A Story of Ratios Module 1 Focus - Grade 6

A Story of Ratios Module 1 Focus - Grade 6
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: X minutes MATERIALS NEEDED: X A Story of Ratios Module 1 Focus - Grade 6 Welcome to A Story of Ratios. Today and tomorrow we will dig deep into this first module of sixth grade and walk away with a firm grasp of ratios, equivalent ratios, unit rates and percents! Introduce session facilitators at the beginning.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Objectives Articulate and model the instructional approaches to teaching the content of the first half of the lessons. Examine how the topics and lessons promote mastery of the focus standards and address the major work of the grade. Examine lesson components including Examples vs. Exercises, Application Problems, Concept Development, Problem Sets, and Exit Tickets. Let’s take a look at the objectives for the first half of today’s session. By the end of this portion, (CLICK TO ADVANCE FIRST BULLET)participants will be able to articulate and model the instructional approaches to teaching the content of the first half of the lessons from Grade 6 Module 1. (CLICK TO ADVANCE SECOND BULLET)Participants will examine how the topics and lessons promote mastery of the focus standards and address the major work of the grade. (CLICK TO ADVANCE THIRD BULLET)Finally, we will examine lesson components including examples and exercises, noting the differences between the two. We will examine application problems, concept development, problem sets and exit tickets. As we move through this session, please ask questions that will help with your immediate understanding of the material. If you have questions that relate to your broader understanding of A Story of ratios or how to implement the curriculum in your school or district, please write those on a sticky note along with your name and place the note on the parking lot. We will look at those questions during the lunch break and address them with the group if they are applicable to all or with you if they are specific to your situation. Principals in particular- You will want to make notes for yourself as a result of your observations to use in later sessions tomorrow. .We will be focusing you on the areas where you will want to make notes for yourself to use later.

Participant Poll Classroom teacher School leader Principal
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Sticky notes (1 per participant) 6 pieces of chart paper Participant Poll Classroom teacher School leader Principal District leader BOCES representative In order for us to better address your individual needs, it is helpful to know a little bit about you collectively. Who of you are classroom teachers? (Call for a show of hands.) Please place your sticky note on the appropriate chart paper. School-level leader? Principal? District-level leader? BOCES representative? All place sticky notes on their prospective chart papers. NOTE TO FACILITATOR: As you poll the participants, take note of the approximate size of each group. This will make it easier for you to re-group the participants for the final portion of this presentation. Regardless of your role, what you all have in common is the need to deeply understand the mathematics of the curriculum and the intentional instructional sequence in which it is brought to life for students. Throughout this session, we ask you to be cognizant of your specific educational role and how you will be able to promote successful implementation in your classroom, school, district, and/or BOCES. Each time we pause to reflect, please do so through the lens of your own professional responsibilities. At the close of this session, you will have the opportunity to share your thoughts, ideas, and concerns with others in a similar role. Let’s take a look at ratios from our data: Write the ratio of each below each heading on the chart paper. What is the ratio of classroom teachers to school leaders? School leaders to classroom teachers? School leaders to Principals? Principals to District Leaders? BOCES representatives to District Leaders? Classroom teachers to total amount of participants? Classroom teachers to Non-Classroom teachers?

Agenda Review of Module Structure
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Agenda Review of Module Structure Examination of the Module Overview and the Topic Openers Lesson Study Coherence Across the Module This portion’s agenda will include the following: We will review the module structure. Next we will examine the module overview and the topic openers. Some of you may have participated in the May 2013 NTI where we examined the module overview in depth. Today we will quickly revisit the module overview for those who were unable to attend, then focus closely on the topic openers. We will spend the bulk of this portion on studying the lessons in the first half of Module 1. We will begin first by examining the lesson components, then move into in-depth study of each lesson. Finally before the break, we will discuss the coherence across the first half of the module. Let’s move into reviewing the structure of the module. (CLICK TO HIGHLIGHT FIRST BULLET)

A Story of Ratios TIME ALLOTTED FOR THIS SLIDE: 1 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X A Story of Ratios Please take a look at the Story of Ratios document. In this section, you will notice that the module we are focusing on is the first module of the school year. The title of the module is Ratios and Unit Rates and it encompasses 35 instructional days.

Review of Module Structure
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Review of Module Structure Module Overview Topic A Topic B Topic C Topic D (CLICK TO ADVANCE MODULE OVERVIEW)We begin with a module overview that provides pertinent information about the entire module. It provides us with a table of contents, including placement of the mid-module assessment and the end-of-module assessment. There is an in-depth overview that steers the instructor from where the students have been, to what students will be accomplishing within the module, and then to where students will be applying what they learned after the module. Focus standards that the module addresses from CCSS are included, as well as prerequisite foundational standards that are essential for student success. There is a study of the mathematical practices that this module represents and provides specific areas within the lessons where these practices are demonstrated. You will note later that this is only a subset of the eight mathematical practices. These practices were determined as they relate to the content and length of the module. This is surely not to say that all eight practices are not included within the lessons, of course. These are the focus practices. New terminology is highlighted in the module overview, as well as a reference to terminology students should have already been exposed to. Suggested tools and representations are provided, with examples, and finally a summary of the mid-module and end-of-module assessments is given. The module is divided into 4 topics. (CLICK TO ADVANCE TOPIC A)Topic A contains eight lessons that focus on representing and reasoning about ratios. (CLICK TO ADVANCE TOPIC B)Topic B includes seven lessons that focus on collections of equivalent ratios. (CLICK TO ADVANCE TOPIC C)Topic C focuses on unit rates and encompasses eight lessons. And finally, (CLICK TO ADVANCE TOPIC D) Topic D focuses on percents, and has six lessons supporting that focus. Lessons 1 - 8 Lessons Lessons Lessons

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: X minutes MATERIALS NEEDED: X Agenda Review of Module Structure Examination of the Module Overview and the Topic Openers Lesson Study Coherence Across the Module Let’s take a closer look at the Module Overview and the topic openers. (CLICK TO HIGHLIGHT EXAMINATION OF THE MODULE OVERVIEW AND THE TOPIC OPENERS)

Module Overview TIME ALLOTTED FOR THIS SLIDE: 10 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: X Module Overview We will take 5 minutes to review the module overview. Please feel free to take notes on the overview. After we have had time to read the overview, we will take 2 minutes to discuss with a neighbor and then take 3 minutes to share with the group our findings. How might you use this information in your role? ( It is a quick summary of what teachers will do for the next few weeks and can be shared with parents and the community, it also summarizes what conversations should be happening in grade level meetings and what resources teachers may be requesting for their classrooms, it can be shared with other teachers in the school for the purpose of thematic unit planning.)

