Module Focus: Grade 6 – Module 4 Sequence of Sessions Overarching Objectives of this February 2014 Network Team Institute Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate how these modules contribute to the accomplishment of the major work of the grade. Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS. Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents. Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the mid-module assessment and end-of-module assessment. High-Level Purpose of this Session ● Implementation: Participants will be able to articulate and model the instructional approaches to teaching the content of the first half of the lessons . ● Standards alignment and focus: Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade. ● Coherence: Participants will be able to articulate connections from the content of previous grade levels to the content of this module. Related Learning Experiences ● This session is part of a sequence of Module Focus sessions examining the Grade 6 curriculum, A Story of Ratios. Key Points
Transcript
Module Focus: Grade 6 – Module 4 Sequence of Sessions
Overarching Objectives of this February 2014 Network Team Institute Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate
how these modules contribute to the accomplishment of the major work of the grade.
Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.
Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents.
Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the mid-module assessment and end-of-module assessment.
High-Level Purpose of this Session● Implementation: Participants will be able to articulate and model the instructional approaches to teaching the content of the first half of the lessons.● Standards alignment and focus: Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the
module addresses the major work of the grade.● Coherence: Participants will be able to articulate connections from the content of previous grade levels to the content of this module.
Related Learning Experiences● This session is part of a sequence of Module Focus sessions examining the Grade 6 curriculum, A Story of Ratios.
Key Points•Students extend their arithmetic work to include using letters to represent numbers in order to understand that letters are simply "stand-ins" for numbers and that arithmetic is carried out exactly as it is with numbers.
•Students explore operations in terms of verbal expressions and determine that arithmetic properties hold true with expressions because nothing has changed—they are still doing arithmetic with numbers.
•Students determine that letters are used to represent specific but unknown numbers and are used to make statements or identities that are true for all numbers or a range of numbers.
•Students understand the relationships of operations and use them to generate equivalent expressions, ultimately extending arithmetic properties from manipulating numbers to manipulating expressions.
•Students read, write and evaluate expressions in order to develop and evaluate formulas. From there, they move to the study of true and false number sentences, where students conclude that solving an equation is the process of determining the number(s) that, when substituted for the variable, result in a true sentence.
•Students use arithmetic properties, identities, bar models, and finally algebra to solve one-step, two-step, and multi-step equations.
Session Outcomes
What do we want participants to be able to do as a result of this session?
How will we know that they are able to do this?
Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate how these modules contribute to the accomplishment of the major work of the grade.
Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.
Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents.
Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the mid-module assessment and end-of-module assessment.
Session Overview
Section Time Overview Prepared Resources Facilitator Preparation
Introduction to Module 25 mins Establish the instructional focus of Grade 6 Module 4 Review Grade 6 Module 4
Grade 6 Module 4. Grade 6 Module 4 PPT
Topic A Lessons 45 mins Examine the lessons of Topic A. Grade 6 Module 4 Grade 6 Module 4 PPT Tape Diagram Manipulative
Prepare tape diagram manipulative
Topic B Lessons 20 mins Examine the lessons of Topic B. Grade 6 Module 4 Grade 6 Module 4 PPT
Topic C Lessons 25 mins Examine the lessons of Topic C. Grade 6 Module 4 Grade 6 Module 4 PPT
Topic D Lessons 45 mins Examine the lessons of Topic D. Grade 6 Module 4 Grade 6 Module 4 PPT
Topic E Lessons 20 mins Examine the lessons of Topic E. Grade 6 Module 4 Grade 6 Module 4 PPT
Topic F Lessons 90 mins Examine the lessons of Topic F and conduct a lesson study/jigsaw presentation.
Grade 6 Module 4 Grade 6 Module 4 PPT
Session Roadmap
Section: Grade 6 Module 4 Time: 305 minutes
TimeSlide #
Slide #/ Pic of Slide Script/ Activity directions GROUP
1. Welcome! In this module focus session, we will examine Grade 6 – Module 4.
1 min 2. Our objectives for this session are:•Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.•Introduction to mathematical models and instructional strategies to support implementation of A Story of Ratios.
