Addressing Unfinished

F R O M G R E A T M I N D S ®

160.01.01P

Addressing Unfinished Learning: Eureka Math Equip™ Grades 6-12Participant Handout

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Addressing Unfinished Learning:Eureka Math Equip™, 6–12 Participant Handout

1Copyright ©2020 Great Minds PBC greatminds.org


Pre-Work:

▪ Complete the Grade 7 Module 1 Equip Pre-Module Assessment on pages 1-4.▪ Read the Grade 7 Module 1 Overview Narrative on page 5.

Addressing Unfinished Learning:Eureka Math Equip™, 6–12 ParticipantHandout

Copyright ©2020 Great Minds PBC greatminds.org

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A STORY OF RATIOS Equip Pre-Module Assessment 7•1

Pre-Work:• Complete the Grade 7 Module 1 Equip Pre-Module Assessment on pages 3-6.• Read the Grade 7 Module 1 Overview Narrative on page 7.

Grade 7 Module 1 Pre-Module Assessment

1. Write a ratio in two ways to describe the relationship of the number of forks to the number of spoons.

The ratio that describes the relationship of the number of forks to the number of spoons is to or : .

2. A bakery can make 30donuts every 15minutes.

The rate at which the bakery makes donuts is donuts per minute.

3. Points 𝐴𝐴, 𝐵𝐵, 𝐶𝐶, 𝐷𝐷, and 𝐸𝐸are graphed on a coordinate plane.

Describe the location of the points on the graph.

Point 𝐴𝐴is located at (,).

Point 𝐵𝐵is located at (,).

Point 𝐶𝐶is located at (,).

Point 𝐷𝐷is located at (,).

Point 𝐸𝐸is located at (,).




Addressing Unfinished Learning: Eureka Math Equip™, 6–12 Participant Handout


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4. Jorge plans to mix red paint and blue paint to create purple paint. The color of purple he has decided to make combines red paint and blue paint in the ratio 4:1. Jorge made the following ratio table to show some combinations of red and blue paint that will create the purple paint.

Blue (𝑩𝑩) Red (𝑹𝑹)

1 42 83 124 165 20

Write an equation that lets Jorge calculate the amount of red paint he will need for any given amount of blue paint.

5. Divide.

1 114÷2

5

A. 8

B. 2

C. 22

D. 3







5

6. The ratio of the number of miles Nash walked to the number of miles Sam walked is 3:10. Together they walked a total of 26miles. How many miles did Nash walk?

Which model would help you solve this problem?

A.

B.

C.

D.

7. What value of 𝑥𝑥makes the equation true?

7𝑥𝑥=84𝑥𝑥=







6

8. Each square on the grid has a length of 1unit.

What is the area of the triangle?

A. 16square units

B. 22.5square units

C. 32square units

D. 45square units





Module 1: Ratios and Proportional Relationships

7•1 Module Overview

Grade 7 • Module 1

Ratios and Proportional Relationships

OVERVIEW In Module 1, students build upon their Grade 6 reasoning about ratios, rates, and unit rates (6.RP.A.1, 6.RP.A.2, 6.RP.A.3) to formally define proportional relationships and the constant of proportionality(7.RP.A.2). In Topic A, students examine situations carefully to determine if they are describing aproportional relationship. Their analysis is applied to relationships given in tables, graphs, and verbaldescriptions (7.RP.A.2a).

In Topic B, students learn that the unit rate of a collection of equivalent ratios is called the constant of proportionality and can be used to represent proportional relationships with equations of the form 𝑦𝑦𝑦𝑦 = 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘, where 𝑘𝑘𝑘𝑘 is the constant of proportionality (7.RP.A.2b, 7.RP.A.2c, 7.EE.B.4a). Students relate the equation of a proportional relationship to ratio tables and to graphs and interpret the points on the graph within the context of the situation (7.RP.A.2d).

In Topic C, students extend their reasoning about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers, such as a speed of 12 mile per 14 hour (7.RP.A.1). Students apply their experience in the first two topics and their new understanding of unit rates for ratios and rates involving fractions to solve multi-step ratio word problems (7.RP.A.3, 7.EE.B.4a).