Topic Openers – Topic A TIME ALLOTTED FOR THIS SLIDE: 3 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Topic Openers – Topic A Please turn to the Topic A Opener. (CLICK TO ADVANCE FIRST BULLET) Please read the descriptive narrative. As you are reading, you will notice that this is a more comprehensive study of the topic. (CLICK TO ADVANCE SECOND BULLET)Please make notes of the important information that you believe will help educators implement these lessons. Let’s take about 3 minutes to read over the opener and take notes. Read the descriptive narrative. Make note of important information that will help educators implement these lessons.

Topic Openers – Topic B TIME ALLOTTED FOR THIS SLIDE: 3 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Topic Openers – Topic B Please turn to the Topic B Opener. (CLICK TO ADVANCE FIRST BULLET)Please read the descriptive narrative. As you are reading, you will notice, again, that this is a more comprehensive study of the topic. (CLICK TO ADVANCE SECOND BULLET)Please make notes of the important information that you believe will help educators implement these lessons. Let’s take about 3 minutes to read over the opener and take notes. Read the descriptive narrative. Make note of important information that will help educators implement these lessons.

Topic Openers – Topics A and B
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: X Topic Openers – Topics A and B How does each topic contribute to the overall instructional goal of the module? How are the Topic Openers useful as a planning tool? What is the relationship between the Topic Opener and the other components of the module? Let’s have a table discussion about the Topic Openers for Topics A and B. As you are discussing with your table, please focus on the following: (CLICK TO ADVANCE FIRST BULLET)How does each topic contribute to the overall instructional goal of the module? (CLICK TO ADVANCE SECOND BULLET)How are the topic openers useful as a planning tool? Be ready to share any ideas you come up with. (CLICK TO ADVANCE THIRD BULLET)What is the relationship between the topic openers and the other components of the module? Let’s share for 3 minutes, then we will come together and share as a whole group. (2 minute whole group share)

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: X minutes MATERIALS NEEDED: X Agenda Review of Module Structure Examination of the Module Overview and the Topic Openers Lesson Study Coherence Across the Module And now for what many of you have been waiting for, let’s dig into these lessons for Topics A and B!! (CLICK TO HIGHLIGHT LESSON STUDY) We are going to begin by looking at how the lessons are designed and the lesson components.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: 4 pieces of chart paper 4 pre-made lesson type headings Lesson Study Examine the development and function of each lesson component. Lesson Type (Socratic, Modeling Cycle, Exploration, Problem Set) Lesson Title Student Outcomes Optional Lesson Notes Classwork: Examples and Exercises Application Problems Concept Development Practice Set* Student Debrief/Exit Ticket Please turn to the first lesson of the Module. (CLICK TO ADVANCE FIRST BULLET)Before we get into the meat of the lesson, lets take a look at how these lessons are designed. Note the blue conversation bubble prior to the lesson title. This graphic means that this is a Socratic lesson. There will be four different lesson types within the module: Socratic, Modeling Cycle, Exploration and Problem Set. (DIRECT ATTENTION TO CHART PAPER)Teachers lead students in a conversation with the aim of developing a specific concept or proof in a Socratic lesson. Teachers ask guiding questions to pull information from the students and draw them into the discussion. In the remaining minutes of the lesson, other activities are likely to occur, like a debrief or application problem. Modeling Cycle Lesson – Teacher and students work through a sequence of examples and exercises to develop or reinforce a concept. This is mostly teacher directed. Students work on exercises individually or in pairs but not for long periods at a time. The majority of the class period is spent alternating between the teacher working through examples with the students and the students completing exercises. Exploration Lesson – Students are given 20 – 30 minutes to work independently or in small groups on one or more exploratory challenges followed by a debrief with the goal of clarifying, expanding upon or developing a concept, definition, theorem or proof. This is typically going to be a challenging problem or question that requires students to collaborate (in pairs or groups) but can be done individually. The class comes back together to discuss the problem for a period of time to draw conclusions and consolidate understandings. Problem Set Lesson –Students are involved in practicing all or part of the problem set lesson. The problem students are working on is ill-defined and has a real world context. Students are likely to work in groups on these types of problems, but teachers may want students to work for a period of time individually before collaborating with their group members. (CLICK TO ADVANCE FOR EACH BULLET)Each lesson is titled with a general description of the lesson. This is followed by student outcomes. Sometimes the lesson will include lesson notes that are optional narratives containing critical pre-instructional guidance. Classwork : Note that there are examples and exercises. If the lesson denotes an example, you will notice that this is teacher-led instruction. Exercises are student-led with teacher guidance. You will note that the lessons include application problems, and of course logical concept development. There is a problem set that is available for each lesson. Directions on how to use these have not been included in the teacher’s notes, but each problem set is provided for the teacher’s discretion on how to use the problems. These problems can be used for additional practice if the timing of the lesson allows. They can also be given as homework. Each lesson ends with a debriefing/closure with student response. This includes an exit ticket. The exit ticket is a daily assessment performance that must be observed and/or collected through an artifact. Exit tickets, debrief questions, or artifacts will enable teacher to assess each student individually.

Lesson 1 Student Outcomes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 1 Student Outcomes Students understand that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students understand that a ratio is often used in lieu of describing the first number as a multiple of the second. Students use the precise language and notation of ratios (3: 2, 3 to 2). Students understand that the order of the pair of numbers in a ratio matters, and that the description of the ratio relationship determines the correct order of the numbers. Students conceive of real-world contextual situations to match a given ratio. (CLICK TO ADVANCE FIRST BULLET) Read the student outcome. (CLICK TO ADVANCE SECOND BULLET) Read the student outcome. (CLICK TO ADVANCE THIRD BULLET) Read the student outcome. (CLICK TO ADVANCE FOURTH BULLET) Read the student outcome. (CLICK TO ADVANCE FIFTH BULLET) Read the student outcome.