1 min 3. We will begin by exploring the module overview to understand the purpose of this module. Then we will dig in to the math of the module. We’ll lead you through the teaching sequence, one concept at a time. Along the way, we’ll also examine the other lesson components and how they function in collaboration with the concept development. Finally, we’ll take a look back at the module, reflecting on all the parts as one cohesive whole.
Let’s get started with the module overview.
2 min 4. The fourth module in Grade 6 is called Expressions and Equations (click for red ring). The module is allotted 45 instructional days. It challenges students to build on understandings from previous modules by:1)Extending previous study of arithmetic operations to understanding identities, properties, and the relationships between operations.2)Applying their knowledge of proportional reasoning and tape diagraming to understand, build and solve equations.
10 min
5. The module focuses on standards (click to advance) 6.EE.A.1, 6.EE.A.2, 6.EE.A.3, 6.EE.A.4, 6.EE.B.5, 6.EE.B.6, 6.EE.B.7, 6.EE.B.8, 6.EE.C.9In your extra materials you will find (click to advance) the Expressions and Equations Progressions Document. Let’s take 5 minutes with a partner and read through pages 2-7, highlighting key points that you find interesting to discuss with the whole group.Let’s discuss (5 minutes).
3 min 6. Turn to the Module Overview document. Our session today will provide an overview of these topics, with a focus on the conceptual understandings and an in-depth look at select lessons and the models and representations used in those lessons.
Take a moment to look at the table of contents at the beginning of the Module Overview. Notice the Module is broken into eight topics which span 34 lessons. Following the Table of Contents is the narrative section. Focus and Foundational standards, as well as the standards for Mathematical Practice are listed in this overview document. You will need to read the entire document at your leisure, following today’s session.
7 min 7. Let’s start by looking at the Module Overview narrative. This narrative will provide you with information regarding progressions from previous grades and to later grades as well as progressions within this module. Please take a few minutes to read through the overview narrative and highlight interesting information that we will share later.Allow two minutes for reading and five minutes for sharing.
0 min 8. Let’s take a closer look at the development of key understandings in Topic A. The plan for today is to speak to three main ideas: operation properties and how they relate to building and solving equations, tape diagrams and the progressions throughout the lessons, and moving from expressions to equations. Topic A focuses on the first two: operation properties and tape diagraming.
3 min 9. Let’s read through the Topic A Opener and discuss any questions or thoughts.
2 min 10. Read the outcome.Click to advance. We use tape diagrams in the first four lessons to model identities and properties of operations. Here, you will see (click to advance) the model represents 3+2. We see that the sum is five, however if we cover up the two, three is left, so we determine that 3+2-2=3. Similarly, not represented in this model, if we had 3 and took two away, then added it back in, the result would be 3, the number we started with. This type of modeling leads into the identity that any number added to another number, when taken away will result in the number we began with, and vice versa; If we subtract a number from another number and then add it back in, the result would be the original number. We are going to model this together.
5 min 11. In your extra materials you will have a set of these tape diagrams. We will be using this set for Lesson 1 (click to advance) and this set (click to advance) for the duration of the next 4 lessons.Switch to document camera:Model the identities w + x – x = w and w – x + x = w.Model and then draw a series of tape diagrams to represent the following number sentences.
3+5-5=3
8-2+2=8
1 min 12. You will see here, that the identity is built for students in the teacher materials and fully explains the progression of the identity.
2 min 13. What’s new in Module 4 is the increased frequency of fluency activities. These begin to appear every 2 to 3 lessons and involve either sprints or (click to advance) these rapid white board exchanges. White board exchanges are designed to be similar to sprints, meaning practice fluency from either the number system as prescribed by PARRC, or fluency on newly introduced concepts. Here, you will see that it is not advantageous to have students complete a sprint because the bulk of the work is too lengthy. Teachers will simply display the questions, one at a time in this exact order, and students will show their work and answer on a personal white board. The teacher then goes around quickly reviewing student work, stating “good job” or “let’s try that again” if the students’ work is inaccurate. Once the majority of the students are ready to progress to the next question, the teacher then has students erase their boards and displays the next question, continuing until either time is up, or until all questions have been exhausted. Note that the level of difficulty increases the further students go, similar to the sprint.
