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Decision One: Topic: Different forms of Rational Numbers Grade: 6 Content Map of Unit Optional Key Learning(s): Unit Essential Question(s): Instructional Tools: Students will understand that: there is Why do we need different forms of Pre-requisites: a need for numbers beyond whole numbers? Comparing fractions; numbers; the meaning of ratio, terminating and repeating proportion, percent, fraction, and decimals; decimal and their relationship to each solving simple equations (mult. Div.) other. Concept: Concept: Concept: Concept: Meaning Strategies Constructing Support Real Life Applications Lesson Essential Questions: Lesson Essential Questions: Lesson Essential Question Lesson Essential Questions: How can the same quantity be How do I change from one form How do I use Constructing Support to How do I know which form of a represented in different ways? of a number to another form? provide support or proof of number to use? How are ratios and proportions used statements? How do I use different forms of to show relationships? What is the best way to change from numbers to show how an F can fractions to decimals? affect my grades? Vocabulary and skills Vocabulary and skills Vocabulary and skills Vocabulary and skills fraction, decimal, percent, Factor, proportion, Constructing Problem Solving denominator, numerator, ratio, cross product Support Culminating Activity equivalent, Vinculum Multiple ways to Everyday Use Common Forms solve problems Models and Setting up and Representations solving Relationships proportions Equivalency Decision Two: The performance or product project Note: Decision One is the Content Map that will be the culminating activity of the unit Students’ Assignment Page for the Culminating Activity Essential Question of the Culminating Activity: How do I use what I have learned about different forms of numbers to show how an F can affect my grade? Paragraph Description of Culminating Activity: Students will use data from a quiz situation to determine what effect an F has on a final grade. This activity requires students to write ratios as fractions and then change fractions to decimals and percents using the methods (including setting up and solving proportions) learned in the unit. Determining how F’s can affect a grade is a real-world situation that students can relate to in order to use the skills and concepts that they have learned. Steps or Task Analysis of Culminating Activity (include Graphic Organizers): Students will work in groups of 4 to determine what effect an F has on a final grade. 1. The groups will designate assigned roles of facilitator, encourager, checker, and recorder to the members. 2. Everyone in the group will work together on each of the 4 given situations. The facilitator oversees that the work gets done while the encourager pulls everyone into the work. The checker verifies the solution of the group and the recorder writes the solution on paper. The recorder calls the teacher over to explain the solution. 3. Once the group has arrived at the correct solution, members must rotate roles within the group. 4. Groups are to complete the worksheet section for each situation and then graph the results, using a different color for each situation. 5. Students answer the questions at the bottom of the assignment page. 6. The rubric will be provided to students prior to the activity. Students should use the rubric to assess themselves during the activity. Playing Catch Up 3 Complete each student chart as we did the other day. Then graph the result of each student on the back. Use different colors to distinguish between the different students. Andy Brenda Carlos Denise Andy usually scores 96% on his Brenda usually scores 100% on her Carlos usually scores 89% on his Denise usually scores 90% on her homework. His first assignment is homework. Her first assignment is homework. He turns in his first homework. She turns her first a zero. How many assignments a zero. How many assignments assignment for half credit (50%). assignment in late and receives half will it take for Andy to get an A- will it take for Brenda to get an A- How many assignments will it take credit (50%). How many (90%)? (90%)? him to get a B- (80%)? assignments will it take her to get an A- (90%)? Andy Brenda Carlos Denise # Fraction Percent # Fraction Percent # Fraction Percent # Fraction Percent 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 Andy Brenda Carlos Denise 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 14 15 15 15 15 16 16 16 16 17 17 17 17 18 18 18 18 19 19 19 19 20 20 20 20 1. Which students achieved his or her goal the soonest? 