Lesson 1 - Ratios Lesson Notes:
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 1 - Ratios Lesson Notes: The first two lessons of this module will develop the students understanding and definition of the term ratio. A ratio is always a pair of numbers, like 2:3, and never a pair of quantities like 2 cm : 3 sec. Keeping this straight for students will require consistently correct use of the term ratio. It will require keeping track of the units in a word problem separately. To help distinguish between ratios and statements about quantities that define ratios, we use the term ratio relationship to describe an English phrase in a word problem that indicates a ratio. Typical examples of ratio relationship descriptions include, “3 cups to 4 cups,” “5 miles in 4 hours,” etc. The ratios for these ratio relationships are 3:4 and 5:4, respectively. (CLICK TO ADVANCE FIRST BULLET) Read the note. (CLICK TO ADVANCE SECOND BULLET) Read the note. (CLICK TO ADVANCE THIRD BULLET) Read the note. (CLICK TO ADVANCE FOURTH BULLET) Read the note.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Lesson 1- Ratios The coed soccer team has four times as many boys on it as it has girls. We say the ratio of the number of boys to the number of girls on the team is 4:1, we read this as “four to one.” Let’s create a table to show how many boys and how many girls are on the team. Thinking about the outcomes and the lesson notes, we are going to dive into the first lesson for our sixth graders. For these next few lessons, we will examine various portions to detail the progression of learning. Please follow along in the lesson documents in front of you. Read the problem to the group. (CLICK TO ADVANCE FIRST BULLET) Let’s create a table to show how many boys and how many girls are on the team. (CLICK TO ADVANCE THE TABLE) We see here that there is a 4 in the number of boys column, a 1 in the number of girls column and a 5 in the total number of players column. (CLICK TO ADVANCE THE 8 IN THE BOYS COLUMN) Notice that now there are eight boys on the team. How many girls would be on the team now, if there are 8 boys? (CLICK TO ADVANCE THE 2 IN THE GIRLS COLUMN) If there are 8 boys and 2 girls, how many total players would there be? (CLICK TO ADVANCE THE TEN IN THE TOTAL PLAYERS COLUMN) Notice how we added four to the boys column to reach 8, and 1 to the girls column to reach 2? If I were to keep that pattern going, how many boys would be in the next row of the boys column? (CLICK TO ADVANCE THE 12 IN THE BOYS COLUMN) How many girls would be in the next row of the girls column? (CLICK TO ADVANCE THE 3 IN THE GIRLS COLUMN) How many total players would there be? (CLICK TO ADVANCE THE 15 IN THE TOTAL COLUMN) (CLICK TO ADVANCE) From the table, we can see that there are four boys for every one girl on the team. # of Boys # of Girls Total # of Players 4 1 5 8 2 10 12 3 15 From the table, we can see that there are four boys for every one girl on the team.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Lesson 1- Ratios Suppose the ratio of boys to girls on a different soccer team is 3:2 Create a table like the one shown below to show possibilities of the number of boys and girls on the soccer team. # of Boys # of Girls Total # of Players 3 2 5 CLICK TO ADVANCE TABLE) What values can I place in the second row of the table? CLICK TO ADVANCE SECOND ROW) What is another set of values for the third row? CLICK TO ADVANCE THIRD ROW) I can’t say there are 3 times as many boys as girls. What would my multiplicative value have to be? There are how many more boys as girls? Can this be easily determined? Here we lead students into finding the fractional representation of 3/2. Students may not come to this conclusion, but based on the previous ratio of 4:1, they notice that there are four times as many boys as girls, so in this example there are 3/2 as many boys as girls. Can you visualize 3/2 as many boys as girls? Students are anticipated to share all thoughts.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: X Lesson 1- Ratios Can we make a tape diagram (or bar model) that shows that there are 3/2 as many boys as girls? Which description makes the relationship easier to visualize? Saying the ratio is 3 to 2 or saying there are 3 halves as many boys as girls? There is no right or wrong answer, have students explain why they picked their choice. Can we make a tape diagram (or bar model) that shows that there are 3/2 as many boys as girls? Students have been exposed to tape/bar diagrams in previous grades, but if students need further instruction, here is where it is appropriate. (CLICK TO ADVANCE TAPE DIAGRAM) Note that there are three units to represent the boys and two units to represent the girls. (CLICK TO ADVANCE DISCUSSION) Which description makes the relationship easier to visualize? Saying the ratio is 3 to 2 or saying there are 3 halves as many boys as girls? (CLICK TO ADVANCE DISCUSSION) There is no right or wrong answer, have students explain why they picked their choice.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: X Lesson 1 - Ratios Read through the rest of the lesson to see how it develops. Share your thoughts with your neighbor and write down key points you would like to discuss and share with the whole group. Five minute share. (CLICK TO ADVANCE DIRECTIONS) Read through the rest of the lesson to see how it develops. (CLICK TO ADVANCE DIRECTIONS) Share your thoughts with your neighbor and write down key points you would like to discuss and share with the whole group. Allow 5 minutes to read through the lesson and 3 minutes to share with table neighbors. (CLICK TO ADVANCE SHARING) Let’s share our thoughts, questions and comments.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 2 - Ratios Students reinforce their understanding that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students continue to learn and use the precise language and notation of ratios (3: 2, 3 to 2). Students recognize ratio language as such. Students demonstrate their understanding that the order of the pair of numbers in a ratio matters. Students create multiple ratios from a context in which more than two quantities are given. Students conceive of real-world contextual situations to match a given ratio. Let’s move on to the second half of the Ratios Lesson – Lesson 2. (CLICK TO ADVANCE EACH OUTCOME) Read each outcome as they appear.

Lesson 2 - Ratios TIME ALLOTTED FOR THIS SLIDE: 5 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 2 - Ratios Let’s walk through Lesson 2 together. Notice that students share and write the examples on the board, being careful to include some of the verbal clues that indicate a ratio relationship: ‘to’, ‘for each’, ‘for every’, which is reinforced by the teacher prompting, “What are the verbal cues that tell us someone is talking about a ratio relationship?” (CLICK TO ADVANCE LINE PLOT) Take 3 minutes to read through Example 2 with a table partner and answer the questions guided by the teacher. (CLICK TO ADVANCE DESCRIPTION OF RATIO RELATIONSHIP TABLE) Take 2 minutes to work with your table partner and highlight/underline the words or phrases that indicate the description in a ratio, then write the ratio for each example. (CLICK TO ADVANCE DESCRIPTION OF RATIO RELATIONSHIP TABLE 2) Here, students are examining the ratio, then creating their own examples and highlighting/underlining the words or phrases that indicate the description in each ratio.