2 min 14. Read the outcome.In this diagram (click to advance), you will se that the model represents 8 divided by 2, with a quotient of four. We see, also that if we multiply four by two, the product would result in the original number, 8, thus understanding the identity when any number is divided by another number and then multiplied by the same number, the product or end result is the original number. This will also work with multiplication where if a number is multiplied by a number and then divided by that same number, the quotient, or end result would be the original number, so long as the number being multiplied by and then divided by is not zero.
5 min 15. We are going to practice this identity using this set of manipulatives.Switch to document camera.Model and then draw a series of tape diagrams to represent the following number sentences.
12÷3×3=12
4×5÷5=4
10 min
16. Let’s practice what we have learned! This is the exact exploratory challenge activity in lesson 2 that students will be completing. Let’s work in our table groups and complete the activity. (Read the bullets from the slide)After five minutes, allow 1 minute per table to share their large paper and discuss with group.
2 min 17. Students in the exploratory challenge are asked to critique the work of other groups. They use this rubric to practice critiquing constructively. Let’s spend a couple minutes modeling this with each others groups.
1 min 18. Lesson two has the module’s first sprint. This sprint is reused throughout the module and is up for grabs any time you think the students need additional practice. This is just to show you that although we suggest fluency placement within lessons, it does not constrain you to only use them when prescribed. You are free to use any fluency activity when you find it necessary with your students.
2 min 19. Read the outcome.In this diagram (click to advance), you will se that the model represents the relationship of multiplication and addition. We see that 3 times g is simply g added to itself three times.(Click to advance twice) We see that this model is represented in three equal parts. It shows that one of the equal parts is four. With their previous knowledge, students will see that this model represents 3 times 4. They go on to make connections to the same tape diagram that if they added 4 three times, they would determine the same answer as if they had multiplied. They discover that 3 times four is equal to 4+4+4, the sum of three fours) and relate it to the second tape diagram shown. Three times g will equal g+g+g, the sum of g three times. The last tape diagram shows that one part is seven and that there six equal parts, so 6 times seven will equal 7+7+7+7+7+7, or the sum of seven six times.
1 min 20. Students will further discover that when they represent 4+4+4 with a tape diagram horizontally, they can rearrange the “groups” of four into a familiar array to show that it is equal to three groups of 4, or, 3 times four.
1 min 21. Students will then move to finding the relationship of addition and multiplication within expressions that have more than one number or variable. They can use tape diagrams or draw diagrams to assist them in determining how to create equivalent expressions. You will see that this also supports student learning from Module 2 when they practiced the order of operations.
2 min 22. Read the outcome.Here, you will see (click to advance) the model represents 8 divided by. We see that the quotient is four. Students will use tape diagraming to determine that when they subtract the divisor, in this case, 2, from the dividend four times (which is the quotient), they will find a remainder of zero.They continue to practice with other examples such as 100 divided by 25 = 4. They continually subtract the divisor from the dividend four times to determine the remainder of zero.From there, students discover the relationship of division and subtraction.
4 min 23. Switch to document camera. Participants practice using tape diagrams, and presenter will follow up with questions and concerns.
18 divided by 318 divided by 6
What is the difference when modeling?
4 min 24. Here you will see a progression of tape diagrams from lesson 4 that reiterates the student discovery, but what is new is students will determine if the quotient is either the number of items or the number of groups and compare the relationship between 20 divided by four equals five and twenty divided by five equals four.
Switch to document camera and model both representations and show the relationship:20 divided by 4 equals five:20-4=16, 16-4=12, 12-4=8, 8-4=4, 4-4=0: We subtracted five times, so the quotient is five.
Similarly 20 divided by 5 equals four:20-5=15, 15-5=10, 10-5=5, 5-5=0: We subtracted four times, so the quotient is four.
1 min 25. By the end of the lesson four, students will see the relationship between all operations. They will see that addition is the inverse of subtraction, and multiplication is the inverse of division and vice versa. They will note that multiplication is a repeat of addition and division is a repeat of subtraction.
