Garden City Schools USD #457

Garden City Schools

USD #457

Eureka Math ~ 5th Grade Math Curriculum Guide

2018-2019

Math Framework and Protocol

Eureka Math Modifications

Customized District Assessments

Pacing and Assessment Guides

Problem Solving Tasks

Updated May 2018

Garden City Public Schools Garden City, Kansas

Updated May 2018

Mathematics Framework

Garden City Public Schools Statement of Purpose:

To support mathematical proficiency and to meet the challenges of preparing students for College and Career, Garden City Public Schools has developed the following mathematics framework. It provides a synthesis of research-based principles and strategies proven effective in promoting all students’ mathematics development—including the critical, creative, and self-regulated thinking processes that underlie the Kansas College and Career Ready Standards (KCCRS). The KCCRS calls for a shift to focus on sense-making, reasoning, and connections to real-world situations. Students will need knowledge and skills that prepare them to apply mathematics in a variety of contexts, including their future lives as responsible citizens. A transformation is required that results in a greater emphasis on the many ways that math helps us understand the world, and less on math for its own sake. There needs to be a focus on understanding and concepts, not just computation or procedures. Developing and applying real-world situations requires new technology tools and new approaches to teaching and learning. It also requires new assessment methods. The goal of the assessments should be to inform students and teachers about the level of understanding achieved, and of the next necessary steps in instruction. Ongoing informal assessment that guides teaching and learning brings about increased learning as well as increased self-esteem for students. Students will need the resources to prepare them for our rapidly changing world. By working on authentic tasks and real-life problem situations, students make connections related to their own learning of mathematics as well as important new connections among graphic, symbolic, and dynamic representations that are critical in order to understand mathematics effectively. They will also need to recognize that studying mathematics in high school is important for their future careers. A commitment to teacher professional development is essential that is collaborative with time allotted for vertical discussions and alignment across grade levels and high school courses. Teachers will need long-term professional development and support, including opportunities for reflection on their practice and guidance in improving it. To achieve the vision of reasoning and sense-making as the focus of students’ mathematical experiences, all components of the educational system – curriculum, instruction, and assessment – must work together and be designed to support students’ achieving these concepts and skills. Through a coherent and cohesive mathematics program with a strong alignment of curriculum, instruction and assessment, students will have the opportunity to be fully prepared for College and Career challenges.

Updated May 2018

A Vision for School Mathematics (National Council of Teachers of Mathematics NCTM)

Imagine a classroom, a school, or a school district where all students have

access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it.

Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically

rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment. Students confidently engage in complex

mathematical tasks chosen carefully by teachers. They draw on knowledge from a wide variety of mathematical topics, sometimes approaching the

same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to

make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques

to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups and with access to

technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage

actively in learning it.

Updated May 2018

Effective Mathematics Teaching and Learning

An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically. (Principles to Action, NCTM)

Updated May 2018

Standards of Mathematical Practice The Common Core mathematical practice standards are the foundation for mathematical thinking and practice for students as well as guidance that helps teachers modify their classrooms to approach teaching in a way that develops a more advanced mathematical understanding. Think of these standards as a guide to creating a more complex and absorbing learning experience that can be applied to everyday life, instead of being left in the classroom.

1. Make sense of problems and persevere in solving them. The first Common Core mathematical practice standard is found in almost every math problem across the board. It means that students must understand the problem, figure out how to solve it, and then work until it is finished. Common Core standards encourage students to work with their current knowledge bank and apply the skills they already have while evaluating themselves in problem-solving. This standard is easily tested using problems with a tougher skill level than already mastered. While students work through more difficult problems, they focus on the process of solving the problem instead of just getting to the correct answer.

2. Reason abstractly and quantitatively When trying to problem solve, it is important that students understand there are multiple ways to break apart the problem in order to find the solution. Using symbols, pictures or other representations to describe the different sections of the problem will allow students to use context skills rather than standard algorithms.

3. Construct viable arguments and critique the reasoning of others This standard is aimed at creating a common mathematical language that can be used to discuss and explain math as well as support or object others’ work. Math vocabulary is easily integrated into daily lesson plans in order for students to be able to communicate effectively. “Talk moves” are important in developing and building communication skills and can include such simple tasks as restating a fellow classmate’s reasoning or even supporting their own reason for agreeing or disagreeing. Prompting students to participate further in class mathematical discussion will help build student communication skills.

4. Model with mathematics Math doesn’t end at the classroom door. Learning to model with mathematics means that students will use math skills to problem-solve real world situations. This can range from organizing different types of data to using math to help understand life connections. Using real world situations to show how math can be used in many different aspects of life helps math to be relevant outside of math class.

Updated May 2018

Standards of Mathematical Practice (pg. 2)

5. Use appropriate tools strategically One of the Common Core’s biggest components is to provide students with the assets they need to navigate the real world. In order for students to learn what tools should be used in problem solving it is important to remember that no one will be guiding students through the real world – telling them which mathematics tool to use. By leaving the problem open ended, students can select which math tools to use and discuss what worked and what didn’t.

6. Attend to precision Math, like other subjects, involves precision and exact answers. When speaking and problem-solving in math, exactness and attention to detail is important because a misstep or inaccurate answer in math can be translated to affect greater problem-solving in the real world. The importance in this step comes in the speaking demeanor of students to explain what is understood and what isn’t.

7. Look for and make use of structure When students can identify different strategies for problem solving, they can use many different skills to determine the answer. Identifying similar patterns in mathematics can be used to solve problems that are out of their learning comfort zone. Repeated reasoning helps bring structure to more complex problems that might be able to be solved using multiple tools when the problem is broken apart into separate parts.

8. Look for and express regularity in repeated reasoning In mathematics, it is easy to forget the big picture while working on the details of the problem. In order for students to understand how a problem can be applied to other problems, they should work on applying their mathematical reasoning to various situations and problems. If a student can solve one problem the way it was taught, it is important that they also can relay that problem-solving technique to other problems.

