Robyn Schlichter is currently the math coach for Livermore Valley Joint Unified School District. The purpose of this blog is to provide information and resources for teachers implementing the Common Core State Standards.
I seen a rekenrek before, but have no clue what I would do with it. Yesterday I was lucky to meet a primary math coach from a neighboring district and she shared so many ways to use a rekenrek.
What is a Rekenrek?
Resources:
Math Learning Center Apps (Apps for iPad/iPhone & Web-Versions):
The Math Learning Center has free apps and online versions of their apps available for many math manipulatives. Virtual manipulatives can be an easy way to have access to a variety of concrete models for mathematics. The complete list can be found here. Each virtual manipulative has a tutorial video, so check it out and explore!
The Number Rack has rows of moveable, colored beads that encourage learners to think in groups
of fives and tens, helping them to explore and discover a variety of
addition and subtraction strategies.
This virtual version of the manipulative is an open-ended educational
tool, ideal for elementary classrooms. (from Math Learning Center catalog).
The one-minute tutorial video here.
The web version is available here.
The Number Frames app or web-version from Math Learning Center allows you to explore number frames: 5-Frames, 10-Frames, 20-Frames or even 100-Frames. You can use various counters and colors to support the addition and subtraction strategies you are working on. The calculator allows you to write equations to match your number frame model.
Check out the one-minute tutorial video, download the app, click here.
To open the web-version or to learn more, click here.
In a recent training with Elementary teachers, I shared with teachers the importance of using manipulatives as well as tips and tricks for managing manipulatives. Our district has adopted a math curriculum, Pearson Investigations3, that uses manipulatives on a regular basis. The importance of manipulatives is crucial to students exploring math and discovering the patterns and rules of mathematics. In general, there is very little attention given to why and how to use manipulatives, and any attention to these topics is typically very brief. I designed this workshop to provide some information on why to use manipulatives and then delve into the practical side of it - how to organize manipulatives for daily math instruction. Understanding the "why" is very important and a great motivator to continue to persevere to find solutions to any problems that might occur with organization or management.
A note before we continue ... this workshop was originally done through YouTube Live and you can watch the recording here. I am continuing to explore ways to deliver professional development for our teachers that make content easy to access. It might also help the problem of travel time after school :) Also, I used a HyperDoc to deliver the content and to allow teacher reflection. The lesson design for this workshop was an "Explore - Explain - Apply" design. I will include the "apply" questions in this post as a way for you to reflect on how content can be incorporated into your classroom.
Workshop Objectives:
Teachers will understand the role of manipulatives and why it is important for students to use manipulatives to enhance math learning.
Teachers will develop a plan for managing classroom math manipulatives that includes procedures for using manipulatives appropriately.
Teachers will see examples of ways to organize manipulatives in the classroom and decide which structures will work for their classroom.
Explore the Problem
To narrow down our discussion, I organized the topics into 3 problems that teachers face when using manipulatives:
Sometimes I feel like our instruction time is used better to practice the standard algorithm. Why should we use manipulatives to teach math?
Often it is a hassle to get out the manipulatives, as there is so much time used to get them out and put them away. It is also challenging to have students constantly playing with the manipulatives. How do I make sure our math time is productive when we use manipulatives?
Sometimes I feel like math manipulatives don’t really help students understand the traditional algorithm better. How can I use manipulatives to help students have a better understanding of math?
Problem #1
Explore
"Sometimes I feel like our instruction timeis used better to practice the standard algorithm. WHY should we use manipulatives to teach math?"
Explain
Manipulatives help students make sense of abstract concepts.
Manipulatives provide students ways to test and verify ideas.
Manipulatives serve as useful tools for solving problems.
Manipulatives make learning the mathematics more fun.
Let’s Check out this video (whole group): or URL here: https://vimeo.com/157768846
Apply
Think about the concept that you are currently teaching (number recognition, addition, multiplication, etc). How can manipulatives help students understand that concept?
Extend
For more information on why manipulatives are important for math instruction, check out these resources:
"Often it is a hassle to get out the manipulatives, as there is so much time used to get them out and put them away. It is also challenging to have students constantly playing with the manipulatives. How do I make sure our math time is productive when we use manipulatives?"
Explain
Organization: There are several ways to organize manipulatives. As you consider how to make this work in your classroom, here are a few things to consider:
Things to consider:
What do you have?
When are students using them?
