Module Focus: Grade 7 – 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 7 curriculum, A Story of Ratios.

Key Points The scale factor is the unit rate (in percent form) Scale drawings may have more than one scale factor (horizontal and vertical scales). Given a drawing A, and scale drawing B of drawing A with a scale factor b/a, drawing A is a scale drawing of drawing B with scale

factor a/b. Work with percents in module 4 ushers in the topics of probability and statistics in module 5.

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.

Participants will be able to articulate the key points listed above.

Session OverviewSection Time Overview Prepared Resources Facilitator Preparation

Introduction to Module 20 minsEstablish the instructional focus of Grade 7 Module 4.

Grade 7 Module 4 PPT Faciliator Guide

Review Grade 7 Module 4.

Topic A Lessons 80 mins Examine lessons of Topic A. Grade 7 Module 4 PPT Faciliator Guide

Review Topic A.

Topic B Lessons 70 mins Examine lessons of Topic B. Grade 7 Module 4 PPT Faciliator Guide

Review Topic B.

Topic C Lessons 100 mins Examine lessons of Topic C. Grade 7 Module 4 PPT Faciliator Guide

Review Topic C.

Session Roadmap

Section: Grade 7 Module 4 Time: 270 minutes

TimeSlide #

Slide #/ Pic of Slide Script/ Activity directions GROUP

3 min 1. Welcome Participants! This module focus session unfolds and examines Grade 7 – Module 4: Percent and Proportional Relationships.

Presenter introductions.

We will be doing a variety of things including some individual and group work. Most of what we do today should be done from the students’ perspectives. Please be aware that when we (the presenters) raise our hands high, we are requesting that the group reconvene and come to order.

We will take a 15-minute break [this morning at approximately 11:00 a.m.] and then break for lunch at 12:30 p.m. Our focus on module 4 will continue in the afternoon session beginning at 1:30 p.m. There will be another 15-minute break at 3:15 p.m. and then we will try something new. At 3:30 we will reconvene for discussions regarding your next steps and planning with an emphasis on addressing, diagnosing, and meeting student needs, calendar and pacing concerns, and parent communications.

Please note that on your table are post-it notes. We have provided parking lots [indicate location(s)] upon which we invite you to leave comments, concerns, questions, and of course any typos that you might

recognize in any of our materials. We will attempt to address these items as soon as we can.

2 min 2. Our session begins by exploring the curriculum overview and identifying how module 4 aligns with the other modules in grade 7.

Next we look at the module overview to paint a big picture of module 4. We continue to focus in on Module 4 by examining each Topic Opener and how that topic is developed through its particular section of lessons. To do this we have compiled lesson examples, discussion topics, and student exercises that you can experience from the lessons themselves.

As we focus our minds on module 4 we ask that you be cognizant of the concept development that you see within each lesson, each topic, and the overall module, and how that development aligns with the grade 7 curriculum as a whole as well as the Story of Ratios.

We also take a look at how the concepts in Module 5 are tied to the Progressions for the Common Core State Standards in Mathematics (Referred to as “Progressions documents”).

Finally, we’ll take a look back at module 4, reviewing its key concepts, and reflecting on your personal experiences from this module focus session.

3 min 3. The 4th module in Grade 7 is called Percent and Proportional Relationships.How does it fit in the G7 curriculum?This module has some similarities with module 1, but uses skills learned in modules 1, 2, and 3.It challenges students to build on understandings from previous modules by:1)Deepening their understanding of the different forms that rational numbers can take on (decimal, fraction, and percent);2)Extending their understanding of percents (from grade 6) to include those greater than 100%, and those less than 1%;3)Using algebraic reasoning (from module 3) to write expressions and find solutions to equations representing multi-step problems that involve percents;4)Using understanding of ratios and proportional relationships (from module 1) to create equations, graphs, and tables for relationships that involve percents;

Module 4 requires 25 instructional days for lessons, remediation, assessments and return.