2. Why? Give the best mathematical reason you can. 3. Which student will never reach his or her goal? 4. Why? Give the best mathematical reason you can. 5. How does an F that is a 50% differ from an F that is a ZERO? 6. How does this assignment apply to your grades? What did you learn from this exploration? Decision 3: Culminating Activity/Project Rubric Scale 4 3 2 1 Criteria Work was successfully All 4 problems were At least 3 problems were At least 2 problems were At least 1 problem was completed in the time completed successfully. completed successfully. completed successfully. completed successfully. allowed. Roles were assigned, Team members worked followed and rotated with At least 3 members were At least 2 members were At least 1 member was cooperatively in all 4 members on task at on task at all times. on task at all times. on task at all times. assigned roles. all times. All 4 problems were At least 3 problems were At least 2 problems were At least 1 problem was solved and graphed in a solved and graphed in a solved and graphed in a solved and graphed in a Recorded work was neat and understandable neat and understandable neat and understandable neat and understandable neat and readable. format. format. format. format. Total: _______________ Students in this group: ______________________________________________________________ Decision 4: Student Assessments Plan for how students will indicate learning and understanding of the concepts in the unit. How will you assess learning? • Short answer tests or quizzes • Student portfolios • Informal Assessment – See Summarizer Lesson 2 for sample questions to be used for informal assessment. • Formal student observations or interviews • Oral or written explanations of daily work • Culminating Activity Decision 5: Launch Activities Develops student interest and links prior knowledge. Provides the content map and key vocabulary to students. Literature Link: The Math Curse by Jon Scieszka and Lane Smith 1) Read this book to the students. This book is about a girl who wakes up one day to find that everything is a math problem. In pairs, students will name as many different forms of numbers as they remember from the story along with the situation in which they were used. They will have 2-3 minutes to do this in pairs. Each member of the pair records the answers on his/her own paper. Then, they will “Give One, Get One” for 2 minutes. They will go back to their pairs and form a cumulative list. Discuss these as a class and reward the pair with the most answers. 2) Use the Content Map to give students the big picture of what they will learn in the unit and to preview the vocabulary. Decision 7: Extending Thinking Activities Have extending activities or lessons for most important concepts/skills Cause/Effect Compare/Contrast Constructing Support Justification Induction Deduction Error Analysis Abstracting Analyzing Perspectives Classifying Example to Idea Idea to Example Evaluation Writing Prompts Lesson 1 – Justification – decimal grid activity Lesson 2 – Classifying, Compare/Contrast – ratio and proportion Lesson 3 – Constructing Support – See Lesson 3 Extending and Refining Activity Lesson 3 – Error Analysis – Summarizer Lesson 4 – Extending Thinking Lesson Culminating Activity - Analysis Decision 8: Differentiating the Unit What accommodations will you make in order to meet the varied interests, learning styles, and ability levels of all students? An acceleration lesson is included for those students considered to be at risk. Performance tasks and word problems included are from a variety of fields of interest. Students will be provided with choices from which they will select real world problems to work. Actually, some of the tasks will be chosen from the list produced by the students during the Launch activity and the first lesson. This unit contains auditory, visual, and kinesthetic activities to meet all learning styles. Scaffolding should be used where appropriate. Decision 9: Lesson/Activity Sequence and Timeline What is the most viable sequence for the experiences, activities, and lessons in order to help students learn to the best of their abilities? Put the Lesson Essential Questions, activities, and experiences in order. The lessons and activities in this unit are in Microsoft Word format and are numbered sequentially at the beginning of the filename. Headers at the top of each page identify the lesson in which the page or activity is included. Also, the Content Map gives an overall picture of the flow of the Unit. Since this is a new unit that has never been taught in 6 th grade there is no time period listed on the lessons. This school year will be used to help gauge the pace of the new Georgia curriculum and approximate timelines will be added at a later date. Decision 10: Review and Revise How will you review this unit in order to improve it prior to using it again or sharing it? What criteria will you use to determine the need to make improvements? List when you will conduct distributed reflection. This unit will be used with hundreds of students during the 2005-2006 school year by 6th grade teachers as the new Georgia Performance Standards are implemented. Teachers will give feedback during reflection meetings and during consortium meetings at RESA. The main criteria used to make improvements will be results from on-going formative assessment. Summarizers