3 min 26. Let’s read through the Topic B Opener and discuss any questions or thoughts.
1 min 27. Read outcomes.Students begin the lesson on noticing patterns to determine that a number with an exponent, or power, is not the same thing as the relationship between multiplication and addition. It is actually a relationship between multiplication, base numbers and powers.
1 min 28. Students are provided visual examples to show the difference between multiplication in two dimensions and multiplication in three dimensions. They take that learning and extend it to finding powers of rational numbers.
1 min 29. You will see that the lesson begins with a review of the relationship of addition and multiplication on purpose. It opens up discussion on why evaluating numbers with exponents is not the same as multiplication and addition.
1 min 30. Students rewrite expressions to determine that numbers with powers is in fact a relationship between bases, exponents and multiplication.
0 min 31. From there, students evaluate expressions after they have been rewritten.
0 min 32. They also move forward to finding powers of rational numbers including but not limited to decimals and fractions.
1 min 33. Read the outcome.Students will discover that in the absence of parentheses, exponents are evaluated first.Click to advance. Note here that there are parentheses, so
2 min 34. This activity opens up the reasoning for use of the order of operations. The students notice that they could potentially solve this problem two ways, but there’s a problem. There are two different answers. Whatever will they do? Students are reminded of the relationship between operations from the first four lessons to show that because (advance slide) addition is a shortcut for counting on, subtraction is a shortcut to counting back. They are reminded that (advance slide) multiplication and division are repeats of addition and subtraction, in order for students to note that multiplication and division are more involved than addition and subtraction, or “more powerful” and thus must be evaluated first in expressions.
2 min 35. Read the note.(Advance slide) Note this diagram represents 3+4x2. Because we need to determine the amount of four groups of two, we multiply first, then add to three. With addition, we are finding the sum of two addends. In this example the first addend is three. The second addend just happens to be the number that is the value of the expression 4x2, so before we can add we must determine the value of the second addend.
3 min 36. Read the note.(Click to advance) Notice students evaluate the expression using the appropriate order of operations. They multiply first from left to right, then divide, and finally they find the sum of the two addends. But, this expression (click to advance) is written differently. Notice that the students appropriately evaluate the expression using the order of operations, finding the product of six squared first, then, dividing, and then finally finding the sum of the two addends. They are asked (click to advance) why the first step was to find the value of six squared and they should be able to answer that in this expression the most “powerful” operation involves exponents and thus should be evaluated first.
3 min 37. Walk through the progression of this slide with participants, asking them questions as teachers would ask their students. The purpose of this activity is so students will see the difference between operations with and without parentheses.
(90 min running total)
1 min 38. Students progress through the order of operations until they understand the difference between evaluating expressions with exponents inside the parentheses and exponents outside of parentheses. What is the difference here? Students should evaluate what is inside the parentheses first in both expressions.
3 min 39. Let’s read through the Topic COpener and discuss any questions or thoughts.
2 min 40. Read the outcome.(Click to advance) Students reflect back on their knowledge of area, and when the side lengths are unknown they can be represented with a variable. They use the area formula to multiply length times width and determine that the area is the square of the side lengths. Then, they are given the side lengths and simply replace the letter (variable) with the appropriate number and evaluate the same exact way.
2 min 41. Here you can see that in the first rectangle, the width is represented by two different values. The first value they see is b cm. The next value you see is 8 cm. Since the two widths are equal, it is obvious students can replace the letter b with 8. In the second rectangle, you see that one of the equal pieces is measured at 4 cm. The entire width of the rectangle is represented by x cm. After much work with tape diagrams, students understand that each of the four equal pieces is 4 cm and can thus multiple 4x4cm to reach the length of 16 cm. From there, students are able to determine the area of the rectangle. They replace the letters for lxw with x times b and replace the 16 cm for x and the 8 cm for b finding the area to be 128 square centimeters.
