More Number Talk Ideas – Part 2

by C. Elkins, OK Math & Reading Lady

As I mentioned in my last post (More Number Talk Ideas – Part 1), there are many ways to conduct Number Talks with your students. The last post focused on Picture Talks and Which One Doesn’t Belong (WODB). This week I am focusing on Estimation Mysteries and Data Talks.

Esti-Mysteries

Steve Wyborney has been super gracious to share his math estimation mysteries with educators via the nctm.org blog and through his website: https://stevewyborney.com/ 

What are they?  Each esti-mystery features a clear container with identical small objects (cubes, dice, marbles, manipulatives, etc.). Students estimate how many are in the container, then proceed through 4-5 clues revealed one at a time in a ppt format.  Clues give information dealing with number concepts such as even/odd, less than/greater than, place value, multiples, prime, composite, etc. With each clue, students can then revise their estimate to try to eventually match the actual amount revealed on the last slide. Different clear containers are used with each mystery to include ones with irregular shapes.

It’s really interesting for students to share how they arrived at their estimate, to list possible answers, then defend their choice.  And of course, the rejoicing when/if their estimate matches the revealed amount!

Data Talks

You may have heard of the youcubed website (https://www.youcubed.org) which is partially commanded by well-known Stanford mathemetician Jo Boaler and her co-hort Cathy Williams. You will be amazed at all of the math resources and task ideas for all grades at this site. I witnessed another webinar hosted by these scholars regarding the increased need for data science. While professionals surveyed rarely actually use the algebra, geometry, and calculus learned from high school or college courses, there is definitely an increase in the need for data science / statistics as noted in almost everything we do. So youcubed has made it their mission to ramp up data science resources. One already in the works is “Data Talks” which provides some real-world, interesting, thought-provoking data presentations ready for class discussion.  The link is right here:  https://www.youcubed.org/resource/data-talks/

You will find graphs and tables of all types (some very creative ones), with topics such as these:

  • Steph Curry’s shooting and scoring % shown on a basketball court diagram
  • Social media use
  • Paper towel hoard in 2020
  • Dice combinations

Before diving into the data presented, get students to notice first . . . “I noticed . . .”  and follow analysis with “I wonder . . .”  The “I wonder” questions promote ideas about trends and change in data.  Here’s a sample graph regarding possible outcomes when adding 2 dice (graphic from google, not youcubed.org):

Possible noticing and wondering:

  • I noticed the graph goes up and then down symmetrically.
  • I noticed there are 11 possible sums using 2 dice.
  • I noticed the bar for 7 is the highest.
  • I noticed numbers on the left side go up by .02 each increment.
  • I wonder why 7 is the highest? What are ways to roll a sum of 7?
  • I wonder what a graph would look like when actually rolling 2 dice numerous times? Will it be similar to this one?

I highly encourage you to check these out! I will add the sites to my resource list (top bar of my blog) for easy access.

Till next time . . .  Cindy

 

More Number Talk Ideas – Part 1

by C. Elkins, OK Math and Reading Lady

I’m back after taking a couple of months off from blogging! I know some of  you are already back at school, while others will be starting this coming week. I wish the best with all the uncertainties that still lie ahead. BUT most of you are back in the classroom this year, which is a good thing, right? 

I am a big advocate of implementing Number Talks as part of a short daily math routine. Most of my previous number talk posts have focused on students sharing strategies for solving problems involving number strings and using known problems to stretch for new problems (such as 3 x 4 and then 30 x 4 or 10 + 8 and then 9 + 8).  Today I would like to start a two-part post about other good quality number talk options which are also designed to elicit critical thinking.

  • Picture Talks
  • Which One Doesn’t Belong (WODB)

Next post will be these two:

  • Esti-Mysteries
  • Data Talks

Tips for Implementing:

  1. There are multiple ways to interpret, so students can participate at different levels.
  2. Project them on a large screen, and allow writing on it to capture the thinking process.
  3. A great question to start with is, “What do you notice?”
  4. These are great to share with a partner before discussing with the whole group.
  5. You may need to assist students with verbally explaining their thinking. Summarize so everyone understands.
  6. Relish the chance to introduce or review new vocabulary.
  7. Design your own, and have students create some as well.
  8. Be amazed at the many different ways to interpret these!

Picture Talks

This involves the use of pictures of objects with the purpose of telling how many and how they were counted (simiar to dot cards, but actual photos of objects arranged in rows, arrays, groups, etc.). A terrific way to practice subitizing, doubles, near doubles, equal groups for multiplication and division, fractions, as well as create story problems with them. Great questions for these picture talks:  How many? How did you see them?

Many of them can be found on google images, but a good resource is via Kristen Acosta.  I participated with her on a recent webinar and was hooked. I have tried many of these with my Zoom online students and they enjoy them because there are multiple ways to analyze a picture to determine how many.

  • This is Kristen Acosta’s website. She has posted her photo images free, although you may need to subscribe to access them. She also has other math treasures on her website!  She has a few using egg cartons, which inspired me to go crazy and make my own photos. Feel free to use these below, or take your own! https://kristenacosta.com/number-talk-images/
  • Char Forsten is well known in the Singapore Math world. I have had this book for many years and love it! It is great for PreK-2nd grade. What’s inside? Nursery rhymes with pictures that are full of math content. Suggestions for questions to help students notice the pictures to find number bonds. Other photographs you can place under your document camera to project as you discuss. The book is rather expensive, but I found the digit version which is $15.
  • Math Talk by Char Forsten (Digital copy for sale by sis4teachers.org)
  • Math Talk by Char Forsten & Torri Richards (Amazon)

Example of different ideas students might have on how to count this:

Which One Doesn’t Belong?

Inspired by the book (or vice-versa), you will see 4 images, numbers, letters, shapes, graphs, etc. To elicit critical thinking, the goal is to have your students select one of the images and tell why it doesn’t belong with the others. BUT, there are many possible responses — as long as the student can explain their reasoning. Follow some of the tips above and have fun exploring all of these free ready-made WODB images!

Image 1 thoughts to get you started:

  • Top right because it’s the only one with no holes.
  • Top left because it’s the only one with no icing.
  • Bottom right: It’s pink and the others all have chocolate

Image 2 thoughts to get you started:

  • 9: because it’s the only single digit
  • 9: because the other numbers have digits that add up to 7
  • 43: because it’s the only prime number
  • 16: because it’s the only even number

WODB book at Amazon

WODB designs: Submissions by many, but website created by Mary Bourassa

Which One Doesn’t Belong: 2D shapes from Miss Laidlaw’s Classroom (FREE on TPT)

Which One Doesn’t Belong: 3D shapes from Miss Laidlaw’s Classroom (FREE on TPT)

Which One Doesn’t Belong: 2D shapes for 2nd-7th grades from Jeannie’s Store (FREE on TPT)

Google images for WODB

Here are more of my egg carton images to get you started!  Please share your experiences with these!

 

 

Multiplication using Ten Frames or Base Ten

by C. Elkins, OK Math and Reading Lady

Yes, you can even use ten frames to teach multiplication concepts! Here are my mini ten-frames with dot cards from 1 – 10:  Click HERE to get a free copy. These are helpful to use, especially if you don’t have enough tens/ones blocks . . .  or you prefer manipulatives that are slightly easier to manage. These provide a strong connection to place value, and the commutiative and distributive properties.

I recommend two sets of the cards (1-9) per student. Each set has multiple copies of the same number. They can be laminated, cut, and placed in a baggie for ease in handing out and storage.

Multiplication Examples:

  1. Single digits (basic facts): 
    • For the problem 3 x 6, the ten frame is really helpful for the student to see 3 x 6 is almost like 3 x 5 with one more group of 3 added on (by being familiar with the fact that the top row on a ten frame is 5).
    • Because of the commutative property, I know these two facts will have the same answer. But which of these below do you think might be “easier” to solve? Students don’t often know they have a choice in how they can use the numbers to their advantage!
  2. Double digit x 1 digit:
    • Use of these also provides a strong connection of place value and multiplication. Notice how students can see the breakdown on the 4 x 12 problem (4 groups of 12 = 4 x 10 plus 4 x 2). Great introduction to the distributive property of multiplication!
    • Here is where application of the commutative property also comes in handy. Which of the methods below would you rather use to solve: count by 4’s or count by 12’s? Again, show students how to use their strengths to decide which way to think about solving the problem.
    • Even though the number of total pieces might seem to be a little overwhelming, it definitely is worth the effort for a few lessons so students get a visual picture of the magnitude of the products.
  3. Here are other ways to model multiplication problems with manipulatives like base ten rods or base ten disks.