should provide teachers with an indication of student understanding in order to review and revise this unit. Distributed reflection will be conducted at the reflection meetings and during consortium meetings. I will ask that teachers keep a portfolio of notes during this lesson to help make any adjustments needed. Also, samples of student work will be used to make improvements in the unit. Decision 11: Resources and Materials for Learning Unit Daily newspapers with current stock quotes or internet access. Bubble Gum – one piece per student Chart Paper Markers Colored Pencils Construction Paper Scissors Glue Individual whiteboards or chalkboards Envelopes Spray Adhesive Acquisition Lesson Planning Form Plan for the Concept, Topic, or Skill --- Not for the Day Essential Question: How can the same quantity be represented in different ways? See Launch Activity Activating Strategies: (Learners Mentally Active) Review terms: fraction, decimal, percent, denominator, numerator, by using the vocabulary game Acceleration/Previewing: “Hit or Miss” prior to the unit. (Key Vocabulary) During the unit the term equivalent will be taught using a word map. Vinculum will be taught using the Frayer Diagram. Teaching Strategies: Use numbered heads to create pairs. Give each pair bags with 10 decimal squares in tenths and (Collaborative Pairs; 10 in hundredths. Ones will work with tenths and 2’s will work with hundredths. Students will need Distributed Guided colored pencils, scissors, construction paper, and glue. Ask 1’s to tell partner how many parts their Practice; grid is divided into. (10). Have 2’s do the same (100). Have 1’s shade in 2 parts of their grid. Have Distributed Summarizing; 2’s shade in 20 parts of their grid. Ask pairs to tell each other how this quantity would be written as Graphic Organizers) a fraction not in simplest form but just as they see it (2/10), (20/100). Write these two fractions on the board. Students will then cut the shaded part of their grids out and compare the quantity by placing one on top of the other. Use the Word Map to define the term equivalent. Go back to the fractions on the board and have them read their fractions aloud to each other while the other one writes the number in words. Add this to the Word Map. Then have pairs brainstorm how the words they have written would look if the amounts were written as decimals. Check understanding and add this to the Word Map. Pairs glue their grids on the construction paper and label them in fraction and decimal form. This is a good time to present the following analogy: I have students to describe how I am dressed for school. I ask them to imagine what I would look like if I were working in my yard, attending a baseball game, going to church, and attending an opera. After pairs discuss, we list responses in columns on the board. Pose the following question: Have I changed who I am or am I still “Miss Laurian?” I am still the same person; I have only changed how I look to fit the situation. This is what we do with numbers. Have pairs discuss how the fractions and decimals they have created are like dressing for various occasions. Students work together to create 4 more equivalent amounts and write them in fraction form and in decimal form. (Tenths should always go first for this activity.) They will trade “denominators” and create 5 more and record as before. Use pairs squared to have one pair check another pair’s work. This is a good time to introduce percent. Ask them to take a look at one of the 100 decimal square grids. Pose the following questions to pairs: If you were to place one penny in each of the squares, how many pennies would you have? How many cents would that be? What if you only placed pennies on 80 of the squares? How many pennies? How many cents? Have pairs write 80 cents as a decimal the way we usually see it and then using what they have learned, write it as a fraction. Introduce the idea that the vinculum (vin” cu’ lum) is a fancy name for the fraction bar. Students will use the Frayer Diagram to learn this new word. There are several different ways to read the vinculum, such as “out of” “divided by” “for every” or “per.” They think of a word and a picture that reminds them of vinculum and record on the Frayer. (My example is “Van Column” and I imagine a van carrying a column for a house on top of it. The column is lying down horizontally on the roof of the van.) Go back to the fraction formed from 80 cents. Remind them that this fraction represents 80 out of 100 squares covered. Have pairs read the fraction to each other in three different ways. If we read it as “80 per hundred” or “80 per hundred cents” then it makes “sense” that “per hundred” means “per cent.” Record this on the Word Map in RED because it is very important that they remember this fact. So, 80/100 is also the same as 80%. Students divide up their sheets with decimal grids and go back and write the % to go with the decimals and the fractions. They trade sheets and check each other’s work. Summarizing Strategies: 3-2-1: Ones pick a fraction with a denominator of 10. Both students write: Learners Summarize & 3 ways to write the quantity; Answer Essential Question 2 pictures to show the quantity is the same written in different ways; and 1 statement explaining why the same quantity can be written in different ways. Write an additional page for the “Math Curse”. Homework: What is it? What is it like? Important stuff to remember: Equivalent What are some examples? 