Updated May 2018

Identifying High-Quality Mathematics Tasks or Supplemental Resources

The following tool identifies characteristics that are consistently found in high quality tasks. The following rating or review tool should be used to help identify if a mathematical task or supplemental resource is of high quality. It is important to keep in mind that there is no perfect task. Every task can be improved. The tool can be applied to print resources as well as online resources.

Identifying High-Quality Tasks The purpose of the task is to teach or assess:

Conceptual

Understanding

Procedural skill and

fluency

Application

Rating Scale:

2 - Fully Meets the Characteristic

1 - Partially Meets the Characteristic

0 - Does Not Meet the Characteristic

The mathematics task

Rating

Aligns to mathematics content standards I am teaching.

Encourages my students to use representations.

Provides my students with an opportunity for communicating their reasoning.

Has multiple entry points.

Allows for different strategies for finding solutions.

Makes connections between mathematical concepts, between concepts and procedures, or between concepts, procedures, and application.

Prompts cognitive effort.

Is problem-based, authentic, or interesting.

(Retrieved from Mine the Gap for Mathematical Understanding By: John SanGiovanni 2017)

Updated May 2018

Identifying High-Quality Mathematics Tasks or Supplemental Resources (pg. 2)


Updated May 2018

Identifying High-Quality Mathematics Tasks or Supplemental Resources (pg. 3)


Updated May 2018

USD #457 Mathematics Framework

Instructional Components of Eureka Math

• Fluency Practice: (whole group)

• promotes automaticity

• students are engaged

• high paced and energetic

• Application Problem: (whole group)

• independent and/or collaborative

• Kagan structures utilized

• student discourse present-discovers, recognizes, and verbalizes connections

• students understand and utilize RDW

• evidence of movement from concrete to representational to abstract

• students are given the opportunity to solve the problem without teacher guidance

Debrief

Application Fluency

Concept Development

Updated May 2018

USD #457 Mathematics Framework (pg. 2)

• Concept Development(6+ Classwork): (whole group)

• evidence of movement from concrete to representational to abstract (CRA)

• appropriate time is given to establish new learning

• teacher checks for understanding and provides immediate feedback

• student engagement structures may be used (ex: Kagan)

• student discourse present

• Problem Set is utilized in the concept development or as a result of the concept

development

• Debrief (6+ Closing): (whole group)

• PINNACLE of the lesson, if you are short on time, PROTECT THE DEBRIEF

• students articulate the focus of the lesson (metacognition)

• students identify connections between parts of the lesson and/or previous taught concepts

• teachers use rigorous questions to engage students in mathematical dialogue

• Exit Ticket (Independent)

• students are accountable for the day’s learning

• teacher uses tickets to inform instruction

• Homework (Independent)

• reinforces already taught concepts

• builds student confidence

• checks for understanding and confirms independent proficiency

• Centers (optional) (small group/independent)

• centers can be utilized after the completion of all lesson components

• a balance must be present between conceptual vs procedural activities (Suggested 50/50

balance)

• aligned to KCCRS and Eureka Math curriculum

• can be a review of skills already taught in current or previous grade levels

Updated May 2018

USD #457 Mathematics Resource Protocol

Grade Levels Core Resources Approved Supplemental Resources

Intervention Programs

(Tier 2 and 3) Elementary (K-5th)

Eureka Math https://greatminds.org

Problem Solving: • Youcubed https://www.youcubed.org/ • Inside Mathematics www.insidemathematics.org • 3-Act Math Tasks K-6 https://gfletchy.com/3-act-

lessons/ • Nrich Enriching Mathematics https://nrich.maths.org • Problem Solving In All Seasons By: Kim Markworth, Jenni

McCool, & Jennifer Kosiak • Federal Way Public Schools Problem Solving Activities

(Activities Aligned to Eureka Math Modules) https://www.fwps.org/page/2060

• Estimation 180 www.estimation180.com • Scholastic Math magazine • Mathematics Georgia Standards of

Excellence www.georgiastandards.org • Robert Kaplinsky Problem Based

Lessons https://robertkaplinsky.com/lessons/ Fluency Support: • Math Fact Strategies Books (Digital Resource book) • Building Conceptual Understanding and Fluency Through

Games – North Carolina (Digital Resource book) • Greg Tang Math www.gregtangmath.com • Mastering Basic Facts Add/Subtraction and

Multiplication/Division By: John San Giovanni • Well Played By: Linda Dacey, Karen Gartland, & Jayne

Bamford Lynch • Elementary Number Talks (Online

Resources) https://elementarynumbertalks.wordpress.com/

Content Support: • Illustrative

Mathematics https://www.illustrativemathematics.org/ • Illuminations http://illuminations.nctm.org/ • K-5 Math Teaching Resources www.k-

5mathteachingresources.com • Mine the Gap for Mathematical Understanding By: John

SanGiovanni • Zearn https://www.zearn.org • Eureka Math Bay Area Regional

Consortium https://embarc.online/ • KSDE Top Math Website

Resources http://community.ksde.org/Default.aspx?tabid=6173

• Mathematics Georgia Standards of Excellence www.georgiastandards.org

Do the Math Number Worlds DreamBox iStation Math Eureka Math (pre-teaching, re-teaching) Zearn http://www.zearn.org ECAM diagnostic assessment and resources (K-2) Number Readiness diagnostic assessment (1st-5th) and resources Mathematics Georgia Standards of Excellence www.georgiastandards.org

https://greatminds.org/

https://www.youcubed.org/

http://www.insidemathematics.org/

https://gfletchy.com/3-act-lessons/


https://nrich.maths.org/

http://www.estimation180.com/

http://www.georgiastandards.org/

https://robertkaplinsky.com/lessons/

http://www.gregtangmath.com/

https://elementarynumbertalks.wordpress.com/

https://elementarynumbertalks.wordpress.com/

https://www.illustrativemathematics.org/

http://illuminations.nctm.org/

http://www.k-5mathteachingresources.com/


https://www.zearn.org/

https://embarc.online/

http://community.ksde.org/Default.aspx?tabid=6173



http://www.zearn.org/




Updated May 2018

USD #457 Mathematics Resource Protocol (pg.2)

