos. Thereis no progress card or paperwork to be turned in for this activity.

Partner Game:

The purpose for the Partner Game is to develop students’ social skills and to promoteacceptance of all classmates. Students are to choose partners and a game to play. The gamesthat students play may be commercial board games or teacher-made games; the only restrictionson the games that students play are that they should age-appropriate, school-environmentappropriate, and they should be able to be played in 15 minutes or less.

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Specific Sentences:

The purpose of this activity (Specific Sentences) is to provide practice in sentence structureand sentence sense. It should help students to understand that sentences are complete thoughtsand that all sentences begin with a capital letter and end with a punctuation mark. It should alsohelp students become aware that a line of print is not necessarily a sentence. Students are tocomplete this activity independently at their desks. Students are to refer to the activity carddisplayed at the Specific Sentences Workshop station. On the card, students are to find textbookreferences written as page number, paragraph number, and sentence number written in ordinalformat.

Ex:

Students are to find each of the three specific sentences described on the card in the textbooknamed. It is important that students write the sentences described and not the line of print.Capital letters and punctuation are to be copied correctly also. When students have written thethree sentences (with one blank line separating each sentence from the next) they are to turn theirwork in by placing it in the correct slot in the Finished Box.

Computer:

The purpose of the computer activity is to increase students’ computer skills. Students are towork at the computer(s) using computer software programs available at the particular school;math programs vary from school to school. Students are to work at the computer(s) station intimed intervals (to be determined by the teacher and the classroom schedule). A timer is to beused to alert students to the beginning and ending (start and stop times) of each timed computer-use interval.

Book: ________________________________

Page Paragraph Sentence14 2 2nd

29 2 1st

63 1 3rd

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Time Allotment Chart Math 7th and 8th

Total class time 40-45 minutes

Time Teacher Activities Student Activities

40-45 minutes Math Lesson Whole Class Lesson5-10 minutes Warm -Up Activity Whole Class15-20 minutes Education Strategies

Instructional ProcedureWhole Class Lesson

10 minutes (twice a week) Math Activity withmanipulatives

Whole Class Activity

10-15 minutes Math Six–Group Free Choice AssignmentMath Workshop

4-6 Self Contained ClassesTotal class time 60 minutes

Time Teacher Activities Student Activities

60 minutes Math Lesson Whole Class Lesson5-10 minutes Warm -Up Activity Whole Class Lesson20 minutes Education Strategies

Instructional FocusWhole Class Lesson

10-15 minutes (twice a week) Math Activity withmanipulatives

Small groups or WholeClass Activity

20 minutes Six -Group Activity Math Workshop

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STRUCTURED CURRICULUM LESSON PLAN

Day: 001 Subject: Mathematics Grade Level: 4

Correlations (SG,CAS,CFS):

ITBS/TAP: ISAT:

Unit Focus/Foci

Introduction to Math Workshop

Instructional Focus/Foci

Math Workshop

Materials

Pilon ® WORKSHOP WAY ®THINKERS ®: (for grade 7)BaggiesBlack marker10 index cards (5” x 7”)1 pack of index cards (3” x 5”)1 large poster boardTape

Educational Strategies/Instructional Procedures

Lesson:

Lay the Math Workshop task signs in a place where you can easily reach them to introduce thetasks one at a time.

Say: In today’s lesson I am going to show you how to do the Math Workshop. The rules for theworkshop are:

♦ You go into the Math Workshop after the Free-Choice Lesson or if the teacher directsyou to.

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♦ You must start at task #1 and move in numerical order through the tasks; skippingaround is not allowed.

♦ It is OK in the first month or so that you do not finish each task; you will grow as timegoes on.

♦ You will be graded on your participation in the workshop.♦ It is OK to ask someone other than the teacher for help.♦ The tasks in the workshop change everyday but the signs will remain the same.♦ Everyday you start at number one and work your way through the tasks.♦ I will do a spot check every day as to what number I think you should have completed,

so make sure you hand your work in as soon as you finish.♦ I am not going to hold it against you if you do not finish every task every day, but I

will if I have given you enough time and you are still working from 1 to 5, and I thinkyou could be farther along.

Start the lesson with the Finished box. Show the students this box and the numbers of the tasksthat go into each slot. When students finish a task, put it in the Finished box. Students shouldhave the freedom to move and put their work in the box. Place the Finished box in a centrallocation where you can keep an eye on what is going on.

Hold up the number 1 and the sign 5-Across. Tell the students that is the first task in the MathWorkshop and this is how it is to be completed. Take out a piece of loose-leaf lined notebookpaper and a pencil. (This activity is always done with a pencil.) Show the students the baggythat holds the number to be used that day. Show the students the two numbers on the card.256,259. Write the numbers on the chalkboard side by side leaving space between the two.Example: 256 259. Explain that the comma between the numbers separates the twonumbers in this activity. Have the students write the numbers on their papers under the title 5-Across the same way you did on the chalkboard. Tell the students that there should be spacebetween the numbers going across and down so they are to skip a line after every row. Have thestudents look at the two numbers and ask the question: Are these numbers going up or down?(up) By how much? (3) What would be the next number if we are counting by 3? (262) Writethat number (leave space) next to 259. Ask: What is the next number? Example: 256 259 262268. Write it next to 262. (265) Continue to ask the same question until there are three columnsof numbers. Tell the students that this is called 5-Across because they are making five rowsgoing across the paper.

Example: 256 259 262 265 268 (skip a line) 271 274 277 280 283 (skip a line) 286 289 292 295 298

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Now ask the students if they see a pattern. They should say yes and see that the numbers in thefirst column at the left have the digits 6, 1, 6 in the ones place. 6, 1, 6, the second (9, 4, 9) thethird (2, 7, 2) the fourth (5, 0, 5) and the fifth (8, 3, 8).

Have the students continue to add numbers on their papers down to the last line of the paper.Tell them that, if they make a mistake, they will know because the pattern of the number in theones place will change. Walk around to see if the students need help. When they have finished,have them turn the paper over and write C- for the column and P- for pattern. Example: C

P. Write it on the chalkboard. Write 1 under the C and have students look for the pattern(6, 1, 6). Write 6, 1, 6 under P (pattern). Instruct students to do the same for all five columns.

Example: C P1 6, 1, 62 9, 4, 93 2, 7, 24 5, 0, 5

Point out the designated slot in the Finished box where this activity should be turned in. Put thenumber 1 and the task sign 5-Across as well as the sign Math Workshop above the tasks inthe area in the classroom designated for the Math Workshop.

Say to the students: The next task is called Rounding Off. This is task number two. Hold upthe task sign Rounding Off . Have the students take out a sheet of paper, fold, and tear it inhalf. (The other half will be used for another task.) Show the number that is in the baggy (Ex. 3,675). Tell the students that this is the number that they are going to round off. Hold upthe card that shows the place values that will be rounded.