Lesson 3 – Equivalent Ratios
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 3 – Equivalent Ratios Students develop an intuitive understanding of equivalent ratios by using tape diagrams to explore possible quantities of each part given the part to part ratio. Students use tape diagrams to solve problems where the part to part ratio is given and the value of one of the quantities is given. Students formalize a definition of equivalent ratios: Two ratios 𝐴:𝐵 and 𝐶:𝐷 are equivalent ratios if there is a positive number, 𝑐, such that 𝐶=𝑐𝐴 and 𝐷=𝑐𝐵. Now that students have a good foundational understanding of what a ratio is, and how it is represented, let’s move on to the third lesson, which is the introduction to equivalent ratios. (CLICK TO ADVANCE EACH OUTCOME) Read each outcome as they appear.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 3 – Equivalent Ratios Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to Mel’s ribbon is 7:3. Create a table. Draw a tape diagram to represent this ratio. Shanni Mel 7 inches 3 inches 7:3 7 to 3 21 inches 9 inches 21:9 21 to 9 2 m 2 m 2 m 2 m 2 m 2 m 2 m 14 meters 6 meters 14:6 14 to 6 In this lesson, students examine and create tape diagrams in order to determine equivalent ratios. (CLICK TO ADVANCE THE EXAMPLE PROBLEM) Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to Mel’s ribbon is 7:3. (CLICK TO ADVANCE THE FIRST BULLET) Here, students will refer back to previous lessons and create a table to represent other ratios based on 7:3 (CLICK TO ADVANCE THE SECOND BULLET) Let’s closely examine the construction and interpretation of tape diagrams. (CLICK TO ADVANCE SHANNI) How many units of our tape diagram should we draw for Shanni? (CLICK TO ADVANCE THE TAPE DIAGRAM) (CLICK TO ADVANCE MEL) How many units of our tape diagram should we draw for Mel? (CLICK TO ADVANCE THE TAPE DIAGRAM) What does this mean? What does each unit represent? (CLICK TO ADVANCE MEANING) So Shanni’s ribbon is 7 inches and Mel’s is 3 inches. The ratio of Shanni’s ribbon length in inches to Mel’s ribbon length in inches is 7:3 or 7 to 3 (CLICK TO HIDE BOX) What if each unit were to represent 2 meters? What would the length of Shanni’s ribbon be? What would we do to find out? (CLICK TO ADVANCE THE LABELING OF EACH UNIT FOR SHANNI’S RIBBON) What would we do to find out the length of Mel’s ribbon? Can we do the same thing? We must! (CLICK TO ADVANCE THE LABELING OF EACH UNIT FOR MEL’S RIBBON) Now, what does this mean? (CLICK TO ADVANCE MEANING) So Shanni’s ribbon is 14 meters and Mel’s ribbon is 6 meters. The ratio of Shanni’s ribbon length in meters to Mel’s ribbon length in meters is 7:3 or 7 to 3. (CLICK THREE TIMES TO HIDE THE MEANING AND THE LABELS IN THE TAPE DIAGRAM) What if the each unit represents 3 inches? (CLICK TO SHOW RATIOS) 2 m What ratios can we say are equivalent to 7:3?

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 7 minutes MATERIALS NEEDED: X Lesson 3 – Equivalent Ratios Take 5 minutes to work through Exercise 4 with your neighbor. Share your thoughts! Allow 5 minutes for participants to work through Exercise 4. (CLICK TO ADVANCE THE DIRECTION) Share your thoughts. Allow 2 minutes for sharing.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 4 – Equivalent Ratios Given a ratio, students will identify equivalent ratios. Students use tape diagrams and the description of equivalent ratios to determine if two ratios are equivalent. Students relate the common factor, c, in the description of equivalent ratios to the tape diagrams they’ve been using to find equivalent ratios. Now that students have a good foundational understanding of determining equivalent ratios, let’s move on to the fourth lesson, which is the second part to equivalent ratios. (CLICK TO ADVANCE EACH OUTCOME) Read each outcome as they appear. Note that the outcomes build upon each other, yet not omitting outcomes from previous lessons.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: X Lesson 4 – Equivalent Ratios Exercise 1 is a recursive exercise to practice outcomes developed in the first 3 lessons. Here for exercise 2, you will see that students bridge their knowledge to the constant, or noted here, the value c. Students are determining if ratios are equivalent. If they are they equivalent, they denoting the constant, which is also referenced as the value of the unit in the tape diagram. If they are not equivalent, students create a situation where the ratios would be equivalent. Note number two in this exercise. What are your thoughts on this? How can we explain to students why this is a ratio if we can’t necessarily determine that the constant is 4? Can’t we make the argument that the product of zero and any number will result in zero? This includes 4.

Lesson 4- Equivalent Ratios
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Whiteboards Dry erase markers Lesson 4- Equivalent Ratios Exercise 3: In a bag of mixed walnuts and cashews, the ratio of walnuts to cashews is 5:6. Determine the amount of walnuts that are in the bag if there are 54 cashews. Use a tape diagram to support your work. Justify your answer by determining equivalent ratios. 54 walnuts cashews Read the problem to participants. Students will have to determine that six equal parts of 54 is 9. The constant is 9. Then they will multiply the units for the walnuts by the constant 9. 5 times 9 is 45. There would be 45 walnuts. Use your whiteboards to show the multiplicative relationship between the values, highlighting the constant, 9.

