Grade 5 GT Program Tools
Elementary Mathematics Course Essentials
All students must have access to high-quality, rigorous mathematics instruction. The Exemplary Elementary Mathematics Program document Links to an external site. identifies how the ideas of exemplary mathematics align to Planning and Preparation, Classroom Environment, Instruction, and Professional Responsibilities as related to the Danielson Framework.
Daily mathematics instruction
- is provided for 75 minutes each day;
- begins with a brief (10 minute) Number Talk for developing fluency or a number routine for developing number sense and numeracy;
- features a high-quality, standards-based instructional task;
- leverages an appropriate grouping structure that maximizes instructional time, student collaboration, engagement, and discussion;
- provides students with opportunity to work with concepts, procedures, and problems before explicit instruction;
- promotes diverse strategies, interpretations, and representations so that students develop their understanding;
- makes use of and connects representations of content;
- is rich meaningful discourse;
- provides appropriate, responsible practice for retaining understanding and using skills efficiently; and
- is evidence of effective teaching practices for equitable mathematics.
Daily high-quality first instruction is described in greater detail on the tab below. Other headings below provide information, resources, and/or links for implementation of the Exemplary Elementary Mathematics Program.
Articulation Guidance
Linked below are articulation recommendations from the Elementary Mathematics Office. Adjustments may be needed for varied reasons such as resource allocation, scheduling challenges, or departmentalization models. NOTE: Title I schools also have their own requirement.
Assessment Resources
A collection of assessment resources are available to help you know where your students are mathematically. These tools include:
-
- First Week Tasks: These tasks are designed to assess mathematics learning behaviors. They are included in the first instructional module, access these tasks from the Scope and Sequence.
-
- Measurement Topic Assessments: These are required assessments and provided for each measurement topic within each quarter. They are included in the Grade 5GT Assessment Package below. This assessment package is available electronically through Canvas or in paper/pencil versions. Arrangements are being made for these assessments to be printed and delivered to schools. More information will be shared 9/1/24.
- Canvas Assessment Package: Grade 5, 5A, and 5G/T assessments will appear in your math Canvas teacher course (shell/blueprint). Directions for how to use them will be shared 9/1/24.
- Grade 5 G/T Paper/Pencil Assessment Package Links to an external site.
- Measurement Topic Assessments: These are required assessments and provided for each measurement topic within each quarter. They are included in the Grade 5GT Assessment Package below. This assessment package is available electronically through Canvas or in paper/pencil versions. Arrangements are being made for these assessments to be printed and delivered to schools. More information will be shared 9/1/24.
Measurement Topic Assessments are Mandatory beginning in the SY 24-25. See FAQ document regarding MT assessments here. Links to an external site.
Alignment Document Links to an external site. to understand suggested timing on when to give which assessment during the quarters.
General Assessments for All Levels
-
-
Grade Level Readiness Assessments: These assessments can be useful in determining student understanding of foundational number concepts needed for grade level instruction. They should be administered in an interview or small group setting.
-
| Grade 4 | Grade 5 | Grade 6 |
|---|---|---|
| All Materials PDF Links to an external site. | All Materials PDF Links to an external site. | All Materials PDF Links to an external site. |
-
- Teacher-Selected Assessments: Each standard page in your Canvas curriculum course has a tab (independent practice) containing options for formative assessment to determine student understanding.
- Teacher Observation: Each lesson you teach offers valuable insight into how students think and reason about mathematics. This observational data is as important as any of the resources noted above. It should play a role in determining student understanding.
CogAT Results Math Placement Guidance
The following guidelines may assist as you determine next steps for students based on CogAT test results and the placement process.
CogAT Results Elementary Math Curriculum Guidance Links to an external site.
Community and Identity
Math Identity
A mathematics identity is the deeply held belief or disposition one has about math and their ability to do math. Our role as teachers is to cultivate and nurture positive math identities. Our work is to make sure we continually learn about who are students are as individuals and how they see themselves as mathematicians. There are a variety of ways to learn about students' identities. Some of those activities are baked into module 1. Others are part of the community activities below.
JOURNAL PROMPTS about DISPOSITION
Remember that these works shouldn't be graded. Grammar, spelling, and punctuation shouldn't matter either. Instead, leave a response to students to let them know you read it and you hear them. To manage work load, rotate the entries you read. Keep in mind this isn't something you need to do daily. Journal prompts could be done once a week or once every two weeks.