Individual
Groups
Location & Space
Classroom Rules & Procedures
Suggestions for Classroom Procedures:
Make sure students know the location for gathering and returning materials.
Support students in becoming responsible for their learning and the tools that they use.
Don’t have a procedure/rule that you are not willing to follow.
Teach students how each of your procedures are expectations should be carried out.
Apply
Where can your math manipulatives have a “home” in your classroom? Consider the location, whether it is a bookshelf, cabinet, or storage drawers.
What are your procedures for gathering and returning manipulatives?
Problem #3
Explore
Sometimes I feel like math manipulatives don’t really help students understand the traditional algorithm better. How can I use manipulatives to help students have a better understanding of math?
Explain
Making the connections between the manipulatives and a written method is extremely important.
Consider using questions that guide students in making comparisons and finding similarities.
How does this model look the same as this expression?
Where do you see the ____ in the model? Where do you see it in the expressions/equation?
How are these two strategies different?
How are these two strategies the same?
Use students understandings to guide your instruction and the strategies you are working on.
Apply
What learning progressions are happening at your grade level? Consider the operations that you teach and the various methods that you are using to deepen student learning. How can you provide learning experiences for students that make connections among concrete and abstract strategies?
References
Burns, Marilyn. About Teaching Mathematics: A K-8 Resource. 4th ed. Sausalito, CA: Scholastic, 2015. Print.
Fletcher, Graham. "The Progression of Addition and Subtraction." Vimeo. Https://gfletchy.com/, 4 Mar. 2016. Web. 21 Sept. 2016.
The article discusses 4 skills that are being developed in math class that can help students be prepared for any career. Check out the article and consider how you are incorporating these skills into your class.
After a lunch break and change of teachers, we experienced our afternoon model lesson. Here we continued to look at kindergarteners and how to all students to own their learning through Math Workshop. There were many similar thoughts and reflections from the morning groups of teachers.
Model Lesson: Afternoon Session
In this unit, students will be exploring measurement by developing strategies for measuring the length of an object. Students will practice recording their measurements.
Model Lesson: Kinder Unit 4 Session 1.3
Date: November 17th, 2016
Presenter: Dr. Sandy Fluck
Math Workshop (Investigations Style)
Math Workshop is designed to:
Provide students with repeated experience with the concepts being learned and time to practice important skills and refine strategies.
Provide time for the teacher to work with individual students and small groups and to assess students' learning and understanding.
Help students develop independence and learn to take responsibility for their own learning as they choose activities, keep track of their work, use and take care of classroom materials, and work with others.
Setting up the Lesson & Math Workshop
The opening and closing discussions are a critical part to the day's lesson. In this conversation, Dr. Fluck was asking students to consider how to measure the strip of paper. Students shared a few different ways:
Should they be lined up (up and down) and lined up across the strip (picture on the left)? or
Should they be lined up around the edges of the paper strip (picture on the right)?
Asking questions that guide students to think about which method might be better here is a challenging task, yet critical in allowing students problem solve.
In Kindergarten, teachers may feel the need to provide structures and support for students to engage in independent learning through Math Workshop. While grade level, class size, physical space, students population and management styles are all factors in designing a Math Workshop for your classroom, do not be afraid to give students full access to choice.
The video above demonstrates a lesson where students engaged in Math Workshop with complete control over the activities they chose for themselves. The introduction to the lesson provides the structure and expectations for Math Workshop. The picture to the right shows the students the 4 options for activities during workshop time:
Counting Jar
Measure paperstrips A, B, & C (with craft sticks)
Measure footprints (with snapcubes)
One the concepts the students will explore through the Unit is measuring various things using different units of measure - some big some small. Students will be ask to think about how many small units it takes compared to how many big units it takes. Which will take more units and why?
Asking students the question early in the unit allows students to begin to think about it and consider it as they gain more and more experiences measuring different items.
Classroom Layout & Manipulatives Management
Every classroom is different in regards to layout and space. However, consider how you can place manipulatives so that students can gather and cleanup manipulatives themselves. For the model classroom, the materials were either on a table or at the front of the classroom. Students selected their materials and were able to work either on the carpet (Counting Jar and measuring footprints ) or at the table (measuring paper strips). In addition, you may consider using various tubs, cups, plastic bags or bins to store manipulatives and materials that allows students self-manage their materials.