Lesson 4- Equivalent Ratios
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Whiteboards and markers Lesson 4- Equivalent Ratios Exercise 3: In a bag of mixed walnuts and cashews, the ratio of walnuts to cashews is 5:6. Determine the amount of walnuts that are in the bag if there are 54 cashews. Use a tape diagram to support your work. Justify your answer by determining equivalent ratios. Read the problem to participants. Students will have to determine that six equal parts of 54 is 9. The constant is 9. Then they will multiply the units for the walnuts by the constant 9. 5 times 9 is 45. There would be 45 walnuts. Use your whiteboards to show the multiplicative relationship between the values, highlighting the constant, 9. Share with group. (CLICK TO ADVANCE THE EXEMPLAR)

Correlations Between Lessons 1-2 and 3-4
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Correlations Between Lessons 1-2 and 3-4 Take 3 minutes to discuss with your table partners the correlations you see between Lessons 1 and 2 to Lessons 3 and 4. Share with whole group. Let’s digest. Now that we have examined the first four lessons, let’s reflect on the correlations between the lessons. How are they building upon each other? What have you noticed in the progression from Lessons 1 -4? (CLICK TO ADVANCE THE FIRST BULLET) Take 3 minutes to discuss with your table partners the correlations you see between Lessons 1 and 2 to Lessons 3 and 4. (CLICK TO ADVANCE THE SECOND BULLET) Share with whole group. (Allow 2 minutes to share)

Lesson 5 – Solving Problems by Finding Equivalent Ratios
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 5 – Solving Problems by Finding Equivalent Ratios Students use tape diagrams to find an equivalent ratio given the part to part ratio and the total of those quantities. Students use tape diagrams to find an equivalent ratio given the part to part ratio and the difference between those two quantities. Students make the connection between the common factor, c, in definition of equivalent ratios and the value of the unit in the tape diagram used to solve ratio problems. Now that students have experience with recognizing and creating equivalent ratios, they will use their knowledge to solve problems by finding equivalent ratios. (CLICK TO ADVANCE EACH OUTCOME) Read each outcome as they appear.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Lesson 5 – Solving Problems by Finding Equivalent Ratios A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his county. In the month of August a total of 192 registrations were purchased for passenger cars and pickup trucks at the local Department of Motor Vehicles. They reported that in the month of August, for every 5 passenger cars registered there were 7 pickup trucks registered. How many of each type of vehicle were registered there in the month of August? 5:7 part-to-part 7:5 part-to-part 5 to 12 part-to-whole 7 to12 part-to-whole 12 equal parts What ratios can we determine from this problem? Describe the ratios (CLICK TO ADVANCE EACH RATIO) (Answer: 5:7 part-to-part, 7:5 part-to-part, 5 to 12 part-to-whole, 7 to12 part-to-whole) Let’s use a tape-diagram to represent the situation. (CLICK TO ADVANCE THE TAPE DIAGRAM) How many total units (or equal parts) are there? (CLICK TO ADVANCE, THEN HIDE) How many total registered vehicles are there? (CLICK TO ADVANCE, THEN HIDE) How can we determine the unit value? (CLICK TO ADVANCE, THEN HIDE) How do we determine the amount of passenger cars? (CLICK TO ADVANCE, THEN HIDE) How do we determine the amount of pickup trucks? (CLICK TO ADVANCE) How many equal sized parts does the tape diagram consist of? 12 What total quantity does the tape diagram represents? 192 vehicles What value does each individual part of the tape diagram represent? Divide the total quantity into 12 equal sized parts: 192/12=16 How many of each type of vehicle were registered in August? 5∙16=80 passenger cars and 7∙16=112 pickup trucks 192 divided by 12 = 16 7 x 16 = 112 pickup trucks 192 vehicles 5 x 16 = 80 passenger cars Passenger Cars Pickup Trucks

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 12 minutes MATERIALS NEEDED: Pre-made center problems 6 pieces of chart paper Lesson 6 – Solving Problems by Finding Equivalent Ratios Students use tape diagrams to solve problems given a ratio between two quantities, and a change to those quantities that changes the ratio. Gallery Walk! Spend 2 minutes at each station to determine the answers to each question. Share with the group the rigor you find in the problems provided in the examples. Lesson 6 furthers students problem solving by finding equivalent ratios. (CLICK TO ADVANCE THE OUTCOME) Because there are many exercises in this lesson, let’s participate in a gallery walk in order for us all to visit each exercise and collaborate with our peers. You will choose a station to begin. We will spend 2 minutes at each station. When time is up you will move to the station to the right. Please record your work on a separate sheet of paper. Once time is up, we will return to our seats and share with the group our thoughts on the rigor you found in the problems. Allow 10 minutes for the gallery walk. After two minute intervals, have participants move to the next station. Once seated, (CLICK TO ADVANCE) have participants discuss the rigor of the exercises/stations.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Correlations Between Lessons 1-4 and 5-6 Take 3 minutes to discuss with your table partners the correlations you see between Lessons 1 -4 and Lessons 5-6. Share with whole group. Let’s digest. Now that we have examined the first four lessons, let’s reflect on the correlations between the lessons. How are they building upon each other? What have you noticed in the progression from Lessons 1 -6? (CLICK TO ADVANCE THE FIRST BULLET) Take 3 minutes to discuss with your table partners the correlations you see between Lessons 1 -4 and 5-6. (CLICK TO ADVANCE THE SECOND BULLET) Share with whole group. (Allow 2 minutes to share) Take one minute to reflect on this session. How do these lessons compare to your past experiences with mathematics instruction? What are the implications for the supports and resources your colleagues will need to fully implement this curriculum with fidelity? Jot down your thoughts. Then you will have time to share your thoughts. Give participants 1 minute for silent, independent reflection. Turn and talk with a partner at your table about your reflections. Allow 2 minutes for participants to turn and talk about their reflections. Then, facilitate a discussion that leads into the key points on the next slide.

Lesson 7 – Associated Ratios and the Value of a Ratio
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 7 – Associated Ratios and the Value of a Ratio Students understand the relationship between ratio and fractions. Students understand that given a ratio A : B, different ratios can be formed from the numbers A and B, such as B : A, A : (A + B), and B : (A + B), that are associated with the same ratio relationship. Students describe the fraction A / B associated with the ratio A : B as the value of the ratio A to B. Now that students have experience with recognizing, creating and solving problems by using equivalent ratios, they will use their knowledge to understand the relationship between ratios and fractions, associated ratios and the value of a ratio. (CLICK TO ADVANCE EACH OUTCOME) Read each outcome as they appear.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 7 – Associated Ratios and the Value of a Ratio Take 2 minutes to read through Example 1 and solve. (CLICK TO ADVANCE) Now take a look at how Example 2 extends Example 1. Take 1 minute to complete the example. Take 2 minutes to discuss with your table why students would need to understand associated ratios. Where later will they need this a prerequisite skill?