Middle (6th-8th)

Eureka Math https://greatminds.org

Problem Solving: • Youcubed https://www.youcubed.org/ • Inside Mathematics www.insidemathematics.org • 3-Act Math Tasks 6-

HS: https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0

• 3-Act Math Tasks K-6 https://gfletchy.com/3-act-lessons/

• Nrich Enriching Mathematics https://nrich.maths.org • Estimation 180 www.estimation180.com • Robert Kaplinsky Problem Based

Lessons https://robertkaplinsky.com/lessons/ Fluency Support: • Math Fact Strategies Books (Digital Resource book) • Building Conceptual Understanding and Fluency Through

Games – North Carolina (Digital Resource book) • Greg Tang Math www.gregtangmath.com • Mastering Basic Facts Add/Subtraction and

Multiplication/Division By: John San Giovanni • Well Played By: Linda Dacey, Karen Gartland, & Jayne

Bamford Lynch Content Support: • Illustrative

Mathematics https://www.illustrativemathematics.org/ • Illuminations http://illuminations.nctm.org/ • K-5 Math Teaching Resources www.k-

5mathteachingresources.com • Mine the Gap for Mathematical Understanding By: John

SanGiovanni • Zearn https://www.zearn.org • Eureka Math Bay Area Regional

Consortium https://embarc.online/ • KSDE Top Math Website

Resources http://community.ksde.org/Default.aspx?tabid=6173

Do the Math Number Worlds DreamBox iStation Math Eureka Math (pre-teaching, re-teaching) Zearn http://www.zearn.org Number Readiness diagnostic assessment (1st-5th) and resources

High (9th – 12th)

Agile Minds (Algebra I and Intensified Algebra)

Problem Solving: • Youcubed https://www.youcubed.org/ • Inside Mathematics www.insidemathematics.org • 3-Act Math Tasks 6-

HS: https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0

• 3-Act Math Tasks K-6 https://gfletchy.com/3-act-lessons/

• Nrich Enriching Mathematics https://nrich.maths.org • Estimation 180 www.estimation180.com • Robert Kaplinsky Problem Based

Lessons https://robertkaplinsky.com/lessons/

Fluency Support:

https://greatminds.org/



https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0







http://www.gregtangmath.com/

https://www.illustrativemathematics.org/

http://illuminations.nctm.org/




https://embarc.online/














Updated May 2018

Content Support:

USD #457 Mathematics Resource Protocol (pg. 3)

Recommended Teacher Resources (K-12) Principles to Action By: NCTM Putting the Practices into Action By: John SanGiovanni & Susanne O’Connell Teaching Student-Centered Mathematics (PreK-2), (3-5), and (6-8) (CCSS updated version) By: John Van de Walle 5 Practices for Orchestrating Productive Mathematics Discussion By: Mary K. Stein & Margaret Schwan Smith Classroom Discussions By: Suzanne Chapin Number Talks (K-5), and (6-8) By: Sherry Parris Taking Action: Implementing Effective Mathematics Teaching Practices (K-5), (6-8), and (9-12) By: Various Authors KATM Mathematics Flipbooks http://community.ksde.org/Default.aspx?tabid=5646 Mathematical Mindsets By: Jo Boaler Mathematics Learning Progressions http://ime.math.arizona.edu/progressions/ KSDE Math Website http://community.ksde.org/Default.aspx?tabid=5255

Home Support Resources Freckle Education www.Freckled.com Khan Academy www.Khanacademy.com Prodigy Math Game www.Prodigy.com Sumdog www.Sumdog.com Eureka Math www.greatminds.org Zearn https://www.zearn.org


http://ime.math.arizona.edu/progressions/


http://www.freckled.com/

http://www.khanacademy.com/

http://www.prodigy.com/

http://www.sumdog.com/

http://www.greatminds.org/


Updated May 2018

Modifications to Eureka Math for 2017-2018

Purpose of Modifications for Eureka Math:

• Provide guidelines that will support teachers. • Create a student focused program that supports students and their achievement. • Improve the program to make it better for students, teachers, and parents. • Create a program that has teacher buy-in where teachers can make it their own. • Make Eureka Math a totally positive curriculum for Garden City. • Maximize effectiveness of curriculum for our students.

Parent Communication

• Parent Newsletters: Parent information letter will be sent home explaining how to access digital newsletters. Parents may request paper copies of the newsletters if needed.

• Teachers, coaches, and administrators will address parent concerns related to Eureka Math when they arise.

• www.greatminds.org (free curriculum access, parent newsletters, roadmaps) • If Eureka Math homework and problem sets are used for homework, they must have correct

classroom examples attached. • Digital Homework Helpers are also available to parents and students for assistance with

homework. Information will be sent home each year on how to access these Digital Homework Helpers.

Pacing

• The district math committee recommends 60-90 minutes of math instruction daily for K-6. • Curriculum Guides are provided that include pacing suggestions. • Math instruction must occur on a daily basis. • All students should receive core math instruction. Students should not be pulled for

supplemental math instruction, intervention, or special services during whole group instruction, (concept development).

• The pacing guides should be used as a guide. Modules should be taught in order to provide for district-wide systemization and to follow the progressions of the KCCRS. This will allow for teacher collaboration during PLC’s and grade level meetings.

Differentiation and Remediation

• Differentiation and remediation have the same goal, to modify instruction until it meets the needs of all learners.

• Differentiation and remediation should occur throughout the lesson as needed. • Scaffolding is folded into the Eureka Math curriculum in such a way that it is part of its very

DNA. Faithful adherence to the modules is the primary scaffolding tool. • If necessary, teachers may use fewer models and/or stay at the concrete level for longer

periods of time, based on individual student needs.