Below are a collection of prompts from Productive Math Struggle (Corwin, 2020) for you to choose from but feel free to create your own.
|
|
STUDENT SURVEYS
Surveying students about their thoughts and beliefs about mathematics provides valuable insight to guide your work. Surveys can be given at various times during the year to see how students are growing and changing. A scale response works well and for young students you might choose to use a smiley face, a frowny face, and a neutral face. Below are questions you might include in your survey. They come from Productive Math Struggle (Corwin, 2020). Questions on the left are intended for younger students and questions on the right are intended for older students. You can add to or change questions as you see fit.
|
|
DEAR MATH LETTERS
Engage your class in a conversation using the prompts below (from Dear Math: Why Kids Hate Math and What Teachers Can Do About It by Strong and Butterfield). Then ask students to write a "Dear Math" letter. Depending on the grade level, provide appropriate writing supports. The goal is to encourage thinking about/talking about math identity and provide teachers with insights about how their students feel about themselves as mathematicians.
- Tell me about a time when you felt successful in math class? What happened?
- Tell me about a time when you struggled in math class? What happened?
- When your friends talk about math, what do they say or do?
- What is one way math has helped you grow?
- What can you thank math for?
- How would you change math classrooms?
- What would you like more of in math class?
COMMUNITY
A classroom community is built and maintained throughout the year. A nurturing classroom community is one built on trust and safety. Students share their ideas freely and listen to the ideas of others. They work collaboratively. They know and respect one another. The activities below can be used to learn about student identity while also building toward a stronger math classroom community. You can use these activities at any time during the year.
Number Quilt: A number quilt gives students an opportunity to show who they are through numbers. Each student writes a number on a small rectangular piece of colored construction paper. They attach it to a larger piece of white construction paper with a line of glue at the top. The piece of paper can be lifted up to reveal a picture or words that describe what the number represents about the student.
My Favorite Number: Students can create name tents and add their favorite number to the name tent. On the inside, students write about why the number is their favorite. Students then use the name tents to introduce themselves to new partners and groups.
Myself in Numbers: Students identify numbers that describe them and record them on a lap board or something similar. Classmates guess what the numbers might represent about the student. The student shares and classmates earn points for how many guesses they got right.
Picture is Worth 1,000 Numbers: Students bring a picture from home or draw something about their lives. Students then use numbers to describe the picture and why it (or the topic) is important to them.
My Math Biography: Students write their math biographies. They discuss how they use math in their everyday lives. They can also discuss experiences they have had in math in the past and goals they have for working with math in the future.
My Math Superpower: Students create themselves as a "math superhero." They identify what they do well in math and announce those as the superpowers of their superhero selves.
My Summer in Numbers: Students use numbers to describe themselves and their experiences over the summer. This activity could be easily modified to describe family events, holidays, and so on.
Computation Strategies
By the end of G/T-4, students are expected to fluently multiply multi-digit whole number using the standard algorithm (5.NBT.5) and to divide whole numbers dividends of up to four-digit by up to two-digit divisors, using strategies based on place value and the properties of operations (5.NBT.6) as well as using the standard algorithm (6.NS.2). In addition, they are expected to add, subtract, multiply, and divide with decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (5.NBT.7) as well as applying the standard algorithm to fluently compute with decimals (6.NS.3). This page describes and illustrates addition, subtraction, multiplication, and division strategies that will help your students become flexible, efficient, and accurate computers.
Exploring Strategies Based on Place Value and Properties of Operations
Closure
The linked page provides descriptions and videos of closure activities. “Closure in a lesson does not mean to pack up and move on. Rather, it is a cognitive activity that helps students focus on what learned and whether it made sense and had meaning.” How the Brain Learns Mathematics (2007) P. 104.
Daily High-Quality First Instruction
High-quality first instruction is an expectation for each and every student, each and every day. It nurtures student identity, agency, and self-efficacy. First instruction creates an opportunity for students to develop conceptual understanding, build procedural fluency, and apply their learning to solve authentic problems. High-quality first instruction is grounded in evidence-based, effective teaching practices (NCTM, 2014). High-quality math instruction should occur everyday for 75 minutes. The link below outlines the expectations and provides related resources.
Extended Tasks and Learning Walls
Extended tasks apply mathematical concepts to the real-world. A collection of extended tasks are linked below. It is also noted when these tasks best align with the course scope and sequence.