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 7 – Associated Ratios and the Value of a Ratio Take five minutes to discuss the duration of the lesson with your neighbor. Take note of how the lesson evolves, noting connections to the past lessons, as well as the rigor that is encompassed within the lesson. Take five minutes to discuss the duration of the lesson with your neighbor. Take note of how the lesson evolves, noting connections to prior lessons.

Lesson 8 - Equivalent Ratios Defined Through Value of a Ratio
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 8 - Equivalent Ratios Defined Through Value of a Ratio Students understand the value of a ratio A:B is A/B. They understand that if two ratios are equivalent they have the same value. Students use the value of a ratio to solve ratio problems in a real-world context. Students use the value of a ratio in determining if two ratios are equivalent. (CLICK TO ADVANCE EACH OUTCOME) Read each bulleted outcome.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 8 - Equivalent Ratios Defined Through Value of a Ratio Recall that given a ratio A : B, where B ≠ 0, we call the quotient, A / B, the value of the ratio. Circle any equivalent ratios from the list below. Ratio: 1 : 2 Value of the Ratio: Ratio: 5 : 10 Value of the Ratio: Ratio: 6 : 16 Value of the Ratio: Ratio: 12 : Value of the Ratio: What do you notice about the value of the equivalent ratios? Note that 1:2 is not the same ratio as 5:10, we don’t say they are equal. The ratios are not the same, but their values are equal. Would this always be the case? Would the values of equivalent fractions always be equal? 1/2 1/2 Read the outcomes. (CLICK TO ADVANCE RATIOS AND VALUES OF RATIOS) Let’s circle the equivalent ratios. (CLICK TO ADVANCE CIRCLES) What would be the value of the ratio 1:2? The value of 5:10? How about the value of the ratio 6:16? The value of 12:32? (CLICK TO ADVANCE BULLET) What do you notice about the value of the equivalent ratios? Read bullet and allow 1-2 minute for participant sharing. 3/8 3/8

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 8 - Equivalent Ratios Defined Through Value of a Ratio Exercise 2: Here is a theorem: If two ratios are equivalent, then they have the same value. Can you provide any counter-examples to the theorem above? Allow students to try this in pairs. Observe the progress of students and question student’s counter-examples. Ask for further clarification or proof that the two ratios are equivalent, but do not have the same value. If students still think they have discovered a counter-example, share the example with the class and discuss why it is not a counter-example. Ask entire class if anyone thought of a counter-example. If students share examples, have others explain why they are not counter-examples. Then discuss why there are not possible counter-examples to the given theorem. It is important for students to understand that the theorem is always true so it is not possible to come up with a counter-example. Walk through the progression of this exercise noting that the teacher is providing students to make a choice whether they agree with the theorem. The students are experimenting and determining on the their own. Student discovery is essential when providing this type of “rule.”

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 7 minutes MATERIALS NEEDED: X Lesson 8 - Equivalent Ratios Defined Through Value of a Ratio Read through the duration of the lesson with a table partner. Be prepared to discuss your findings with the group. SHARE! (CLICK TO ADVANCE BULLET) Let’s take 5 minutes to walk through the rest of the lesson and discuss with your table partners. Allow 5 minutes. Allow 2 minutes to share.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Correlations Between Lessons 1-6 and 7-8 Take 3 minutes to discuss with your table partners the correlations you see between Lessons 1 an- 6 to Lessons 7 and 8. Share with whole group. Have tables discuss the close connections between all of the lessons thus far in the module. Allow 2 minutes for group discussion.

Lesson 9 – Tables of Equivalent Ratios
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: X Lesson 9 – Tables of Equivalent Ratios Students understand that a ratio is often used to prescribe the relationship between the amount of one quantity and the amount of another quantity as in the cases of mixtures or constant rates. Students understand that a ratio table is a table of equivalent ratios. Students use ratio tables to solve problems. The approach of this lesson and those that follow is for the teacher to model the use of tables in problem solving. There is no need to engage in an explanation of why or how they are useful; simply modeling their use in this lesson, examining their structure in the next lesson, and repeated use for problem solving in the remaining lessons of the topic should sufficiently promote tables as a tool for problem solving with collections of equivalent ratios. (CLICK TO ADVANCE EACH STANDARD) Read each standard.

Lesson 9 – Tables of Equivalent Ratios
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 9 – Tables of Equivalent Ratios Read through Example 1 of Lesson 9 in the Teacher Materials. Highlight and label with lesson numbers where previous skills from the module prepare students for this lesson. Notice Example 2 moves the students from the model to independent creation of the table. What skills are being addressed in this lesson? Allow 5 minutes for reading of Example 1. (CLICK TO ADVANCE BULLET) Notice example 2 moves the students from the model to independent creation of the table? (CLICK TO ADVANCE BULLET) What skills are being addressed in this lesson?

Lesson 10 – The Structure of Ratio Tables
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 10 – The Structure of Ratio Tables Students identify both the additive and multiplicative structure of a ratio table and use the structure to make additional entries in the table. Students use ratio tables to solve problems. Take 5 minutes to read through Lesson 10. Talk with your table partners to make correlations to Lesson 9. How does Lesson 10 extend Lesson 9? Share with whole group. Read each standard. (CLICK TO ADVANCE BULLET) Take 2 minutes to read through lesson 10. (CLICK TO ADVANCE BULLET) Talk with your table partners to make correlations to Lesson 9. How does Lesson 10 extend Lesson 9? Allow 3 minutes for reading and discussing. (CLICK TO ADVANCE BULLET) Allow 2 minutes for group discussion.

Lesson 11 – The Structure of Ratio Tables
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Lesson 11 – The Structure of Ratio Tables Students solve problems by comparing different ratios using two or more ratio tables. Take 5 minutes to read through Lesson 11. Talk with your table partners to make correlations to Lessons 9 and 10. How does Lesson 11 extend Lessons 9 and 10? Share with whole group. Read the standard. (CLICK TO ADVANCE BULLET) Take 5 minutes to read through lesson 11. (CLICK TO ADVANCE BULLET) Talk with your table partners to make correlations to Lesson 9 and 10. How does Lesson 11 extend Lesson 9 and 10? Allow 3minutes for reading and discussing. (CLICK TO ADVANCE BULLET) Allow 2 minutes for group discussion.