Example: to the nearest 10 to the nearest 100 to the nearest 10000

Ask the question: What number is the tens place? (7) Say: The chart says to round to thenearest ten. What number are we looking at to use the rule for rounding? (5) Should we roundup or down? (up) What is the new number? (3,680) What number is in the hundreds place?(6) What number do we look at to round 6 to the nearest hundred? (7) Should we round up ordown? (up) What is the new number? (3,700) As the students answer, write the answer on thechalkboard. Ask: What number is in the thousands place? (3) What number should we look atto round the 3? (6) What is the new rounded number? (4,000)

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3,675 – 3,6803,675 – 3,7003,675 – 4,000

Show the students where they should put the assignment in the Finished box. Hang the numberand task up in the Workshop. Ask for any questions about the Rounding Off task.

The next task is called Precision Cards . Show the students the task card and number of thetask. Show the students where the Precision Cards will be kept. Tell the students that whenthey have finished with the card they should put it back where they got it from. Have thestudents look in their Workshop folders and take out the Precision Cards Progress Sheet. Havea student distribute the Precision Cards . Tell the students that they are going to read an articleand answer the questions at the top of the card by using math strategies. Say: Use the progresssheet to record your answers, then turn the card over to check to see if you were correct. Mark acorrect sign by the ones that were correct. Anybody can turn the card over and write theanswers and cheat themselves. When you are finished, put the progress sheet back in the folder.When the progress sheet is filled, give it to the teacher for another card. The activity is to bedone once a day. Hang the number and task sign in the Workshop. Ask the students if they haveany questions.

Hold up the task sign Three in a Group. Have the students take out their math textbooks.Show them the card in the baggy. Ex. p. 11

36, 37, 38

Write the questions asked on the chalkboard.

Example: Problem State the Fact What is the question Draw the situation

Choose the equation Answer

Explain the categories to the students. The problem is the page number and problem separatedby a decimal. Example: 11.36. 11 is the page and 36 is the problem. Tell students that thisactivity is done with three people who are on this task, and it is done a 8” by 11” unlined paper ifavailable. If not have students do it on notebook paper. Students need a ruler and a pencil to dothis activity. Draw the box on the chalkboard and fill in the categories. Ask the studentsquestions about what goes into the box according to what the problem asks. Do all threeproblems the same way and tell the students that this is what to do when the group meets; theproduct should look like the one on the chalkboard. Show the students where in the Finishedbox you want this assignment. Each group member is responsible for a paper. Hang the numberof the task in the Workshop and place the baggy under the task sign. Answer any questionsabout this activity.

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Hold up the task card Daily Dozen and the number. Tell the students that these are problemstaken from yesterday’s lesson. Tell the students that they may move to another location in theroom so that they can copy the problems. This activity is to be done independently. Tell thestudents to use the other half of the paper that they used for Rounding Off. Show studentswhere this completed activity sheet should be placed in the Finished box. (Change the problemseveryday.) Hang the task in the Math Workshop and the twelve baggies under the task sign.

Hold up the task sign Thinkers® and show the students where in the room they are located.Tell the students that when they get to this task, they should take out the Progress Sheet to see ifthey have done the Thinker already. Give each student a Thinker and have them spread thecontents out on their desks. Tell them that this activity is to be done on their desks or in anempty space on the floor. Explain to students that most of the Thinkers have guide pieces thatare different colors. When the students have finished, tell them that you are going to ask them aquestion: Why did you put this here? The student will give you an answer; accept it even if it iswrong. (*Note: If you notice that a lot of students are getting a particular Thinker wrong,conduct a Six-Group Activity using that Thinker.

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Say: If you notice that I am in the middle of teaching a Six-Group Activity, lay your progresssheet over your Thinker and move on to the next task. When I say I am ready to checkThinkers , stop what you are doing and bring them to me to be checked. When you get youranswer to the Thinker question, find the number of the Thinker on the Progress Sheet and writeOK in the space. Ask if there are any questions. Have students put the Progress Sheets back intheir folders when they are done with them. Hang the number and the task in the Workshop Askif there are any questions.

Hold up the number and task sign Math-5. Tell the students that this task has a baggy that willhold the operation to be done on that day. Ex.: + . Show the students the card with thenumbers on it. Write the numbers on the chalkboard 3756,7. Have students look at the operationin the baggy. This tells them what to do with the two numbers. The sign says add, so studentsare to add 3756 + 7 = 3763. Instruct students to complete the remaining problems the same way.There are four possible signs (+, -, ÷ × ); this covers four days. On the fifth day, add all of thecolumns going straight down.

Example: 3756 7 5461 8 7955 37+5760 +2522932 77

Show the students where you want this completed activity to be placed in the Finished box.Hang this number and task in the Workshop. Ask if there are any questions.

Ten Statements

Review the ten statements and have the students write yes if they heard it in today’s lesson andno if they did not. If the answer is no, say: The statement is true, but it was not heard in today’slesson.

No Ten Statements today

Free-Choice Lesson

Have the students choose a lesson from the Free-Choice Activity sheet (one box per day).

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Six-Group Activity

No Six-Group Activity today.

Math Workshop

Have the students work in the Math Workshop after completing their Free-Choice Lesson.

Integration with Core Subject(s)

LA: Understanding explicit, factual informationUnderstanding the meaning of words in context

SC: Apply scientific method to solve problemsAnalyze and interpret data

SS: Read and interpret maps, charts, tables, graphs, and cartoonsSequence information, especially using timelinesSelect appropriate information for intended purpose

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Homework

Teacher Notes

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Math Workshop

256;259

Rounding Off1 2 3 Precision Cards

3,675

to the nearest 10to the nearest 100to the nearest 1000

5-Across

p. 63, 4, 5

Daily Dozen3 4 5 ThinkersThree in a Group

2× 5

69× 3

5

9÷ 2

4

7÷ 3

510× 7

8

4× 5

6

8÷ 4

43× 4

3

2÷ 1

3

20÷5

8× 1

4

5× 3

5

Five Sentences7 8 9 PuzzlesMath-5

+

3756 75461 87955 375760 25

Tangos10 11 12 Partner GameGraph-it

24-Game

Computer13 14Specific Sentence

Page: Par: Sent:5 3 2nd

3 4 1st

10 6 4th

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Correlations (SG,CAS,CFS):

ITBS/TAP:Perform arithmetic operations involving

integers, fractions, decimals and percentsChoose and apply appropriate operational

procedures and problem-solving strategiesto real-world situations

Understand number systemsUnderstand geometric properties and

relationships; apply geometric concepts andformulas

Apply a variety of estimation strategies:standard rounding, order of magnitude,front-ending, compatible numbers, andcompensation

Use variables, numbers, and sentences, andequations to represent solutions and solveproblems

Analyze and interpret data presented in charts,graphs, tables, and other displays

Understand and apply principles of probability,central tendency and variability

Demonstrate understanding of measurementconcepts and apply measurement skills

ISAT:Solve word problems requiring computations

with whole numbers, fractions, decimals,ratios, percents, and proportions

Understand and apply geometric concepts andrelationships

Use mathematical skills to estimate,approximate, and predict outcomes and tojudge reasonableness of results

Identify, analyze, and solve problems usingequations, inequalities, functions, and theirgraphs

Understand and use methods of data collectionand analysis, including tables, charts, andcomparisons

Demonstrate an understanding of measurementconcepts and skills

Unit Focus/Foci

Introduction to Math Workshop


Math Workshop

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Materials

Pilon ® WORKSHOP WAY ®WORKSHOP WAY® FIVE SENTENCES TASK-General ContentWORKSHOP WAY ® PUZZLESTangosA language bookComputer


Lesson:

Tell the students that today they will be introduced to the remaining tasks in the Math Workshop.

