Introduction to Tape Diagrams

Introduction to Tape Diagrams
21st Century Lessons Introduction to Tape Diagrams Primary Lesson Designer: Lisa Schad

This project is funded by the American Federation of Teachers.

21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson: Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets. Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly. Feel free to customize this file to match the language and routines in your classroom. *1st Time Users of 21st Century Lesson: Click HERE for a detailed description of our project.

Lesson Overview (1 of 3) Lesson Objective
Content Objective: SWBAT solve ratio problems by using a tape diagram. Language Objective: SWBAT discuss ratio problem solving with a partner and in groups. Lesson Description The lesson begins with a review of what a ratio is and has students identify various ratios for a given situation. They will also watch a short video that showcases ratios in use in everyday life. There is an overarching question that is introduced before the mini-lesson that can be solved using the tool they learn today: tape diagrams. Students will be shown how tape diagrams are created based on information in a problem. They will practice in a heavily-scaffolded worksheet to fill in and later create tape diagrams. At the end of the lesson, for the exit ticket, students revisit the problem introduced before the mini-lesson and solve it using the tape diagram tool.

Lesson Overview (2 of 3) Lesson Vocabulary Materials Scaffolding
Ratio – a relationship between two or more amounts Tape diagram – a drawing that looks like a segment of tape, used to illustrate number relationships. It is also known as a strip diagram, bar model, fraction strip, or length model. These models work particularly well to show comparisons between part-to-part or part-to-whole ratios. Materials Required: All students have a notebook and pen or pencil. Teacher has board space for student work. Optional: Teacher can use large student whiteboards to put up student work for sharing with the class. Scaffolding Opportunities to discuss and to write about the math content give ELL students the chance to practice the language of mathematics. The Thinking Blocks video provides a visual aid to any struggling students. Enrichment Students who finish work quickly can work on additional tape diagram problems at the Thinking Blocks site given below. Online Resources for Absent Students How different professionals use ratios to solve problems at work Thinking Blocks website for a video demo of how to use tape diagrams to solve ratio problems and practice problems with feedback.

Lesson Overview (3 of 3) Common Core State Standard Before and After
6RP3 Use ratio reasoning to solve real-world problems and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Before and After This lesson builds off of previous lessons that introduced students to the idea of a ratio and the language of ratio by introducing them to problem solving with ratios. The tool, tape diagrams, will be helpful for solving many ratio problems involving two or more similar parts. (For more, see slide notes below.) Topic Background Ratios have a real and practical purpose in the lives of adults. Many use ratios in their work lives, but also any home cook has had to increase or decrease a recipe. Even mixing juice from concentrate requires the use of ratios. The tape diagram model is heavily used in high performing Asian and European curricula, but rarely seen in current American curricula. This lesson and those that follow in this unit will help to bridge that gap. Before this lesson: Students should have a foundation in fraction basics. Students will rely on many ideas from their study of fractions to help them to manipulate and better understand this new topic of ratios. Helpful prior learning includes: equivalent fractions and fraction as a relationship between part and whole. They will also greatly benefit from thinking using multiplicative reasoning (rather than additive). After this lesson they will learn a few more tools including ratio tables and double number lines. They will continue to develop facility in scaling up and iterating using a given ratio. They will also learn how to compare ratios (which will greatly rely on the ability to compare fractions) as well as find and use unit rates. Using ratios to think about calculating percents lays the foundation for later proportional reasoning work in grade 7 and beyond.

Warm Up Write each ratio as a fraction in lowest terms.
OBJECTIVE: SWBAT solve ratio problems by using a tape diagram. Language Objective: SWBAT discuss ratio problem solving with a partner and in groups. Write each ratio as a fraction in lowest terms. What is the ratio of… Girls to boys? People wearing pants to people who are not? People wearing white to people who are in jeans? 1:1 4:1 (Time on this slide – 5 min) Time passed 5 min In-Class Notes Only the simplified answers will come up when you click through. #2 is originally 8:2 then simplifies to 4:1 (4 white tops, 1 white dress, 1 pair of white sneakers) #3 is originally 6:4 then simplifies to 3:2 #4 possible answer: For every four people wearing pants, one person is not. Preparation Notes We are looking to see that students remember how to identify a ratio, simplify it, and can use the language of ratio to explain its meaning. 4. Write a sentence about what your answer to #2 means. 3:2 Agenda