In the final topic of this module, students bring the sum of their experience with proportional relationships to the context of scale drawings (7.RP.A.2b, 7.G.A.1). Given a scale drawing, students rely on their background in working with side lengths and areas of polygons (6.G.A.1, 6.G.A.3) as they identify the scale factor as the constant of proportionality, calculate the actual lengths and areas of objects in the drawing, and create their own scale drawings of a two-dimensional view of a room or building. The topic culminates with a two-day experience of students creating a new scale drawing by changing the scale of an existing drawing.

Later in the year, in Module 4, students extend the concepts of this module to percent problems.

The module is composed of 22 lessons; 8 days are reserved for administering the Mid- and End-of-Module Assessments, returning the assessments, and remediating or providing further applications of the concepts. The Mid-Module Assessment follows Topic B. The End-of-Module Assessment follows Topic D.

A STORY OF RATIOS

©2016 Great Minds. eureka-math.org

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Question 1 Question 2






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Grade 7 Module 1

Bridging Gaps in Foundational Knowledge

Fill gaps in essential foundational knowledge (as identified by the pre-module assessment) using the supporting content provided in the table below. Refer to guidance that follows to customize your plan to address gaps for the entire class or for individuals or small groups of students.

Teach the supporting lesson(s) and insert fluency activities and/or previous grade-level components using the recommended pacing guide. The module adjustments listed below are suggestions. However, make customizations to the lessons based on the needs of your students.

Essential Foundational Knowledge Pre- Module Assessment

Item

Supporting Content When This Knowledge Is

Needed

How Could the Supporting Content BeIntegrated?

A. Write a ratio that describes therelationship between two quantities.

1 Supporting Fluency A (WBE: Ratios)

G7 M1 L1 Insert fluency at the beginning of G7 M1 L1.Omit Example 2.

B. Identify the rate associated

with a ratio a:b presented in context.

2 Supporting Component B (adapted from G6 M1 L16 Example 1)

G7 M1 L2 Insert component at the beginning of G7 M1 L2.Omit Exercise 1.

C. Name the coordinate points in acoordinate plane.

3 Supporting Component C (adapted from G6 M3 L14 Exercises 1 and 2)

G7 M1 L5 Insert component at the beginning of G7 M1 L5.Omit Opening Exercise.

D. Write an equation that models theratio relationship represented by atable of values.

4 Supporting Lesson D (adapted from G6 M4 L31)

G7 M1 L8 Teach lesson prior to G7 M1 L8.

E. Calculate the quotient of a mixednumber and fraction.

5 Supporting Fluency E (WBE: Dividing Fractions)

G7 M1 L11 Insert fluency at the beginning of G7 M1 L11. Omit Example 2.

F. Recognize a model that can be usedto solve a ratio word problem.

6 Supporting Lesson F (adapted from G6 M1 L5 and G6 M1 L6)

G7 M1 L13 Teach lesson prior to G7 M1 L13.

G. Solve a one-step equation involvingmultiplication of a whole number.

7 Supporting Fluency G (WBE: Solving One-Step Equations)

G7 M1 L14 Insert fluency at the beginning of G7 M1 L14.

H. Calculate the area of a right trianglepresented on a grid where each squarehas a length of one unit.

8 Supporting Fluency H (WBE: Area of Right Triangles)

G7 M1 L19 Insert fluency at the beginning of G7 M1 L19. Omit Exercise 2.

ab



F R O M G R E A T M I N D S ® Addressing Unfinished Learning: Eureka Math Equip™, 6–12 Participant Handout


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7 •1 Equip Supporting Fluency A A STORY OF RATIOS

Essential Foundational Knowledge A: Write a ratio that describes the relationship between two quantities.

Supporting Fluency A: WBE: Ratios

Suggested Integration: Insert at the beginning of G7 M1 L1. Omit Example 2.

Whiteboard Exchange

A ratio is an ordered pair of nonnegative numbers, which are not both zero. The ratio is denoted AA :: BB or AA ttoo BB to indicate the order of the numbers. In this specific case, the number A is first, and the number BB is second. Let’s find the ratio of the number of circles to the number of triangles. How many circles do we see?

Four How many triangles do we see?

Two What is the ratio of the number of circles to the number of triangles?

4 to 2 We can also write this ratio with a colon, 4 : 2.