Updated May 2018

• Teachers should consider the following, which are contained in strategically placed margin notes/scaffolding boxes within the lessons:

o Multiple means of representation o Multiple means of action and expression o Multiple means of engagement o https://www.engageny.org/sites/default/files/resource/attachments/how_to_impl

ement_a_story_of_units.pdf pg. 14-20 This document contains charts for English Language Learners, Students with Disabilities, Students Performing Above Grade Level and Students Performing Below Grade Level.

o https://www.engageny.org/resource/scaffolding-instruction-english-language-learners-resource-guides-english-language-arts-and This document suggests visual or concrete representations, graphic organizers, Kagan, sentence frames, building background knowledge, teacher modeling, and additional strategies.

o This document also contains lesson plans for specific grade levels with suggestions for differentiated instruction.

• Differentiation and remediation can be done during whole group instruction, small group and/or independent work times.

• If gaps in student knowledge exist, teachers should use material from previous Eureka Math lesson(s) whenever possible. Use the search tab to locate material from modules across grade levels. If necessary, supplemental materials aligned with KCCRS (coherence, focus, rigor, 8 SMPs) and Eureka Math may be used. Students still need to be exposed to grade level content, even if you stay at a concrete level longer.

• Problems in daily instruction can be modified by changing numbers, names, and/or context to increase real-world relevancy. These changes should not change the overall problem type of the objective of the problem. Adjustments can NOT be made to the Mid and End Module Assessments.

• Resource links: Greatminds.org Zearn.org – created to go with Eureka Math (Grades K-5) Embarconline.org See USD#457 Math Protocol for additional resources.

https://www.engageny.org/sites/default/files/resource/attachments/how_to_implement_a_story_of_units.pdf

https://www.engageny.org/sites/default/files/resource/attachments/how_to_implement_a_story_of_units.pdf

https://www.engageny.org/resource/scaffolding-instruction-english-language-learners-resource-guides-english-language-arts-and

https://www.engageny.org/resource/scaffolding-instruction-english-language-learners-resource-guides-english-language-arts-and

Updated May 2018

Complex reading level and vocabulary

• Vocabulary and Reading Level: Through differentiation practices teachers may restate directions so students can better understand the expectations. Teachers may rewrite problems for relevancy and better understanding with the exception of the Mid and End Module Assessments.

• Use a variety of strategies to reinforce vocabulary; word walls, anchor charts, sentence stems, student journals with vocabulary sections, introduce prior to instruction, make connections to math words, show pictures, use visual models, gestures, positive reinforcement, Kagan strategies, connect to concrete or pictorial, etc. See pg. 16 in A Story of Units.

• Try to embed vocabulary throughout the lesson and review during debriefing.

Centers

• All components of the Eureka lesson (fluency, application problem, concept development, problem set, and debrief) should be completed prior to students completing centers.

• Center activities should include a balance (approximately 50/50) of conceptual vs. procedural activities.

• All center activities need to be aligned to KCCRS and/or Eureka curriculum. • Center activities should cover concepts and skills that have already been taught in the

current school year or previous grade levels.

Special Education

• Special Education teachers are encouraged to use on grade level modules as much as

possible. Teachers should scaffold lessons to meet individual needs and/or IEP goals. • If necessary, SPED teachers may use fewer models and/or stay at the concrete level for

longer periods of time. Whenever possible, students in resource should be exposed to the grade level curriculum and be present for core instruction. The teacher providing support may pull the student from the core classroom after the concept development has been completed to provide accommodated support for the problem set and/or IEP goals.

• Self-contained SPED teachers should teach Eureka Math with fidelity as much as possible. They may use modules from lower grade levels for their instruction and/or go at a slower pace. Supplemental materials should be aligned with the Eureka Math curriculum unless otherwise stated in the student’s IEP.

• Writers of Eureka Math & MTSS team believe that if students are only instructed at a lower grade level, or pulled from core instruction, it increases achievement gaps and increases holes in student knowledge.

Updated May 2018

Fluency

• Teachers may adjust or repeat Eureka Math fluency activities and sprints multiple times. • When there are multiple fluency activities in an Eureka Math lesson, teachers may choose

the fluency activity(ies) with Eureka that will best prepare students for the lesson. • Students should be active at this time. • When students are counting, teacher may begin with them, but allow students to continue

on their own. • Sprints should not be graded, just trying for student personal best. • Sprints were created with deliberate patterns and sequencing. ( See quadrant example.) • Teachers should facilitate discussion with students about patterns and sequences found

within the Sprints. • Core fluencies are built into the lessons. These can be used as assessments and be graded.

These are particular to grade levels. The page will have a “CF” at the top of the page. The quadrants will also apply to Core Fluencies. 80% of the first column is considered mastery.

• Celebrate successes and aim to get at least one more on the second attempt. • Additional resources can be utilized to support instruction, but not should not replace all

the Eureka fluency activities.

Homework Guidelines

• When homework is assigned, teachers should use the following guidelines. • Homework should be at the independent level of the students, (80% accuracy). We

suggest teachers utilize homework to reinforce facts, computational fluency, and concepts. Do not send work home that is frustrating to students and parents. When Eureka Math homework is used, they must have correct classroom examples attached.

• Absent Students –Teachers should develop a system for absent students that includes notes, examples, peer coaching, etc. Small group time may be used for helping students who have missed instruction. Teachers may video instruction to be watched by students. Homework can be differentiated; students should not be expected to complete all problem sets or homework for extended absences. Teachers should note the overall objectives and teach the big ideas.

• Another option is to copy the lesson from the Teacher’s Manual to send home. • You may send home Sprints for additional practice, since it is not graded and you are trying

for students’ personal best. • Refer to USD #457 Homework Policy and Recommendations prior to assigning homework.

Assessments

• There are two categories of assessments used in Eureka Math, formative and summative. The Customized Mid-Module assessments should be used as formative and/or summative tests. The Customized End-of-Module assessments will be used as summative assessments.

Updated May 2018

Prior to teaching the module, teachers should preview the assessments to establish focus that will guide instruction.