Lesson 12- From Ratio Tables to Double Number Line Diagrams
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Pre-made cards Double Number Line Reproducible Lesson 12- From Ratio Tables to Double Number Line Diagrams Each participant is given a card with a ratio on it. Move around the room in search of other participants who have ratios that are equivalent to theirs. Those with equivalent ratios will form a group and create a ratio table, which contains all of the equivalent ratios. Examine Exercise 3 and Example 1 in the Teacher Materials. Share with the group your thoughts on the questioning strategies in Exercise 3. What major points do you walk away with from Example 1? Allow 5 minutes for the activity.

Lesson 13 - From Ratio Tables to Equations Using the Value of a Ratio
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Unifix Cubes Lesson 13 - From Ratio Tables to Equations Using the Value of a Ratio Jorge is mixing a special shade of orange. He has mixed 1 gallon of red paint with three gallons of yellow paint. Based on the ratio of gallons of yellow paint to gallons of red paint, which of the following statements are true? 3/4 of a 4-gallon mix would be yellow. Every 1 gallon of yellow requires 13 gallon of red. Every 1 gallon of red requires 3 gallons of yellow. There is 1 gallon of red in a 4-gallon mix of orange paint. There are 2 gallons of yellow paint in an 8-gallon mix of orange paint. Each participant is given a pre-made Unifix cube model consisting of 1 red and 3 yellow cubes to be used as a model for the scenario below. Allow participants to discuss each question with a partner or group. As a whole group, participants explain one of the statements, and whether their groups feels the statement is true or false, and why. (The first 4 statements are true, while the 5th statement is false.) How can we make the last statement true? To be made true, it should read “There are 6 gallons of yellow paint in an 8 gallon mix of orange paint.

Lesson 13 - From Ratio Tables to Equations Using the Value of a Ratio
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 7 minutes MATERIALS NEEDED: X Lesson 13 - From Ratio Tables to Equations Using the Value of a Ratio Take 5 minutes to work through the rest of the lesson with a partner or at your table. Share your thoughts! Allow 5 minutes for examination of the lesson. (CLICK TO ADVANCE BULLET) Allow 2 minutes for sharing of the lesson.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Lesson 14 - From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane Students associate with each ratio A : B the ordered pair (A, B) and plot it in the x-y coordinate plane. Students represent ratios in ratio tables, equations and double number line diagrams, then represent those ratios in the coordinate plane. (CLICK TO ADVANCE EACH OUTCOME) Read each outcome.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 6 minutes MATERIALS NEEDED: X Lesson 14 - From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane Based on their previous knowledge from earlier lessons in this module, and with predetermined groups, students complete tables to satisfy missing values, create double line diagrams to support the values, and develop an equation to support the values. From there, a Socratic approach is used in order to guide students to build a graph on the coordinate plane. Read through the questioning in Lesson 14 and discuss with your table partner(s). What do you notice about the questioning? (CLICK TO ADVANCE EACH BULLET) Based on their previous knowledge from earlier lessons in this module, and with predetermined groups, students complete tables to satisfy missing values, create double line diagrams to support the values, and develop an equation to support the values. From there, a Socratic approach is used in order to guide students to build a graph on the coordinate plane. Read through the questioning in Lesson 14 and discuss with your table partner(s). What do you notice about the questioning? Allow 2 minutes for reading, 2 minutes for sharing with table. Allow 2 minutes for sharing with whole group.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 8 minutes MATERIALS NEEDED: Chart paper Markers Lesson 15 - From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane Gallery Walk! Spend 2 minutes at each station to determine the answers to each question. Share with the group the rigor you find in the problems provided in the examples. (CLICK TO ADVANCE THE OUTCOME) Because this lesson culminates the first half of the module, let’s participate in a gallery walk in order for us all to visit each representation and collaborate with our peers. You will choose a station to begin. We will spend 2 minutes at each station. When time is up you will move to the station to the right. Please record your work on a separate sheet of paper. Once time is up, we will return to our seats and share with the group our thoughts on the connections you found in the problems. Allow 8 minutes for the gallery walk. After two minute intervals, have participants move to the next station. Once seated, (CLICK TO ADVANCE) have participants discuss the connections between Lessons 1 – 15 from the exercises/stations.

Biggest Takeaway What is your biggest takeaway from this session?
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Biggest Takeaway What is your biggest takeaway from this session? Be ready to share. Take one minute to reflect on this session. What, for you, is the biggest takeaway? What would you add to our list of key points Jot down your thoughts. Then you will have time to share your thoughts. Give participants 1 minute for silent, independent reflection. (CLICK TO ADVANCE ANIMATION ON SLIDE.) Turn and talk with a partner at your table about your reflections. Allow 2 minutes for participants to turn and talk about their reflections. Then, facilitate a discussion that leads into the key points on the next slide. PARTICIPANTS WRITE ALL questions, concerns, comments on post its/paper etc. and leave in center of table. We will review them all this evening and be better prepared to support you tomorrow.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: X Key Points Modules Overviews and Topic Openers provide essential information about the instructional path of the module and are key tools in planning for successful implementation. Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Standards to life. The Exit Ticket is an essential piece of the Student Debrief and provides daily formative assessment. Opportunities to nurture the Standards for Mathematical Practice are embedded throughout the lesson. Now that we’ve examined all aspects of the module, let’s consider your plans for training, implementation, and differentiation. Take a minute and tie all that we have together and think about it from the lensed of the role you fill. Teacher- time to read through the modules, discuss the lessons with a co-teacher, solve the problems, find/order materials, highlight key questions School Leader- identify areas that may need the most support, consider how to bridge the gaps in student understanding, identify what teachers need to know to effectively implement the modules, find/order materials Principal- provide time for teachers to plan, facilitate discussions around modules to encourage team problem solving, consider how the module impacts the way teachers demonstrate lesson planning, consider how this impacts what will been seen during an observation, organize/support the process of gathering/ordering materials District Leader – provide funding and resources necessary for staff development, curricular materials, and assessment. Consider implications of new curriculum and new tests and prepare stakeholders for change. BOCES Representative – Identify economies of scale for staff training. Consider implications of new curriculum and new tests and prepare stakeholders for change. Turn and talk with a partner at your table about your reflections. What, for you, is the biggest takeaway? Jot down your thoughts. Allow 2 minutes for participants to turn and talk about their reflections. Then, facilitate a brief discussion that leads into the key points on the next slide.