After students get practice using these manipulatives (concrete), then proceed to pictorial models to draw them as simply as possible.  This will give them a good foundation to apply to the abstract (numbers only) problems.  I always pitch for the CPA progression whenever possible!!!

I will pause a while for the summer and just post once a month until school starts up again.  Take care, everyone!  But please don’t be shy.  Post your comments, ask your questions, etc.

Multiplication strategies — Equal groups

by C. Elkins, OK Math and Reading Lady

Thanks for checking in on another multiplication strategy! The focus for this post will be on the equal groups strategy — looking at how students can efficiently use this strategy to help learn basic multiplication facts. My angle will be at the conceptual level by using concrete and pictorial methods. Be sure to see the links at the end for books and my free equal groups story cards.

Basics:

  • Instead of in array or area format, equal groups are separate groups.
  • The “x” means “groups of.”  So 3 x 4 means “3 groups of 4.”

What things normally come in equal groups? Conduct a brainstorming session. I love the book “What Comes in 2’s, 3’s, and 4’s” as a springboard. After reading the book, let students brainstorm other things that come in equal groups. See the pictures below for some more ideas. After some internet research, I also made this attached list to use (in case you or your students draw a blank): click here: Equal groups pictures and list template

Use these lists to help students generate stories about equal groups. When students can create (and maybe illustrate) their own stories, they are much better at solving problems they must read on their own. This also helps students think carefully about what in the story constitutes a “group” and what the “groups of” represents:  

  1. There were 5 bowling balls on the rack. If you count all of the holes (3 per ball), how many holes are there all together? (5 x 3). The bowling balls are the groups. The holes are what is being counted in each group.
  2. How many numbers are shown on 3 clocks? (3 x 12). The clocks are the groups. The numbers are what is being counted in each group.
  3. I bought 8 pair of earrings. How many earrings are there? (8 x 2). The pairs are the groups.
  4. Seven ladybugs were crawling on the leaves. How many legs would there be? (7 x 6). The ladybugs are the groups. The legs are what is being counted in each group.

Ways to show equal groups with objects and drawings:

  • Hula hoops (great to use these in PE class to emphasize multiplication)
  • Embroidery hoops
  • Circles of yarn
  • Dishes:  cup, bowl, plate, tray
  • Baskets
  • Shelves

Objects to use to show equal groups:

  • people
  • cubes
  • tiles
  • mini erasers
  • teddy bear manipulatives
  • base ten materials
  • food: pinto beans, macaroni, cereal, candy
  • practically anything you have an abundance of!!

Teaching concepts regarding equal groups:

  • When students are placing objects or drawing inside, do they randomly place objects? Or do they organize them to enable ease in counting? Showing students how to organize the objects in each set contributes to their knowledge of equal groups — AND it’s a big help to you as the teacher as you check on students. If the dots are randomly placed, the teacher and student must count one at a time to check. If they are organized, teacher and student can tell at a glance if the amount in each group is correct. Notice the difference below: Which ones show a student’s understanding of 9? Which ones can a student or teacher check rapidly?

  • When counting the objects or drawings to determine the product of these equal groups, are students counting one at a time? Or are they counting in equal groups (such as by 2’s, 5’s, 3’s, etc.)? If we allow students to just count by ones, then they are not practicing multiplication . . .just counting!!

Activities to practice equal groups strategy:

  1. Circles and Stars:  Roll a dice once. This is the number of circles to draw. Roll a dice again. This is the number of stars to draw inside. If played with a partner, students can keep track of their totals to determine a winner. Dice can be varied depending on the facts that need to be practiced. A spinner can also be used. (See picture at beginning of this post.)
  2. Variation of above:  Use other materials (such as those listed above).
    • Dice roll #1 = # of cups. Dice roll #2 = number of cubes
    • Dice roll #1 = # of hoops. Dice roll #2 = # of pinto beans
    • Dice roll #1 = # of plates. Dice roll #2 = # of Cheerios
  3. Write and illustrate stories:  Provide a problem for students to illustrate (example:  6 x 3 or 3 x 6).  Then each student can decide how to form the story and illustrate. I always tell students to choose items they like to draw to make their story. Here are some examples.  See some examples from former students.
    • There were 6 monsters in the cave.  Each monster had 3 eyeballs. How many eyeballs all together?
    • Six princesses lived in the castle. They each had 3 ponies. How many ponies in all?
    • There are 3 plants in the garden. They each have 6 flowers. How many flowers are in my garden?
    • I made 3 pizzas. Each pizza had 6 slices. How many slices of pizza did I make?
  4. PE Class activities:  If your PE teacher likes to help you with your learning objectives, let them know you are working on equal groups strategies. While I’ve not done this personally, I think having relay races related to this would work perfectly. For example, the teacher presents a problem and each team must use hula hoops and objects to show the problem (and the answer).
  5. Try these story books about multiplication:
  6. Equal groups story problems to solve:  Here are some story problem task cards and templates for solving multiplication and division problems using the equal groups strategy. Click to see the blog post on equal groups story problems and get my FREE set of story problem cards:  HERE

Enjoy!!  Many of you are now off for a well-deserved summer break. Use your summer time to catch up on my postings from this past year, or email me for more information. Also, feel free to comment on any article about your experience or additional tips. 

Multiplication strategies — using arrays

by C. Elkins, OK Math and Reading Lady

In the last post, I shared my thoughts about multiplication strategies using the repeated addition strategy. This time I will focus on using arrays. Do you have some arrays in your classroom? Look for them with bookshelves, cubbies, windows, rows of desks, floor or ceiling tiles, bricks, pocket charts, etc. Students need to know arrays are everywhere! It is also very helpful for students to build arrays with objects as well as draw them. This assists students with moving from concrete to pictorial representations — then the abstract (numbers only) can be conceptualized and visualized more easily. Some good materials for arrays:

  • cubes
  • tiles
  • circular disks
  • flat stones
  • pinto beans (dry)
  • grid or graph paper
  • bingo stamper (to stamp arrays inside grids)
  • mini stickers
  • candy (Skittles, M&Ms, jellybeans)

Array Basics:

  1. Arrays form rectangular shapes.
  2. Arrays are arranged in horizontal rows and vertical columns.  This vocabulary is very important!
  3. The number of objects in each row (and column) in an array are equal.
  4. Arrays can be formed by objects, pictures, or numbers.
  5. Arrays can be described using numbers:  If there are 4 rows and 3 columns, it is a 4 by 3 array.
  6. The number of rows and number in each row are the factors. The product is the total.
  7. When an array is rotated, this shows the commutative property.

Ways to incorporate arrays into story problems:

  • Desks in a class (5 rows, 4 desks in each row)
  • Chairs in a classroom or auditorium (10 rows of chairs, 8 chairs in each row)
  • Plants in a garden (6 rows of corn, 8 corn plants in each row)
  • Boxes in a warehouse (7 stacks, 5 boxes in each stack)
  • Pancakes (3 stacks, 5 pancakes in each stack)
  • Cars in a parking lot (4 rows, 5 cars in each row)
  • Bottles of water in a crate (3 rows, 8 bottles in each row)
  • Donuts or cupcakes in a box (how many rows? how many in each row)

Activities to encourage concrete and pictorial construction of arrays:

  • Start off using manilla grid paper you probably have available with the construction paper supply at your school. This will help students keep their rows and columns even. Pose a problem and allow students to use manipulatives you have available to construct the array.  If you say, “Build an array for this multiplication problem: 3 x 5,” do they know the 3 refers to # of rows and the 5 refers to the number in each row?  Starting off using this graph paper may help when students freehand their own array (to help keep rows and columns lined up and not going astray).
  • Turn the paper after building the above array to see the commutative property. Now the picture shows 5 x 3 (5 rows with 3 in each row). The product is still 15.
  • Use the manilla grid paper along with bingo dobbers to create the array.  The grids can also be completed with mini stickers (I get them all the time in junk mail) or drawings.
  • When using pictures of arrays, direct your students to always label 2 sides of the array (the rows and columns). Try to label different sides of the array so it’s not always presented in the same format.
  • Find the product:  The whole point of using an array as a multiplication strategy is to visualize the rows and columns to help calculate the product. If students create rows and columns and then just count the objects one-by-one, then this does not accomplish the objective.  Show students how to skip count using the # of objects in the rows or columns. Believe me, students don’t always know to do this without a hint from the teacher.  Or better yet, before actually telling them to do this, ask students this question: “How did you get the total number of objects?” When you pose this question, you are honoring their strategy while secretly performing an informal assessment. Then when the student who skip counted to find the total shares their strategy, you give them the credit:  “That is an efficient and fast way to count the objects, thank you for sharing! I’d be interested to see if more of you would try that with the next problem.” Plus now students have 2 strategies.
  • Use the distributive property to find the product: Let’s suppose the array was 6 x 7.  Maybe your students are trying to count by 6’s or 7’s to be more efficient – but the problem is that counting by 6’s or 7’s is difficult for most students. Break up (decompose) the array into smaller sections in which the student can use their multiplication skills.  Decomposing into rows or columns of 2’s and 5’s would be a good place to start. This is the distributive property in action – and now the students have 3 strategies for using an array!! This is a great way to use known facts to help with those being learned.Here is a link to Math Coach’s Corner (image credited above) and a great array resource: Multiplication arrays activities from TPT $5.50.  Here is my FREE guided teaching activity to help students decompose an array into 2 smaller rectangles. Click HERE for the free blank template.
  • Use the online geoboard I described in a previous post to create arrays using geobands. Click here for the link: Online geoboard  Click here for the previous post: Geometry websites (blog post)
  • Try these freebies:  Free array activities from k-5mathteachingresources.com. Here’s a sample.

     

  • Play this game I call “Block-It.” This is a competitive partner game in which students must create arrays on grid paper. Click here for a FREE copy of the directions: Block-It Game Directions
  • Relate use of arrays when learning strategies for division and area.

In a future post I will show some ways to use manipulatives and pictures arrays for double digit multiplication problems. Stay tuned!!

Multiplication: Repeated addtion

by C. Elkins, OK Math and Reading Lady

The next few posts will continue to focus on the basic multiplication concepts one at a time. This will allow the opportunity to dig deeper into the concepts we want students to understand. This one will focus on the concept that multiplication is repeated addition. These posts will be helpful to teachers introducing multiplication to students in 2nd and 3rd grade as well as those in 4th, 5th, 6th and beyond who have missed some of these basic concepts. Future posts will focus on the area (array), set (equal groups), counting, decomposing, and doubling/halving models as well as the associative and distributive properties.  Freebies below!!

Do your students know what the “times” sign means? They may hear it frequently, but not realize what it means. I like to interpret it as “groups of.”  So a problem like 3 x 4 can be said as “3 groups of 4.”

To show repeated addition, that same problem would be 4 + 4 + 4 = 12.

Repeated addition can be shown with numbers, and also with arrays and equal groups. These pictorial models are great for developing multiplication concepts (and will be topics of future posts). However, when students are presented with these models they often count the individual pieces one at a time rather than adding the same amount repeatedly. Observe your students to see how they are counting. . . and encourage counting in equal groups to promote a growth of the multiplication mindset.

Do your students apply the commutative property of multiplication? This means if the problem is 3 x 4, it can also be solved by thinking of 4 x 3 (which is 4 groups of 3 OR  3 + 3 + 3 + 3). I want students to know even though the answers are the same, the way the factors are grouped is different. When used in a story, 3 x 4 is a different scenario than 4 x 3.

Do your students practice repeated addition, by combining 2 or more numbers? See the following for an illustration of 15 x 6:

Do your students apply the concept of repeated addition to multiple digit multiplication problems as well? I have witnessed students numerous times who only try a problem one way and struggle. For example, on a timed test I witnessed a 5th grader attempt the problem 12 x 3. I observed him counting by 3’s.  He was trying to keep track of this by skip counting by 3’s twelve times (using his fingers). I could tell he had to start over frequently, thus spending a lot of time on this one problem. It became obvious he had no other strategy to try. He finally left it blank and went on. Just think if he had thought of 12 + 12 + 12. This should have been relatively easy for a 5th grader.  He also could have decomposed it to this: (3 x 2) + (3 x 10).

Do your students always go to the standard algorithm when they could perhaps mentally solve the problem by repeated addition? If the problem was 50 x 3, are they thinking 50 + 50 + 50? Or are they using paper-pencil and following the steps?

What about a problem such as 45 x 4?  Using repeated addition, is your student thinking of 40 + 40 + 40 + 40 combined with 5 + 5 + 5 + 5? This is then solved as 160 + 20 = 180.

Here are a few resources (FREE) that might help with this strategy:

Students who are able to use repeated addition skillfully are showing a healthy understanding of place value and multiplication. This strategy also enhances mental math capabilities. Conducting daily number talks are highly advised as a way to discuss multiple ways to solve a given problem such as those mentioned above. Check out “Number Talks” in my category list for more information on this. Also check out some recommended videos about conducting number talks (above black bar “Instructional Resources”).

Multiplication — Developing an understanding

by C. Elkins, OK Math and Reading lady

Are you looking for some ways to help your students learn the multiplication facts? Or ways to help them solve multiplication problems while they are in the process of learning the facts? One way is to skip count or repeatedly add the number over and over again. While this is one acceptable strategy, I see many students skip count using their fingers, often starting over numerous times. And if the child miscounts just one number in the sequence, then all of the remaining multiples/products are incorrect. Sometimes the student will write down the sequence in a horizontal row (better than using fingers in my opinion), but again – if they miss one number . . . all the rest of the numbers in their list are wrong.

What I want to show you today (in Part I of my series about multiplication strategies) are ways to relate the multiples/products in recognizable patterns which may facilitate recall and help with committing the facts to memory. Yes, students should also know the following about multiplication – and I will focus on all of these in future articles:

  1. Multiplication is repeated addition. For example: 3 x 4 means 3 groups of 4 or 4 + 4 + 4 = 12
  2. Multiplication is equal groups. 3 x 4 might be shown with 3 circles and 4 dots in each one. Be cautious about continued use of this one. Students are good at drawing this out, but then are they actually adding repeated groups or just counting one dot at a time. Observe students to see what they are doing. Transition to showing 3 circles with the number 4 in each one.
  3. Multiplication is commutative. If solving 7 x 2 (7 groups of 2), does the student count by 2’s seven times, or perhaps make it more efficient by changing it around to make it 2 x 7 (2 groups of 7 — and adding 7 + 7)?
  4. Multiplication can be shown with arrays. If students are drawing arrays to help solve, watch how they are computing the product. Are they counting one dot at a time? Or are they grouping some rows or columns together to make this method more efficient. I will focus on this one in Part 2.
  5. Multiplication facts have interesting relationships — stay tuned for future posts or check out my blog archives for more
    • An even number x an even number = an even number
    • An odd number x an even number = an even number
    • An odd number x an odd number = an odd number
    • 2’s, 4’s, and 8’s are related
    • 5’s and 10’s are related
    • 3’s, 6’s, and 9’s are related
  6. Multiplication can be shown by skip counting.  Aside from my comments above about errors students make with skip counting, there are some ways to arrange skip counted numbers in distinctive organized groupings so the patterns become more noticeable, perhaps leading more to memorization than just a horizontal list of numbers, or using fingers.
    • I have included 2 visuals to see some of my favorite ways to relate skip counting to unique patterns (for the 2’s, 3’s, 4’s, 6’s, 8’s, and 9’s). Visualizing and explaining the patterns is a good exercise for the brain.  Can your students come up with another way to visualize the patterns with these numbers?

 

Stay tuned for more blog entries about multiplication!

Building a Classroom Community – Learning Names and Other Teamwork Activities

by Cindy Elkins – OK Math and Reading Lady

Since many of you may just now be coming back together with your students in person due to hybrid or virtual teaching models, I thought I’d revise this post I wrote 3 years ago concerning establishment of a classroom community.  While you may feel extra pressure to get back into some serious catch-up learning lessons, time spent on creating a genuine classroom community is definitely worth it and should pay off.

Creating a sense of community within your classroom puts emphasis on establishing a climate of mutual respect, collaboration, kindness, a positive atmosphere, and a feeling that each one is a valued member of the class. This is also critical to help you prepare for small group collaborative practices for your reading and math instructional program. See the freebie of fun teamwork activities in the last paragraph!