Hold up the number card and task sign entitled Five Sentences. Show the students where thistask activity is located. Choose a volunteer to give each student a Five Sentences envelope.Explain to the students that prior to choosing this activity, they should look at the Progress Sheetin their Workshop folder to see whether or not Five Sentences has been completed. Instructstudents to spread the contents of the envelopes on their desks. Point out that there are fivedifferent colors and that the pieces should be sorted in piles according to color. Explain that theobject of this activity is to create sentences using one color for each sentence. Tell students thatsome cards contain a word that begins with a capital letter and some cards contain punctuationmarks; these cards indicate the first and last words of the sentences.

Tell the students that they should have the teacher check their work when they have completedcreating all five sentences. If the teacher is not available, tell the students that they should covertheir work using their Progress Sheet until their work has been checked. Hang this baggy in theWorkshop. Ask students if they have any questions about the Five Sentences task.

Display the task sign entitled Puzzles. Show the students the classroom location for this activity.Choose a volunteer to distribute an envelope containing a puzzle to every student. Explain thatthere are a total of 100 different puzzles in four different subject areas. Ask the students tospread the contents of the envelopes on their desks. Tell the students that the picture on the frontof their envelope looks exactly like the picture they are trying to create with their puzzle pieces.Present the following helpful hints:

1. Assemble the puzzle pieces next to the picture on the folder/envelope; do not placethe puzzle pieces on the picture.

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2. The pieces that have a black line along the edge(s) are border pieces.

3. It will be easier to assemble the puzzle if the border pieces are put together first.

The Puzzles activity should only take about eight to ten minutes.

As with previous task activities, explain to the students that their work is to be checked by theteacher; however, if the teacher is not available, students should cover their completed workusing their Progress Sheet.

The next task is called Tangos. Show the students where in the classroom this can be located.Open up the game and show the students the game pieces and accompanying cards. Explain tothe students that when they choose a card with a figure on it, they should use the tango pieces tomake that figure. There is no Progress Sheet for this activity; students should have a classmatecheck their work. Place the task card in the Workshop area. Ask students if they have anyquestions.

Next, hold up the task number sign that reads Specific Sentences. Students of grades 4 and 5will use their English textbooks and students of grades 6, 7, and 8 will used their Social Sciencetextbooks for this activity. Students will open their English/Social Science books to the pagenumber, paragraph, and sentence shown on the first line of display on the card inside the baggy.

The Specific Sentences task card should look like the following:

Discuss the abbreviations with the students.

p. - pagepar. - paragraphsent. - sentence

Explain to the students that they are to turn to the page number given on the task card, thenlocate the paragraph and sentence given, and, finally, write that specific sentence on a sheet ofnotebook paper. Students are to repeat these directions for the remaining two sets of page,paragraph, sentence numbers given. When all three sentences have been recorded on notebookpaper, students are to put the completed task assignment in the Finished box. Answer anyquestions students may have about this activity.

p. 262 par. 2 sent. 1p. 154 par. 3 sent. 2p. 310 par. 1 sent. 3

22

Hold up the task sign entitled Computer and the timer that will be used for this activity. Explainto the students that the timer will be used to indicate when it is time to change groups working atthe computers. (Computer activities will be generated by the math program used at eachindividual school. The length of the timed intervals for computer use will be determined by theindividual teacher depending on what best fits the schedule in place at that school. Teachers willset the time that will fit in their class schedules.) When the timer/bell/buzzer sounds, groups willchange places; if they have been using the computer, they must go to a different task to allowother students time at the computers.

Ten Statements


No Ten Statements today

Free-Choice Lesson


Six Group Activity

No Six-Group Activity today.

Math Workshop






23

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Homework

Teacher Notes

24



Correlations (SG,CAS,CFS): 6A1

ITBS/TAP:Understanding number systems

ISAT:

Unit Focus/Foci

Place Value


Introducing place value vocabulary

Materials

Six-Group Activity: Addition (words to numbers)Math journalsTransparencies of warm-up problems, and place value chart (optional)Homework worksheetsOverhead projector


Warm-up:

Read aloud the 20 problems below and have students write the corresponding answers on theirpapers. Allow a five second response time.

1. 6 + 7 = 7. 4 + 7 = 13. 8 + 5 = 18. 8 + 6 =2. 19 - 7 = 8. 13 - 4 = 14. 14 - 7 = 19. 15 - 6 =3. 9 + 9 = 9. 18 - 9 = 15. 5 + 4 = 20. 7 + 9 =4. 2 + 8 = 10. 16 - 8 = 16. 17 - 9 =5. 12 - 6 = 11. 5 + 7 = 17. 16 - 7 = 6. 9 + 8 = 12. 15 - 9 =

25

Prepare a transparency in advance with the 20 problems and answers. Read each problem one ata time and call volunteers to give answers. After a student displays the answer continue until allproblems are completed.

Lesson:

Present and explain the following vocabulary terms using examples: 1) place value 2) standardform 3) expanded form 4) word form 5) digit 6) period 7) order.

Write 862 on the chalkboard, then explain the difference between a number and a digit by statingthat 8, 6 and 2 are the digits that make up the number 862. Write 137,468 and have students tellhow many digits there are. Repeat procedure with the numbers 1249, 8, and 17,245. Be surestudents understand that the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are numbers that have only 1digit.

Point to the number 862 and say that this way of writing a number is called the standard form.Ask for other ways to write a number. One way is the expanded form. Write 800 + 60 + 2.Explain that, if you add all the numbers together, they will equal the original number. Write7,591 and have a student go to the chalkboard or overhead projector and write it in expandedform. Introduce word form by writing “eight hundred sixty-two” and state that this is the wordform of the same number.

Place value is the value of a digit in a number. The value of 9 in 29 is 9 ones; in 94, its value is90, or 9 tens; and in 926, its value is 900, or 9 hundreds.

Students may refer to the place value chart in the text or the teacher can prepare the place valuechart given in teacher notes on a transparency. A period is a group of three digits in a numberthat can be set off by commas. There can be up to three digits in a period. A period must havethree digits in it if there is a comma to the left of it. Remind students that commas are placedevery three digits counting from the right. For example: In the number 16,437 you would countfrom the right three places and write the comma between the 4 and 6. Next, write the number45,806,396. Have students refer to place value chart and identify the periods in this number.Then have them identify how many digits are in each period.

Explain that the term order means to arrange numbers in some way. Example: order thesenumbers from least to greatest: 5, 9, 1, 6 1, 5, 6, 9

least greatest

26

Write the following numbers on the chalkboard or overhead projector transparency: 13, 12, 8,10. Have students order them from least to greatest. Write these numbers 28, 32, 29, 27, 31, andhave the students order them from greatest to least.