• Formative Assessments: The goal of formative assessments is to gather feedback that can be used by the instructor and the students to guide improvements in the ongoing teaching and learning context. Exit tickets are not required to be entered as grades, but should be used to drive instruction.

• Teacher Flexibility o Teachers have the flexibility to assess as needed to drive instruction. The

components of each lesson that may be used as formative assessments are teacher observations, debriefing questions, exit tickets, and problem sets.

• Summative Assessments: The goal of a summative assessment is to measure the level of proficiency that has been obtained at the end of an instructional unit. End-of-Module assessments will be used as summative assessments.

Technology

• When students use technology, students should be accountable for the practice. Teachers and students should be able to communicate a desired outcome. Rigor should be evident.

• Technology used to strengthen conceptual understanding, fluency, and skill mastery should support the curriculum, not supplant the curriculum.

• Technology appropriate for use by students during core instruction may include virtual manipulatives and student response activities.

• Teachers can use technology to enhance instruction as long as it is aligned to KCCRS and supports the Eureka Math curriculum.

• Please refer to the District Math Protocol for approved curriculum-aligned websites and resources.

USD #457 Customized Eureka Math Assessments The original Eureka Math Mid and End Modules Assessments have been customized by teacher writers from Garden City Public Schools to include a balance of the higher DOK level 2 and 3 questions from the original assessment as well as skill based questions from throughout the module. The purpose of this customization is to ensure all students are being given access to the challenging high level questions throughout the curriculum, while also accessing the foundational skills students need in place to successfully complete those higher level questions. At the beginning of each customized assessment you will find a reference page identifying the standard each question on the customized assessment addresses as well as the original location of that test item, and if the question is procedural, conceptual, or application. Grades 5-8 will also have a converting a rubric score to % conversion chart with each assessment. To ensure consistency with the administration and grading of these assessments, the following must be followed when giving the assessments.

• Assessments are to be completed independently by students. (Questions may be read aloud to students in lower grade levels as needed.)

• Testing accommodations that students receive on state and other classroom assessments, may be provided to students on the customized district assessments.

• Tests are designed to be completed either in one class period or by breaking the assessment apart based on the curriculum pacing. Test administration should be no more than 60 minutes if being administered in one setting.

• Assessments are to be graded using the district customized assessment grading rubric.

• If customized assessment grades are going to be entered into the gradebook, the converting a rubric score to % conversion chart must be used.

• Previewing or giving “practice tests” of the assessments is not allowed. • Review of the assessments may only occur after the assessment has been

administered. • Data entry of student assessment scores are to be entered no later than 2

weeks after the module is finished based on the pacing guide provided.

You can also download the Customized District Assessments directly for your grade level at https://www.gckschools.com/cms/One.aspx?portalId=54924&pageId=4234075 or at www.gckschools.com under Curriculum and Instruction Resources, Math, and then USD #457 Custom Eureka Assessments..

https://www.gckschools.com/cms/One.aspx?portalId=54924&pageId=4234075

http://www.gckschools.com/

Fifth Grade Pacing 2018-2019

Within the development of the pacing guides, it is expected that these will be reasonably flexible depending on the needs of your class. The pacing guide for Fifth Grade has 150 days of instruction including 114 days for core instruction, 24 days for assessment administration and feedback, and 12 days for problem solving tasks. In addition to the 150 days of core instruction listed above, there are 15 additional days that can be flexed based on state and district assessments and your students’ needs.

Skills spiral throughout the year and students may not be at mastery by the end of an individual lesson. In fact, many lessons anticipate that students will need more practice in concepts. Therefore, it is recommended that if re-teaching needs to happen, it occurs as a part of the next day’s lesson. By doing this, teachers are able to present concepts in several ways and will not remain within the same lesson for multiple days. Module Map for Fifth Grade Module 1 Module 2 Module 3 Module 4 Module 5 Module 6 14 Core Lessons

24 Core Lessons

12 Core Lessons

27 Core Lessons

17 Core Lessons

18 Core Lessons

2 Days for Problem Solving Tasks






4 Days for Assessment and Feedback






Suggested 20 Days

Suggested 30 Days

Suggested 18 Days

Suggested 33 Days

Suggested 23 Days

Suggested 24 Days

USD #457 5th Grade Eureka Math Pacing and Assessment Guide 2018-2019

Module # of Curriculum Days (Lessons &

Assessments)

Instruction Date Range

Assessment Testing Window

Data Entry Due Date

1: Place Value and Decimal Fractions 20 Aug. 20 – Sept. 17

MM: Aug. 28 – Sept. 11 September 11 EM: Sept. 14 – Sept. 28 September 28

2: Multi-Digit Whole Numbers and Decimal Fractions

32 Sept. 18 – Nov. 6 MM: Oct. 9 – Oct. 23 October 23

EM: Nov. 5 – Nov. 19 November 19

3: Addition and Subtraction of Fractions 18 Nov. 7 – Dec. 6

MM: Nov. 19 – Dec. 4 December 4 EM: Dec. 5 – Dec. 19 December 19

4: Multiplication and Division of Fractions 33 Dec. 7 – Feb. 8

MM: Jan. 9 – Jan. 23 January 23 EM: Feb. 7 – Feb. 20 February 20

5: Addition and Multiplication with Volume and Area

23 Feb. 11 – Mar. 26 MM: Feb. 20 – March 7 March 7

EM: March 25 – April 8 April 8

6: Problem Solving with the Coordinate Plane 24 Mar. 27 – May 1

MM: April 3 – April 17 April 17

EM: April 30 – May 7 May 7 Note: This pacing guide allots one day per lesson, 2 days per assessment (one day for administration and one day for reteaching), and 2 days for problem solving activities in each module. Combining lessons may need to occur

to adjust for state assessments or other scheduling conflicts.

Suggestions on How to Combine Eureka Math Lessons Effectively

Fluency

• If both lessons include a Sprint activity, choose one to complete.

• Examine the objective of each fluency activity and if several have the same objective or cover the same standard, select one activity to complete.