There are many ways to accomplish this, of course. But I will share my favorites. Before Great Expectations came to SW Oklahoma, I became familiar with an organization called Responsive Classroom (click to link to their website). They are similar to GE, but primarily train teachers in the NE part of the U.S.  Like GE, they also focus on a strong link between academic success and social-emotional learning. You can subscribe to their newsletter and order wonderful books via their website. I started with one of their books called “The Morning Meeting Book” (click on title). It promotes ways to create a classroom community by having a daily “Morning Meeting.”

In my classroom, we formed a circle every morning and greeted each other by name in fun ways. See some ideas below in the bulleted section.  You might be surprised to know that students often don’t know their classmates names, even after several weeks of school! Knowing and using a child’s name is a sign of respect. Through this circle, we also shared successes and concerns for one another, began discussion topics about how we should behave and respect one another, welcomed new students, made group decisions, and set the tone for the day. Every student was acknowledged and felt valued every day. Students don’t want to disappoint a teacher or classmate they respect, and it almost eliminated the need for time consuming behavior plans.  For a great plan to get students in a circle in a timely manner see Activity #22 in the Teamwork Activities linked below (last paragraph)

Name Greetings:

  • One student starts. Student #1 offers a type of handshake to the person to their right -Student #2 (handshake, pinky shake, salute, wave, high five, fist bump), and says, “Good Morning, ________ (name).” Student #2 returns the greeting (also with eye contact), “Good morning, ________.” Then Student #2 greets Student #3, and it goes all the way around the circle.  I usually only introduce one type of hand gesture at a time. After we learn all of them, then I often give them a choice. I have to teach eye contact, sincerity, how to give a proper handshake, and what to do if you don’t know/remember their name.
  • After we have mastered the above, I introduce some other way to greet. One is to write each student’s name on an index card and place the stack face down in the middle of the circle. Turn over the top 2 names and they greet each other. Keep turning over 2 names at a time until the whole stack is completed.
  • Learn a greeting in another language (such as Hola or Buenos Dias, Guten Morgen, Bonjour, etc.).
  • Using a ball, student #1 rolls it to a student across the circle to greet them (student #2). Then student #2 rolls the ball across the circle to greet #3, and so on.
  • If we are crunched for time, we shake to the left, shake to the right, say “Good Morning, ____” and are all done!!

Teamwork Activities:

Through my years of GE training, I added teamwork activities to our classroom routines – especially at the beginning of the year. And then we continued them once a week because caring has to be practiced. We loved “People to People” and “Black Socks” and the “Woo Game.” I am attaching a pdf of  22 Movement, teamwork, energizer activities – I hope you will try some. Many of them require no advance preparation. I feel taking the time to create a caring atmosphere was worth every minute. When students have the opportunity to engage in fun activities together and learn their names and interests, they are more likely to show genuine respect toward one another.

Enjoy your time together!  Share your favorite teamwork activity!

Interactive math lessons and activities on NCTM

Review by C. Elkins, OK Math and Reading Lady

Resource – http://illuminations.nctm.org

This is a math resource I absolutely love! It is a product of the National Council for the Teachers of Mathematics (NCTM).

This site includes lesson plans and interactive activities. Search in several ways: by topic, by standard, or by grade level. Need some strategy games? Check out “Calculation Nation” (some of which can be played against other players), and “Brain Teasers.” I have just added this link to my Resources page (on my blog home page).  Pass this along to parents for them to use with their children at home!

Many of the lessons connect to exploration projects and literature. The interactive features are outstanding!! These are perfect for the smartboard, on laptops, or tablets. Doing Zoom lessons? Then these are also wonderful for sharing the screen to introduce or review concepts. Once you are on the home screen, click the Interactives box (right side) and then the desired grade level. There are dozens of great applets, but here are a few you might really like. I have linked them for easy reference, so just click on the  title and you’ll be there:

Dynamic Paper: Customize graph paper, number lines, spinners, nets, number grids, shapes (to include pattern blocks, color tiles, and attribute blocks), and tessellations. You can also choose inches or cm. These can be customized, saved and printed as jpeg or pdf. I created the spinner shown here from this application.

Five Frame and Ten Frame tools: Geat activities to build number sense using five or ten frames. These may take 1-2 minutes to load.

Cubes: Build a rectangular prism one cube, or row, or layer at a time and then compute the volume or surface area.

Coin Box: Drag and exchange coins. There is also a feature I like (the grid at the bottom right corner), which puts coins in blocks (by 1s for pennies, 5s for nickels, 10s for dimes, and 25s for quarters). This really helps see the value of the coins. Want more info about coin blocks? Once on the Coin Box page, click on the “Related Resources” tab.

Try these for fractions: Fraction Models (which includes decimal and percent equivalencies) and the Fraction Game.

Geometric Solids: Create a shape (either transparent or solid) and swivel it around to see all of the faces, vertices, and edges. It has a cube and pyramid as far as basic 3D shapes are concerned. I wish it had more that 3rd-5th students would encounter.

Here’s a nice multiplication game:  Product Game  Two players (or a player vs. the computer) choose factors from the bottom bar to create products shown on the game board grid to get 4 in a row (and try to block your opponent from getting 4 in a row).  Be sure to see the directions included.

Some of the interactives require an NCTM subscription.  The ones I have listed above should be okay to access without membership. I have subscribed for years and just paid $94 for this coming year. Well worth it if you plan on using their site extensively.  This subscription also entitles you to a print and and online journal, blog capabilities, and more.

Enjoy these and so many more!!! Let us know if there are others you recommend.  I’ll highlight more on my next post.

 

Sight Word Activities

by C. Elkins, OK Math and Reading Lady

This post contains some of my favorite sight word activities and resources to help your students practice those sight words and high frequency words.  If you haven’t read part 1 (Sight word instructional tips), be sure to do that as it contains information about research based teaching strategies. These all focus on ways for the child to actually read / say the word and use in a sentence, not merely matching, copying, or building the word. Here goes!!

  1. Sight word tic-tac-toe:
    • Played with partners or teacher vs. students
    • Materials needed:  tic-tac-toe template on a small whiteboard or on a laminated page
    • Two-color counters so each student can mark their spot
    • Select 9 sight words you would like to review.  Have students write them in randomly in the 9 tic-tac-toe spaces
    • Each player selects a word to read.  If read correctly, they can put their counter on the space.  You may also require students to use the word in a sentence.
    • 3 in a row wins the game. Then play again!
    • You may choose to give corrective feedback regarding missed words:  Example:  “No, this word is ________. You say it.”
  2. Sight word sentence cards:

    from thisreadingmama.com

    • Using the words in sentences (or phrases) helps students put the word into context.
    • Try these sight word cards from a blogger I follow (www.thisreadingmama.com).  If you subscribe to her blog, you will find these and dozens of other good reading resources for free. Check out: Sight Word Cards with Sentences (Link to free resources)
    • I mentioned this in the last post, but a great research-based method for using these with individual students is to select no more than 10 words. Show the word. If it is known, put it in a separate pile. If it is unknown or the child is hesitant or guesses, tell the child the word, read the sentence so they can hear it in context, have the child say the word, then put the card 2-3 spaces back in the pile so they will see it again in a short amount of time. Repeat with other cards.
  3. Sight word teaching routine:
    • Please take a look at this KG teacher’s routine for teaching and practicing sight words.  It is called “Sight Word 60” because through this routine, students get a chance to hear and use the word 60 times during the week. Sight Word 60 by Greg Smedly-WarrenLook for videos for each day, plus center and celebration activities. This routine can also be followed in 1st and 2nd grade classes or small groups.  Especially good for use with tutors, paraprofessionals, or volunteers!
  4. Sight word path game:
    • This simple path game scenario is well-researched. You are likely to find several versions available. Here is mine (also pictured below): Reading Race Track for Sight Words CE   In part 1 (last post), I linked one from another popular blogger (Playdough to Plato). Here is another editable one from Iowa Reading Research: Reading Race Track (editable).
    • Teacher fills in the words being practiced (5-7 words repeated 4x each placed randomly).
    • The track can be used by students for practice (they can roll a die, move to the space, pronounce the word, and perhaps use it in a sentence).
    • The track can be used by teachers and students for timed practice after they have been introduced. A recording sheet is included with my version as well as the Iowa version.

      Page 2 of Reading Race Track by C.E.