Display the following for students:

Ask the following questions out loud:

1. What is the ratio of the number of circles to the number of squares?4 to 3 or 4 : 3

2. What is the ratio of the number of squares to the number of circles?3 to 4 or 3 : 4

Module 1: Ratios and Proportional Relationships 2 Copyright © 2020 Great Minds PBC Eureka Math EquipTM greatminds.org/math




7 •1 Equip Supporting Fluency A A STORY OF RATIOS

3. What is the ratio of the number of triangles to the number of circles?2 to 4, 1 to 2, 2 : 4, or 1 : 2

4. What is the ratio of the number of triangles to the number of squares?2 to 3 or 2 : 3





Essential Foundational Knowledge B: Identify the rate 𝑎𝑎𝑎𝑎𝑏𝑏𝑏𝑏

associated with a ratio 𝑎𝑎𝑎𝑎:𝑏𝑏𝑏𝑏 presented in context.

Supporting Component B: G6 M1 L16 Example 1

Suggested Integration: Replace G7 M1 L2 Exercise 1 with suggested additional component.

Introduction to Rates Ratios can be transformed to rates. A rate is a quantity that describes a ratio relationship

between two types of quantities. For example, 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 miles/hour is a rate that describes aratio relationship between hours and miles.

If an object is traveling at a constant 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 miles/hour, then after 𝟏𝟏𝟏𝟏 hour it hasgone 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 miles. How far will the object travel after 𝟐𝟐𝟐𝟐 hours? 𝟑𝟑𝟑𝟑 hours?It has gone 30 miles after 2 hours. It has gone 45 miles, after 3 hours.

Diet cola was on sale last week. It cost $𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 for every 𝟒𝟒𝟒𝟒 packs of diet cola. a. How much do 𝟐𝟐𝟐𝟐 packs of diet cola cost? How do you know?

2 packs of diet cola cost $5.00. I know this because half of 4 is 2 and half of 10 is 5.

b. How much does 𝟏𝟏𝟏𝟏 pack of diet cola cost? How do you know?

1 pack of diet cola costs $2.50. I know that half of 2 is 1 and half of 5 is 2.5.

The rate is $𝟐𝟐𝟐𝟐.𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 per pack.

Packs of Diet Cola 4 2

Total Cost 10 5

Packs of Diet Cola 2 1

Total Cost 5 2.50

7 •1 Equip Supporting Component B A STORY OF RATIOS





Lesson D: Problems in Mathematical Terms (adapted from G6 M4 L31)

Student Outcomes Students analyze an equation in two variables to choose an independent variable and a dependent variable.

Students determine whether or not the equation is solved for the second variable in terms of the first variableor vice versa. They then use this information to determine which variable is the independent variable andwhich is the dependent variable.

Students create a table by placing the independent variable in the first row or column and the dependentvariable in the second row or column. They compute entries in the table by choosing arbitrary values for theindependent variable (no constraints) and then determine what the dependent variable must be.

Classwork Example 1 (10 minutes)

Example 1

Marcus reads for 𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑 minutes each night. He wants to determine the total number of minutes he will read over the course of a month. He wrote the equation 𝒕𝒕𝒕𝒕 = 𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑 to represent the total amount of time that he has spent reading, where 𝒕𝒕𝒕𝒕 represents the total number of minutes read and 𝟑𝟑𝟑𝟑 represents the number of days that he read during the month. Determine which variable is independent and which is dependent. Then, create a table to show how many minutes he has read in the first seven days.

Number of Days (𝟑𝟑𝟑𝟑)

Total Minutes Read (𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑)

𝟏𝟏𝟏𝟏 𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑 𝟐𝟐𝟐𝟐 𝟔𝟔𝟔𝟔𝟑𝟑𝟑𝟑 𝟑𝟑𝟑𝟑 𝟗𝟗𝟗𝟗𝟑𝟑𝟑𝟑 𝟒𝟒𝟒𝟒 𝟏𝟏𝟏𝟏𝟐𝟐𝟐𝟐𝟑𝟑𝟑𝟑 𝟓𝟓𝟓𝟓 𝟏𝟏𝟏𝟏𝟓𝟓𝟓𝟓𝟑𝟑𝟑𝟑 𝟔𝟔𝟔𝟔 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟑𝟑𝟑𝟑 𝟕𝟕𝟕𝟕 𝟐𝟐𝟐𝟐𝟏𝟏𝟏𝟏𝟑𝟑𝟑𝟑

When setting up a table, we want the independent variable in the first column and the dependent variable inthe second column.

What do independent and dependent mean?