• Do not remove all fluency activities, as they are intentionally included in each lesson to scaffold past learning or prepare students for future topics.

Application Problem • Application Problems review

skills previously learned. Either application problem will achieve this objective.

• Completing both Application Problems is not necessary.

Concept Development/Instruction • Prepare concept development

parts in advance by taking problems from both lessons.

o Identifying your “must dos”, “could dos” and “should dos” on the Problem Sets first and then choosing the Concept Development problems to complete will ensure that instruction matches what students will be expected to do.

• Remaining parts of the concept development can be used to remediate, or extend in small groups.

• It is not suggested to cut out the conceptual development pieces of any lesson. (Ex: student use of models, manipulatives, etc)

Problem Sets/Homework • Combine parts of both Problem Sets

to match parts taught in the Concept Development.

• Customize problems carefully by choosing the most appropriate problems for students.

• Be mindful to not remove all of the deeper level or more challenging problems.

• Creating homework to match your Problem Set is necessary if assigning homework.

Exit Tickets • Combining the Exit Tickets

from both lessons is an excellent way to formatively assess students’ understanding of the content of both lessons.

USD #457 Specific Pacing Guide Suggestions ~ Eureka Math 5th Grade

Lesson Topics and Objectives Days Instructional NotesTopic A: Multiplicative Patterns on the Place Value Chart

3

Standards 5.NBT.1 | 5.NBT.2 | 5.MD.1Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.Lesson 3: Use exponents to name place value units and explain patterns in the placement of the decimal point.Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.

Focus is on metric conversion.

Topic B: Decimal Fractions and Place Value Patterns 2

Standards 5.NBT.3 | 5.NBT.3.a | 5.NBT.3.bLesson 5: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning.

Lesson 6: Compare decimal fractions to the thousandths using like units, and express comparisons with >, <, =.

Add problems with ≠ symbol. (2017 KS Standard)

Topic C: Place Value and Rounding Decimal Fractions 1

Standards 5.NBT.4Lesson 7: Round a given decimal to any place using place value understanding and the vertical number line.

Repeated objective in Lesson 7 and 8.

Lesson 8: Round a given decimal to any place using place value understanding and the vertical number line.MID-MODULE ASSESSMENT 2Topic D: Adding and Subtracting Decimals 2Standards 5.NBT.2 | 5.NBT.3 | 5.NBT.3.a | 5.NBT.3.b | 5.NBT.7Lesson 9: Add decimals using place value strategies and relate those strategies to a written method.Lesson 10: Subtract decimals using place value strategies and relate those strategies to a written method.

Module 1: Place Value and Decimal Fractions


Topic E: Multiplying Decimals 2Standards 5.NBT.2 | 5.NBT.3 | 5.NBT.3.a | 5.NBT.3.b | 5.NBT.7

Lesson 11: Multiply a decimal fraction by single-digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used.

Lesson 12: Multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point.

Topic F: Dividing Decimals 4Standards 5.NBT.3 | 5.NBT.3.a | 5.NBT.3.b | 5.NBT.7Lesson 13: Divide decimals by single-digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method.Lesson 14: Divide decimals with a remainder using place value understanding and relate to a written method.Lesson 15: Divide decimals using place value understanding including remainders in the smallest unit.Lesson 16: Solve word problems using decimal operations.END-OF-MODULE ASSESSMENT 2

Total Number of Instructional Days 18


Lesson Topics and Objectives Days Instructional NotesTopic A: Mental Strategies for Multi-Digit Whole Number Multiplication

2

Standards 5.NBT.1 | 5.NBT.2 | 5.OA.1

Lesson 1: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties.

Lesson 2: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication

6

Standards 5.OA.1 | 5.OA.2 | 5.NBT.5Lesson 3: Write and interpret numerical expressions, and compare expressions using a visual model.Lesson 4: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

Enrichment lesson.

Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.Lesson 6: Connect area models and the distributive property to partial products of the standard algorithm with renaming.Lesson 7: Connect area models and the distributive property to partial products of the standard algorithm with renaming.Lesson 8: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.Lesson 9: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

Module 2: Multi-Digit Whole Numbers and Decimal Fractions


Topic C: Decimal Multi-Digit Multiplication 3Standards 5.NBT.7 | 5.NBT.1 | 5.OA.1 | 5.OA.2

Lesson 10: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

Lesson 11: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal.

Lesson 12: Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation.

Topic D: Measurement Word Problems with Whole Number and Decimal Multiplication

3

Standards 5.NBT.5 | 5.NBT.7 | 5.MD.1 | 5.NBT.1 | 5.NBT.2Lesson 13: Use whole number multiplication to express equivalent measurements.Lesson 14: Use fraction and decimal multiplication to express equivalent measurements.Lesson 15: Solve two-step word problems involving measurement conversions.MID-MODULE ASSESSMENT 2Topic E: Mental Strategies for Multi-Digit Whole Number Division

2

Standards 5.NBT.1 | 5.NBT.2 | 5.NBT.6Lesson 16: Use divide by 10 patterns for multi-digit whole number division.Lesson 17: Use basic facts to approximate quotients with two-digit divisors.

Lesson 18: Use basic facts to approximate quotients with two-digit divisors.

Review of Lesson 17. Teach lesson if extra instruction is needed.


Topic F: Partial Quotients and Multi-Digit Whole Number Division

5

Standards 5.NBT.6

Lesson 19: Divide two- and three-digit dividends by multiples of 10 with single-digit quotients, and make connections to a written method.

Lesson 20: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients, and make connections to a written method.

Lesson 21: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients, and make connections to a written method.

Lesson 22: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

Lesson 23: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

Topic G: Partial Quotients and Multi-Digit Decimal Division

4

Standards 5.NBT.2 | 5.NBT.7Lesson 24: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method.

Lesson 25: Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the placement of the decimal point.

Lesson 26: Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method.Lesson 27: Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method.Topic H: Measurement Word Problems with Multi-Digit Division

1

Standards 5.NBT.6 | 5.NBT.7

Lesson 28: Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown.