8 min 4. Please turn to the Module Overview (page 3 of the module). Read through the overview document and look for major conceptual ideas that determine how the content will develop through each topic and lesson.•How many days are allotted for lessons? (18) Assessments? (3) Assessment return and remediation? (4)•How many topics are in this Module and what are they? (4 topics)•A: Finding the Whole•B: Percent Problems Including More than One Whole•C: Scale Drawings•D: Population, Mixture, and Counting Problems Involving Percents•What are some of the concepts, topics, and representations discussed in the narrative?•Finding the “whole” quantity•Quantity versus sub-quantity•Quantity versus a distinct quantity•Application of percent in contextual problems•Continued use of expressions and equations

5 min 5. What do you expect to see in Topic A? [Pause for participant inquiry]•Mental conversion between forms of numbers (percents, fractions, decimals)•Solving percent problems involving part-to-whole relationships [part = percent x whole]•Solving percent problems comparing distinct quantities [quantity = percent x whole]•Emphasis on identifying the whole quantity (or whole quantities) in percent problems•Percent increase and decrease•Alternative strategies (other than equations) for solving percent problems (numeric representations, double number lines, mental math)

2 min 6. Read student outcomes.

There is a fluency sprint to open the lesson and the module that asks students to draw upon their knowledge of percents from grade 6.

6 min 7. Please complete the Opening Exercise in lesson 1.

Discussion Questions:•How are these fractions and representations related to percents?•What are some equivalent representations of 30/100? (30%, 30/100, 15/50, 3/10, 0.3)•If these representations are all equivalent to 30/100, then what else are they all equivalent to? (30%)•Why do these representations all equal 30%? (The numerator-denominator comparison is a part-to-whole relationship

There are a number of ways that this grid can be shaded to represent these fractions.

3 min 8. Discussion Questions (continued):•If these representations are all equivalent to 30/100, then what else are they all equivalent to? (30%)•Why do these representations all equal 30%? (The numerator-denominator comparison is a part-to-whole relationship, each equivalent to 30/100, or 30%)

There are a number of ways that this grid can be shaded to represent these fractions.

2 min 9. Discussion Questions (continued):•What are equivalent representations of (1/3)/100?

There are a number of ways that this grid can be shaded to represent these fractions.

6 min 10. Complete example 1 at your tables. In a few moments, we will cover some discussion questions from the lesson.

•What is the pattern or process that you recall or notice when converting percents to fractions?•Place the value of the percent over 100 and reduce if possible.•If I gave you a number as a fraction, could you tell me what percent the fraction represents? How would you do this?•Find the equivalent fraction with a denominator of 100.•What mathematical process is occurring for the percent to convert to a decimal?•The percent is being divided by 100.•If I gave you a number as a decimal, could you tell me what percent the decimal represents? How would you do this?•Yes, multiply by 100, or by 100%.

What are we not “teaching” here that is typically taught in many classrooms and why?

Move the decimal two places. Students lose track of what direction to move the decimal and they further do not understand what they are doing by moving the decimal place. This method is a great shortcut, but it should come naturally through fluency.[Show the conversion of the fraction 2/7 by finding an equivalent fraction with a denominator of 100

5 min 11. Color Sequence:Red…Blue…Red…Blue…Maroon…Brick…Navy…Denim…Azure…Folly…Carmine…Iris….ZaffreDiscussion questions:

Who can tell me the point of this exercise? (likely no one will guess this) There are several points to this exercise:

Everybody could do this right away; why? (The color names were easy to recognize)

Why did you raise your right hand when I said red? (Because the “teacher” told me to)

What happened when the colors were not so easily recognizable? (We didn’t know which option to do)

Who raised their hand when I said Zaffre? Why did you raise your hand? (It was a guess)

Now can anyone tell me why we did this exercise? (possible that someone will guess this time)

Teaching percents using the strategy of “key words” (ie: is and of) typically does not teach understanding because students start looking for the is and the of a word problem instead of thinking about the quantities and their relationship. For this reason, our focus will be identify the quantity that represents the whole, or the 100%. If you can identify the whole, the part is easy, and the percent that corresponds with the part is

obvious (in general). This forces students to think about the quantities and how they are being compared.

5 min 12. Review the student outcomes for lesson 2.

What do part-of-a-whole percent problems involve?comparison of generic numbers, or comparison of

quantities where quantity A is a subquantity of

A big focus of the next few lessons is exercising the ability to identify the whole, or the 100%. How should students identify the whole in a given problem?

The whole will be the number or quantity that another number or quantity is being compared to.

6 min 13. Read Example 1 aloud. This is an excerpt from Example 1.Which quantity represents the whole? Explain how you know. (The 30 students in the class represents the whole because the number of students that got an A is being compared to the total number of students in the classroom.)Use a double number line to model the problem.Because 30 students is the whole, 30 aligns with 100%. We know that there are 100 intervals of 1% in 100%. What number of students does each 1% correspond with? (0.3 of a student)If 0.3 students corresponds with 1%, then what number of students corresponds with 20%? (6 students)

We refer to this method as finding the 1% first and is an essential skill for students. Some will recognize a more efficient route (divide by 5) but this should not be

forced upon them. Continued practice of finding the 1% will develop better understanding of percents and students will eventually recognize more efficient methods on their own.