5 4 3 2 1 A B C D E Hit or Miss Directions: Mary Kunzman and Mary Higham adapted this strategy from The Mailbox (1998) to promote knowledge of content vocabulary. Select 10-12 vocabulary words for the game. Students copy the words from the word list in random order somewhere on the gameboard as if placing ships on a Battleship game. Using numbered heads, ones call out a set of coordinates. If twos have a word in that box, they say “HIT” and call out the word. Ones then define the word, give an example of the word or use the word in a sentence according to the teacher’s directions. If they are correct, the box gets crossed off, ones get a point, and it is twos’ turn. If incorrect or if there is no word in the box, twos say “MISS” and then twos take a turn. The first person to get all of the points wins – the loser will have all of his/her words crossed off. Make copies of the grid to send home as homework so that parents can play with their children. Make extra copies available for students to use when they complete their work or when more vocabulary practice is needed. Ones: Pick a fraction with a denominator of 10. Tell your partner. Each person must hand in a response: Different ways to write the quantity: Pictures to show that two of the above are the same: Statement explaining why the same quantity can be written different ways. Chat Box: Frayer Diagram 1 What is it? What does it sound like? Vinculum What does it mean? Picture Acquisition Lesson Planning Form Plan for the Concept, Topic, or Skill – Not for the Day Essential Question: How are ratio & proportion used to show relationships? Activating Strategies: 3 Corners: Adaptation of 4 corners: See LFS Math 6-12 Activating Tab (Learners Mentally Active) Place signs in 3 corners of the room. Each sign has one of the following terms on it: percent, decimal, fraction. Each student draws a card from the hat with a number on it and writes the equivalent forms on post-its and posts them on the corresponding sign. Have one student share responses from the signs with the class. Blowing Bubbles – LFS Math 6-12 Numbers and Operations page 10 Materials: One piece of bubble gum per student, recording sheet Have students chew gum until they are able to blow a bubble with it. Students will work in partners and collect data on the number of bubbles each student can blow in 30 seconds. Acceleration/Previewing: Factor, proportion, ratio, cross product – taught in context during the lesson. (Key Vocabulary) Teaching Strategies: This lesson uses an adaptation of the graphic organizer from LFS Math 6-12 to record understandings (Collaborative Pairs; during the lesson. Discuss the meaning of ratio, ways to draw, write, and say it. Use counters to model it. Distributed Guided Practice; Have students model sample ratios with counters in pairs. Relate ratios to fractions, equivalent fractions, Distributed Summarizing; and percents with the graphic organizer from Lesson 1. Graphic Organizers) Brainstorm where ratios are used in everyday life along with examples. Record on G.O. Give students real-life examples such as batting averages, miles per gallon, miles per hour, recipes, calories per serving, etc. Record these on G.O. and stress that the order that the ratio is written is important. This goes in the “The Scoop” graphic. Using Baseball Stats 1 handout students will write ratios that represent batting averages. They may bring up the fact that batting averages are read as decimals. If so, tell them that they will convert the fractions to decimals, but a ratio must be formed first. Refer to the essential question and stress that in this lesson we are looking at the meaning of ratio and proportion and how they are used to show relationships. Students should note that on this sheet, there is a column for decimals and percents. We already learned that every number can be represented as a fraction, a decimal, and a percent. This does not change the quantity that is represented – only what it looks like. (Ask them to tell their partners the metaphor used to remember this – how we dress doesn’t change who we are, only what we look like.) Notice that the handout uses simple batting statistics such as 5/10, 3/10, and 23/100 to relate writing these as a decimal and percent the way they did in Lesson 1. Have 1’s write a matchbox summary of what the ratios stand for and 2’s write a matchbox summary of why they can be written in different ways. Pairs have two minutes to share their responses and check their partner’s accuracy. Pairs get together with another pair (pairs