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Do you remember as a kid saving up coins in a jar or piggy bank? You probably thought about the toy you’ve been saving up to buy! Do you remember hearing all the coins jingle and jangle when you shook the jar or piggy bank? And, yet, there were no CoinStars back then!
I had to count the money! I would empty the jar, sort the coins, then begin counting. Then I would use the coin wrappers to get them ready to take to the bank. Before going, I would add up all the coins. Of course, it was always an amount less than I thought it would be!
Now think of all the math involved in completing the task. We estimate the total amount of money, sort the coins by their values, and count the sorted coins to fill the wrapper according to the printed coin wrapper amount. Finally, adding up all the coin wrappers for the final total. Does this sound like an idea for teaching place value?
Counting is a path which leads to place value understanding!
Yes! Integrated into this counting task was place value! The task of sorting and counting by 1s, 5s, 10s, or 25 is developing unitizing. Unitizing is part of teaching place value. You can read more about unitizing in this prior blog post.
Keeping track of the counting – counting out ten pennies or ten dimes or ten nickels or four quarters – was part of my strategy for filling the coin wrappers. Each coin wrapper had to have a certain amount such as 50 pennies (50 cents), 40 nickels ($2), 50 dimes ($5), and 40 quarters ($10). Do you see how place value is woven into this task?
Using Authentic Tasks as an Idea for Teaching Place Value
Though place value can be taught explicitly through direct instruction, you can develop place value understanding indirectly through counting tasks. What’s an idea for an authentic counting task? You may not like my first idea for teaching place value. Why? It will take some effort on your part, your students, and your students’ parents to get it done.
What am I talking about? They’re counting collections! Yes, similar to the task of counting coins, having students count objects can develop a conceptual understanding of place value. Like our ancestors developed our current place-value system out of the necessity to measure and record more significant quantities, students naturally develop counting strategies. These strategies align with unitizing, which is an essential component of place value.
Why did I say you wouldn’t like it? Because to use counting collections, you will need to have materials ready ahead of time. If you’re teaching virtually, you’ll have to rely on your students and their caregivers to put together a counting collection.
If you’re unfamiliar with counting collections, check out this site by Stanford University.
Putting Together Counting Collections for Students
How are you going to get students to put together their counting collections? I have some ideas on how to do this. The two most important factors to consider are time and materials. Students will need time to gather the materials. Parents will have to either look through their homes or buy some inexpensive materials for the collections.
Help Parents Understand the Purpose of Counting Collections
Parents might wonder what counting collections are and how they work. This video by the UCLA Math Project explains counting collections to parents while explaining all the math learned through this process. Share the video with your parents!
Time – I would ask families to have a counting collection ready in one week, which should be enough time to gather a collection.
Materials – below are my suggestions for materials for a counting collection. Store in a sealable baggie. The quantity depends on your grade level and standards regarding place value.
Kindergarten should start with a collection from 0 – 10, then eventually move to 20 or more. First graders should begin with collections less than 50 and then move up gradually to 100 or more. Second-graders should start with at least 100 (larger quantities will use base ten blocks).
Students also need a way to organize their counting to keep track. I suggest paper plates, paper bowls, plastic cups, etc. Students can use any container which will hold their objects. Use rubber bands for the bundling of items such as straws. Students can also use pie tins, cupcake molds, muffin pans, etc. Egg cartons are great ten frames if you cut off two of the parts.
Where to find it around the house
- beans (lima beans work best – they’re large and don’t roll around)
- macaroni (any kind)
- pebbles or small stones (from the front or backyard – wash them first!)
- coins (best if they’re all one type such as pennies)
- paper squares (card stock or thin cardboard from cereal boxes or similar cut into one-inch squares)
- buttons (better if the buttons are a similar size)
Inexpensive items which can be purchased at dollar-type stores
- buttons (they should all be similar size and color)
- straws (can be cut in half or used whole)
- popsicle or craft sticks
- aquarium or river stones (they should all be similar size and color)
- paper clips (be careful as they can be bent and cause injury)
- craft pom-poms
- school supplies like small erasers
Some items I would avoid
- food items (kids will eat them – if not, the ants will!)
- seeds (depends on the seed, but some kids might eat them)
- large objects over one-inch in length or diameter (hard to store and manage)
- stickers (students will stick them down, and you can’t reuse them.)
- small toys (too much of a temptation to play with them)
- beads (they’re usually too small and roll everywhere)
Some Ideas for Teaching Place Value Using the Counting Collections
When working with students in a distance learning model, place value lessons will be a combination of synchronous and asynchronous learning.
For the synchronous part, the teacher should have images of distinct quantities to screen share. You can find images using Google Image search. Alternately, the teacher can do the same with a document camera to show a number of objects from her own counting collection.
I have created a Place Value Tool Kit you can share with your students. They contain math tools to aid counting: 5 frames, ten frames, 100s and 1000s charts, counters, base ten blocks, and place value charts. The students would have to print out the pages to use. If not possible, you would have to prepare packets for caregivers to pick up from a location you have designated.
If you want to get the Place Value Tool Kit, sign up below for my newsletter. Students will also need to cut out some of the tools ahead of time.
Moving the Students to More Efficient Counting Strategies
- Get started with showing the students the image or collection.
- Have students notice and wonder what they see.
- Have students estimate how many.
- Also, elicit estimates which are too high or too low so students have some parameters to work with so they can develop reasonableness of answers.
- Then ask the students: How would we count these objects? Which math tools might help us?
By asking these questions, you can discover what strategies students use to count (touching each object, moving one by one to the side, lining up the items in a row, using a math tool to keep track, grouping or bundling by set amounts, etc.).