Lesson 29: Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown.

Repeated objective from Lesson 28.

END-OF-MODULE ASSESSMENT 2Total Number of Instructional Days 30


Lesson Topics and Objectives Days Instructional NotesTopic A: Equivalent Fractions 2Standards 4.NF.1Lesson 1: Make equivalent fractions with the number line, the area model, and numbers.Lesson 2: Make equivalent fractions with sums of fractions with like denominators.Topic B: Making Like Units Pictorially 5Standards 5.NF.1 | 5.NF.2Lesson 3: Add fractions with unlike units using the strategy of creating equivalent fractions.Lesson 4: Add fractions with sums between 1 and 2.Lesson 5: Subtract fractions with unlike units using the strategy of creating equivalent fractions.Lesson 6: Subtract fractions from numbers between 1 and 2.Lesson 7: Solve two-step word problems.MID-MODULE ASSESSMENT 2Topic C: Making Like Units Numerically 5Standards 5.NF.1 | 5.NF.2Lesson 8: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.Lesson 9: Add fractions making like units numerically.Lesson 10: Add fractions with sums greater than 2.Lesson 11: Subtract fractions making like units numerically.Lesson 12: Subtract fractions greater than or equal to 1.Topic D: Further Applications 0Standards 5.NF.1 | 5.NF.2Lesson 13: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

Enrichment lesson.

Lesson 14: Strategize to solve multi-term problems. Enrichment lesson.Lesson 15: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

Enrichment lesson.

Lesson 16: Explore part-to-whole relationships. Enrichment lesson.END-OF-MODULE ASSESSMENT 2


Module 3: Addition and Subtraction of Fractions


Lesson Topics and Objectives Days Instructional NotesTopic A: Line Plots of Fraction Measurements 1Standards 5.MD.2

Lesson 1: Measure and compare pencil lengths to the nearest 1/2, 1/4, and 1/8 of an inch, and analyze the data through line plots.

Topic B: Fractions as Division 4Standards 5.NF.3Lesson 2: Interpret a fraction as division.Lesson 3: Interpret a fraction as division.Lesson 4: Use tape diagrams to model fractions as division.

Lesson 5: Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers.

Topic C: Multiplication of a Whole Number by a Fraction 3

Standards 5.NF.4.aLesson 6: Relate fractions as division to fraction of a set.

Lesson 7: Multiply any whole number by a fraction using tape diagrams.

Lesson 8: Relate a fraction of a set to the repeated addition interpretation of fraction multiplication.

Lesson 9: Find a fraction of a measurement, and solve word problems.Lesson extension or review of measurement conversions.

Topic D: Fraction Expressions and Word Problems 3Standards 5.OA.1 | 5.OA.2 | 5.NF.4.a | 5.NF.6

Lesson 10: Compare and evaluate expressions with parentheses.

Lesson 11: Solve and create fraction word problems involving addition, subtraction, and multiplication.Lesson 12: Solve and create fraction word problems involving addition, subtraction, and multiplication.MID-MODULE ASSESSMENT 2

Module 4: Multiplication and Division of Fractions


Topic E: Multiplication of a Fraction by a Fraction 8Standards 5.NBT.7 | 5.NF.4.a | 5.NF.6 | 5.MD.1 | 5.NF.4.bLesson 13: Multiply unit fractions by unit fractions.Lesson 14: Multiply unit fractions by non-unit fractions.Lesson 15: Multiply non-unit fractions by non-unit fractions.Lesson 16: Solve word problems using tape diagrams and fraction-by-fraction multiplication.Lesson 17: Relate decimal and fraction multiplication.Lesson 18: Relate decimal and fraction multiplication.Lesson 19: Convert measures involving whole numbers, and solve multi-step word problems.Lesson 20: Convert mixed unit measurements, and solve multi-step word problems.Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems

2

Standards 5.NF.5.b | 5.NF.5.a | 5.NF.5 | 5.NF.6Lesson 21: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.

Enrichment lesson.

Lesson 22: Compare the size of the product to the size of the factors.

Lesson 23: Compare the size of the product to the size of the factors.

Lesson 24: Solve word problems using fraction and decimal multiplication.

Topic G: Division of Fractions and Decimal Fractions 5

Standards 5.OA.1 | 5.NBT.7 | 5.NF.7 | 5.NF.7.a | 5.NF.7.b | 5.NF.7.c

Lesson 25: Divide a whole number by a unit fraction.Lesson 26: Divide a unit fraction by a whole number.Lesson 27: Solve problems involving fraction division.Lesson 28: Write equations and word problems corresponding to tape and number line diagrams.Lesson 29: Connect division by a unit fraction to division by 1 tenth and 1 hundredth.

Lesson 30: Divide decimal dividends by non-unit decimal divisors.

Lesson 31: Divide decimal dividends by non-unit decimal divisors.

Topic H: Interpretation of Numerical Expressions 1Standards 5.OA.1 | 5.OA.2Lesson 32: Interpret and evaluate numerical expressions including the language of scaling and fraction division.

Enrichment lesson.

Lesson 33: Create story contexts for numerical expressions and tape diagrams, and solve word problems.END-OF-MODULE ASSESSMENT 2



Lesson Topics and Objectives Days Instructional NotesTopic A: Concepts of Volume 3Standards 5.MD.3 | 5.MD.3.a | 5.MD.3.b | 5.MD.4

Lesson 1: Explore volume by building with and counting unit cubes.

Lesson 2: Find the volume of a right rectangular prism by packing with cubic units and counting.

Lesson 3: Compose and decompose right rectangular prisms using layers.

Topic B: Volume and the Operations of Multiplication and Addition

3Standards 5.MD.3 | 5.MD.3.a | 5.MD.3.b | 5.MD.5 | 5.MD.5.a | 5.MD.5.b | 5.MD.5.cLesson 4: Use multiplication to calculate volume.

Lesson 5: Use multiplication to connect volume as packing with volume as filling.