Measuring Footprints
Students used snap cubes to measure pre-drawn footprints. Snapcubes were located in one large bin in the middle of the carpet area for everyone to use. Students collected a footprint paper from the table and sat on the carpet to measure and record.
Monitoring Students
The teacher's role during math workshop is to walk around and monitor student progress. Many Investigation sessions provide Assessment Checklists or questions to guide teachers in what to look for. There is a careful balance between guided students and allowing students to make discoveries on their own.
The picture to the right shows students measuring their own feet (which they did earlier in the week). However, today students needed to measure pre-drawn footprints that students had brought in from home.
While you may check for understanding before releasing students to Math Workshop time, there may be a need to check-in with each group or "station". Guiding students to stay on track to the goal of the activity may involve careful questioning so that students problem-solve themselves, or you may need to correct off-task activities.
The Counting Jar
The Counting Jar is a very important classroom routine that support students' Number Sense. While Number Sense is a cognitive skill that is related to brain development, young students need plenty of experiences and a variety throughout the year to target where they are at developmentally.
Students are working on a variety of skills that impact Number Sense:
one-to-one correspondence
number conservation
number sequence
cardinality
subitizing
When students are counting objects from the counting jar, can they:
count in number sequence
count each object once (1:1 correspondence)
know how many (total)
represent the quantity with a numeral
represent the quantity with the same number of a different object
Measuring and Recording
Keeping track of student sheets can be a lot of work. There may be piles of papers everywhere is your classroom. What might be some solutions to managing all the student papers? Here are a few suggestions. Consider what might work in your classroom and tweak it to fit you and your students.
Possible ideas:
using a student folder
"station" bins for done work
math notebook
Lesson Closure: The Discussion
Probably the most important part of the lesson is the closure discussion. Here students share what they noticed. As mathematicians, we are always looking for patterns. What did you notice about today's math investigations?
It may also be a time to just listen. Listen to what your students notice about the activities. Used this information to inform how to move forward with tomorrow's math time. It may guide you in what the emphasis might be in your work.
In the discussion, you can also gather students insights and expand on them to provide students the formal understanding for the lesson.
There are a variety of purposes to the discussion time. Use the "Ongoing Assessment Questions" and the "Discussion Check-in" to guide your conversations. Each session included these two components.
With a new adoption and and shifting our teaching practice to inquiry-based learning, there is so much for us to learn as teachers. Luckily for our Kindergarten teacher, we were able to have a consultant come in to model a lesson. This is not something that the publisher deos regularly, however, due to some not-up-tp-par experiences in our Professional Development day, the publisher agreed to do this for our district. And WOW! It was amazing! Sometime seeing really is believing.
Here I am going to share some the major ah-ahs from the day, including videos and pictures. Hopefully this will give you an example of what Math Workshop can look like in your classroom and you can take it and make it your own! Ok, let's get started!
Model Lesson : Morning Session
In this unit, students will be using a variety of manipulatives for learning about 2-D shapes. Organizing the manipulatives and having students own their learning through Math Workshop can be a challenge. Below are pictures and videos that show possible ways to organize the manipulatives and MathWorkshop time with students.
Model Lesson: Pearson Investigations3 Kindergarten Unit 3 Session 1.4
Date: November 17th, 2016
Pearson Trainer: Sandy Fluck
Playdough Shape Mats
As a scaffolding technique, you can use these mats for students to form shapes with the playdough. By providing the outline of the shape, students can match the playdough either as an outline or filled in shape.
Removing the mat provides a different skill. This forces the student to form the shape without the outline.
Math Workshop (Investigations Style)
Math Workshop is designed to:
Provide students with repeated experience with the concepts being learned and time to practice important skills and refine strategies.
Provide time for the teacher to work with individual students and small groups and to assess students' learning and understanding.
Help students develop independence and learn to take responsibility for their own learning as they choose activities, keep track of their work, use and take care of classroom materials, and work with others.
Math Workshop menu using pictures
In Kindergarten, teachers may feel the need to provide structures and support for students to engage in independent learning through Math Workshop. While grade level, class size, physical space, students population and management styles are all factors in designing a Math Workshop for your classroom, do not be afraid to give students full access to choice.