  5. Sight words in context:
    • Of course students benefit from practicing sight words in context.  In your guided reading group, allow students to use mini magnifying glasses (check the dollar stores) or those fancy finger nails that slip over a finger to locate sight words you call out. Example:  “Find the word said on this page.  Can you find it on another page?  Read the sentence it is in to your partner.”
    • My favorite way to practice sight words in context is through short, fun poetry. Here is a great resource (sorry, it’s not free) full of poems which target specific sight words. I’m sure there are others out there – let us know of ones you have found!  Sight Words Poems for Shared Reading by Crystal McGinnis (TPT for $4.00)
  6. SWAT!
      • Find some new flyswatters.  If you are working with a small group, you just need 2.
      • Lay out 4-8 sight words you are working on (table top or floor). You could also write them on the board. Teacher calls out a word.
      • The object is for the students to locate and hold their swatter on the word you call out.
      • The student who found it first will have their swatter under the second student’s swatter — proof of who found it first.
      • This is also great for other vocabulary practice or math facts!!

    Find the word “said”

  7. Memory / Concentration:
    • Make 2 copies of each sight word on index size cards. You might limit to 8 cards for KG students and 12 cards for 1st or 2nd.
    • Arrange the cards in a rectangular array.
    • First player selects 2 cards to turn over and read. If they are a match, they can keep them.
    • STRESS to students to just turn the cards over and leave them down — don’t pick them up. This is because the other students are trying to remember where these are located – and they need to be able to see them and their location. It’s a brain thing!!

Notice that in all of these methods, the students need to read and say the word (and perhaps use it in a sentence). Be sure your sight word activities reinforce these. Activities in which students just merely match, stamp, copy, write in different colors, recreate with letter tiles, etc. do very little to help them really know the word. Have FUN!!!

What other sight word activities have you tried that you’d like to share? Take care, friends!

Sight Words Instructional Tips

by C. Elkins, OK Math and Reading Lady

Sight words are those which students can identify automatically without the need to decode. They often do not follow phonics “rules.” Examples: who, all, you, of. They may include some high frequency words (HFW). High frequency words are those which occur most often in reading and writing. By learning 100 of the HFW, a beginning reader can access about 50% of text.  According to Fry, these 13 words account for 25% of words in print:  a, and, for, he, is, in, it, of, that, the, to, was, you.

When are students ready to learn sight words?  According to the experts from Words Their Way (Bear, Invernizzi, Templeton), student need to have a more fully developed concept of word.  Concept of Word is the ability to track a memorized text without getting off track, even on a 2-syllable word. In other words, does the child have a one-to-one correspondence with words? When tracking, does their finger stay under a 2-syllable word until it is finished, or are they moving from word-to-word based on the syllable sounds they hear? In the sentence shown, does a student move their finger to the next word after saying ap- or do they stay on the whole word apple before moving on? Students in the early Letter-Name Stage (ages 4-6) start to understand this concept. It becomes more fully developed mid to later stages of Letter Names (ages 5-8).

Students with a basic concept of word are able to acquire a few words from familiar stories and text they have “read” several times or memorized. Students with a full concept of word can finger point read accurately and can correct themselves if they get off track. They can find words in text. Therefore, many sight words are acquired after several rereadings of familiar text.

Instructional Strategies KG-2nd Grade

1. To help children gain concept of word:

  • Point to words as you read text to them (big books, poetry on charts, etc.).
  • Invite children to point to words.
  • Pair memorized short poems with matching word cards for students to reconstruct. Using a pocket chart is helpful.

2. Explicit Instruction: Dedicated time each day for sight word work

  • KG: 1-3 words per week; 1st grade: 3-5 words per week
  • Introduce with “fanfare and pageantry”.
  • Read, chant, sing, spell, write.
  • Use them in a sentence and ask children to do the same.
  • Use letter tiles, magnetic letters, word cards.
  • Use with a word wall (see more info later in this post).
  • Locate in text you are reading (poems, big books, stories in small group).

    a box of juice

  • Many sight words are hard to explain the meaning (the, was, of). Associate with a picture and phrase or sentence such as: a box of juice.
  • Reinforce with small group instruction.
  • Practice at learning stations:  CAUTION — activities should be done with previously learned  words to promote fluency. If the words are not known, then stamping them in playdough or writing them multiple times may not help you achieve your objective. Saying them correctly along with visual recognition is key. Go to this blogger’s link for many free resources for reinforcing sight words.  http://www.playdoughtoplato.com/pirate-sight-word-game/   She has a simple path board game which is editable. You can put in 1-5 sight words to practice – students must say the word to their partner to advance along the path. I often require students to use the word in a sentence as well. She is a great resource for KG-2nd grade!!
  • I (and experts) do not recommend using sight words on weekly spelling lists. Research suggests  spelling words should follow typical orthographic patterns, which many sight words do not have (ex: who, was, all, of). If you practice sight words in ways mentioned above, students will get better at spelling them or can refer to the word wall when needed for writing assignments.

3. Flash Card Practice (Research based method) with no more than 10 words: Continue reading

Rounding activities (whole numbers and decimals)

by C. Elkins, OK Math and Reading Lady

Last week I reposted my blog regarding use of number lines to assist students with number sense and rounding. Check it out for free activities and rounding charts. Today I am sharing some more rounding activities I developed and used with students to practice (with either whole numbers or decimals). These activities can be varied to suit your students’ needs.

These grid templates are to use the activities with 2-4 students (or teacher vs. student if working one-on-one online). I developed 3 different grid sizes (4 x 4, 5 x 5, and 6 x 6).  You will also need something to generate numbers for each set of players:

  • Grid for playing board:  Get here FREE  Grid 4 x 4   Grid 5 x 5   Grid 6 x 6
  • 2 dice (1-6)
  •  2 dice (1-9)
  • digit cards (0-9) — get your free set here:  0-9 digit cards
  • deck of playing cards (with tens and face cards removed)
  • spinner (with digits 0-9) — 1 is ok, 2 is better

The objective of the game is for a player to capture 4, 5, or 6 squares in a row (horizontally, vertically, diagonally).  You decide based on the size of the grid and the skill level of the players how many captured squares are needed.

The teacher can write in possible answers on the grid and laminate for continued use (samples below). Then students can use a game piece  (flat stones, two-color counters, etc.) or different color dry erase marker to mark their square.

  • Using a paper form, students can write in answer choices randomly on the grid (supplied by the teacher for accuracy). Then each player can use a different colored crayon to mark their square.

Here are some different variations of the game (whole number rounding to nearest 10, 100, 1000 and decimal rounding to the nearest tenth or hundredth).

Rounding to the nearest ten:  You can use the blank grid to write in your own numbers randomly.  Consider which number generated options you are using.  If you use 1-6 dice, the biggest number on the board has to be 70 and remember there’s only 2 ways to achieve 70 (by rolling a 6 and 5 or a 6 and 6).  If you use 1-9 dice or number cards, then you can place numbers from 10-100 on the board.  This gives a few more options and a chance to round higher numbers.

  • Roll 2 dice (or turn over 2 number cards, spin spinner twice)
  • Generate a 2 digit number.  If a 3 and 5 are rolled, the player can decide to make it 35 or 53.
  • Round that number to nearest 10.
  • Find that number on the grid.
  • If using a laminated board, place a colored “chip” on it. If using paper, each player colors their chosen # with a crayon.
  • Player #2 follows same steps.
  • Each player is trying to get 4, 5, or 6 in a row (depending on which grid size you choose).
  • It’s more fun if you try to block the other player and use strategies about your choice of a number to round (should I use 35 — rounded to 40?  Or 53 — rounded to 50?)

Rounding to the nearest hundred:

  • Follow same steps as above, except use 3 dice or 3 number cards.
  • Place numbers such as 0, 100, 200, 300 . . . randomly on the board. In the samples pictured I numbered to 1000 since I used 0-9 dice. I didn’t show a 0 on the boards pictured below, but should have since a number less than 50 could actually be generated. If using 1-6 numbered dice, the highest would be 700.
  • Example:  Roll a 2, 5, 6 — player can make these numbers 256, 265, 526, 562, 625, 652.  The number choice becomes part of the strategy of the game to see which spot is available on the board.

Rounding to the nearest thousand:

  • Follow same steps as above, except use 4 dice or 4 number cards.  If using 1-6 numbered dice, the highest would be 7000.

Rounding to the nearest tenth:

  • Follow steps similar to rounding to nearest tenth, except answer choices on the grid would look like this:  .1, .2, .3 . . .
  • If using number cards (as pictured below) or a spinner with digits up to 9, be sure to include a space on the grid for 1 (which is what you would round these numbers to:  .95, .96, .97, .98, or .99.
  • Again, be mindful of randomly placing numbers because it depends on which number generating options you are using.  If using 1-6 dice, I would only include a couple of spaces with .7 because there’s a limited number of ways to round to .7 with dice numbered 1-6.  The only way to round to .7 would be to roll a .65 or a .66.