Ten Statements


1) There are six digits in the number 389,263. (yes)2) 2 + 3 ⋅ 4 is an example of the order of operations. (no)3) The number 862 written in expanded form is 800 + 60 + 2. (yes)4) There can be up to three digits in a period. (yes)5) Place value is the value of a digit in a number. (yes)6) 6/3 is an improper fraction. (no)7) 8, 6, and 2 are the digits that make up the number 862. (yes)8) In the number 862, the digit 6 has the value of 60. (yes)9) On the number line, positive numbers are to the right of the zero and negative numbers are to

the left of zero. (no)10) In the number 16,437, the comma would be written between the 4 and the 6. (yes)

Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete teacher-directed activitysheet. (Addition: words to numbers)

Math Workshop




27



Connection(s)

Enrichment:

Fine Arts:

Home: Family members can help students learn terms by helping develop a math glossary.Terms can be written on the front of index cards. Their explanations, along with examples, canbe written on the back of the cards. A family member can read the term and have the studentgive the meaning or the family member can give an explanation and have the student give theterm.

Remediation: See Six-Group Activity Sheet “Addition: Words to Numbers” (attached).

Technology:

Assessment

Students’ responses during lesson, Warm-up Activity, Ten Statements.

Homework

Say: Choose three of today’s vocabulary terms and learn them thoroughly. You should be ableto do the following: 1. When you see/hear the term, be able to give the correct definition. 2.When you see/hear the definition, be able to give the correct term. 3. Be able to give your ownexamples of each. 4. Be able to ask/answer questions about each of your terms.

If you don’t want the teacher to actually say this, but you want to describe it, it should read asfollows: Have students choose three of the vocabulary words introduced in today’s lesson.

28

Teacher Notes

Millions Thousands

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

29

Six Group Activity

Addition (Words to Numbers)

Materials:10 index cards (5” x 7”)1 black marker1 pencil1 envelope (9 ½” x 6 ½”)

Prepare the following index cards using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the back of the cards. Write one number on eachcard.

Five hundred nineSeven hundred threeTwo thousand, one hundred sixteenFive thousand eightSix thousand, eight hundred forty-threeSeventy-four thousand-nine hundredSeven thousand fourThree hundred seventeen million, fifty-two thousandNine thousand, fifteenTwenty thousand, forty-five

Answers:509 703 2,116 5,008 6,843

74,900 7,004 317,052,000 9,015 20,045

Copy this study board and use it to reteach this lesson.

30

Place Value ChartHUNDRED

BILLIONS

TEN

BILLIONS

BILLIONS

HUNDRED

MILLIONS

TEN

MILLIONS

MILLIONS

HUNDRED

THOUSANDS

TEN

THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

Use this place value chart to review writing words as numbers. Use this example and ask thesequestions.

Example: 6,093

What number is the hundreds place? (0)How many thousands are there? (6)How could you write this number in expanded form?( 6 × 1000 )+( 0 × 100 )+( 9 × 10 )+( 3 × 1 )What number is in the ones place? (3)How many tens are there? (9)

Prepare index cards for the study board by writing the ten numbers given in the Six GroupActivity, one number on each card. Tell the students that they are going to do an activity thatinvolves changing words into numbers. Lay a card on the table and have the students write theanswer. As you reveal the answer, say: The answer is…… Store the activity cards and studyboard in the 9 ½” x 6 ½” envelope.

31



Correlations (SG,CAS,CFS): 6B1

ITBS/TAP:Understanding number systems

ISAT:

Unit Focus/Foci

Place Value


Reading and writing numbers

Materials

Six-Group Activity: Addition: Place ValueMath journals


Warm-up:

Have students work in groups of two or three with students who have studied the same terms.Together, they will review the terms, they have studied.

For the next seven to eight minutes, have the students work in groups of two or three again. Thistime work with students who studied different terms. Students will then teach their terms to eachother.

Review all terms orally with the students. Give an explanation of each term and have studentsname the term or vice versa.

32

Lesson:

Show the following numbers to students one at a time and have volunteers read them aloud:1.) 2,758 2.) 903 3.) 54,212 4.) 600,000 5.) 697,421,0006.) 400,002 7.) 111,808,217 8.) 14,065 9.) 60,005 10.) 8,070

Using the same numbers that students read aloud, ask students to identify various periods and tellhow many periods a number has. For example: In number 7, which period contains the digits808? (thousands). In number 10 how many periods are there? (two). Next have studentsidentify the place value of some of the digits. For example: In number 6, what is the place valueof the 4? (four hundred thousand). In number 2, which digit is in the tens place? (zero).

To introduce dictation to the students, have them open their journals and number from 1 to 5.Tell the students to listen as the teacher says a number. The teacher will say a number, repeat thenumber, and have students write it in their journals next to number 1. The teacher should tellstudents that there can be only three digits in a period, and discuss where to place commas. Tellstudents to count the digits from right to left and write a comma to the left of each third digit (ormultiple of three). Example: 21,469. Have students count from right to left three digits and askwhere to place the comma (between the 1 and the 4.). Tell students to continue counting fromright to left three digits and determine whether another comma is needed (no).

Explain that a comma should be written in place of any period name that the student hears duringthe dictation. For example: The teacher dictates the number 8,492. The student hears 8thousand 492 and writes an 8 followed by a comma, then 492. The teacher will dictate thefollowing numbers: 1.) 687 2.) 3,925 3.) 84,450 4.) 871,604 5.) 409,299. Theteacher should dictate each number and then discuss it as soon as the students have written it.Have students go to the chalkboard and write the numbers. Allow students to make anynecessary corrections in their journals.

Ten Statements


1) When writing a number, the periods are separated by commas. (yes)2) There can be up to three digits in a period. (yes)3) The number 18 is divisible by 2. (no)4) In the number 3,925, the comma is written between the digits three and nine. (yes)

33

5) In the number 871,604, the digit 1 is in the thousands place. (yes)6) In the problem 6 + 5 = 11, the 6 and 5 are addends. (no)7) The number 400,002 has two periods. (yes)8) When writing the number 2,758, you will need to write only one comma. (yes)9) A square has four equal sides. (no)10) In the number 400,002, a zero is in the ten thousands place. (yes)

Free- Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet. (Addition: Writing Numbers)

Math Workshop

Have the students work in the Math Workshop after completing their Free Choice Lesson.





Connection(s)

Enrichment:

Fine Arts:

Home: Family members can help students by dictating numbers between 1 and 999,999 to thestudent and having the student write them. Family members can also write numbers and havethe student read them.

34

Remediation: See attached Six-Group Activity Sheet

Technology:

Assessment

Students’ responses during review, lesson, dictation and Ten Statements review.

Homework

Have students practice reading and writing these numbers:

1.) 386 2.) 490 3.) 2,729 4.) 8,206 5.) 13,9986.) 70,000 7.) 5,684 8.) 6,901 9.) 43,875 10.) 7,707

Teacher Notes

35

Six Group Activity

Addition: (Place Value)


Prepare the following index cards using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the back of the cards. Write one number inexpanded form on each card.