squared) and discuss the following: How do you find the unknown percent when given a ratio in fraction form with a denominator of 5, 10, 20, 25, 50, or 100? What methods do you use? Are they all the same? Is one way any better than another? Come to some consensus to prove your method works and record it to explain to the class. They have 5-7 min. (Before they begin they must designate a timekeeper, a recorder, a mediator, and a speaker. Have speakers share with the whole class (use overhead if needed). They go back to their pairs and discuss the following: What happens when you are given a ratio such as 4/7 or 9/17. Give them about 5-10 min. to struggle with this. Suggest that they go to their math notebooks and refer to their graphic organizer from a previous unit on comparing fractions. Ask: How do you know if two fractions are equal? (cross products are equal) Given 12/18 and 2/3 show how you know by writing all of the steps. So if we were missing one of the numbers, say 2, then we would have 12*3=n*18. Since we have solved simple equations before, how would you find out what n is equal to? When you write two equivalent ratios, this means that you know that their cross products are equal. Let’s go back to our word map from lesson 1 and review what equivalent means. So, if we write the steps below the ratios, using a variable for the unknown, then all we need to do is to solve for the variable. When two ratios are equivalent, this is called a proportion. If we have to find out what one of the numbers in the proportion is equal to, we are “solving proportions.” How would you check your work? Let’s record what we know about proportions on our G.O. for this lesson. Give some numerical and word problem proportions and have students solve them and share with their partner. Samples are included. After they have done a few through guided practice, take out whiteboards. Using whiteboards 1’s will write the equation and 2’s will solve for 5 problems. Then switch roles for 5 problems. (These are numerical). Then do the same for 10 word problems where they write the ratios and set up proportions and solve. Given the proportion 3/7=n/22, what does this mean. Record on G.O. Massed Practice: Bubble Gum recording sheets. Use pairs checking. Distributed Guided Practice/ All questioning above is done in pairs. Summarizing is explained above, also. Summarizing Prompts: (Prompts Designed to Initiate Periodic Practice or Summarizing) Summarizing Strategies: The Envelope Please Puzzle Questions – Directions found in both LFS Math books. (Learners Summarize & Answer Essential Question) Sample problems: Answers: 3 x 3 9 1) 12 28 8) 7 a 1) 7 2)45 6 x 8 x 2) 10 75 9) 10 15 3)15 4)9 8 12 x 15 3) 10 n 10) 100 20 5)15 6)18 a 3 4) 21 7 7)16 8)21 85 c 5) 100 20 9)12 10)15 7 x 6) 14 36 4 6 7) x 24 1. The weight of the brain is about 2.5% of the total body weight. How much would the brain of a 120 pound person weigh? 2. Starting at age 35, humans lose approximately 7,000 brain cells a day that are never replaced. How many is this in a week? A month? A year? 3. In one day, humans shed about 10 billion skin flakes. How many billion would they shed in the year 2005? 4. Six people out of 40 are left-handed. What percent of the population is this? 5. On your first test you got 40 out of 45 correct. On your second test you got 25 out of 30 problems correct. Which test had the better percentage? 6. TRUE FACT: In making peanut butter and jelly sandwiches, 96% of the people put on the peanut butter first. Out of 12,000 people making sandwiches, how many people would spread the peanut butter first? 7. In a bizarre turn of events, 2 people in a certain family stubbed their toe, developed gangrene, and died. If there were 16 people in the whole family (including aunts and uncles), what percent stubbed their toe? 8. “Arachibutyrophobia” (pronounced I-RA-KID-BU-TI-RO-PHO-BI-A) is the fear of peanut butter getting stuck to the roof of your mouth. What percent of the letters in that word is an “a”? 9. After an extended advertising campaign, the “Don’t Kick Your Poodle” Organization hopes to reduce poodle abuse by 15%. If last year there were 548 incidents, how many would there be this year? 10.Yesterday, out of 50 students who were tardy, 80% had lame excuses. How many people is this? Sources: www.pleasanton.k12.ca.us , www.funnyfact.com 1 3 7 47 8 2 4 10 100 50 0.45 0.32 0.05 0.7 0.4 97% 14% 56% 78% 6% 9 55 7 2 3 10 100 100 10 5 22% 37% 8% 40% 60% 0.21 0.26 0.9 0.11 0.3 The Swamp Gravy Mathletes have had a great baseball year! Their stats are shown below. Use the batting information for the Mathletes to find the information needed to fill in the table. Player Hits At Fraction Decimal Percent Bats Jackson Wilson 5 10 Jesse Erwin 7 10 Josh Phillips 10 20 Eli Wilson 12 20 Cody Phillips 15 20 Michael Boyd 20 25 Adam Phillips 25 50 Colt Calhoun 45 50 Billy Grimsley 46 50 Kameron Whitaker 72 100 Ratio What is it? Say It Draw It Write It “THE SCOOP” Examples Uses in the Real World Proportion What is it? Solve