Example 2 is a similar problem that students solve using this numeric method on the screen. They then discuss their steps in solving the problem and using properties are able to generalize the formula: part = percent x whole.

5 min 14. These discussion questions are based on the solution process from Example 1.1.Is the expression ________ equivalent to _______ from the steps in Example 1? Why or why not?Yes, any order any grouping property of multiplication.2.What does 20/100 represent?20/100 is 20%.3.What does 30 represent?30 represents the whole quantity.4.What does their product represent?Their product (6) represents the part.5.Write a true multiplication sentence relating the part, the whole, and the percent.(20/100)(30) = 66.Translate your sentence into words. Is the sentence valid?

20% of 30 is 6. Yes the sentence is valid.7.Generalize the terms in your multiplication sentence by writing what each terms represents.Part = Percent x WholeStudents can now begin using this percent formula and algebraic reasoning to solve percent problems.

2 min 15. Outcome 1: You can see here that identifying the whole is still a major focus.

Outcome 2: The wording in this formula permits use in both types of percent problems that we’ve discussed. The reason that the “part” has been replaced is that is can present a misconception to students that all parts are smaller than the whole quantity.

Outcome 3: The percent more and percent less introduces students to lesson 4 in which they work with percent increase and decrease.

There is a fluency sprint at the end of the lesson that asks students to find the part, the whole or the percent of generic percent problems.

5 min 16. In lesson 3, students change the wording of the percent formula [“part”= percent x whole] to [“quantity”=percent x whole] so that it applies to a greater variety of problems.

If two disjoint quantities are being compared as in this example, identifying which quantity represents the whole is a little bit trickier. Students continue to practice identifying the whole quantity first and justifying why that quantity represents the whole. What should a student’s response sound like when identifying the whole?

(The number of bracelets that Anna produced is the whole since the number that Emily produced is being compared to it.)

In this lesson students are introduced to a visual model that is a combination of the double number line and a tape diagram. This visual model is an excellent

resource for organizing the quantities given in the problem and identifying how and where to enter into solving the problem. This model will come in very handy in lesson 5.

3 min 17. Following these examples the teacher prompts students to think about the percent more (or less) one quantity is of the other. By this point students associate whole quantity A with 100% and that a quantity B, greater than quantity A, must be greater than 100% of quantity A. This question helps prepare the students for lesson 4 which is Percent Increase and Decrease.

[Problem set #12 is a 7-part question that compares several pairs of quantities on a graph and connects percents to proportional relationships] – Provide the problem separately and complete if time is available.

1 min 18. Read the student outcomes for the lesson.

3 min 19. Following Example 1 students discuss a percent decrease situation and compare it to the previous percent increase problems. They use this discussion to write expressions that represent the situation, then show the equivalence of those expressions using familiar properties of operations.

What does this statement imply? (Think like a student)How does this problem differ from the percent increase problems?

Instead of the percent being added to 100%, it is less than 100% so must be subtracted from 100%.What expressions represent your implications?

“I will only pay 90% of my bill” : 0.90(bill)“10% of my bill will be subtracted from the

original total” : (original) – 0.10(original)

These expressions are equivalent. Show or explain why.

1 min 20. Read the student outcomes for the lesson.

5 min 21. The opening exercise in lesson 5 helps students identify more efficient means for working with percents. Take a few minutes and complete the opening exercise.

How do you think we can use these whole number factors in calculating percents on a double number line?The factors represent all the ways that 100% can be broken into equal intervals. The multiples would be the percents represented by each cumulative interval. The number of multiples is equal to the number of intervals.

5 min 22. Lesson 5 offers students alternatives to using equations in solving percent problems. The first is the modified double number line that was introduced in lesson 3, and then the use of the factors of 100% and their multiples. The opening exercise of Lesson 5 asks students to identify the factors of 100, and their multiples (through 100). The factors of 100 represent the ways in which we can break 100% into equal intervals of equal (whole number) size. The number of multiples for that factor represents the number of those intervals.

Give one example from the opening exercise…for example, 20.Which quantity represents the whole? (Adam’s points)[DOCUMENT CAMERA]Draw a percent number line and a bar representing the whole quantity (Adam’s points). The bar representing Nick’s points must extend to 120% because it is given that Nick has 20% more than Adam, or 100% + 20% = 120%.