Agenda: OBJECTIVE: SWBAT solve ratio problems by using a tape diagram.
Language Objective: SWBAT discuss ratio problem solving with a partner and in groups. 1) Warm Up - independent 2) Launch – partners 3) Explore: Predict - independent Mini-Lesson – whole class Practice & Discuss – independent & partners (Time on this slide – 1 min) Time passed 6 min In-Class Notes Briefly introduce but don’t spend too much time here. 4) Summary - independent 5) Exit Ticket - independent 6) Assessment - independent

Launch Abby and Zack are mixing red and yellow paint to make an orange color to paint their kitchen table. They each think they have the perfect shade of orange. (Time on this slide – 1 min) Time passed 7 min In-Class Notes Brief introduction Preparation Notes This begins the narrative of Abby and Zack that continues throughout the next lesson. Agenda

Launch Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow. This sounds like a ratio. What are ratios again? (Time on this slide – 1 min) Time passed 8 min In-Class Notes Let students think for a moment about what a ratio is. You could even do a Think, Pair, Share if time permits. Preparation Notes This sets up a review of vocabulary. Agenda

Launch Here’s the definition:
A ratio is a relationship between two or more quantities. But, why would I want to use or think about a ratio? Here’s a short video that will show how ratios are used in a few real life situations.  (Time on this slide – 2 min) Time passed 10 min In-Class Notes Make sure students have the definition for a ratio in their notes somewhere. Acceptable if they can turn to it from prior lesson. Click “www” symbol for link to video. Reflection questions on video follow. Preparation Notes Clicking the internet symbol will bring you to a very short video clip (1:19) you can play that will show students how ratios are used in a variety of jobs. Agenda

Launch – Think, Pair, Share
Think for one minute about an answer to these questions: What is a job that uses a ratio? How was a ratio useful in that job? Lefty share your answers with Righty. Now Righty share your answers with Lefty. Does anyone want to share what their partner told them? (Time on this slide – 2 min) Time passed 12 min In-Class Notes Get students to reflect on what they have seen: ratios are useful in many different kinds of jobs Preparation Notes In a Think-Pair-Share the teacher will need to have pre-chosen pairs of students to have a quick conversation to process the lesson at a “check-in” such as this. The name “Righty” designates the student in the pair sitting to the right in the pair and “Lefty” the student on the left. This might require clarification if students are not sitting side-by-side. Still having names for each person in the pair can be helpful to cue all students to participate and to take turns. The idea is not to spend too much time discussing the video but to encourage students to think about what they have seen. Agenda

Launch – Think, Pair, Share
Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. Lefty – Tell Righty the ratio of red to yellow in Zack’s orange paint. 3:5 Righty – Tell Lefty the ratio of yellow to red in Zack’s orange paint. Class – What is the ratio of red to yellow in Zack’s orange paint? Partner Share (Time on this slide – 2 min) Time passed 14 min In-Class Notes Students should see that 3:5 is a different ratio than 5:3 and to make sure to read carefully. Preparation Notes Anytime students take time to talk to each other about the content you are increasing the language usage and helping your ELL students. 3 to 5 or 3:5 or 3 5 Agenda

3:5 Explore – Strategize Zack bought 24 cups of red paint.
How much yellow paint will Zack need to buy to make his shade of orange paint? 3:5 Write down in your notes any ideas you have about how to answer this question. (Time on this slide – 1 min) Time passed 15 min In-Class Notes Students are NOT meant to solve this problem before the lesson. This slide is a preview of the overarching question that gives students a clear need for the Tape Diagrams tool. The teacher may want to point out or highlight from any student questions that Zack’s original ratio is 3 red to 5 yellow. Some students may get the answer right away. Some may only write down the question. That’s ok. The point is to establish a need for the tape diagram tool. They will all have to prove the answer using the tool for the exit ticket. Let speedy students know this. “Nice work. We are going to learn about a way to visually show how you get this answer. It’s a pretty nice tool for ratio problems – I really think you will like it.” For students who don’t know how to begin, “I see that you are struggling with your strategy for this problem. Lucky for you we are going to learn a really helpful tool for solving this problem. I really think you will like it.”  Agenda