1 min 42. This example shows students that because the units can be counted on this diagram, the area of the square is easily found. They use the area of a square formula, replace the letter s with the measure of 3 units and find the area by squaring the 3 units. This leads to…. Click to advance to next slide
1 min 43. ….students being able to determine the area of a square without countable units.Read the problem aloud to participants.Since they know the formula for the area of a square, students simply – again – replace the letter s in the formula with the side length of this labeled square, which is 23. They square the side length and determine the area to be 529 square centimeters.
1 min 44. Students then use tables in order to find the area of a square by replacing the letter that stands for the side length with the given measure.
1 min 45. They further this use of substitution with the volume formula for right rectangular prisms in preparation for Module 5.
2 min 46. Read the outcomes to participants.(click to advance slide) Look at the diagram. How many of these statements are true? How many of those statements would be true if the 4 was replaced with the number 7 in each of the sentences? Would the number sentence be true if the four was replaced by any other number? Participants should note that all numbers would work except zero.Division by zero is undefined. You cannot make zero groups of objects and group size cannot be zero. It appears we can replace the number 4 with any non-zero number and each of the number sentences will be true. A letter in an expression can represent a number. Look at the next diagram. (click to advance) Are all these true (except for g=0) when dividing? Each of these properties will be looked further into on the next set of slides.
1 min 47. Read through the slide with participants.
1 min 48. Read through the slide with participants.
1 min 49. Students focus on the commutative property of addition and multiplication in lesson 8. (Click to advance)Let’s look at this first set of properties. Are all of these statements true? (click to advance)Let’s replace the number 3 with the letter a. Are all of these statements true? (Click to advance)Finally, let’s replace the number four with the letter b. What are you noticing? Participants should note that all of the statements are true, with the exception of b being not equal to 0.
30 sec
50. Throughout lesson 8, students are exposed to tape diagrams and models to make abstract ideas more concrete. Here they use bar diagrams and …(click to advance)
30 sec
51. … here is a good example of a model to prove the commutative property of multiplication. Notice that students have been using arrays like this since grade 3.
5 min 52. Students write expressions that record addition and subtraction operations with numbers. They identify parts of an expression using mathematical terms for addition and subtraction.Participants use whiteboards to show the expressions.
5 min 53. Let’s take a look at the topic opener for Topic D and discuss information you find valuable and interesting. Take 2 minutes to read the opener and discuss briefly with your table groups.Allow at least 2 minutes to share.
3 min 54. Let’s practice writing some expressions using the language of the statement. Record your answers on your personal whiteboards. We can use this as a practice rapid white board exchange!
Click to advance through each question and note when participants are correct or when they need extra time.Explain the difference between subtract and subtracting from. Participants should discuss the placement of the minuend and the subtrahend depending on the language of the statement. When a number is subtracted from another, it is the subtrahand. When a number is being subtracted from, that is the minuend.
3 min 55. Change to document camera. Have participants try alone. They should model with you if they find difficulty in the following examples:Prove a+b=b+aProve that 6a=a+a+a+a+a+aProve that a-b does not always equal b-aWhen would a-b=b-a?
1 min 56. Read the outcome. Students in this lesson discover the various ways multiplication is represented in expressions, ranging from using the multiplication “x” sign, to the dot, parentheses and letters and/or numbers being placed directly next to each other with no space. We encourage students to represent the value using the least amount of symbols instead of asking them to simplify the expression.
2 min 57. Advance through slide and discuss writing multiplication expressions. Discuss that the number is the coefficient and also a factor, the letters are variables and also factors. When represented with the least amount of symbols, we call that a term.Discuss that students are directed in the lesson to write the number first in a term, then variables in alphabetical order.
2 min 58. Advance through slide and discuss expanding multiplication expressions. Note that students use their previous knowledge of factoring from Module 2. Continue advancing through the slide discussing the process of expanding expressions to finding the product of expressions.
3 min 59. Read the outcome.(Click to advance) Notice this tape diagram. How many sixes are there? How many fours are there? What is the sum of these two terms? Participants should state that the sum is 2 x 6 + 2 x 4.Let’s move the units to make 2 equal units of 6+4. (Click to advance) How many 6+4’s do we have?What multiplication expression is represented here? Participants should share that it is 2 x (6+4) or 2(6+4)Discuss with your partner why the following equation is true: (Click to advance slide). Share.