It Your Turn Step 1: m 1 4 2 2 m 1 4 Step 2: 2m 4 Step 3: m2 Acquisition Lesson Planning Form Plan for the Concept, Topic, or Skill – Not for the Day Essential Question: How do I change from one form of a number to another form? Activating Strategies: Today’s Number: p. 19 in LFS 6-12 Activating (Learners Mentally Active) Acceleration/Previewing: Review division when you need to add a decimal and annex zeros; repeating decimals 3-4 days prior to the (Key Vocabulary) lesson. Teaching Strategies: Make a 3 flap foldable. This is the G.O. to record key understandings and memory aids as the lesson is (Collaborative Pairs; taught. Distributed Guided Practice; Show decimal to % and % to decimal by moving the decimal point. This is the easiest. May use Tootsie Distributed Summarizing; Roll PowerPoint found at www.sw-georgia.resa.k12.ga.us on the math page. Will need to adapt it to fit this Graphic Organizers) lesson. Remember that the words and the motions do not coincide. This would defeat the purpose of practicing with problems if all they did was move the direction that the song states. They must look at the problem to decide which way to move the decimal point. Show fraction to % and % to fraction using proportions. Include repeating and terminating decimal answers and explain that the remainder should be written as a fraction. Show fraction to decimal by reading the vinculum as “divided by.” Show decimal to fraction for both terminating and repeating. Use the equation method to explain repeating decimals and the shortcut. See attached. Show that fraction to decimal can be done by using a proportion to change to % and then moving the decimal point to change to decimal. Distributed Guided Practice/ Students should be encouraged to learn the most common equivalent forms such as ½=0.5=50%. Play Summarizing Prompts: “Concentration”, “MATHO”, or “I Have – Who Has” to help them memorize these. (Prompts Designed to Initiate Periodic Practice or Summarizing) Summarizing Strategies: Stick-It-Up: (Learners Summarize & Use spray adhesive on a three column grid. Columns read fraction, decimal, and percent. One of the three Answer Essential Question) is given in each row. Students draw cards from the hat and show their work on a sheet of paper to change the number on the card to the other two forms. They “stick” their card in the appropriate place on the grid as they leave. They hand in the paper to be checked. The teacher can then give individual feedback the next day and there is very little paperwork to be done. Extending and Refining: Error Analysis – Switch some of the correct answers on the grid and as an activator the next day they must figure out which ones are in the wrong place and tell where they should be and why. I have 50%. I have 1 2 . Who has this as a fraction? (Beginning Card) Who has this as a decimal? I have 0.5. 1 Who has the fraction for 25%? I have . 4 Who has this as a decimal? I have 0.25. I have 0.75. Who has this plus 0.5? Who has this as a percent? I have 75%. 3 Who has this as a fraction? I have . 4 1 Who has this plus written as a percent? 4 I have 100%. I have 1.0. Who has this as a decimal? 9 Who has this minus ? 10 1 I have 10%. I have . Who has this as a decimal? 10 Who has this as a percent? I have 0.1. I have 0.7. Who has this plus 0.6? Who has this as a fraction? 7 I have 70%. I have . Who has this plus 20%? 10 Who has this as a percent? I have 90%. I have 0.9%. Who has this as a decimal? Who has this as a fraction? 9 1 I have . I have . 10 3 17 Who has this as a percent ? Who has this minus ? 30 1 I have 0.3 . I have 33 % . 3 Who has this plus 0.3 ? Who has this as a decimal? I have 0.6 . 2 I have . Who has this as a fraction? 3 Who has this as a percent? 2 I have 30%. I have 33 % . Who has this as a decimal? 3 2 Who has this minus 36 % ? 3 I have 0.3. 3 Who has this as a fraction? I have . 10 1 Who has as a percent? 2 1 3 7 2 4 10 0.5 0.75 0.7 50% 75% 70% 9 1 4 1 10 90% 25% 100% 0.9 0.25 1.0 1 2 1 3 3 10 1 0.6 33 % 3 0.3 3 10% 30% 10 0.1 0.3 Put the following numbers on the board: 1 3 1 2 1 1 9 2 4 3 3 4 1 10 10 7 3 10 10 50% 75% 33 1 % 66 2 % 25% 100% 3 3 10% 90% 70% 30% 0.5 0.3 0.6 0.25 1.0 0.1 0.9 0.7 0.3 M A T H O Decimal Decimal Decimal Decimal Decimal for for for for for 1 3 1 9 1 2 4 4 10 3 Decimal Decimal Decimal Decimal Decimal for for for for for 2 66 % 3 100% 10% 70% 30% Fraction Fraction Fraction Fraction Fraction for for for for for 1 2 50% 75% 33 % 3 66 % 3 25% Fraction Fraction Fraction Fraction Fraction for for for for for 1.0 0.1 0.9 0.7 0.3 Percent Percent Percent Percent Percent for for for for for 3 7 2 1 3 10 10 3 3 4 Percent Percent Percent Percent Percent for for for for for 1 1 9 1 4 10 10 1 2 1 3 7 47 2 4 10 100 0.5 0.75 0.7 0.47 50% 75% 70% 47% 1 55 7 2 3 72 8 25 1 7 1 8% 33 % 76 % 87 % 3 18 2 0.3 0.7638 0.875 0.08 3 8 15 50 20% 0.16 0.2 16% Acquisition Lesson Planning Form Plan for the Concept, Topic, or Skill – Not for the Day Essential Question: How do I use Constructing Support to provide support or proof