Explore – Mini-Lesson Before we solve Zack’s problem, let’s look at some simpler problems to get ready. Read this problem. Example 1) The ratio of boys to girls in a class is 2 to 3. 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – ½ min) Time passed 16 min In-Class Notes Students are NOT solving this problem. It is an example used to illustrate the tape diagrams tool. Click through to get to the heart of the lesson: the introduction to the tape diagram Preparation Notes You will want to spend a good deal of preparation time reviewing the next slides so that you thoroughly understand how a tape diagram is created and used. Drawing an accurate model is very important. Agenda

Explore – Mini-Lesson Let’s learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – ½ min) Time passed 16 min In-Class Notes We want students to be very clear that there are several very useful tools for working with ratios. The tape diagram is the first of these tools that they will learn about. Preparation Notes This lesson is an introductory lesson for students on a visual model for ratio problem solving called here, the tape diagram. It is also referred to as a “unit bar model” in Singapore Mathematics. Many high-achieving countries use this visual model for ratio problem solving. Students can just watch the diagram creation without writing anything unless your students have trouble with this kind of instruction. Then have students draw the diagram with you. This will obviously take more time and require the lesson to be broken into 2 days. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. boys girls Each box represents a number in the original ratio. 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 3 min) Time passed 19 min In-Class Notes Go slowly and make sure that students realize that the “4 boys” in the problem belongs written above or below the appropriate tape. Now let’s look at the question. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. If this tape shows 4 boys then… boys girls 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 1 min) Time passed 20 min In-Class Notes Make sure they see that the first step is to set up the tape diagram with information that is given to us. This can take time but it is time well-spent. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 4 How many students are in one box? This tape is 4 boys. So we put 4 above the tape. 2 2 boys girls 2 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 2 min) Time passed 22 min In-Class Notes This slide can be replayed over and over to show students how we get to “2” in each box. You distribute the 4 into the two boxes in the tape. Agenda

The number in each box must be the same for every tape.
New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 4 We don’t yet know the number of girls so we put a ? for the length of that tape. 2 2 Important Rule: The number in each box must be the same for every tape. boys 2 2 2 girls ? 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 1 min) Time passed 23 min In-Class Notes Very important rule. This is the key to students being able to recreate and use a tape diagram. Preparation Notes Make sure you spend time to make sure you fully understand the model and how to explain it. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 4 2 2 Now we can answer the question. boys 2 2 2 girls ? 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 1 min) Time passed 24 min In-Class Notes If you use the tool correctly it is extremely simple to find the answer to the question asked. 6 Agenda

? 8 Explore – Mini-Lesson Let’s try another one.
New Tool: Tape Diagram Explore – Mini-Lesson Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? We can label what we know. 8 girls. boys girls First, draw the tapes. We can put a question mark for what we don’t know. 8 2. If there are 8 girls in the class, how many boys are there? (Time on this slide – 2 min) Time passed 26 min In-Class Notes Make sure students realize that this is a different problem. Now let’s look at the question. Agenda

4 ? 8 Explore – Mini-Lesson Let’s try another one.
New Tool: Tape Diagram Explore – Mini-Lesson Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? How many students does each box represent? boys This makes 8 girls. 4 4 girls 4 8 2. If there are 8 girls in the class, how many boys are there? (Time on this slide – 2 min) Time passed 28 min In-Class Notes Again, here is a very important step. If there are 8 girls and the ratio indicates we must make 2 boxes for a ratio of 3:2 then we can distribute the 8 into the 2 boxes. Students may, of course, realize this “distribution” as division. This would be desired but does not need to be pushed early. Agenda

Every box must have the same quantity.
New Tool: Tape Diagram Explore – Mini-Lesson Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? Remember: Every box must have the same quantity. boys 4 4 4 4 4 girls 8 2. If there are 8 girls in the class, how many boys are there? (Time on this slide – 2 min) Time passed 30 min Preparation Notes Advanced box comes as a click at the end of this slide. Use if you want to. 12 Can you answer the question using the diagram? Advanced: Think of one way you could prove that the numbers in each box should be 4. Tell your partner. Agenda

Explore Tape Diagrams can be a helpful tool for solving problems.
Check this out for more about how tape diagrams work: Click “Watch video” for a demonstration. (Time on this slide – 5 min) Time passed 35 min In-Class Notes Click the internet symbol to link to the Thinking Blocks website that has an interactive applet for using tape diagrams to solve ratio problems. Preparation Notes You can further explore this website with students to practice using tape diagrams or what they call “Thinking Blocks”. If you have access to a computer lab this would be a great activity to have students work on. Agenda