Use digital manipulatives within other lessons within this topic to address this objective.

Lesson 6: Find the total volume of solid figures composed of two non-overlapping rectangular prisms.Lesson 7: Solve word problems involving the volume of rectangular prisms with whole number edge lengths.Lesson 8: Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.

Enrichment lesson.

Lesson 9: Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.

Enrichment lesson.

MID-MODULE ASSESSMENT 2Topic C: Area of Rectangular Figures with Fractional Side Lengths

6

Standards 5.NF.4 | 5.NF.4.b | 5.NF.6Lesson 10: Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths by tiling, record by drawing, and relate to fraction multiplication.Lesson 11: Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths by tiling, record by drawing, and relate to fraction multiplication.Lesson 12: Measure to find the area of rectangles with fractional side lengths.Lesson 13: Multiply mixed number factors, and relate to the distributive property and the area model.

Lesson 14: Solve real-world problems involving area of figures with fractional side lengths using visual models and/or equations.

Lesson 15: Solve real-world problems involving area of figures with fractional side lengths using visual models and/or equations.

Module 5 Addition and Multiplication with Volume and Area


Topic D: Drawing, Analysis, and Classification of Two-Dimensional Shapes

5

Standards 5.G.3 | 5.G.4Lesson 16: Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes.Lesson 17: Draw parallelograms to clarify their attributes, and define parallelograms based on those attributes.

Lesson 18: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.

Lesson 19: Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes.Lesson 20: Classify two-dimensional figures in a hierarchy based on properties.Lesson 21: Draw and identify varied two-dimensional figures from given attributes.

Enrichment lesson.

END-OF-MODULE ASSESSMENT 2Total Number of Instructional Days 21


Lesson Topics and Objectives Days Instructional NotesTopic A: Coordinate Systems 5Standards 5.G.1Lesson 1: Construct a coordinate system on a line.Lesson 2: Construct a coordinate system on a plane.Lesson 3: Name points using coordinate pairs, and use the coordinate pairs to plot points.Lesson 4: Name points using coordinate pairs, and use the coordinate pairs to plot points.Lesson 5: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.Lesson 6: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.

Enrichment Lesson

Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

0

Standards 5.OA.2 | 5.OA.3 | 5.G.1

Lesson 7: Plot points, use them to draw lines in the plane, and describe patterns within the coordinate pairs.

5.OA.3 No longer 5th grade KS Standard (2017)

Lesson 8: Generate a number pattern from a given rule, and plot the points.


Lesson 9: Generate two number patterns from given rules, plot the points, and analyze the patterns.


Lesson 10: Compare the lines and patterns generated by addition rules and multiplication rules.


Lesson 11: Analyze number patterns created from mixed operations.5.OA.3 No longer 5th grade KS Standard (2017)

Lesson 12: Create a rule to generate a number pattern, and plot the points.


MID-MODULE ASSESSMENT 2

Module 6: Problem Solving with the Coordinate Plane


Topic C: Drawing Figures in the Coordinate Plane 5Standards 5.G.1 | 5.G.2

Lesson 13: Construct parallel line segments on a rectangular grid.

Lesson 14: Construct parallel line segments, and analyze relationships of the coordinate pairs.

Lesson 15: Construct perpendicular line segments on a rectangular grid.

Lesson 16: Construct perpendicular line segments, and analyze relationships of the coordinate pairs.Lesson 17: Draw symmetric figures using distance and angle measure from the line of symmetry.Topic D: Problem Solving in the Coordinate Plane 3Standards 5.G.2 | 5.OA.3Lesson 18: Draw symmetric figures on the coordinate plane.Lesson 19: Plot data on line graphs and analyze trends.

Lesson 20: Use coordinate systems to solve real world problems.

END-OF-MODULE ASSESSMENT 2Topic E: Multi-Step Word Problems 5Standards 5.NF.2 | 5.NF.3 | 5.NF.6 | 5.NF.7.c | 5.MD.1 | 5.MD.5 | 5.G.2

Lesson 21: Make sense of complex, multi-step problems, and persevere in solving them. Share and critique peer solutions.Lesson 22: Make sense of complex, multi-step problems, and persevere in solving them. Share and critique peer solutions.Lesson 23: Make sense of complex, multi-step problems, and persevere in solving them. Share and critique peer solutions.Lesson 24: Make sense of complex, multi-step problems, and persevere in solving them. Share and critique peer solutions.Lesson 25: Make sense of complex, multi-step problems, and persevere in solving them. Share and critique peer solutions.Topic F: The Years in Review: A Reflection on A Story of Units

0

Lesson 26: Solidify writing and interpreting numerical expressions. Enrichment Lesson

Lesson 27: Solidify writing and interpreting numerical expressions. Enrichment Lesson

Lesson 28: Solidify fluency with Grade 5 skills. Enrichment LessonLesson 29: Solidify the vocabulary of geometry. Enrichment LessonLesson 30: Solidify the vocabulary of geometry. Enrichment LessonLesson 31: Explore the Fibonacci sequence. Enrichment LessonLesson 32: Explore patterns in saving money. Enrichment LessonLesson 33: Design and construct boxes to house materials for summer use.

Enrichment Lesson

Lesson 34: Design and construct boxes to house materials for summer use.

Enrichment Lesson


Problem Solving Tasks

During each module you teach, students will participate in 2 days of

problem solving tasks. It is at the discretion of the classroom teacher as to when the 2 days of problem solving will take place during each module, as well as which problem solving tasks will be completed. A list of suggested curriculum-aligned resources can also be found within the USD#457 K-12 Mathematics Framework. Direct digital links to the resources listed can also be found at www.gckschools.com/candi/math.

Additional problem solving tasks can be used if they are identified as being

high quality mathematical tasks. An Identifying High-Quality Tasks or Supplemental Resources tool can be found within the USD #457 K-12 Math Mathematics Framework. The tool identifies characteristics that are consistently found in high quality tasks.

http://www.gckschools.com/candi/math

Garden City Schools USD #457

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