3 min 60. Here you will see students will practice this skill of factoring with letters and numbers. (Click to advance) How many units of ‘a’ are here? How many units of ‘b’ are here? What is the sum of these two terms? 2a+2b or two ‘a’s plus two ‘b’s. Let’s move the units to make 2 equal units of (a+b) (click to advance slide) What expression is now represented with this diagram? 2x(a+b) or 2(a+b) Discuss with your partner why the following equation is true (Click to advance).
5 min 61. Switch to document camera.Model with participants the following:Prove that 3(a+b) is equivalent to 3a+3b.Show that students move to using the greatest common factor and the distributive property to write equivalent expressions for 4d+12eWhat is the question asking us to do? Rewrite the expression as an equivalent expression in factored form which means the expression is written as the product of factors. The number outside the parentheses will be the GCF.
62. Read outcome.How would you write 2 x a with the least amount of symbols? 2aHow would you write 2x(a+b) with the least amount of symbols? 2(a+b)(Click to advance slide) In this model, how many ‘a’s are there? 2How many ‘b’s? 2(Click to advance slide) We moved the 2 ‘a’s and the 2 ‘b’s so they would be together. What is 2(a+b) equal to when distributed? 2a+2bIn the model, is (a+b) the number of units or the size of the unit? size
1 min 63. Read through the teacher/student discussion with participants to make sure they understand that factors can be either the number of groups or the number of items within each group.
5 min 64. Switch to document camera.Model with participants how to model how to write an expression that is equivalent to “double (3x+4y)”How can we rewrite double (3x+4y)? Double is the same as multiplying by two: 2(3x+4y)Is this expression in factored form, expanded form, or neither? Factored form.Make the model of 3x+4y.How can we change the model to show 2(3x+4y)? Make an exact copy of the model.Are there terms that we can combine in this example? The x’s and the y’s. There are 6 x’s and 8 y’s.2(3x+4y)=6x+8y or 2(3x)+2(4y).Summarize how you would answer this question without the model. When there is a number outside the parentheses, I would multiply it by the terms on the inside.)
2 min 65. Students use their knowledge of area models to write expressions in expanded form that is equivalent to the factored form represented in the model.What factored expression is represented in this model? y(4x+5).How can we rewrite this expression? (Click to advance) y times 4x is 4xy following alphabetical order, (click to advance) y times 5 is 5y making sure the coefficient is first. 4xy+5y
2 min 66. Note that lessons 13 and 14 are parts 1 and 2 of a two day lesson.Read the outcome.Students begin lesson 13 with a model of 1 being divided by 2. Students see that they can write the expression as one divided by two or as one divided by two using the fraction bar, or one half. They extend this to dividing a variable by a number written both ways, and then to a variable divided by a variable. They note that when using the division symbol, it is read “dividend divided by divisor” and when it is in fractional form, the numerator is the dividend and the divisor is the denominator.
3 min 67. Place the equivalent expressions graphic organizer in your whiteboard sleeve. Use the whiteboards to complete the graphic organizer with each expression.Click to advance all three examples and allow time for participants to complete the organizers for each.
3 min 68. Take a few minutes to read through the topic opener for Topic E and highlight interesting areas to discuss with your table groups.
3 min 69. Read the outcomes to participants.(Click to advance) Students begin the lesson by brainstorming words that could indicate a specific operation. They understand that some words may be used for more than one operation depending on the context of the problem.(Click to advance) They then move from this organizer to determine how to read expressions where letters stand for numbers. Read through the examples.
3 min 70. Students underline key words practiced in Lesson 15 to determine how to write algebraic expressions that record all operations with numbers and letters standing for numbers. (Click to advance the table)(Click to advance) Read the story in column B. Note that the key word here is lost, so we assume that the operation would involve subtraction. From the expressions in column A, which expression would best represent this story?Read the next story in column B. (Click to advance) Note that the key words here are times and combined. From the expressions in column A, which expression would best represent this story?Read the next story in column B. (Click to advance) Note that the key words here are and, together and distributed. From the expressions in column A, which expression would best represent this story?Read the next story in column B. (Click to advance) Note that the key words here are quadrupled and deposited. From the expressions in column A, which expression would best represent this story?Read the next story in column B. (Click to advance) Note that the key words here shared it equally. From the expressions in column A, which expression would best represent this story?