Practice You will have 15 minutes to work on solving some ratio problems using the tape diagrams tool. You might feel a little confused and want to talk about it. Don’t worry – you will discuss it when you are finished. (Time on this slide - 15 min) Time passed 50 min In-Class Notes This screenshot is a cue for students so that they know what page to have in front of them. Answers will be provided later in the slideshow. Agenda

Discuss Check with a partner to see if you have the same answers. See if you used your tape diagram tools in the same way. You have 10 minutes. (Time on this slide – 10 min) Time passed 60 min In-Class Notes Have students put a star next to any problems that have different solutions. Agenda

If you and your partner cannot agree on a diagram, put a star next to the problem.
Discuss Let’s look at questions 3 and 4. Check to see if you and your partner completed the tape diagrams in the same way. (Time on this slide – 4 min) Time passed 64 min In-Class Notes Students will star problems that they are having trouble agreeing about. Take a poll to find out how many students had trouble with #3? How many had trouble with #4? Etc. You can then decide if you want to go over each problem or only those that many students had trouble with. Answers including tape diagrams are found by clicking a button on this or any of the next 2 slides. Preparation Notes If you only have a 60 min block the slides from here on out may be used for another day. Students review their work together. Answer button can be used to walk students through the tape diagram drawing process. Then small group discussion, reflection, independent exit ticket and assessment for understanding. Agenda

Discuss Answers 6 8 6 6 6 6 6 6 sour oranges 4 4 4 4 4 8 red marbles
(Time on this slide – 1 min) Time passed 65 min 4 4 8 red marbles 8 Agenda

Discuss Did you and your partner complete the tape diagrams the same way? Did you get the same answers? (Time on this slide – 4 min) Time passed 69 min In-Class Notes Click “answers” button for detailed answer diagrams. Agenda

Discuss Did you and your partner complete the tape diagrams the same way? Did you get the same answers? 24 children playing 10 apples 24 10 (Time on this slide – 1 min) Time passed 70 min playing 8 8 8 apples 5 5 resting 8 oranges 5 5 5 Agenda 8 15 Agenda

Discuss (optional) Each pair will share with another pair to see if you have the same answers. See if you used tape diagrams the same way. Each group of four will be assigned one problem (3, 4, 5, or 6) from the class work. One person will need to put their group’s work on the board. (Time on this slide – 5 min) Time passed 75 min In-Class Notes If there is no time for this exercise, then click back for the button to see the answer slides. Preparation Notes Having students discuss the math is not only good for ELL students but allows students with learning differences to experience the content through a different modality. It also increases attention to the topic and student engagement. You will have 10 minutes. No time? Click for Answers Slides Agenda

Summary – Write in your notebook
What is one thing you like about the tape diagrams as a tool? What is one thing that is difficult? Is there anything that is confusing about using tape diagrams as a tool? (Time on this slide – 5 min) Time passed 80 min In-Class Notes Have students take 3-5 minutes to write sentences that answer these three questions. Select 3 students at random to answer one of the questions by reading their writing. Agenda

New Tool: Tape Diagram Exit Ticket Now that you learned a new tool use it to solve Zack’s paint problem. Remember: Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. He bought 24 cups of red paint. (Time on this slide – 4 min) Time passed 84 min In-Class Notes For the exit ticket it is important that students make a tape diagram to prove that they have mastered the objective for the lesson. Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint. Agenda

24 8 8 8 8 8 8 8 8 ? 40 cups of yellow paint Exit Ticket
New Tool: Tape Diagram Exit Ticket Let’s solve this problem using a tape diagram. The question is: How many cups of yellow paint does Zack need to make his shade of orange paint? We know: Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. And, we know: he bought 24 cups of red paint. Since every box must have the same quantity… Now we can figure out how many cups each box represents. If 3 boxes are 24 then… This is a 3:5 ratio of red to yellow. 24 Let’s label the diagram. red yellow 8 8 8 Let’s draw the tapes. 8 8 8 8 8 (Time on this slide – 1 min) Time passed 85 min In-Class Notes For the exit ticket it is important that students make a tape diagram to prove that they have mastered the objective for the lesson. ? 40 cups of yellow paint That means the answer is: Agenda