1. 700 + 30 + 52. 50 + 53. 600 + 20 + 74. 1000 + 400 + 85. 9000 + 10 + 16. 8000 + 107. 600 + 20 + 98. 10,000 + 200 + 109. 2000 + 600 + 20+110. 3000 + 200 + 1

Answers:1. 7352. 553. 6274. 1,4085. 9,0116. 8,0107. 6298. 10,2109. 2,62110. 3,201


36

MILLIONS

H TU HN OD UR SE AD N D S

TEN

THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

Say: When writing a number in expanded form, you are writing the value of that number.Example: 856 Expanded: 800+50+6 = (8 × 100)+(5 × 10)+(6 × 1)

When writing a number in standard form, write the cardinal number. Example: 856

Review with the students how to write numbers from the expanded form. Write the number7,695 and ask what place the digits are in.

Example: What place is the seven in? (thousands) What is the expanded form of the 6? (6 x 100) What place is the number 9 in? (tens)

Tell the students that you want them to risk writing the answers to these problems. The name ofthe activity is Place Value. Write the standard form of a number. Lay a card with a numberwritten on it on the table and have the students write the answer. As you reveal the answer, say:The answer is…… Store the activity cards and study board in the 9 ½” x 6 ½” envelope.

37



Correlations (SG,CAS,CFS): 6B1

ITBS/TAP:Understand number systems

ISAT:

Unit Focus/Foci

Place Value


Ordering numbers

Materials

Six-Group Activity: Addition (Place Value)Two 0-5 number cubesTwo 5-10 number cubesOverhead projectorMath journals


Warm-up Activity:

Have the students number from 1 to 10 in their math journals. Dictate the following ten numbersand have students write them:1.) 597 2.) 309 3.) 6,318 4.) 245,690 5.) 300,0086.) 502,158 7.) 3,960,425 8.) 19,002 9.) 97,063 10.) 8,146.

Instruct the students to listen to the number the first time it is dictated and begin writing it thesecond time. Ask for volunteers to go to the chalkboard to write their answers and read themaloud. Instruct the students to correct any errors in their math journals.

38

Lesson:

Call on volunteers to define the word order, which means to arrange numbers in some way. Askstudents: What does least mean? (smallest or lowest)? Ask students: What does greatestmean? (largest)? Write the following group of numbers on the chalkboard: 24, 36, 14, 32.Have students write these numbers from least to greatest. (14, 24, 32, 36)

Write these numbers on the board and have the students write them from greatest to least:247, 284, 274, 248. (247, 248, 274, 284)

Write the next groups of numbers on the chalkboard: 1.) 475, 472, 469, 470 2.) 1100, 1103,1099, 1101 3.) 896, 900, 890, 895 4.) 3,257, 3,248, 3,250, 3,247. Have students go to thechalkboard and rewrite these groups of numbers in order. Have the students order the first twogroups from least to greatest and the last two groups from greatest to least.

Write 29, 36, 34, 28 on the chalkboard. Have students order the numbers from least to greatestand greatest to least (28, 29, 34, 36 and 36, 34, 29, 28).

Write 64, ___, 66 on the chalkboard. Ask students: What number comes after 64 and before 66?(65)

Write the following on the chalkboard, and have students copy and complete in their journals: 1.38, ___, 40 2. 57, ___, 59 3. 49, ___, 51 4. 603, ____, 605 5. 799, ____, 801 6.2,840, _____, 2,842.

Write 79 and 85 (leaving space between them) on the chalkboard. Ask: What number comesafter 79 and before 85? Students should recognize that there is more than one answer (80, 81,82, 83, 84). Repeat this with the following: 1. 627 and 635 2. 4,796 and 4,803.

Write the following on the chalkboard: A B C116 ____ 125 126 ____ 135 136 ____ 145

Tell students that you are going to say some numbers. The students are to tell in which blank thenumber belongs.

1. 132 (B)2. 120 (A)3. 119 (A)

39

4. 141 (C)5. 137 (C)6. 134 (B)7. 147 (none)

Ten Statements


1) The numbers 14, 24, 32, and 36 are arranged in order from least to greatest. (yes)2) 34 rounded to the nearest ten is 30. (no)3) To order is to arrange numbers in some way. (yes)4) The least number would be the smallest number. (yes)5) 50 comes after 49 and before 51. (yes)6) The answer to an addition problem is called the sum. (no)7) The numbers 36, 34, 29, and 28 are arranged from greatest to least. (yes)8) You can estimate when an exact number is not needed. (no)9) The greatest number would be the largest number. (yes)10) The numbers 80, 81, 82, 83, and 84 come between 79 and 85. (yes)

Free Choice Lesson

Have the students choose a lesson from the Free-Choice Activity Sheet (one box per day).

Six Group Activity

Have a group of six students, two from each ability level, complete teacher-directed activitysheet. (Addition: Place Value)

Math Workshop




40



Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six Group Activity Sheet: Addition: Place Value

Technology:

Assessment

Informally assess students’ responses during lesson and game, Warm-up Activity, TenStatements review.

Homework

Distribute the prepared homework sheet (attached).

Teacher Notes

41

Day 5: Homework

1. Define the word order. _______________________________________ __________________________________________________________

Write these numbers in order from least to greatest.

2. 35, 39, 34, 37 _____________________________________________ 3. 1248, 1243, 1250, 1249 _____________________________________

Write these numbers in order from greatest to least.

4. 15, 19, 16, 12 ____________________________________________ 5. 375, 370, 376, 374 ________________________________________

Write the missing numbers.

6. 47, ___, 49 7. 999, ____, 1001

Write in all missing numbers.

8. 4279, ______________________________, 4284

42

Six Group Activity

Addition: (Place Value)


Prepare the following index cards using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the back of the cards. Write one number inexpanded form on each card.

1. 700 + 30 + 52. 50 + 53. 600 + 20 + 74. 1000 + 400 + 85. 9000 + 10 + 16. 8000 + 107. 600 + 20 + 98. 10,000 + 200 + 109. 2000 + 600 + 20+110. 3000 + 200 + 1

Answers:1. 7352. 553. 6274. 1,4085. 9,0116. 8,0107. 6298. 10,2109. 2,62110. 3,201


43

MILLIONS

H TU HN OD UR SE AD N D S

TEN

THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

Say: When writing a number in expanded form, you are writing the value of that number.Example: 856 Expanded: 800+50+6 = (8 × 100)+(5 × 10)+(6 × 1)

When writing a number in standard form, write the cardinal number. Example: 856

Review with the students how to write numbers from the expanded form. Write the number7,695 and ask what place the digits are in.

Example: What place is the seven in? (thousands) What is the expanded form of the 6? (6 x 100) What place is the number 9 in? (tens)

Tell the students that you want them to risk writing the answers to these problems. The name ofthe activity is Place Value. Write the standard form of a number. Lay a card with a numberwritten on it on the table and have the students write the answer. As you reveal the answer, say:The answer is…… Store the activity cards and study board in the 9 ½” x 6 ½” envelope.

44



Correlations (SG,CAS,CFS): 6A1, 6B1, 4


ISAT:

Unit Focus/Foci

Place Value


Comparing numbers and finding numbers on a number line

Materials

Six-Group Activity: Addition: Commas


Warm-up Activity:

Draw the chart below on the chalkboard and have students copy and complete it.Say: For each group of digits give the greatest possible number and the least possible number.