A Story of Ratios G6-M1 : Mid-Module Assessment
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: A Story of Ratios G6-M1 : Mid-Module Assessment This afternoon we will be focusing our attention on the Grade 6 Mid-Module Assessment for Module 1.

Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: Objectives To articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the mid-module assessment Is there anyone present this afternoon who was not here for the morning session? (Call for a show of hands.) As we focus on the objectives for this session, we ask you to be cognizant of your specific educational role and how you will be able to promote successful implementation in your classroom, school, district, and/or BOCES. Principals- Consider the implications of this data (quantitative and qualitative) for the professional development needs of the staff, the resources needed to support struggling students, and the conversations held in the data analysis meetings. You will want to make notes on ideas you have as a result of your observations to use in later sessions tomorrow.

Agenda Experience the Mid-Module Assessment from a student-standpoint.
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: Agenda Experience the Mid-Module Assessment from a student-standpoint. Link the Assessment back to the Focus and Foundational standards. Complete and score the assessment using the rubric Identify the Mathematical Practices embodied in each assessment task. Let’s take a look at our agenda for this afternoon. For administrators, please think of the implications of using rubrics on your current grading policies, what are teachers going to need to discuss and agree upon when using rubrics versus their current grading structures?

G6-M1: Ratios and Unit Rates
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: G6-M1: Ratios and Unit Rates We will be focusing on the first assessment in Module 1: Ratios and Unit Rates.

G6-M1 Mid-Module Assessment
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: G6-M1 Mid-Module Assessment You will notice from the Table of Contents in the Module Overview, that the Mid-Module Assessment follows Topic B, after the 15 lessons that comprise Topics A and B. (1 minute)

Standards Assessed Which Standards and Topics will be assessed?
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: Standards Assessed Which Standards and Topics will be assessed? Look through the lessons and standards referenced in the Module Overview Table of Contents, and at the Assessment Summary at the end of the Module Overview. Discuss with your table members the topics and standards you would expect to see on the Mid-Module Assessment. (After 2 minutes) Ask participants to share out answers with the whole group. The participants should identify: Topic A: Representing and Reasoning About Ratios (6.RP.1, 6.RP.3a) Topic B: Collections of Equivalent Ratios (6.RP.3a) What are the Foundational Standards that serve as a prerequisite? 4.OA.2, 5.NF.3, 5.MD.1, 5.G.1, 5.G.2

Understanding the Assessment
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 16 minutes MATERIALS NEEDED: G6-M1 Mid-Module Assessment Copies Pencils Understanding the Assessment (Hand out copies of the assessment to participants, so that they can keep their binder copy clean for future turn-key training and photocopying). “Spend the next 15 minutes completing the Mid-Module Assessment. You may wish to take the test as if you were a student, so that you can better understand the rubric and scoring.”

A Progression Toward Mastery
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: A Progression Toward Mastery Please turn to the rubric and student work for the assessment. Student responses fall into 1 of 4 categories on the rubric, which is a Progression Toward Mastery. Please note that steps 1-4 are not necessarily assigned point values that you will total when scoring the assessment; but rather they designate the student’s level of mastery of concepts. Now that we have gathered our data, we are ready to score using the rubric. But first, what is the purpose of a rubric? Possible answers: To assess the student understanding of the standards To provide context and language to discuss student work To plan next steps for future instruction To grade (This is not the intention of the writers.) Principals- Consider the implications of this data (quantitative and qualitative) for the professional development needs of the staff, the resources needed to support struggling students, the conversations held in the data analysis meetings. You will want to make notes on ideas you have as a result of your observations to use in later sessions tomorrow. Take the next 2 minutes to score Topic A using the rubric. If you finish early, continue with Topics B and C. NOTE TO FACILITATOR: Allow 2 minutes for participants to work independently.

Scoring Student Work TIME ALLOTTED FOR THIS SLIDE: 10 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: Pens Scoring Student Work (Participants exchange papers and score work according to the rubric and sample student work.) Participants share in conversations at their table about the scoring of the assessment according to the rubric.

Sharing Student Work TIME ALLOTTED FOR THIS SLIDE: 10 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: Document Camera Sharing Student Work Various participant volunteers bring their work up to the document camera and share the score they assigned to it based on the rubric.

Standards for Mathematical Practice
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 8 minutes MATERIALS NEEDED: Copies of the 8 Mathematical Practices Pencils Highlighters Standards for Mathematical Practice Locate the Standards for Mathematical Practice Listing in your materials. Take 7 minutes to identify the mathematical practices that are addressed in each assessment question. Discuss it as a table, and record the Mathematical Practice number in the margin aside each assessment question.

Evidence of the Mathematical Practices
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 15 minutes MATERIALS NEEDED: Post-it Notes Pens and Markers Posters of Assessment Questions stationed around the room Document Camera Evidence of the Mathematical Practices How and where do they appear in the assessment items? Participants are directed to get up and stick a post-it note with a Mathematical Practice Number(s) on the poster of each assessment question. Presenter walks around the room and goes from assessment question to assessment question, stating the Mathematical Practices that were referenced the most according to the post-it notes. At each stop (assessment question poster), the presenter elicits an explanation from a participant. Participants verbally explain why they selected that Mathematical Practice and if necessary, the document camera is used to show where and how they saw the mathematical practices reflected in the assessment item.

Biggest Takeaway TIME ALLOTTED FOR THIS SLIDE: 5 minutes
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Biggest Takeaway Each table is directed to take a minute to brainstorm their biggest takeaway. The presenter calls upon each table’s spokesperson to state their group’s biggest takeaway.

Key Points Assessment Questions Scoring Rubric
Header July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Key Points Assessment Questions Are directly aligned to the CCSS May address Multiple Focus Standards Invoke Higher-Level Thinking and the Mathematical Practices Scoring Rubric Progression Toward Mastery Standards Referenced for each Assessment Item In closing, these are the key points from our session this afternoon.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Pulse Check Please go to and fill out the online plus-delta for the Math session. Thank You! EngageNY.org

A Story of Ratios Module 1 Focus - Grade 6

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