- Now count the objects using some of those strategies. Students can count with you. Emphasize a counting strategy you think your students need to practice.
- If you’re screen sharing, you can use the annotation tools in Zoom to cross out or circle objects you count.
- If you’re using a document camera, put a contrasting color under the objects to be certain the students can see the items as you touch or move them to count. You could even put them under a whiteboard to draw circles or lines or other annotations.
- If it’s a larger quantity, take a video of yourself counting out the objects and speed it up. In Zoom, share your iOS device and your video (or have the video on Google Drive to share).
Can I use virtual math manipulatives?
Yes, you can use virtual manipulatives. Below are sites I recommend for counting and place value. I suggest using them for demonstration or teaching purposes. Before using these sites with your class, be certain you know how to use the site tools, have the counting task arranged ahead of time, and have a backup plan in case the site is down.
- toytheater.com – the teddy bear counters can put on a grid for counting to be more manageable and visually show grouping by 10.
- mathlearningcenter.org – The Number Pieces virtual manipulative allows you to work with 1s, 10s, and 100s using base ten blocks. Allows annotation and sharing.
- ictgames.com – The Arrow Card virtual manipulative builds numbers visually with base ten blocks and the digits. When digits reach a ten or hundred, they automatically regroup.
- coolmath4kids.com – The Base Ten Blocks virtual manipulative builds number sense through base ten blocks, grouped and ungrouped.
- Once you have counted, discussed the strategies and tools used. This is a chance to have a rich discussion of how we might group objects to keep track or to count on from. Suggest to the students they can use these strategies or tools when they count.
Now have students work asynchronously to count their counting collection.
- The students should count their collection using any strategy and tool.
- The student should write the total on a piece of paper or index card next to the collection.
- Then the student should record their counting on a paper or take a photo to share (of the paper or the collection).
- The student should be able to explain their process of counting.
As a reminder, use the paper place value blocks in the Place Value Tool Kit with first graders in the second half of the year and second graders all year. They’re not appropriate for kindergarten students. Why? I explain in great detail how grouped, and ungrouped math tools can pose a problem to students acquiring number sense and place value. More information is here: Teaching Place Value? How NOT to do it the Wrong Way!
But how will the teacher know what the student counted?
Remember how excited I was to count the coins from my piggy bank? Your students are going to be excited and proud to tell you how many were in their collection! But how are they going to share it with you?
There are several ways to do this, depending on the available technology, tech-savviness of students, and available assistance from caregivers. Here are some possibilities:
- Have the student take a picture of their counting to share with you via email or to upload to a learning management system (Google Classroom, Seesaw, Canvas, ClassDojo, etc.)
- The student records a video explaining how they counted and shares it to you via email or Flipgrid or Screencastify.
- The student draws a picture of their counting to share with you via Zoom, or use their webcam to snap a photo to share with you
The easiest way to share is if the caregiver can snap a photo using their phone or the student’s tablet to upload it or email it to you. If you use Remind or ClassDojo, parents can attach a picture to send to you. Here’s a tutorial on how to take a picture with a Chromebook (this is for students who have drawn their counting collection) and add it to Google Classroom.
If the student is to draw their counting collection, teach them to draw quick models – circles, squares, lines, etc. The drawing does not need to be a work of art! Squares can represent the 100 base ten block while lines can be the tens, and dots can be the ones. If they’re loose objects, use the shape of the item to represent it (circles, squares, rectangles).
Sharing and Discussing Ideas for Counting
When you have all these photos, what do you do with them? The teacher should analyze them for strategies the students used.
- Did the student arrange the items in groups?
- How many in each group?
- Is the total accurate?
- If the student recorded a video, did the student give enough detail on how the collection was counted?
You’re looking for consistent use of strategies. Take the photos and put them in a Google Slides or PowerPoint presentation one to a slide. Then share these for the next lesson. However, strategically choose ahead of time 3 – 4 students whom you want to have them share their thinking.
- Tell the class students will be sharing their thinking about how they counted their collection.
- Before the student begins sharing, show the slide with the student’s collection, and ask the other students what they notice and wonder.
- Then ask the sharing student: how did you count these ______?
- Ask the other students who else used the same strategy or tool to count their collection.
What is the End Goal for Place Value Instruction?
For kindergarten students, the teacher is working towards the students understanding the teen numbers are composed of a 10 + another number. Ten frames provide a visual model for this. Counting collections provide the concrete experience needed to develop this first step towards place value understanding.
First grade students are working towards an understanding of 10 units being grouped or bundled into one ten unit. This is unitizing. They use this understanding to build 2 digit numbers. I would continue using counting collections until the students have developed this idea of 10 units is now counted as one unit of 10. Once students have a grasp of this concept, a switch to base ten blocks can begin.
Second-grade students expand on first-grade learning. They learn how to bundle ten tens into hundreds and build three-digit numbers. Second-grade students should practice bundling those ten tens into hundreds. Place value blocks provide an excellent visual and concrete way of unitizing into greater numbers. More abstract thinking and learning about place value can occur using place value charts, expanded form, and word form.
In an up and coming blog post, I will further delve into teaching place value specifically to second-grade students. I will show you how to work virtually with second graders to build, expand, and reinforce their understanding of place value. Stay tuned!
Need a Resource NOW?
I created this PowerPoint to use with second and third graders to build a conceptual understanding of place value. It teaches place value with 2 and 3 digit numbers. Students work along with printables to learn how to represent numbers in standard form, word form, expanded form, and base ten units. Check out the preview below. The resource can be found in my TpT Store!
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