Use these digits Greatest Number Least Number1.) 5, 32.) 6, 7, 13.) 2, 9, 94.) 4, 8, 4, 85.) 1, 2, 3, 2, 0

1. 53, 352. 761, 1673. 992, 2994. 8844, 44885. 32, 210 10,223

45

Lesson:

Introduce the comparison of two numbers by explaining that when comparing two numbers,students should show that one value is larger or smaller than the other(s). Say: The symbols thatare used to show greater than or less than are called chevrons. The less than sign points to theleft and the greater than sign point to the right. Remind the students that the point of thechevron points to the smallest number. For example: 4 < 6 is read 4 is less than 6, or 6 > 4 isread 6 is greater than 4. [Less than (<), greater than (>).] Other vocabulary terms that can beused to show comparing of numbers is “ascending order” arranging from smallest to largest, and“descending order” arranging numbers from largest to smallest.

Have individual students go to the chalkboard and write two numbers leaving a space betweenthem. Have the student write the number, then call on another student to go to the chalkboardand write the correct chevron symbol between the two numbers and read the number sentencealoud. If the student does both steps correctly, then he/she may write two new numbers on thechalkboard and call on another student to complete the new number sentence. If the studentanswers incorrectly, he/she must sit down and the teacher can call on another student to go up tosolve the problem.

Finding numbers on a number line: These number lines can be prepared ahead of time on atransparency). Draw the number line shown below on the chalkboard.

A B C D E F G ↓↓ ↓↓ ↓↓ ↓↓ ↓↓ ↓↓ ↓↓

0 5 10 15 20 25 30 35 40 45 50

Have students identify the numbers being represented by the letters. (A = 8, B = 14, C =21, D =32, E = 38, F = 43, G = 49)

Ask what numbers can be found between 20 and 25 on this number line. (21, 22, 23, 24)

Draw the number line shown below on the chalkboard.

H I J K L M N ↓↓ ↓↓ ↓↓ ↓↓ ↓↓ ↓↓ ↓↓

0 10 20 30 40 50 60 70 80

46

You may need to explain that this number line increases in increments of two.Have students identify the numbers being represented by the letters. (H = 4, I = 12, J = 28, K =36, L = 52, M = 65, N = 79)

Ask what numbers can be found between 30 and 40 on the number line. Students may tell you32, 34, 36, 38. Make sure that students understand that 31, 33, 35, 37 and 39, must be included,also.

Draw the number line shown below on the chalkboard.

O P Q R S ↓↓ ↓↓ ↓↓ ↓↓ ↓↓

0 25 50 75 100 125 150

You may need to explain that the number line increases in increments of five. Have studentsidentify the numbers being represented by letters. (O = 20, P = 35, Q = 70, R = 105, S = 140)

Ten Statements


1) When comparing two numbers, the point of the chevron always points to the smaller number.(yes)

2) When comparing two numbers, you show that one value is larger or smaller than anothervalue. (yes)

3) 548 rounded to the nearest hundred is 500. (no)4) To order is to arrange numbers in some way. (yes)5) In the number sentence 4< 6, the chevron points to the four. (yes)6) The symbols for less than and greater than are called chevrons. (yes)7) The symbol for greater than is a chevron that points to the right. (yes)8) The answer in addition is called the sum. (no)9) You can estimate when an exact answer is not needed. (no)10) The numbers 75 , 80, 82 and 90 are arranged in ascending order from least to greatest. (yes)

Free Choice Lesson


47

Six Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet. (Addition: Commas)

Math Workshop

Have the students go into the Math Workshop after completing their Free-Choice Lesson.





Connection(s)

Enrichment:

Fine Arts:

Home: Family members should play the Order game with the student, to help the studentpractice reading and writing numbers.

Remediation: See attached Six Group Activity Sheet: Addition: Commas.

Technology:

48

Assessment

Informally assess students responses during lesson and game, Warm-up Activity, Ten Statementsreview

Homework

Have students write 10 comparison problems without symbols. Instruct students to write theanswers on the back of the paper. Students should also practice reading and writing numbers.

Teacher Notes

49

Six-Group Activity

Addition: (Commas)

Materials:10 index cards (5” x 7”)1 black marker1 pencil1.envelope (9 ½” x 6 ½”)

Prepare the following index cards using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the back. Write only one comparison numbersentence on each card.

1433962 964821 217924 11682371 143929743268 1436849 576243912 6954 102635

Tell the students that when you lay a card on the table they are going to write the commas in thecorrect place in the number.

Answers:

1,433,962 964,821 217,924 11,682,371 1,43929,743,268 1,436,849 576,243,912 6,954 102,635


Commas

Say: Commas are used to separate the hundreds, thousands, millions, and billions. You start atthe right and count three places. Every three places, write a comma.

6734 695734271

6,734 695,734,271

Use the study board to show the students where and how to place commas in numbers. Askthese questions:

50

Example: 9656

How many digits are in 9656? (4)How many places should you count before you place a comma? (3)What side of the number do you start on? (right)Where would the comma belong in 9656? (between the 9 and 6)

As you ask these questions, write the answers on the chalkboard so that the students can seethem.

Tell the students that they are going to do an activity like the one they just did. Lay an indexcard with numbers written on them on the table and tell the students to write commas where theybelong. As you reveal the answer, say: The answer is…… Store the activity cards and studyboard in the 9 ½” x 6 ½” envelope.

51



Correlations (SG,CAS,CFS): 6A1; 6B1


ISAT:

Unit Focus/Foci

Whole Numbers


Writing numbers in standard form, expanded form, and word form

Materials

Six-Group Activity: Addition: Expanded FormHomework worksheet (attached)Prepared transparency of problems for standard, expanded and word formsMath journals


Warm-up Activity:

Have students exchange their homework problems with a classmate. Have students write theappropriate comparison symbol (< or >) in the spaces provided between the pairs of numbers.After completing the problems, tell students to turn over the papers, and using the answer key,correct their answers.

Lesson:

Have the students write in their math journals the three ways to write numbers. The first way towrite a number is the standard form; this is when you write a number using digits. Ex.: 58,275Expanded form is showing the place value of each digit in a number. Ex.: 58,275 = 50,000 +8,000 + 200 + 70 + 5.Word form is the number written in words. Ex.: One hundred fifty-eight thousand, two hundredseventy-five. Remind students to use commas to separate the periods.

52

(Because writing expanded form and word form problems can be time consuming, you mightwant to prepare a transparency or have a student go to the chalkboard to write a seven-digitnumber in standard form.)

Write these numbers on the chalkboard and have the students write them in expanded form andword form.

1) 5,6232) 12,0003) 6914) 185,9755) 87,402

Answers:

1) 5,000 + 600 + 20 + 3; five thousand, six hundred twenty-three2) 10,000 + 2000; twelve thousand3) 600 + 90 + 1; six hundred ninety-one4) 100,000 + 80,000 + 5,000 + 900 + 70 + 5; one hundred eighty-five thousand, nine

hundred seventy-five5) 80,000 + 7,000 + 400 + + 2; eighty-seven thousand, four hundred two.

Dictate these numbers to the students and have them write the standard form:

1) 3,8612) 8953) 4,9804) 5,2895) 769,458.

Write the answers on the chalkboard after the students have been given time to write theanswers.