Learning Walls help students develop conceptual understanding through the use of inquiry. The page linked below provides an overview of and suggestions on implementing and using Learning Walls.
Famous Mathematicians
Everyone needs a mathematics hero. Learning about famous mathematicians can inspire our students. Learning about their challenges, fears, and achievement can support our students as they face challenges. It can also help students identify what they can do with mathematics.
The Famous People Links to an external site.
Famous Mathematicians (Links to an external site.) Links to an external site.
Greatest Mathematicians of the Past (Links to an external site.) Links to an external site.
The Story of Mathematics (Links to an external site.) Links to an external site.
Famous Mathematicians (Links to an external site.) Links to an external site.
Hidden Figures (Links to an external site.) Links to an external site.
Family Communication and Support
The linked page provides to access to a variety of resources for supporting parents.
HCPSS Family Math Support Center: This site provides information about grade level topics, vocabulary, practice materials, and related videos.
Math Milestones: These video clips give parents an idea of what mastery of important concepts looks like at each grade level.
Homework
Homework is an opportunity for students to practice skills and concepts.
HCPSS Homework Guidelines Links to an external site.
Homework Considerations
- It should be a task that students can complete independently.
- Academic grades should not be jeopardized because of incomplete homework.
- Homework should be purposeful rather than "just something to do." (Vatterott, 2009)
- The task is as important as the time required for homework. In other words, quality is greater than quantity. (Vatterott, 2009)
Maximizing Instructional Time
Instructional time is lost when too much time is dedicated to homework review and/or correction. Time to discuss problems can happen in different ways. Mathematics engagement and momentum can also be lost when the class opening is dedicated to homework. Discussing homework may be a small portion of small group discussion.
It may also be a part of independent time. Strategies for going over homework during independent time include:
- Post answers to questions and tell the students two answers are incorrect. Ask which ones. Share their thinking with a partner.
- Working with partners, students share answers for particular questions and explain how they found solutions. (Or problems of their choice.)
- Students self-assess by reviewing homework answers displayed on the board or with a completed copy.
Other options include:
- Collect the homework and correct it outside of class.
- Have a co-teacher, paraeducator, or volunteer record completed homework.
- Ask students to vote on a problem they would like to discuss.
- Go over a small subset of the problems. This shouldn't take place during the first five minutes of class.
Reflecting on Homework
Teachers or students can use homework for feedback. Students may reflect on problems or homework as a whole in the general categories below (primary options in parenthesis).
- Got it/understood ("smiley" face)
- Sort of got it/not sure ("straight" face)
- Didn't get it/totally lost ("frowny face") (Vatterott, 2009)
Other ideas for student self-reflection include:
- What questions/undertaintities do you still have about ____?
- What was most effective in ____?
- What was least effective in ____?
- How difficult was ____ for you?
When reviewing homework during independent time, students might record
- item number
- reason missed
- correction
Homework Resources
Resources are available under the "Independent Work" tab on each standard page. These resources can be adjusted to meet the needs of your students. Playing math games or practicing math facts are also good choices for a homework assignment.
Vatterott, Cathy. (2009) Rethinking Homework: Best Practices That Support Diverse Needs
Instructional Level Identification
A mathematics instructional level is determined by a student’s performance. Performance should equally measure concepts, procedures, and application of mathematics. The Instructional Level Guide provides information about which indicators should be used to determine a student's mathematics instructional level. The Instructional Level Change Form can be used to document and report a change in an individual student's instructional level. Contact your Mathematics Support Teacher or the Elementary Mathematics Office with questions.
Instructional Level Identification Guide Links to an external site.
Planning for Mathematics
what is collaborative planning in Elementary mathematics (HCPSS)?
Collaborative planning can be done with or without a Math Coach. Participants discuss upcoming math standards and make purposeful selections of instructional material.
Collaborative planning…
- Is intentional and purposeful.
- Is a shared responsibility.
- Is time to discuss upcoming standards and learning targets, that were reviewed by all before the collaborative planning meeting.
- Confirms the meaning of the mathematics inherent in the standard and considers “what comes before” and “what comes after” within the grade and across grades.
- Identifies and selects tasks that promote student reasoning and that are aligned with the established mathematical goal(s).
- Is a time to do the selected task.
- Is an opportunity to anticipate student responses and misconceptions.