Students recognize that 100 and 120 have the common factor of 20 and that there is no need to find the 1% as was done in earlier lessons. This provides opportunities to use mental math in certain situations. Strategies for using mental computations using factors of 100 and their multiples are covered in greater depth in the second half of the lesson.

Adam has 6000 points in the fantasy baseball league.

5 min 23. Students are further challenged to use their knowledge of percents to begin problem solving by mental calculation. Example 2 is a multi-part questions in which the part is constant, but the percent that it represents changes, and hence the value of the whole also changes.

Take a moment to complete parts a-e of Example 2.

(1%, 3900); (10%, 390); (5%, 780); (15%, 260); (25%, 156)

<<<TAKE A 15-MINUTE BREAK at the conclusion of this slide>>>

1 min 24. Read the student outcomes for the lesson.

There is a fluency sprint at the end of the lesson that asks students to answer percent questions involving percent more or percent less.

5 min 25. Lesson 6 is initially a day of extra practice with a variety of percent problems and an extension into problems with more steps. One such example is a percent problems involving unit conversions.

Provide time for participants to complete the problem.

5 min 26. What do you expect to see in Topic B? [Pause for participant inquiry]•Markup and markdown problems•Connection to proportional relationships•Percent error•Problems involving changing percents•Simple Interest, tax, commission, other fees•Modeling real world scenario using percents

2 min 27. Read the student outcomes for the lesson.

5 min 28. Students discuss and understand what markups and markdowns are, and why we have them. They then develop the formulas used to calculate markups and markdowns, and are able to effectively use those formulas in solving multi-step problems.

Complete Example 2.

5 min 29. a.p = (1+0.25)(s)

b. On document camera

c. On document camera

d.(0,0) represents an item with a price of $0 and its markup price of $0. So an item that costs $0 has no markup. The point (1,1.25) is the unit rate representing the percent that each markup price is of the original price.

2 min 30. Read the student outcomes for the lesson.

5 min 31. How many teachers have seen students get stuck because they can’t seem to remember if the denominator of the formula is the measured value or the actual value? To gain the best understanding of what percent error is, it is important that students understand absolute error first. Then percent error is the percent that the absolute error is of the exact value. Once absolute error is understood, finding the percent error is a comparison of two very similar to the problems from previous lessons.

In the beginning of lesson 8 students develop the concept of absolute error by considering the amount of error in three measurements of the diameter of a computer monitor. This can be simulated using almost anything of which you know the exact measurement. We will use a standard 8 ½ by 11 sheet of paper and follow the student/teacher dialog.Step 1: Measure like the typical 7th grader would measure•Display 3-4 measurements that are above and below the known value and reveal that known value of 13.901 inches.•How could you determine the error of each measurement to the actual diameter? (x – a or a – x )•What is the difference of table ___’s measurement and the actual measurement? (2 possible answers)•Which is correct? Why? (the positive answer because we are working with measurements and measurements must be positive)•How can we make sure that the error is always a positive value? (absolute value)•You have just developed what is called absolute error, which is |a – x| where a is a is the approximate value and x is the exact (or accepted) value.

5 min 32. Provide time to calculate the absolute errors of the given measurements.•Do you think that absolute error should be large or small? Why? (small…approximate should be as close to the exact as possible)•If we found the percent that the absolute error is of the exact value, what would this tell us? (tells us by how much our approximation differs from the exact measurement)•Additional question to consider: Why does percent error matter? Can’t we just always aim for an absolute error of less than 0.01 units?•Consider using the given absolute errors on much larger exact measurements and how the percent error is affected.

5 min 33. Extending the concept of percent error, students understand that it is possible to estimate the percent error where the exact value is not known, but that value lies within a known interval (inclusive endpoints). The problem on the screen is an example of one such problem.

Solution to problem: Since the counts and the actual number both lie on the interval 573 to 589, the absolute error cannot be greater than the difference of the upper and lower bounds, which is 16, and cannot be less than exact. If the count was exactly the same as the known attendance, then the percent error would be 0%. If the count was 589 and the actual attendance 573 (or vice versa), the absolute error would be 16, giving a percent error of 2.8%. So the percent error of the count of attendance is less than 2.8%.

1 min 34. Read the student outcomes for the lesson.

5 min 35. Try to solve this problem…but remember…equations with variables on either side of the equal sign are an 8th grade skill!