53

Ten Statements


1) When writing numbers, you must use commas to separate the periods. (yes)2) Three ways to write a number are standard form, expanded form, and word form. (yes)3) 2,576 is a four digit number. (no)4) 54,271 in expanded form is 50,000 + 4,000 + 200 +70 + 1 (yes)5) Standard form is a number written using digits. (yes)6) The number 725 comes between the numbers 724 and 726. (no)7) The answer in to a division problem is called the quotient. (no)8) 300 + 50 + 2 is the expanded form of 352. (yes)9) Ascending and descending order are vocabulary words used to show ordering of numbers.

(yes)10) Three-tenths is less than six-tenths. (no)

Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet. (Addition: Expanded Form)

Math Workshop






54

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity Sheet Addition: Expanded form

Technology:

Assessment

Informally assess students’ responses during Warm-up Activity lesson, and Ten Statementreview.

Homework

Have the student complete the teacher-prepared worksheet. Also have students practice readingand writing numbers.

Teacher Notes

55

Six Group Activity

Addition: Expanded Form

Materials:5 index cards (5” x 7”)1 black marker1 pencil1 envelop 9 ½” x 6 ½”

Prepare the following index cards, using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the back of the cards.

79 196 6093 94,089 5,146

Have students write each number in expanded form.

Answers:

(7 × 10) + (9 × 1)(1 × 100) + (9 × 10) + (6 × 1)(6 × 1,000) + (0 × 100) + (9 × 10) + (3 × 1) or (6 × 1000) + (9× 10) + (3 × 1)(9 × 10,000) + (4 × 1,000) + (0 × 100) + (8 × 10) + (9 × 1) or (9 × 10,000) +(4× 1000) + (8 × 10) + (9 × 1)(5 × 1,000) + (1 × 100) + (4 × 10) + (6 × 1)


Expanded Forms

Say: You multiply the number times the place it is in.

Examples: 356 3 × 100, because 3 is in the hundreds place

5 × 10, because the 5 is in the tens place6 × 1, because 6 is in the ones place

689 = (6 × 100) + (8 × 10) + (9 × 1) = 600 + 80 + 9

56

23,154 = (2 × 10,000) + (3 × 1,000) + (1 × 100) + (5 × 10) + (4 × 1)= 20,000 + 3,000 + 100 + 50 + 4

Use the study board to do this sample problem and ask the students these questions:

Example: 295 3567

Write the number on a piece of paper so the students can see the work. Write 295 first.Have students write the number 295.

Ask:

How many digits are there in this number? (3)Name the place values in this number from right to left (ones, tens, and hundreds)Does this number need a comma? (no)

Write down 3567 Ask: How many digits are in this number? (4)

What number is in the hundreds place? (5)What would we multiply 3 times in expanded form? (1000)What would it give us? (3000)What would we multiply 5 times? (100)What would it give us? (500)What would we multiply 6 times? (10)What would the answer be? (60)What would we multiply 7 times? (1)What would the answer be? (7)Does 3,000+500+60+7 give us 3567? (yes)

Say to the students: We are going to do activity just like the one we just did. I am going to showyou a card and I want you to risk writing the expanded form of the number. Lay an index cardwith a number written on it on the table and give the students time to write the answer. As youreveal the answer, say: The answer is…… Store the activity cards and study board in the 9 ½” x6 ½” envelope.

57



Correlations (SG,CAS,CFS): 6E3

ITBS/TAP:Understand number systemsPerform arithmetic operations

ISAT:

Unit Focus/Foci

Whole Numbers


Using the order of operations with parentheses

Materials

Six-Group Activity: Addition: Ordering NumbersMath journalsTransparency


Warm-up Activity:

List the following problems on the chalkboard or a transparency.

Write the following numbers in standard form.

1) 20,000 + 6,000 + 400 + 52) One hundred thirty-thousand, two hundred three

Write in expanded form.

3) 5,9064) Fifty-four thousand, nine hundred

58

Write in word form.

5) 918,0606) 30,000 + 4,000 + 300 + 60 + 8

Have the students write the answers in their math journals. Call on volunteers to go to thechalkboard and write their answers. This is a part of the review for the test.

Lesson:

Tell the students that when more than one operation is used, there is an order in which theyshould perform the operations within a problem. Explain that this is important so that everyonewill get the same solutions.

Write the following on the chalkboard. Ask the students to copy the mnemonic device in theirjournals.

PleaseExcuseMyDearAuntSally

Tell them that a mnemonic is a device, such as a rhyme, that is used to help remembersomething. Tell students that this mnemonic will help them learn the order of operations. Havestudents underline the first letter of each word. (P, E, M, D, A, S) Next have them write thefollowing in a column next to the mnemonic.

ParenthesesMultiplicationDivisionAdditionSubtraction

Students should note that these mathematical words begin with the same letters as the words inthe mnemonic.

59

Next write the rules.

1. Do all operations within parentheses first.2. Next multiply and divide in order from left to right.3. Then add and subtract in order from left to right.

The equation 3 + 5 x 6 can have two solutions when parentheses are used. The order in whichstudents perform the operations will determine the solution. Write (3 + 5) x 6 and 3 + (5 x 6)onthe chalkboard. Ask students to solve them in their journals. (8 x 6 = 48 and 3 + 30 = 33.) Askstudents what was different about the two problems. (The parentheses were in different places.)Ask them how this affected their answers. (Example: Because they performed differentoperations first in each problem, the solutions were different.)

Write 18 - 8 ÷ 2. Ask students how they should solve this problem. Students should state thatthe division operation (8 ÷ 2) should be performed first, and then 18 - 4. The solution is 14. Askstudents why they did not perform the subtraction operation (18 - 8) first. (Because order ofoperations says that division is to be performed before subtraction.)

Ask what could be done to the problem to get a different solution. (Parentheses could be addedaround the 18 and 8.) Write (18 - 8) ÷ 2. Have students solve. (18 - 8 = 10, 10 ÷ 2 = 5)

Assign the following problems for students to complete in their journals.1. 7 x (3 + 2) 2. (7 x 3) + 23. 18 ÷ (6 ÷ 2) 4. (24 ÷ 6) ÷ 25. 3 + (9 x 3) 6. (3 + 9) x 37. 12 ÷ (3 + 7 - 4) 8. (9 + 5) ÷ (8 - 1)9. 8 - (24 ÷ 4) 10. (24 ÷ 8) x 5

Solutions:1. 35 2. 23 3. 6 4. 2 5. 306. 36 7. 2 8. 2 9. 2 10. 15

Review days 003-007 unit vocabulary, reading and writing numbers, ordering numbers,comparing numbers, and finding numbers on a number line.

60

Ten Statements


1) When doing chain calculations without parentheses, you work from left to right. (yes)2) The problem 24 ÷ 6 - 2 can have 2 solutions when parentheses are used. (yes)3) The number 63,475 has five digits. (no)4) According to the order of operations, multiplication is done before subtraction. (yes)5) The numbers you multiply are called factors. (no)6) Please Excuse My Dear Aunt Sally is a mnemonic device used to help us learn the order of

operations. (yes)7) 727 rounded to the nearest hundred is 700. (no)8) The order in which you work the operations in a problem will determine the solution. (yes)9) When more than one operation is used, there is an order in which the operations must be

performed. (yes)10) The word “Dear” in the mnemonic represents division. (yes)

Free-Choice Lesson


Six-Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet, (Addition: Ordering Numbers)

Math Workshop





61


Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation: See attached Six-Group Activity Sheet: Addition: Ordering Numbers

Technology:

Assessment

Informally assess students’ responses during the lesson and Ten Statement reviews.