- Discusses which representations and strategies are appropriate to highlight and what connections students might make between representations.
- Identifies what manipulatives may be needed to support student understanding.
- Considers which grouping structure to select based on the task and purpose of the day.
- Includes discussions about purposeful questions to ask students in order to advance students’ reasoning and sense making.
- Complements provided timelines by considering evidence of student progress and understanding
- Can include professional development “shorts” provided by MST to enhance understanding of standards.
Collaborative planning is not...
- Providing all of the activities to the entire group by one individual (ITL, Math Coach, or any teacher)
- Grabbing activities or finding worksheets so that copies can be made
- Filling in a plan book for five or more full days of instruction. The process (in column to left) takes time.
- Dividing to conquer the task where one person plans all the homework for the team, one person plans all the routines for the team, or in which each person plans a different day of the week.
planning for task implementation
Planning for a task is different than selecting materials for copying and preparing. There a few steps that we may not be familiar with. These steps are critical for being well-prepared for a rich mathematics class. Keep in mind that none of these steps should take more than a few moments but can have far-reaching implications on the orchestration and intentionality of a lesson.
Do the Task Yourself
Take a few moments to complete the task ourselves. This helps us consider how we would prefer the task to be solved. It also gives us an idea about possible missteps or even shortcuts that students might take.
How Might They Solve It?
After doing the task, we have a sense of what they might do to solve the problem or complete the task. Anticipating what they might do helps us consider what questions to ask, what strategies might be highlighted, and what representations might be used.
What Might They Misunderstand?
Learning mathematics is grounded in making mistakes and proving that misconceptions are just that. Doing the task helps us anticipate what students might do. It also helps us consider what misconceptions they might have and how they might be countered. Misconceptions and errors are not a bad thing. They can be leveraged to develop a deep understanding of the mathematics.
What Misconceptions Might I Have?
We all have perspectives of mathematics. It's possible that as adults we have incomplete thoughts about concepts or possible misconceptions. This usually results in a focus on procedure so that the misconception or misunderstanding doesn't arise. This is completely natural. It's important to check in with MSTs and colleagues to confirm ideas about upcoming standards. This is just part of the importance of collaborative planning.
What Will I Circle Back To?
What in the task will I use to circle back to other ideas? What connections will I make to other ideas that students have already learned? Like any other content, mathematics is not an isolated collection of ideas. Each task and activity is an opportunity to make connections. Students who make connections have a deeper understanding that they can apply and transfer more easily.
A lesson Plan organizer
Planning for mathematics has many parts. The lesson planning templates provided below are recommended but not required. The template aligns with the concepts of Understanding by Design in that we plan with the end in mind. The template also helps teachers think about what students might do during the mathematics lesson and plan for questions to react to student thinking and guide the discussion. The electronic version can be copied into your Google account and completed there.
Daily Planning Organizer Links to an external site. (electronic version)
Daily Planning Organizer Links to an external site. (print version)
This template focuses on the planning of the mathematics. It is not the traditional "teacher-centered" form. Instead, it asks for us to think about intended outcomes, assessment of those outcomes, task selection, and anticipation of student understanding. It also asks for teachers to select both a routine and a structure for the class that day. The upper righthand section of the template prompts for "teacher moves." Those actions are general academic strategies or approaches for introducing, managing, or engaging students in the task or discussion. Some moves are listed below. Not all are intended to be recorded. Teachers should highlight the big ideas that need to be kept in mind. The moves include:
Teacher Moves:
How will I
- Give directions or introduce the task?
- Scaffold student support?
- Monitor student thinking during the task?
- Work or visit with small groups during the task?
- Facilitate discussion?
- Record or chart ideas?
- Sequence student work?
Talk Moves:
How will I use
- Think, Pair, Share?
- Turn and Talk?
- Use wait time?
- Whole group or small-group discussion?
- Partner talk?
- Revoicing (“So you’re saying that it’s an odd number”)?
- Student revoicing (students revoicing ideas of classmates)?
- Prompt for further participation or discussion. (“Would someone like to add on?”)
Problem Solving
Problem solving is not an isolated activity. It doesn't occur every Friday. Instead problem solving is a skill that favors every mathematics lesson. Problem solving is more than just one-step word problems. Problem solving should feature rich tasks, authentic purposes, and multiple ways to be solved. This linked page offers suggestions and resources for developing your students' problem solving capabilities.