10 min
71. Participants walk through the Mid-Module Assessment and collaborate with their peers to highlight points of interest and questions that they would like to have discussed during whole group share.
3 min 72. Participants walk through the topic opener for Topic F. They discuss their questions or concerns with their tables prior to discussing in whole group.
2 min 73. Read the outcomes.Click to advance story problem.Continue clicking to advance to complete the activity.
180 minutes running total
2 min 74. Read the outcomes.Click to advance story problem.Continue clicking to advance to complete the activity.
2 min 75. Read the outcomes.Click to advance story problem.Continue clicking to advance to complete the activity.
2 min 76. Read the outcomes.Click to advance story problem.Continue clicking to advance to complete the activity.
2 min 77. Read the outcomes.Click to advance story problem.Continue clicking to advance to complete the activity.
2 min 78. Read the outcomes.Click to advance tables.Discuss the meaning of each symbol and the example for each.
2 min 79. Student record what will make statements true and false.Click through the slide in order to reveal what will make each of the statements true or false.
20 min
80. Allow partners or table groups to read through lessons 24 and 25, highlighting areas of interest that they would like to discuss, as this is most likely new information for many teachers. Spend 10 minutes discussing questions, comments and concerns.
0 min 81. Read through outcomes
5 min 82. Switch to document camera.Model the following one step equations with addition and subtraction, as well as the check:a+2=812=8+cd-5=7f-10=15
0 min 83. Read through outcomes.
5 min 84. Switch to document camera.Model the following one step equations with multiplication and division as well as the check:3z=9y/4=22=h/7
0 min 85. Read through outcomes.
5 min 86. Switch to document camera.Model the following equations:Juan has gained 20 lb. since last year. He now weighs 120 lb. Rashod is 15 lb. heavier than Diego. If Rashod and Juan weighed the same amount last year, how much does Diego weigh? Allow j to be Juan’s weight last year (in lb.) and d to be Diego’s weight (in lb.).
Marissa has twice as much money as Frank. Christina has $20 more than Marissa. If Christina has $100, how much money does Frank have? Let f represent the amount of money Frank has in dollars and m represent the amount of money Marissa has in dollars.
0 min 87. Read through outcomes.
5 min 88. Switch to document camera.Model the problem in the slide.Switch back to slide show presentation.Another organizational tool students use in Lesson 29 is a table. Click to advance. Talk through table and the relationships involved in the columns and rows.
If time permits model: The school librarian, Mr. Marker, knows the library has 1,400 books, but wants to reorganize how the books are displayed on the shelves. Mr. Marker needs to know how many fiction, nonfiction, and resource books are in the library. He knows that the library has four times as many fiction books as resource books and half as many nonfiction books as fiction books. If these are the only types of books in the library, how many of each type of book are in the library?
1 min 89. Revisit the story.(Click to advance)Students also create tables to organize information to write equations.(Click to advance) Students use this information to write their equations.(Click to advance) They use their knowledge from the Module to solve the equation.
30 min
90. Assign each group one lesson between lesson 30-34. Provide time for them to research the information in the lessons, then groups will present student outcomes, lesson notes/opening exercises, key points of the lesson and will model at least one example from the lesson.
1 min 91. Let’s take a few minutes to reflect on the purpose of today’s session.
2 min 92. Take two minutes to turn and talk with others at your table. During this session, what information was particularly helpful and/or insightful? What new questions do you have?
Allow 2 minutes for participants to turn and talk. Bring the group to order and advance to the next slide.
3 min 93. Let’s review some key points of this session. I would like each tables’ members to take one minute to write down a key point from today’s session. I will then call on each table to share out. (Click to advance and show key points.)
Use the following icons in the script to indicate different learning modes.
Video Reflect on a prompt Active learning Turn and talk