Homework

Have students explain (in their math journals) how parentheses can change the value of thisnumber sentence: 40 ÷ 4 + 6.

Teacher Notes

62

Six Group Activity

Addition: Ordering Numbers

Materials:5 (5” x 7”) index cards1 black marker1 pencil(9 ½” x 6 ½”) envelope

Prepare the following index cards using the black marker to write the problems on the front ofthe card and the pencil to write the answers on the back. Write only one column of verticalnumbers on each card.

6,59232,5671,956

325

36,25436,59137,21137,115

2,956956

3,2412,413

20,35621,21129,3515,699

5,3675,3005,9535,826

Answers:325

1,9566,592

32,567

36,25436,59137,11537,211

9562,4132,9563,241

5,69920,35621,21129,351

5,3005,3675,8265,953

Tell the students that they are going to do activity that involves putting numbers in order fromleast to greatest. Lay a card with the four numbers in one vertical column on it on the table andallow the students time to write the answer. As you reveal the answer say: “The answer is……”Store the activity cards and study board in the 9 ½” x 6 ½” envelope.

63



Correlations (SG,CAS,CFS): 6A1; 6B1

ITBS/TAP:Understand number sentences

ISAT:

Unit Focus/Foci

Place Value


Assessing place value; order; comparing; standard, expanded, and word forms of numbers

Materials

Six-Group Activity: Addition: Comparing Numbers


Warm-up Activity:

Write the following problems on the chalkboard:

1) (2 x 3) + 5 2) 2 x (3 +5) 3) (18 ÷ 2) x 3 4) 18 ÷ (2 x 3)5) (10 x 6) + 4 6) 10 x (6 + 4) 7) (2 + 5) x (10 - 2) 8) 2 + (5 x 10) - 2

How many different answers can you get by putting the parentheses in different places?

9) 3 x 5 x 4 10) 16 ÷ 4 + 6

Have students complete the answers for problems 1-8 and answer the question for problems 9-10.

Answers: 1) 11 2) 16 3) 27 4) 3 5) 64 6) 100 7) 56 8) 50 9) 1 10) 2

Duplicate the following test for students.

64

Place Value, Order, and Comparing Test

Dictate these numbers and have the students write them on lines 1 - 4:(985,876; 45,234; 333,890; 234,000) 1) _________________ 2) _________________ 3) _________________

4) _________________

How many digits are there in the following numbers?

5) 47,568,428 _________________________________________________________________ 6) 149,263 ___________________________________________________________________ 7) Write sixteen thousand, four hundred seventy-eight in standard form ___________________

8) Write 698,512 in expanded form ________________________________________________

9) Order these numbers from greatest to least. 8247, 8428, 8248, 8427 ___________________ 10) How many periods are there in the number 348,922?________________________________ 11. Write 600,000,000 + 80, 000, 000 + 8, 000, 000 + 400,000 + 5,000 + 200 + 50 + 2 in word

form ______________________________________________________________________

Compare the following numbers. Write < or > in the boxes.

12) 275 � 257 13) 6,802 � 6,082 14) 89,999 � 90,000 15) 700,999 � 700,900

16) Order these numbers from least to greatest: 35,597, 35,793, 35,953, 35,739 _____________

___________________________________________________________________________

65

17) Write seventy-three thousand, eight hundred twenty-four in expanded form _____________

___________________________________________________________________________

18) In the number 180,237,462 what is the value of the 7?______________________________

__________________________________________________________________________

19) In the number 180,737,462 what is the value of the 2?______________________________

Put commas where they belong in these numbers.

20) 68436 21) 175896243

22) Is the number sentence “165>164” read 165 is less than 164 or 165 is greater than 164?____

__________________________________________________________________________

23) In the number 84,605,217, what is the name of the period that contains the digit 6 ? ______

__________________________________________________________________________

24) Write 16,203 in word form._______________________________________________

25) Write 200,000,000 + 10,000,000 + 5,000,000 + 900 ,000 + 50,000 + 5,000 + 400 + 20 + 1 instandard form_____________________________________________________________

66

Ten Statements


No Ten Statements today.

Free Choice Lesson


Six Group Activity

Have a group of six students, two from each ability level, complete the teacher-directed activitysheet. (Addition: Comparing numbers.)

Math Workshop

Have the students work in the Math Workshop after completing their Free Choice Lesson.





Connection(s)

Enrichment:

Fine Arts:

Home:

67

Remediation: See attached Six Group Activity Sheet. (Addition: Comparing Numbers)

Technology:

Assessment

Answer Key:

1) 4,805 2) 97,235

3) 254,103 4) 175,800

5) 8 6) 6

7) 16,478 8) 600,000 + 90,000 + 8,000 + 500 + 10 + 2

9) 8428, 8427, 8248, 8247 10) 2

11) six hundred eighty-eight million, fourhundred five thousand, two hundred fifty-two

12) >

13) > 14) <

15) > 16) 35,597; 35,739; 35,793; 35,953

17) 70,000 + 3000 + 800 + 20 + 4) 18) 7 thousand

19) two hundred thousands 20) 68,436

21) 175,896, 243 22) 165 is greater than 164

23) thousands 24) sixteen thousand, two hundred three

25) 215,955, 421

Homework

Teacher Notes

68

Six Group Activity

Addition: Comparing numbers


Prepare the following index cards using the black marker to write the problems on the front ofthe cards and the pencil to write the answers on the back. Write only one comparison numbersentence on each card.

105__1110 2,202__2,020150__130 52,904__42,5091,394__1,349 210__1201,005__1,005 41,052__41,042269__268 671__761

Answers:105 < 110 2,202 > 2,020150 > 130 52,904 > 42,5091,394 > 1,349 210 > 1201,005 = 1,005 41,052 > 41,042269 > 268 671 < 761


Comparing Numbers

Symbol Meaning Examples= is equal to 5 = 5

5 is equal to 5.< is less than 7 < 8

7 is less than 8.> is greater than 6 > 3

6 is greater than 3.

69

Use the story board to teach the students how to use symbols to compare numbers. Havestudents write these numbers on a piece of paper:

84__48 315__135 924__924

Write 84 and 48. First ask these questions:

Are these pairs of numbers in the same place value? (yes)Name the two places. (ones and tens)Which number is larger than the other is? (84 is larger than 48)What symbol do we use? (>; - greater than: 84>48)

Remind students that the chevron or arrow will always point to the smaller number.How do we read the number sentence? (84 is greater than 48)

Instruct students to do the rest of the problems the same way.

Tell the students that they are going to do an activity just like the one they just did. Lay a cardwith two numbers to be compared on the table and give the students time to write the answer. Asyou reveal the answer, say: The answer is…… Store the activity cards and study board in the 9½” x 6 ½” envelope.

Note to the Teacher

Documents

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