The video above demonstrates a lesson where students engaged in Math Workshop with complete control over the activities they chose for themselves. The introduction to the lesson provides the structure and expectations for Math Workshop. The picture to the right shows the students the 4 options for activities during workshop time:
Counting Jar
GeoBoards
PlayDough
Pattern Blocks
Classroom Layout & Manipulatives Management
Every classroom is different in regards to layout and space. However, consider how you can place manipulatives so that students can gather and cleanup manipulatives themselves. For the model classroom, the pictures show a table where all the math manipulatives were located for that day. Tubs, cups, plastic bags and bins are all used to help students self-manage their materials.
Student taking their bag of playdough
Each student has an individual ziplock with playdough. Names are written on the outside of the bag.
Geoboards and cups of rubberbands
Paper cups are used to store the rubber bands for the GeoBoards. Students take a cup and a GeoBoard to their table to work on creating shapes.
Table used for gathering, seleting, and return supplies
Remember, there is no right way or wrong way to set-up your classroom and your math materials. Each teacher has a personal style and classroom management routine that will influence how classroom materials are handed out. Consider organization strategies that allow students to take ownership of classroom math manipulatives. Here are a few suggestions:
Location: Math Bookshelf or Cupboard
Storage: bins, buckets, ziplocks, etc. You can even use clear food containers that can be donated by families.
My District is using Pearson Investigations3 math instructional materials. One component of the daily lessons is the Classroom Routines or Ten-Minute Math time. Classroom Routines occurs in Grades 3-5, while Ten-Minute Math is for Grade K-2. Even though the title is different, some of the routines are the same and the purpose of this time is consistent across the grade levels. Let's take a look at why Classroom Routines/Ten-Minute Math is an essential part to our daily math lesson and a few strategies that will support our routine time is really 10 minutes (and not turn into a 30 minute mini-lesson).
Overview of Classroom Routines/Ten-Minute Math
Adapted from Implementing Investigations:
Classroom routines are a critical piece of the review and practice that is built into the investigations curriculum. These short, 10-15 minutes activities provide daily practice and review that support and balance in-depth work of each curriculum unit. They are introduced as a session activity and are then used outside of math time (e.g. during morning meeting, just before or after lunch or recess, or at the beginning or end of the day) or integrating into the math lesson as the first 10 minutes of the 70 minute math block. Classroom routines offer ongoing skill building, practice, and review to support students understanding and retention key mathematical ideas, reinforcing the work of previous units and helping students increase the repertoire of strategies for mental confrontation and problem-solving.
Let's take a quick glance at the various routines across the grade levels.
Classroom Routines in Investigations3
Additional information about Classroom Routines and Ten-Minute Math can be found in Part 4 of the Implementing Investigations manual.
Classroom Routines
Ten -Minute Math
Kinder
Gr 1
Gr 2
Gr 3
Gr 4
Gr 5
Attendance
Build It
Fact Fluency
Closest Estimate
Closest Estimate
Closest Estimate
Calendar
Quick Images
How Many Pockets
Counting Around the Class
Counting Around the Class
Guess My Rule
Counting on the Number Line
Start With/Get To
Quick Images
Guess My Rule
Practicing Place Value
Order of Operations
Story Problems
Tell a Story
Today’s Number
Practicing Place Value
Quick Images
Practicing Place Value
Today’s Question
Time
What Time is it?
Quick Images
Quick Survey
Quick Images
Today’s Number
Today’s Number
Today’s Number
What Time is it?
What Time is it?
You can see from the table that there are some routines that are done at each grade. This consistency supports students as they engage in the routine again and again with deeper content as the move from one grade level to the next. Some of the routines are common math routines that are discussed in other instructional resources. For those familiar with Number Talks: Helping Children Build Mental Math and Computation Strategies, the routine Quick Images will be familiar. While investigations3 takes a slightly different approach to Quick Images, it is perfectly fine to adapt the routine for your students as use both approaches. A couple of other resources that I really love for the K-2 classroom, is the It Makes Sense series. There are some routines describe in these two books that are similar to the routines we are using in Investigations3.
Certainly it is not necessary to have these books in order to implement your Classroom Routines/Ten-Minute Math, but if you have these available or you are familiar with these books, go ahead use them! One of the main differences between the approach in these resources and the Classroom Routines/Ten-Minute Math from Investigations3 is using the routine as pure mental math. One of the resources that I think is really useful is the hand signals. These hand signals allow for students to participate in mental math while informing you, the teacher, where they are at in their thinking process. Using thumbs up, thumbs sideways, and showing the number of fingers to match additional strategies communicates whether students are done, need more time, or have more than 1 strategy. Click here: Hand Signals PDF