This problem can be easily solved with a visual model like those used in earlier lessons. The key is to identify the whole(s) in the context of the problem.

The first whole is Sally’s beginning money. The second whole is Sally’s ending money.

5 min 36. Equation method first: Let x represent Kimberly’s final amount after spending $50. Mike only spent $25 so he now has $25 more than Kimberly. Since Mike’s money is 50% more than Kimberly’s, the $25 must correspond with the 50%, so the resulting equation is: 0.5x=25

Visual method next: Start at the end…Mike’s money is 50% more than Kimberly’s, or 150% of Kimberly’s. The 50% more must be the $25 difference, so each bar represents $25.

Each persons started with $100.

1 min 37. Read the student outcomes for the lesson.

There is a fluency sprint at the end of the lesson that asks students to solve generic problems involving fractional percents.

5 min 38. Lesson 10 begins with a look at how simple interest works to give students a better understanding of what exactly simple interest is.Read the problem aloud to the group then follow up with discussion questions below.What pattern do you notice from the table? (Each year, the balance of the account increases $4.50)What does that $4.50 represent? (interest earned per year)How is that interest calculated? (it’s a percentage of the $100 invested)Can you create a formula to represent the pattern of change in the table? (I=100(0.045)t) where I represents the interest earned and t represents the number of years.)What kind of relationship is represented by your formula? (A proportional relationship)At this point you would reveal the simple interest formula I=Prt, define the variables, and model how the values would be substituted in to calculate a year ending balance.

What is the importance of this first example? (it shows that simple interest earned represents a proportional relationship and also encourages students to understand what simple interest is and how it works rather than just a formula to use.)

5 min 39. It is important for students to understand that the units on the interest rate and the time in a simple interest problem must be compatible. For example, if an interest rate is given as 4% per year, and the time given is 6 months, then either the 6 months must be converted to ½ year, or the 4% per year must be converted to 2% per 6-months (obviously the first of these is more desirable).

Problems in this lesson not only vary in time units, but also vary in units of time for the interest rate.

Take a few moments to complete Lesson 10, Problem Set #3. We’ll reconvene for the answers and some reflections in a few minutes.

2 min 40. Read the student outcomes for the lesson.

5 min 41. Exercises 1 and 2 are part of a modeling lesson in which students apply their knowledge of percents to realistic situations.

4 min 42. If time allows, complete problem #1 from the mid-module assessment without looking at the rubric or sample student responses. When finished, compare participant answers to the rubric and student sample response.

<<<THIS IS IDEAL TIME FOR LUNCH>>>

43. This concludes the Grade 7 the first half of the Module 4 focus session.

5 min 44.What do you expect to see in Topic C? [Pause for participant inquiry]•Scale factors in scale drawings expressed as percents•Horizontal and vertical scale factors•Scale factors of scale drawings A and B have reciprocal relationships A/B and B/A•Comparing scale factors between three (or more) scale drawings•Using scale drawings and scale factors to determine actual measurements•Area problems in scale drawings

2 min 45. Read the student outcomes for the lesson.

5 min 46. Complete Exercise 1. Discuss with a partner how you completed your drawing. (have a participant share their strategy) Students need to imagine auxiliary horizontal and vertical lines.

Students have worked with several scale drawings to this point where they drew in any diagonal line segments by joining the corresponding vertices from the original drawing. For this exercise they must imagine (or draw in) auxiliary lines to obtain the vertices of the scale drawing.

When a scale factor is given as a percent, why is it best to convert the percent to a fraction? (as opposed to a decimal)Sometimes a fractional percent results in a repeating decimal which may lead to an approximate answer. Percents can always be converted to a fraction by dividing the percent value by 100 and reducing the fraction.

Consider 152 1/3%. Describe the scale drawing this creates (enlargement) and the scale factor in fraction form (457/300)

5 min 47. [From Example 3]: Sometimes it is helpful to make a scale drawing where the horizontal and vertical scale factors are different, such as when creating diagrams in the field of engineering. Having different scale factors may distort some drawings. For example, when you are working with a very large horizontal scale, you sometimes must exaggerate the vertical scale in order to make it readable. This can be accomplished by creating a drawing with two scales. Unlike the scale drawings with just one scale factor, these types of drawings may look distorted.

We can compare this to using different scales on a coordinate grid.

1 min 48. Read the student outcomes for the lesson.

5 min 49. Students find the scale factors that exist between three drawings of an octagon and write equations to illustrate the relationships between measurements in those drawings.