Progressions
Mathematics is not learned in isolation. It is an interconnected collection of skills and concepts. Each standard builds on previous learning while contributing to future learning. This link connects to progressions developed by the Common Core writing team.
Routines
Routines are a desirable way to begin math class. They develop number sense by connecting critical math concepts on a daily basis. They should be used in place of a traditional warm-up or reviewing homework. This linked page provides descriptions, examples, and videos of routines.
SBIR (Standards Based Instruction and Reporting)
Measurement Topics and Instructional Standards Crosswalk
This file aligns instructional standards with the measurement topic that they roll up to. It also identifies the instructional quarter that each measurement topic is reported.
Mathematics Measurement Topics Crosswalk Links to an external site.
Report Card Comments Bank by Quarter
This is the collection of prepared report card comments in Synergy. Teachers can use these comments and/or write their own. Reminder: A comment is needed for students learning standards from the next grade.
Mathematics Report Card Bank Links to an external site.
SBIR Canvas Course
This course houses a collection of SBIR information including directions for using the Canvas grade book, SBIR FAQs, and other resources.
SBIR Family Canvas Course
This course houses a collection of resources to help parents understand Standards Based Instruction and Reporting.
SBIR CANVAS SBIR Family Canvas Course
August SBIR Professional Learning Session
Professional Development from August 19th Links to an external site.
How can I collect evidence of student understanding
- Observe students during instruction, while they use centers, or while they play games
- Evaluate written work
- Rubric for Tasks Links to an external site.
What can I Use to collect evidence of student understanding?
- Any item found on the Independent Work tab can be used to collect evidence
- Teacher-created items
- Anecdotal notes
- Observation of students working on centers and games from the Independent Work tab
- Items from Quarterly Measurement Topic/Canvas assessments that align to this standard
Reminders
- You do not need to grade all of the evidence you collect.
- If a student's work is inconclusive, get more evidence of the individual. You don't need to reassess the entire class.
- Some evidence with be evaluated using the rubric. Other evidence will use percentages.
- The assessments provided by the mathematics office should not be the only evidence used for grading and should not be valued more greatly than other data points.
- Report card comments: Students learning standards from the next grade level must have a comment that stating that. Students with an L must get a comment about their performance in that measurement
guidance for determining if students should be instructed on the next grade level's mathematics standards
The following document provides guidance for determining students’ instructional level/which curriculum is appropriate in mathematics. All students should receive instruction at their chronological grade level at a minimum. This document provides guidance in determining if a student is better matched with the next grade level curriculum.
Guidance for determining appropriate instructional math standards Links to an external site.
Structures for Math Class
The models on the linked page outline options for structuring your mathematics class. Your mathematics class is not required to use the same model everyday. The model for each day should be selected intentionally to support the needs of your students and the goals of the lesson.
Suggested Math Materials
The linked page offers a list of suggested and additional materials for this specific grade level curriculum.
Standards for Mathematics Practice
The Standards for Mathematical Practice identify the behaviors of mathematically proficient students. The "practices" are not taught in isolation. They are developed intentionally through mathematics instruction. This page identifies student and teacher behaviors of these practices and also provides resources for developing these habits of mind in your students.
Student Learning Objective (SLO)
Reminders about mathematics SLOs.
- Your SLO is determined by you and your principal.
- It is recommended that the SLO focuses on a major work or big idea from a grade level.
Recommended Option 1:
Select a Major Work (topic) from the appropriate mathematics course. Those assessments are linked below and within each grade level course. Note: Major Works Assessments are not available for grade 4 G/T and/or grade 5 GT due to the compaction of grade level standards in these courses.
Recommended Option 2:
Use a math practice rubric with an appropriately aligned task.
Recommended Option 3:
Select a Measurement Topic from your grade level's report card and use the aligned Measurement Topic Assessments from your grade level content. For example, if you select Understanding of Addition in grade 1 you would then use the measurement topic assessments aligned to that topic. NOTE that this would include multiple assessments to pre-test.
Walkthrough Tools
The folder linked below includes walkthrough tools for administrators and teachers to use when visiting mathematics class. They are designed to look for evidence of high-quality mathematics instruction. These tools are provided as examples. Schools may select the tool that aligns most closely to their School Improvement Plans and/or professional learning activities. Users may choose to focus on a select number of practices for the Effective Teaching Practices tool or the Standards for Mathematical Practice (SMP) tool.