Rounding to the nearest hundredth:

  • Follow steps similar to rounding to the nearest hundred by using 3 dice or turning over 3 number cards.  Be sure to include a space or two for an answer of 1.

Other tips for playing:

  1. Provide students with a blank white board to draw an open number line to check out their answer.
  2. Provide a sentence frame such as:  I made the number  ______ which is rounded to ________.
  3. Remind the players that it is their job to watch their opponent and challenge anything they think may not be correct (in a friendly, helping manner of course).
  4. Shorter time frame for playing?  Choose the 4 x 4 grid.  Longer time frame?  Choose the 6 x 6 grid or use the 6 x 6 grid with the winner being one to get 5 in a row.
  5. Consider creating a box of 4 completed squares in addition to 4 in a row.
  6. This can be played as teacher vs. students in a virtual setting.
  7. This can be played in a one-on-one online setting by using a document camera or posting a screen shot on the screen.

Let me know if you try these!  Pass along any extra tips you have.

Also, a reminder to contact me if you would like personalized professional development over any reading or math strategy.  I can do a Zoom session with you or a group of teachers.  Flexible payment options.  Also, check out my link on the side bar for Varsity Tutors regarding the opportunity for you to tutor students online or in person (and earn a bonus for using my name).

Take care, stay safe!!!  

 

Rounding and Number Lines

by C. Elkins, OK Math and Reading Lady 

I get requests from many teachers to help with instructional strategies regarding rounding, so I am happy to share my thoughts (and freebies) with you. Difficulty with rounding usually means students lack number sense. The essential goal of rounding is: Can you name a benchmark number (whole, tens, hundreds, thousands, tenths, hundredths, etc.) that a given number is closer to? I have found the more experience a student has with number lines, the better they will be with number sense, and the better they are with rounding to the nearest ___.  Then this rounding practice must be applied to real world problems to estimate sums, differences, products, or quotients.

When doing a google search for tips on rounding (ie Pinterest), you very often find an assortment of rhymes (such as “5 or more let it soar, 4 or less let it rest”) and graphics showing underlining of digits and arrows pointing to other digits. These steps are supposed to help children think about how to change (or round) a number to one with a zero. Many students can recite the rhyme, but then misunderstand the intent, often applying the steps to the wrong digit, showing they really don’t have number sense but are just trying to follow steps.

My answer (and that of other math specialists) is teaching students how to place any number on a number line, and then determining which benchmark number it is closest to. Continue reading to see examples and get some free activities. And watch next week for some new rounding activities for grades 2-6 (whole numbers and decimals).

Continue reading

Listening to your students read Part 2: Running Records and the Structural Cueing System

by C. Elkins, OK Math and Reading Lady

This is part 2 of a series on ways you can efficiently listen to your students as they read, identify cueing systems the child is using / neglecting, and offer helpful prompts that will guide them as they read.  This blog will focus on the Structural Cueing System. Even though this is considered an early reading strategy, there are many intermediate elementary students (and higher) with reading difficulties who would benefit from this type of analysis and prompting.

The second cueing system is the use of (S) Structure or Syntax of our English language. Much of a child’s knowledge about language structures comes as a result of speaking or listening to how language naturally sounds. A reader attempts to make it sound right. Below are 3 possible scenarios with analysis of a child’s possible response.

Using this text:  She runs with the puppy.

1. Suppose a student read it this way:

  √        ran      √       √         √.

She     runs   with   the   puppy.

This student is using structure because “She ran . . .” sounds right. He/She is also using M (meaning) because it makes sense. And the child is using visual (V) cues because ran / runs are visually similar.

2. Suppose a student read it this way:

√       runned       √      √         √.

She    runs       with  the   puppy.

This student is not using structure because “She runned . . .” does not sound structurally / grammatically correct. However, it still makes sense (M) and is still visually similar (V).

3. Suppose a student read it this way:

√      chased      –        √         √.

She   runs      with   the   puppy.

This student is using structure because “She chased the puppy” sounds right. He/She is also using (M) meaning because it makes sense. The child is not using (V) visual cues because chased and runs are not visually similar.

When a child is not using structure, their errors in reading are typically with verb tenses. Often with -ed ending words they will use the wrong pronunciation (such as look-ded), or they will generalize by adding -ed to words which don’t use it to make past tense (runned, swimmed, bited). Or a student may be an English Language Learner – be sensitive to their needs. They may not know what “sounds right.” In that case, you as the teacher should model what it should sound like.

Helpful teacher prompts to help a student monitor for (S) Structure / Grammar:sound-icon

  • Did that sound right?
  • Does that sound the way we talk?
  • Is there a better way to say it?
  • What word would sound right there?
  • Can you say it another way?
  • Try ______. Would that sound right? Listen as I read it. Now you try.
  • Listen to this (give 2 choices). Which sounds better?

Remember, it is often most helpful to wait until the child completes the whole sentence before prompting or trying to correct an error. This gives the child an opportunity to monitor themself and perhaps self-correct. If the teacher (or parent) jumps in right away after the error is made, it is the teacher doing the monitoring, not the student.

To assist you with documentation about the child’s cueing system, see part 1 about Running Records. In your notes for the child’s oral reading, write the word they said above the word from the text. Analyze to see if they are making meaning, structural, or visual errors. Does the child tend to use one cueing system over another? What prompts can you offer to help the child monitor their reading and self-correct?

Finally — be sure to let the student know when you notice their self-corrections and montoring.  For example:  “I noticed you changed the word ‘runned’ for ‘runs’ in the sentence. You made it sound right! Good for you!” This reinforces use (and hopefully continued repetition) of the strategy.

Happy Listening! Next time Visual Cues – Part 3

Clip art courtesy of MS Office.

Happy Holidays

by C. Elkins, OK Math and Reading Lady

This has been an incredibly difficult year in so many ways.  But during these difficult times, you teachers do what teachers have always done — you show unbelievable flexibility, you adapt to changing situations with a variety of resources, spend countless hours making sure you have the best lessons, and continue to show compassion and caring for your students — because that’s who you are!! I am proud of you, and I want to thank you for hanging in there with me this year. I hope I was able to provide some help as you navigated through uncharted waters.

We are all looking forward to 2021, and hope to get closer to “normal.”  I wish the best for you, your family, and your school. May you have a brief respite here at the end of December and time to enjoy it and relax a little bit.  Happy Holidays to you!  I will resume my blog articles in January.

Take care, be safe!!  Cindy Elkins, OK Math and Reading Lady

Listening to your students read Part 1: Running Records and the Meaning Cueing System

By C. Elkins, OK Math and Reading Lady – with adaptations from Marie Clay and Scholastic

Taking a running record is written documentation of a child’s oral reading. It consists of listening to a child orally read a passage while you document it as best you can on paper. As the listener, you note errors (such as omissions, insertions, substitutions),  pay attention to strategies they are using or neglecting, and are alert to what is easy and what is hard. Many publishers now provide a written page of the text for you to keep track of the child’s reading page by page, while experienced notetakers can do it at a moment’s notice on any blank paper.

I attended a Reading Recovery workshop about mid-way into my teaching career, and heard from two teachers who described how to take a running record and then analyze the results to determine which strategies students were using or neglecting. That one workshop forever changed how I listened to my students read, and how I talked to parents about their child’s reading successes or difficulties.  About 8 years after that I had formal training in Reading Recovery methods, and subsequently completed a Masters in Reading . . . all because of that workshop!  I learned all mistakes are not equal and provide a huge clue as to what cueing system a child is using. I learned that I can help steer a child toward a neglected strategy by carefully crafted teacher prompts. I learned that there are much more effective prompts than the standard, over-used:  “Sound it out.”

The benefits of running records

  • Identifies accuracy of reading (independent, instructional, or hard)
  • Provides a record of strategies used, errors, corrections, phrasing, fluency
  • Helps teachers identify cueing systems the child is using / neglecting (meaning, visual, structural)
  • Documents progress over time
  • Can help determine a level for guided reading purposes (Fountas and Pinnell, Reading A-Z, DRA, etc.)

Continue reading

Number Talks with Dot Cards: Subitizing, Number Sense, Facts (Part 2)

by C. Elkins, OK Math and Reading Lady

Hi!  This is Part 2 regarding ways to do number talks using dot cards. This post will feature random dot cards. See the last post for strategies with ten frame dot cards and some background information about why and how (click HERE).