of statements? Activating Strategies: Situation: (Learners Mentally Active) The school is considering a new dress code. Our class has been asked to give input for the new dress code. Brainstorm ideas in pairs (3-5 min.). Choose one of your ideas to submit to the committee for approval. Acceleration/Previewing: Constructing Support (Key Vocabulary) Teaching Strategies: The teacher models the steps in Constructing Support. These steps should be posted. (Collaborative Pairs; 1. Write a position statement. Distributed Guided Practice; 2. Decide if it is fact or opinion. (If fact, you will provide proof. If opinion, you will provide support.) Distributed Summarizing; 3. Determine if the situation warrants support. (If so, give reasons.) Graphic Organizers) 4. Use facts, evidence, examples, or appeals to support your argument. Use the graphic organizer from the LFS strategies book or the Extending and Refining flipchart to record information as you model the steps. Distributed Guided Practice/ Prompts: Why is this skill important? Where might it be used in jobs? In school? At home? In other real Summarizing Prompts: life situations? (Prompts Designed to Initiate Periodic Practice or Summarizing) Summarizing Strategies: The Important Thing about Constructing Support is … (Learners Summarize & Answer Essential Question) Constructing Support Position Statement Extending Thinking Lesson Planning Form Essential Question: What is the best way to change fractions to decimals? Mini-Lesson: Situation: You have been asked to tutor 5th graders on how to change fractions to decimals. You must decide if you think it is best to teach them to set up the fraction as a division problem where you place the decimal point, annex zeros, and divide or to set up a proportion and solve. Task: Groups of four: Using a graphic organizer for Constructing Support, prepare a presentation on why you think that 5th graders should be taught to use the method of your choice. This presentation will help you get the job to tutor 5th graders. Remember to include all of the steps in Constructing Support. A rubric is attached that will be used to grade your presentation. Note to teacher: These steps should be posted. 5. Write a position statement. 6. Decide if it is fact or opinion. (If fact, you will provide proof. If opinion, you will provide support.) 7. Determine if the situation warrants support. (If so, give reasons.) 8. Use facts, evidence, examples, or appeals to support your argument. Summarize/Sharing: Students will present their method to the entire class. Assignment: Batting Stats 2 : A worksheet with statistics from the Atlanta Braves’ 2004 season is included. A blank worksheet is included if you would like to have students search the internet to find their favorite baseball payers’ statistics. If this is not possible, go to http://mlb.mlb.com/NASApp/mlb/mlb/stats/index.jsp and select a team and print out stats. Be sure to elimate or cover up the column that gives the batting average. They should complete the discussion athe the bottom of the sheet analyzing the stats and explaining their thinking. (Mathenese is what we call “Math Talk.”) Use pairs checking. Need On- You’ve Got Go Back to the-Job the Job School Training Believable but Logical and not related to What reasons and Position directly related to some of the facts? Statement reasons and facts facts and reasons. Variety of devices such as facts, Some devices evidence, No devices used to Support or used to support examples, and support the argument Proof the argument appeals support the argument Clear and Clear and Unclear or accurate, close accurate, within inaccurate, no time to time frame, the time frame, frame, and visual visual Presentation and visual absent or does not somewhat enhances the add to the enhances the presentation presentation presentation From the information given, choose 10 baseball players and find their batting averages as fractions, decimals, and percents. Player Hits At Fraction Decimal Percent Bats Pick one player and analyze his stats. Explain what each statistic means in detail. Use “Mathenese” words to explain your thinking. Batter Up! Player Hits At Fraction Decimal Percent Bats A. Jones 119 570 R. Furcal 157 563 J. Drew 158 518 C. Jones 117 472 J. Estrada 145 462 M. Giles 118 379 A. LaRoche 90 324 J. Franco 99 320 M. DeRosa 74 309 Pick one player and analyze his stats. Explain what each statistic means in detail. Use “Mathenese” words to explain your thinking. Extending Thinking Lesson Planning Form Essential Question: How do I know which form of a number to use? Mini-Lesson: Carousel Chairs: Instead of moving around the perimeter of the room, students will be in groups of 4 and will change seats after working one problem on each sheet. This can also be done by students staying in the same seat and passing the sheets around in a circle. See attached for what should be on each sheet. Be sure to include questions as well as problems. Check student understanding by comparing answers from each group. Task: Problem solving lesson: Use ROPES and the flipchart to have students solve problems involving various forms of numbers. There should be an emphasis on the “P” – Plan. This is where students should look for clues in the problem that tell them which form of the number is best to use and which form the final answer should be in. Students must be able to explain why they worked the problem the way that they did and why they chose the form that they chose. They will be working in small groups on this task. Summarize/Sharing: Students will share their solutions and reasons with the whole class. This is a great time to point out that all of them did not work the problem the same way. They should, however, be able to explain their thinking and why they chose to use the form of the numbers that they chose. The answer must be in the correct form. Assignment: Massed Practice: Each group is given authentic problems dealing with situations of choice. Students will work individually and then get together to check their work. Problems can be found at: http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade6/Proportions/Proportions_Index.html Each student will work the following two problems: http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade6/Percents/PlayingCatchUp1and2/PlayingCatchUp1.html http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade6/Percents/PlayingCatchUp1and2/PlayingCatchUp2.html Are the following ratios equivalent? Solve each proportion. Prove your answer. 8 12 8 x , 1) 12 8 1) 12 8 1 3 , 9 6 2) 2 4 2) n 18 4 6 x 7 , 3) 14 21 3) 5 100 16 17 4 6 , 4) 32 33 4) 14 x Set up the proportion and solve. Answer the questions. 1) Franco uses 2 teaspoons of 1) How do you remember what fertilizer for each gallon of equivalent means? water. How many gallons can he make with 15 teaspoons of fertilizer? 2) Furcal has an ERA of 0.381. 2) How do your remember what How many hits did he get if he the vinculum is? went to bat 21 times? 3) What does it mean when we 3) Goodwin of the Chicago Cubs say that two ratios are had 21 hits out of 105 at bats. equivalent? What is his hitting percentage? 4) A recipe for muffins calls for 2 1 4) How are fractions, decimals cups of flour for each 1 cups and percents alike and how are 2 of sugar. How much sugar is they different? (in just a few needed if 8 cups of flour are words) used? Snapshot of Webpage for massed practice problems. Ratios, Proportions, and Percents Ratios and Proportions Statue of Liberty Tree Problem Can be used as an introductory activity or a pre- An activity that actually utilizes (in an authentic way) assessment. ratios. Pulling Cubes Swimming Pool Problem After pulling cubes from a can and recording the Students use proportions to create a table to be used by results, students use proportions to "predict" the swimmers for their work-out. number of cubes of each color that are in the can. Nautical and Statutes Water, Juice, and Punch Similar to the Swimming Pool Problem, students use Can be used as an assessment activity. proportions to create a conversion table between nautical and statute miles. Giant Hand Another cool activity that can be used as an assessment. It is very similar to the Statue of Liberty problem, so makes for a great "before/after" comparison. Percents Playing Catch Up 1 Playing Catch Up 2 Playing Catch Up 3 FDP Organizer How bad does it after your Further investigation of Another extension. A visual method for grade to get a ZERO on a how your grade is affected memorizing common homework assignment? by ZEROS rather than fraction, decimal, and This cool activity answers "half credits". percent equivalencies. that question. Growing Pyramids Coke Pie Chart Percents with Pattern Cuisenaire Percents Blocks Converting between Take actual Coca-Cola Using Cuisenaire Rods to fractions and percents. data and convert it into a Each block gets a chance investigate what percent Cool patterns. pie chart. Converting to be 100%. one rod is of another rod. fracitons, decimals, and percents. Cuisenaire Back and Forth Percent Painter Dividing The Dollars Human Percentages Using Cuisenaire Rods to Using multi-link cubes to Divinding up a certain What percent of your body investigate what percent convert fractions into amount of money is your head? Lots of other one rod is of another rod. percents. Lots of cool according to percentages. cool questions. Backwards and forwards. patterns. Business Percents Science Fair Anita's Cake Percent Practice 1 Which payment plan is Students convert between A problem involving Word problems. best for you? fractions, decimals, and fractions and percents. percents to solve a real-life problem. Percent Practice 2 Percent Practice 3 Percent Practice Review Percent Increase and Decrease Word problems. Lots of word problems. Lots and lots of word problems. Calculating percent increase and decrease of real-life problems. Bigger and Smaller Percent Review 1999/2000 Problems taken from actual product labels! Just like it says. Playing Catch Up 1 Playing Catch Up 2