5 min 50. In this example, students use the scale factors between 2 of 3 scale drawings to determine the remaining scale factor(s).

1 min 51. Read the student outcomes for the lesson.

5 min 52. Good example of MP1 – students may overthink this problem and give up when they are unsure what to do. However, all that is needed is to determine the scale factor using two corresponding vertical measurements and two corresponding horizontal measurements.

1 min 53. Read the student outcomes for the lesson.

5 min 54. Students were introduced to the relationships between areas of scale drawings in module 1, and lesson 15 in this module is much the same, but the scale factors are instead in percent form.

5 min 55. Students were introduced to the relationships between areas of scale drawings in module 1, and lesson 15 in this module is much the same, but the scale factors are instead in percent form.

5 min 56. What do you expect to see in Topic D? [Pause for participant inquiry]•More word problems related to percents•Population and mixture problems related to percents (extending use of percent to other areas of math and science)•Counting problems involving percent to prepare for future work with probability.

1 min 57. Read the student outcomes for the lesson.

5 min 58. Students are faced with multi-step percent problems in which there are multiple whole quantities to consider, some of which are sub-quantities, and multiple percents as well. They use visual modeling to organize and make sense of the information given and algebraically solve problems.

Have participants complete Example 1 then go over the solution.

5 min 59. This is a different type of “population” problem that can be solved using the same methods.

Have participants complete Example 3 then go over the solution.

5 min 60. This problem is a little trickier. Do this problem with participants if time allows.

1 min 61. Read the student outcomes for the lesson.

5 min 62. Have participants attempt exercise 1(a) before moving forward.

Let’s take a look at a strategy used for mixture problems. Organize the information in a mixture problem using a table to compare and combine the amounts of liquids (or matter) that are combined and the amount of the ingredients within them.

How much of liquid 1? (6-pints)How much of liquid 2? (3-pints)How much total liquid then when they are combined? (9-pints)

How much oil is in liquid 1? (0.25(6)=1.5-pints)How much oil is in liquid 2? (0.4(3)=1.2-pints)How much oil is in the combined liquids? (2.7-pints)

What percent of the total combined mixture is oil? (2.7/9)x100%=30% oil

Let’s take the information from the table and put it into equation form: (0.25 x 6) + (0.4 x 3) = (p x 9) where p represents the percent oil in the final mixture.

At the end of lesson 17, students reverse this process by dissecting an equation that represents a mixture problem. [Do if time allows, otherwise move to lesson 18]

5 min 63. Propose exercise 1(a) before moving forward.

Let’s take a look at a strategy used for mixture problems. Organize the information in a mixture problem using a table to compare and combine the amounts of liquids (or matter) that are combined and the amount of the ingredients within them.

How much of liquid 1? (6-pints)How much of liquid 2? (3-pints)How much total liquid then when they are combined? (9-pints)

How much oil is in liquid 1? (0.25(6)=1.5-pints)How much oil is in liquid 2? (0.4(3)=1.2-pints)How much oil is in the combined liquids? (2.7-pints)

What percent of the total combined mixture is oil? (2.7/9)x100%=30% oil

Let’s take the information from the table and put it into equation form: (0.25 x 6) + (0.4 x 3) = (p x 9) where p represents the percent oil in the final mixture.

At the end of lesson 17, students reverse this process by dissecting an equation that represents a mixture problem. [Do if time allows, otherwise move to lesson 18]

1 min 64. Read the student outcomes for the lesson.

5 min 65. In Lesson 18, counting problems are presented that require understanding and use of percents. This lesson serves as an introduction to probability (module 5) without formally computing combinations or permutations.

Discussion questions

7 min 66. The End-of-Module Assessment is given over two days. The first of two days is completed with the use of calculators whereas the second day does not.

We’ve left this time for you to complete the End-of-Module Assessment using the concepts and strategies that we discussed in today’s session.

5 min 67. Allow 1-minute for participants to reflect on the module focus session and identify a key takeaway(s) to share with the group.

5 min 68. Many, if not all of these key points were brought up but we’ll review them now in case anything was missed.

5 min 69.

70.

Use the following icons in the script to indicate different learning modes.

Video Reflect on a prompt Active learning Turn and talk

Turnkey Materials Provided

Grade 7 Module 4 PPT Grade 7 Module 4 Faciliatator Guide Student Examples and Exercises

Additional Suggested Resources

A Story of Ratios Curriculum Overview