My pictures below feature dot cards provided via an extra purchase from this great resource regarding Number Talks. I blacked out the number in the small print at the bottom of each card because I was using them online and didn’t want the magnification to show the number.  When showing them in person, the number is too small really for a student to notice or I can use my hand to cover it when showing the card.  Anyway . . . that’s for those of you wondering what the little black smudge was. Here’s an amazon link to the cards which you can get digitally for $19.95 (279 pages worth): Number Talk Dot Cards

My previous post (linked above) also listed 2 resources for ten frame and random dot cards.  Here is another one you might like and is great to use with partners as well.  I’ll describe an activity with them below.  Dot Cards for Number Sense ($2 from mathgeekmama.com)

You may like checking out mathgeekmama for other wonderful FREE resources.

Random Dot Cards

While I refer to these as “random” dot cards, it really doesn’t mean the dots are just scattered willy-nilly.  The dots on these cards are still organized, but just not on ten frames.  When using these cards, the goal is for students to “see” patterns with the dots to aid their subitizing and quick recall of number pairs.  You might start with dot dice first, then look for these on the dot cards:

  • groups of 2
  • groups of 3 (such as triangles)
  • groups of 4 (such as squares)
  • groups of 5 (like on a dice)
  • groups of 6 (like on a dice)
  • doubles
  • near doubles

I also often point out to students how I mentally “move” a dot to visualize one of the above scenarios. This will be shown in the pictures below with an arrow.

Procedures for whole group (either in person or on Zoom):

  1. Flash the card (longer for more dots).
  2. Students put thumb up (I prefer thumb in front of chest) when they have decided the amount.
  3. Randomly select students to tell you how many they saw. No judgement yet on who is correct and who isn’t.
  4. Then ask the VERY important question, “How did you see it?”  This should elicit various responses which will help reinforce different ways numbers can be decomposed.
  5. If desired with in-person sessions, you can have students pair-share their response first before calling on students to tell you. This way all students get a chance to share their way with a ready listener.  Click on this link for a way to silently signal  “Me too” in sign language. I find this very helpful especially for those students who want to respond — and helps avoid the “he took my answer” complaint.
  6. Record the different responses on a chart tablet.
  7. On the occasions where there are limited responses, here are some options:
    • Ask students if they see a way another student might have seen it. Be prepared — you might get some amazing (or long-winded) responses.
    • If students don’t see something I think it worth mentioning, I might say, “Here’s a way I saw a student think about this one last year.”
    • Or you could  just show the card another day to see if there are some new responses then.

What do you see with these?  . . . Plus some examples:

How do you see these? . . . Plus suggested outcomes:

Procedures for individual or partners (great for online tutoring or class center activity)

  1. Flash the card (longer if more complicated).
  2. Student tells you how many.  If not correct, show the card again.
  3. Ask, “How did you see them?”
  4. If the card is laminated, circle the parts the child describes.
  5. Tell how you (teacher) saw it.
  6. Ask, “How might another student see it?”  This gets them to see other possibilities.
  7. Record responses.

With the activity I mentioned earlier from mathgeekmama.com, this is a great with partners. I would recommend dot cards with no more than 8 dots for this activity:

  • Start with a stack of dot cards (face down).  Provide a blank laminated square to record dots on.
  • Partner 1 selects the top card and flashes it to partner 2 (perhaps 2-3 seconds).
  • Partner 2 uses a laminated blank square to try to draw the dots (with dry erase marker) to match what partner 1 showed them.
  • Both students reveal their dot cards to see if they match.
  • Switch roles and repeat.

As an individual activity, provide the laminated dot cards and a dry-erase marker.  Circle the dots.  Write a math problem to match it. Take pictures to record answers. (Recommendation: Do this after you have already modeled it during a Number Talk session.)

Take care. Share your experience with using dot cards for Number Talk sessions. I love success stories!

Interesed in personal professional development, or PD for your grade level team or school? Please contact me for special rates. I can meet via Zoom for just about any need you have (math or reading).  I’d love to help!

Number Talks with Dot Cards: Subitizing, Number Sense, Facts (Part 1)

by C. Elkins, OK Math & Reading Lady

Do you see 3 + 4 =7 or perhaps 5 + 2 = 7? Maybe you see 3 + 2 + 2 = 7.

I have been using dot cards for many years with K-2 students as part of my Number Talks routine. I’d like to share some ways to follow this routine using both ten frame dot cards and random dot cards.  These are also easy to use via distance learning situations.

If you haven’t tried this before, you are in for a treat!  It is so nice to listen how students process their thinking. I never cease to be amazed at how developed a child’s thoughts can be expressed . . . and how many children take this as a challenge to see how many ways a dot picture can be explained.  I often feel I learn so much about my students capabilities (or sometimes the deficits) during this type of Number Talk session.  Look for my recommended links below (FREE).

What are the benefits?:

  1. Students gain the ability to subitize (tell a quantity without physically counting).
  2. Students gain number sense by noticing more dots, less dots, patterns aid counting, the same quantity can be shown different ways, sequencing numbers, skip counting, and many more.
  3. Students gain the ability to see many different ways a number can be composed or decomposed which assists with addition and subtraction facts.
  4. Students gain practice with strategies such as counting on, add/subtract 1, doubles, near doubles, adding 9, adding 10, missing addends, and equal groups.
  5. Teachers are able to observe students’ processing skills in an informal math setting.

Materials needed:

  1. Ten frame dot cards:  This set is FREE from TPT and includes ten frame cards as well as random dot cards. Great find!!  https://www.teacherspayteachers.com/FreeDownload/Number-Talks-Early-Level-Starter-Pack-10-Frames-and-Dot-Cards-4448073
  2. Random dot cards (not on ten frames)

General procedures:

  1. Decide how you are going to show the cards:
    • Show to students who are seated near the teacher?
    • Show to students via a document camera projected to a screen?
    • Show to students online with a split screen?
    • Show to students via a ppt?
  2. Depending on the grade level, you may want to flash the card quickly to encourage subitizing or shorten/extend the time the card is shown.
    • To encourage subitzing to 5, I recommend flashing the card for a couple of seconds for dots from 1-5 for all age groups.
    • Depending on the number of dots and the complexity of the dots, you may choose to shorten or extend the time you display the card for amounts more than 5.  The goal is for the students to look for patterns, equal groups, doubles, dots making squares, rectangles, or triangles, determine a quantity, and then explain how they arrived at that amount.
  3. Students put a quiet thumbs up when they have decided the quantity.  They should not say the amount outloud at this point. This shows respect for others who are still processing.
  4. The teacher observes to see who is counting, who is participating, who uses fingers, who is quick /slow, etc.
  5. Teacher asks random students, “How many dots?”
  6. Teacher asks random students, “How did you see them?”
  7. Results can be stated verbally or written down by the teacher.

Here are some examples with sums less than 10:

Here are examples using 2 ten frames to illustrate quantities greater than 10:

Next post:  I will feature ways to use the random dot cards for your Number Talk sessions.

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Number Pairs / Number Bonds Activities (PreK-2): Part 2

by C. Elkins, OK Math and Reading Lady

This post will feature some more number pairs / number bonds activities as well as ideas for informal assessment (along with some FREEBIES).  See the previous post for Part 1.  Also, here is another cool virtual manipulatives site:  https://toytheater.com/category/teacher-tools/  You will find lots of materials for students to use to help with these activities:  counters, bears, two-color counters, whole-part-part templates, Rekenreks, etc.  Check it out!

For all of these activities, the student should be working with the number of manipulatives to match their focus number.  They should do several different activities using that same amount to get lots of different experiences making the same number pairs repeatedly.  After a generous amount of practice, assess the child and move to the next number when ready. An important feature of each activity is for the student to verbalize the combination being made. Using a sentence frame they can have with them or putting it on the board for all to see is a plus:  “____ and ____ makes _____.” Students will usually need reminders that you should hear them saying this.  It takes if from just playing to being cognizant this is a serious math activity.