The independent variable changes, and when it does, it affects the dependent variable. So, thedependent variable depends on the independent variable.

In this example, which would be the independent variable, and which would be the dependent variable?

The dependent variable is the total number of minutes read because it depends on how many daysMarcus reads. The independent variable is the number of days that Marcus reads.

How could you use the table of values to determine the equation if it had not been given?

The number of minutes read shown in the table is always 30 times the number of days. So, theequation would need to show that the total number of minutes read is equal to the number of daystimes 30.

Independent variable _________________

Dependent variable _________________

Number of days

Total minutes read

MP.1

7 •1 Equip Supporting Lesson D A STORY OF RATIOS





Lesson D: Problems in Mathematical Terms

Classwork

Example 1

Marcus reads for 30 minutes each night. He wants to determine the total number of minutes he will read over the course of a month. He wrote the equation 𝑡𝑡𝑡𝑡 = 30𝑑𝑑𝑑𝑑 to represent the total amount of time that he has spent reading, where 𝑡𝑡𝑡𝑡 represents the total number of minutes read and 𝑑𝑑𝑑𝑑 represents the number of days that he read during the month. Determine which variable is independent and which is dependent. Then, create a table to show how many minutes he has read in the first seven days.

Independent variable

Dependent variable

7 •1 Lesson D A STORY OF RATIOS




F R O M G R E A T M I N D S ® Addressing Unfinished Learning: Eureka Math Equip™, 6–12 Participant Handout


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IntroductionThis resource contains all supporting content connected to the Essential Foundational Knowledge (EFK). All supporting lessons, lesson components, and fluencies associated with the essential foundational knowledge as well as supporting content for branch items (e.g. EFK E-i) are included.

EFK E: Calculate the quotient of a mixed number and fraction. If students need more support, refer to G6 M2 Topic A.

EFK Branch E-i: Identify equivalent expressions that show the decomposition of a fraction greater than 1 into the sum of smaller fractions.

Supporting Fluency E-i-1 is adapted from G4 M5 L7. Supporting Fluency E-i-2 is adapted from G5 M3 L16. Supporting Fluency E-i-3 is adapted from G4 M3 L24.

TableofContentsEFK E Supporting Content ..................................................................................................................... 2

Supporting Fluency E (WBE: Dividing Fractions) ................................................................................ 2

EFK Branch E-i Supporting Content ....................................................................................................... 4

Supporting Fluency E-i-1 (WBE: Break Apart Fractions) ..................................................................... 4

Supporting Fluency E-i-2 (WBE: Break Apart a Whole) ...................................................................... 5

Supporting Fluency E-i-3 (WBE: Equivalent Expressions of a Mixed Number) .................................... 6

A STORY OF RATIOS Equip Supporting Content E 7•1




Notes and ReflectionsEquip Pre- Module Assessments

Assessment Data




Supporting Content Recommendations

Branching




The Preparation and Customization Process

Information on the Preparation and Customization Process can be found in the Teacher Edition in the Module Overview of Module 1 in every grade level.

Webinar: Preparation and Customization: Making Intentional Decisions to Meet Students’ Needs

https://eurekamath.greatminds.org/preparation-customization-webinars

Additional Resources

Website: www.greatminds.orgBlogs: https://greatminds.org/math/blog/eureka Facebook: Eureka MathTwitter: @eureka_mathPinterest: https://www.pinterest.com/0130/

Final Reflection and Next Steps

What are your next steps to successfully implement Eureka Math™ Equip with your students?




Distribution of Learning: Sprinkling versus Clumping

Rather than clumping remedial instruction to address a significant learning gap, a practice that usually disrupts the coherence of the math story, we recommend sprinkling carefully sequenced instruction across a larger body of lessons. Sprinkling, or distributed learning, immediately contextualizes the work in the curriculum’s thoughtfully sequenced objectives. Inevitably, sprinkling slows pacing somewhat, but it maintains the forward movement of the mathematical story. We can compare the situation to the familiar classroom experience of a teacher reading a chapter in a book aloud to students. Consider the scenario in which a student is absent. On the student’s return, the teacher might question her to find the last point in the plot she remembers, and then fill in some additional details the student missed while still moving forward with the story. Contrast this with rereading the entire missed section to the student.

In the images below, the lower strip is a proportional representation of a grade level’s modules showing no customizing or pace changes, and the upper strip is a representation of a grade level’s modules showing either sprinkling or clumping of remedial instruction. Take a moment to analyze the two images below and how each strategy affects pacing.