Assessment Carefully review the tape diagram tool and solution. What is wrong here? The ratio of grapes to strawberries in a fruit salad is 4 to 1. If there are 20 grapes in the salad then how many strawberries are there? grapes strawberries 20 20 20 20 20 (Time on this slide – 5 min) Time passed 90 min In-Class Notes This is a very quick assessment and is not meant to take a long time. Students can write answers to this question in their notebook or on a small paper to be turned in with only their suggestions on what to do to correct the problem. Answer: So the number of grapes is 20. Agenda

1st Time Users of 21st Century Lessons
Description of 21st Century Lessons: Welcome to 21st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Next Slide Back to Overview

Standards for This Unit The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: 6RP3 Use ratio reasoning to solve real-world problems and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Next Slide Back to Overview

Requirements to teach 21st Century Lessons: In order to properly use 21st Century Lessons you will need to possess or arrange the following things: Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Scissors – at least 1 for every pair Next Slide Back to Overview

Strongly Suggested to teach 21st Century Lessons: Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with a student’s name on each one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students’ attention. (“hands- up”, Count from “5” to “0” etc.) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Next Slide Back to Overview

Lesson Preparation (Slide 1 of 2) We suggest spending minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you. Note: All of our lessons are designed to be taught during a minute class. If your class is shorter than this you will have to decide which sections to condense/remove. If your class is longer we suggest incorporating some of the “challenge” questions if available. Next Slide Back to Overview

Lesson Preparation (Slide 2 of 2) After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for the lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the content, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Next Slide Back to Overview

Features built into each PowerPoint lesson There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include: Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Click the agenda button on any slide to return to the agenda. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Next Slide Back to Overview

Overview Slide Tab Descriptions (Slide 1 of 3) # Category Description 1 Lesson Objective A description of what your students should know or be able to do by the end of the lesson. We also include a “Student-Friendly Objective,” written in a manner students can more easily comprehend and digest. 2 Lesson Math Vocabulary A list of the math vocabulary used in this lesson, with student-friendly definitions. 3 Common Core State Standard Over 40 states have adopted the Common Core State Standards. This tab lists the Common Core Standard being taught in the lesson. (Massachusetts state standards are usually identical to the Common Core, if the MA standard is different it is also listed here.) Next Slide Back to Overview

Overview Slide Tab Descriptions (Slide 2 of 3) # Category Description 4 Lesson Description This is probably the most important tab on the overview slide. Here, in a narrative form, the lesson designer takes you from beginning to end of the lesson. We often describe the pedagogical approach that we are using as well as the rationale for using this approach. We also discuss the big ideas of this lesson as well as any essential understandings. 5 Background Information This tab covers: a) interesting historical facts related to the day’s objective, b) how the lesson’s mathematics is used in the real world, and c) a brief description of the research supporting the practices used in the lesson (sometimes with a link to the source). 6 Scaffolding Description of what supports the lesson utilizes for ELL students, Special Education students, and those who may be struggling to learn the concept/skill. Next Slide Back to Overview

Overview Slide Tab Descriptions (Slide 3 of 3) # Category Description 7 Enrichment On this tab we state an “advanced” objective for students who have already mastered (or master quickly) the standard objective. We also give a short description on how teachers can support these students. 8 Materials This is a list of materials required for this lesson. Some of these items may be hyperlinked to the actual document or website. In addition, there is a lesson outline which can be printed out. 9 Online Resources for Absent Students Links to videos and practice problems that students who are absent (or need a review) can use independently to learn the day’s objective. 10 Before and After An explanation on how the concept and skills in the day’s lesson fit into the larger mathematics picture (i.e. what related concepts have students learned previously and what future concepts are we helping build a foundation for). Back to Overview

21st Century Lessons The goal…
The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to: Support an increase in student achievement; Engage teachers and students; Align to the National Common Core Standards and the Massachusetts curriculum frameworks; Embed best teaching practices, such as differentiated instruction; Incorporate high-quality multi-media and design (e.g., PowerPoint); Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; Be available, along with videos and supporting materials, to teachers free of charge via the Internet. Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers.

21st Century Lessons The people…
Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21st Century Lessons Brian Connor – Technology Coordinator

Introduction to Tape Diagrams

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