  1. Heads or Tails:  Use coins and a whole-part-part template.  The student shakes and gently drops some coins (stick to one type of coin). Then sort according to how many landed on heads vs. tails by placing them on one of the templates.  Say the combination outloud:  “5 heads and 2 tails makes 7.”  Repeat.  Here’s a FREE Coin Toss recording sheet.
  2. Paper Cups:  The student finds different ways to place small paper cups up or down to match their focus number.  Example:  To make 7 I could have 5 up and 2 down, or 6 up and 1 down, or 4 up and 3 down, etc.
  3. Hiding or “Bear in the Cave”:
    • Use a small bowl, clean plastic butter tub, etc. and some objects (cubes, stones, beans, cheerios, M&Ms).
    • With a partner and the number of objects matching the student’s focus number, partner 1 closes their eyes while partner 2 hides some of the counters under the tub and the rest outside or on the tub.
    • Partner 1 opens his eyes and names how many outside the tub and then tries to determine the number hiding.
    • Partner 2 can then reveal if partner 1 was correct or not.
    • Calling it “Bear in the Cave” was the idea of a math specialist I follow and clicking on this link will take you to her site with the opportunity to get the directions and recording sheet (Math CoachsCorner:  mathcoachscorner.com Bears in the Cave freebie)
    • Be sure when students are playing that they say the number pairs outloud such as, “3 and 4 make 7.”
  4. Roll and Cover Game / Four in a Row:
    • Items needed:  A blank grid template (4×4 or larger), counters or crayons for each player (up to 3), and one of the following to create numbers needed to play (spinner, number cards, custom dice).
    • With the grid template, create the game board by randomly placing all of the numbers making up the number pairs for the focus number and fill up the grid. If working on number pairs of 6 as pictured, place these randomly:  0, 6, 5, 1, 2, 4, and 3
    • Using a spinner, custom dice, or number cards, select the first number (example 5).  Make this sentence frame:  “2 goes with ____ to make 6.”  Locate the missing number on the grid and put a counter there (or color if using a printed worksheet). How to create an easy spinner: Draw one with the number of spaces needed and duplicate for multiple students. To use, students place a pencil vertically on the center of the spinner to hold a paper clip at the center. Spin the clip.
    • The object is to try to get 4 of your counters (or colors if using a worksheet) in a row (vertically, horizontally, or diagonally).  Blocking your opponents may be necessary to keep them from getting 4 in a row.
    • A freebie attached for Number Pairs of 6 (same as picture):Capture A game of six CE
  5. Stories:  Students can create stories using pictures from clip art or other art work:

    6 children and 1 adult = 7 OR 4 girls and 3 boys = 7  Or 2 pink shirts + 5 other shirts = 7

Assessment:

  1. This page can be used to record a student’s mastery of the number pairs / bonds.  On all assessments, observe if student names hiding amount immediately (meaning fact is known) or uses fingers or other counting methods such as head-bobbing, etc. For mastery, you want the student to be able to name the missing amount quickly.Click here for free PDF copies: Number Bond Assessment by CE and Number Pairs assessment class recording sheet CE
  2. The Hiding Game above can also be used as an assessment as the teacher controls how many showing / hiding.  Ask the same questions each time:  “How many showing?”  and “How many hiding?”
  3. Folding dot cards:  Hold one flap down and open the other. Ask, “How many dots?”  Then ask, “How many hiding?”I got these free at one time from www.k-5mathteachingresources.com, but not sure they are available now. At any rate, they look easy to make.These are also good to practice with a partner.Here is a similar one I made for FREE with the PDF copy :Number Bond 3-10 assessment in part-whole format
  4. Whole-Part-Part Template:  Using a circular or square template, place a number or objects in one of the parts.  Ask student how many more are needed to create the focus number.  This can also be done with numbers only as shown in this picture.

Let us know if you have tried any of these, or if you have others that you’d like to share!  

As I’ve mentioned before, as a consultant I am available to help you as an individual, your grade level team, or your school via online PD, webinar, or just advice during a Zoom meeting.  Contact me and we can make a plan that works for you.  If you are interested in tutoring during your “spare time” check out my link for Varsity Tutors on the side bar.  Mention my name and we both get a bonus. Have a wonderful, SAFE week.  Mask up for everyone!

Number Pairs / Number Bonds Activities (PreK-2): Part 1

by C. Elkins, OK Math and Reading Lady

Learning the combinations for numbers (number pairs / numbers bonds) is critical for both operations — addition and subtraction. This is slightly different than fact families, but it’s related.  With number bonds, students learn all of the possible ways to combine 2 numbers for each sum.  Think of whole / part / part.  If five is the whole amount, how many different ways can it be split or decomposed?  For example these combinations illustrate ways to make 5:

  • 5 = 1 and 4  (also 4 and 1)
  • 5 = 2 and 3  (also 3 and 2)
  • 5 = 5 and 0  (also 0 and 5)

Knowing these combinations will aid a student’s understanding of the relationship of numbers as they also solve missing addend and subtraction problems.  For example:

  • For the problem 2 + ___ = 5.  Ask, “What goes with 2 to make 5?”
  • For the problem 5 – 4 = ____.  Ask, “What goes with 4 to make 5?”

I suggest students work on just one whole number at a time and work their way up with regard to number bond mastery (from 2 to 10). You may need to do a quick assessment to determine which number they need to start with (more of assessment both pre and post coming in Part 2). Once a student demonstrates mastery of one number, they can move on to the next. It is great when you notice them start to relate the known facts to the new ones. Here are a few activities to practice number pairs.  They are interactive and hands-on.

One more thing:  PreK and KG students could work on these strictly as an hands-on practice, naming amounts verbally.  Using the word “and” is perfectly developmentally appropriate:  “2 and 3 make 5”.  With late KG and up, they are ready to start using math symbols to illustrate the operation.

  1.  Shake and spill with 2-color counters: 

    Shake and Spill

    Use 2 color counters.  Quantity will be the number the child is working on.  Shake them in your hand or a small paper cup. Spill them out (gently please). How many are red? How many are yellow?  Record on a chart.  Gradually you want to observe the child count the red and then tell how many yellow there should be without counting them. This will also aid a student with subitizing skills (naming the quantity without physically counting the objects). To extend the activity, you can create a graph of the results, compare results with classmates, and determine which combinations were not spilled. Click on this link for the recording sheet shown:  Shake and Spill recording page

  2. Connecting cubes:  Use unifix or connecting cubes.  Quantity will be the number the child is working on. Two different colors should be available.  How many different ways can the child make a train of cubes using one or both colors?  If working with 5, they might show this:  1 green and 4 blue; 2 green and 3 blue; 4 green and 1 blue; 3 green and 2 blue; 5 green and 0 blue; or 0 green and 5 blue.  They could draw and color these on paper if you need a written response.
  3.  Ten frames: 

    Use a ten frame template and 2 different colored objects (cubes, counters, flat glass stones, candy, cereal, etc.) to show all of the cominations of the number the student is working on.  Using a virtual ten frame such as the one here Didax.com virtual ten frame or here Math Learning Center – Number Frames are also cool – especially if you are working from home or don’t want students to share manipulatives.

  4.  On and Off:  This is similar to shake and spill above.  Use any type of counters (I especially love the flat glass tones for this myself) and any picture.  For my collection, I chose some child-friendly images on clip art and enlarged each one separately  to fit on an 8.5 x 11 piece of paper (hamburger, football, flower, Spongebob, ice cream cone, unicorn, etc.).  Put the page inside a sheet protector or laminate for frequent use.  Using the number of counters the student is working with, shake them and spill above the picture.  Count how many landed on the image and how many landed off the image.  Like mentioned above, the goal is for the student to be able to count the # on and name the # off without physically counting them.  1st and above can record results on a chart or graph.  Often just changing to another picture, the student feels like it’s a brand new game!  You might also like to place the picture inside a foil tray or latch box to contain the objects that are dropped.  The latch box is a great place to store the pictures and counters of math center items.
  5.  Graphic organizers:  The ten frame is a great organizer as mentioned earlier, but there are two whole/part/part graphic organizers which are especially helpful with number pairs – see below.  Students can physically move objects around to see the different ways to decompose their number.

Check out Jack Hartman’s youtube series on number pairs from 1 to 10. Here’s one on number pairs of 5:   “I Can Say My Number Pairs: 5″ He uses two models (ten frames and hand signs) and repetition along with his usual catchy tunes.

Also, please check out the side bar (or bottom if using a cell phone) for links to Varsity Tutors in case you are interested in doing some online tutoring on the side or know students who would benefit from one-on-one help. Please use my name as your reference — Cindy Elkins.  Want some PD for yourself?  Contact me and I’ll work out a good plan to fit your needs!

Next post:  More activities for learning number bonds and assessment resources (both pre- and post-).  Take care!!