As you can see, clumping means squishing the balance of the modules into a shorter time frame. Sprinkling, in contrast, may lengthen some modules because we remediate daily, but the remedial work is much more likely to integrate fluidly into the current instructional goals.

One example of distributed learning appears below. Let’s assume that the teacher has reviewed the curriculum map and anticipates that her students lack background knowledge and skill related to fractions, a requirement for working at grade level in Modules 3 and 4. Take a moment to consider the following questions: How has the remedial instruction been sprinkled in? What effect might the sprinkling have on pacing throughout the year?

Preparation and Customization of a Eureka Math Module: A Story of Ratios®

Copyright © 2018 Great Minds® greatminds.org 22

Reading Activity

Distribution of Learning: Sprinkling versus Clumping Rather than clumping remedial instruction to address a significant learning gap, a practice that usually disrupts the coherence of the math story, we recommend sprinkling carefully sequenced instruction across a larger body of lessons. Sprinkling, or distributed learning, immediately contextualizes the work in the curriculum’s thoughtfully sequenced objectives. Inevitably, sprinkling slows pacing somewhat, but it maintains the forward movement of the mathematical story. We can compare the situation to the familiar classroom experience of a teacher reading a chapter in a book aloud to students. Consider the scenario in which a student is absent. On the student’s return, the teacher might question her to find the last point in the plot she remembers, and then fill in some additional details the student missed while still moving forward with the story. Contrast this with rereading the entire missed section to the student.






Reading Activity

Distribution of Learning: Sprinkling versus Clumping Rather than clumping remedial instruction to address a significant learning gap, a practice that usually disrupts the coherence of the math story, we recommend sprinkling carefully sequenced instruction across a larger body of lessons. Sprinkling, or distributed learning, immediately contextualizes the work in the curriculum’s thoughtfully sequenced objectives. Inevitably, sprinkling slows pacing somewhat, but it maintains the forward movement of the mathematical story. We can compare the situation to the familiar classroom experience of a teacher reading a chapter in a book aloud to students. Consider the scenario in which a student is absent. On the student’s return, the teacher might question her to find the last point in the plot she remembers, and then fill in some additional details the student missed while still moving forward with the story. Contrast this with rereading the entire missed section to the student.







Another example of distributed learning appears below. In this example, the anticipated learning gap is prerequisite knowledge for the content in the first or second module. How might the need to address a learning gap immediately affect the pacing of the module?

Both plans above rest on the idea that it is preferable to distribute, or sprinkle, rather than clump remedial work. Ideally, the school schedule is structured with time set aside for Response to Intervention (RTI) or teachers temporarily place students in a math support class that focuses on remediation of targeted skills. If this is not your situation, we encourage you to think flexibly as you plan a module to honor the rigor of your grade-level content while meeting the needs of all students. Remediation minutes often have the dual objective of shoring up learning gaps while supporting current instruction.

In either case, we recommend that these remedial experiences be distributed over time. It’s always easier to conduct a sustained review of a concept or skill that will benefit the whole class or period. And it is our experience that a simpler lesson structure is better for pacing and consistency. The following chart shows five different ways to use a class period’s instructional minutes.

The rationale for doing the work almost daily is to provide a rhythm to the sessions, which simplifies management issues and allows students to feel comfortable in a predictable structure so the focus can be on learning rather than on organization.






Minutes for Math

Instruction Remediation

Grade-Level Content (Look for ways to apply the remedial content in the grade-level

content to affirm the relevance of the remediation.) Closure

45 10 minutes 30 minutes 5 minutes





90 every other day 30 minutes 55 minutes 5 minutes







Minutes for Math

Instruction Remediation

Grade-Level Content (Look for ways to apply the remedial content in the grade-level

content to affirm the relevance of the remediation.) Closure






90 every other day 30 minutes 55 minutes 5 minutes





CREDITS

Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this presentation.

WORK CITED

National Council of Teachers of Mathematics, National Council of Supervisors of Mathematics. 2020. “Moving Forward: Mathematics Learning in the Era of COVID-19.” National Council of Teachers of Mathematics. June. Accessed June 18, 2020. https://www.nctm.org/uploadedFiles/Research_and_Advocacy/NCTM_NCSM_Movin g_Forward.pdf.

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