Counting Collections

Counting

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Counting is a foundational number sense skill that should be practiced K-5. Take a look at this video to see how and why.

Here are some resources and routines that can help make counting an important part of your math week:

Counting together:

Counting Objects:

Counting Images:

Money Counting Printouts

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Don’t have plastic coins or enough real coins? No problem.

We have designed a handy student counting page that can be used as part of an ongoing routine:

Notice that the page is designed with an extension task box that is left empty. Here are some challenges for you to use. Simply feature one each time you try this routine. Write it on the board for for early finishers to try.

  • Extension 1: Split the money evenly! You decide on how many groups.
  • Extension 2: Ask them to determine double, triple, quadruple (etc.) the amount they counted.
  • Extension 3: Ask them to design a treat that will sell for the amount they counted. Then get them to determine how much they would earn if they sold ___ (you decide) numbers of this treat.
  • Extension 4: Ask them to design a gizmo that will sell for the amount they counted. Then ask them how many they could buy for $____ (you decide). How much money would they have left over?

Moth Party Level 1

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Looper moths are everywhere! How many can you find?

If you can easily find moths outside (on your house or on a tree), grab some paper and a pencil and go outside to do some counting! Keep track of what you find. Here are some challenges for you:

  1. How many moths did you find? Record your count by using tally marks.
  2. Half of the moths are male (boys) and half are female (girls). If that is so, how many moths in your collection are male? How many are female?
  3. Each moth has 4 wings. If you had to count the wings on ten moths, how many would there be?
  4. If you had to count the wings on all of your moths, how many wings would there be?
  5. Each female moth lays 5 eggs. If 10 females laid eggs, how many eggs would there be?
  6. If all the females in your collection laid eggs, how many eggs would there be?

If you can’t make it outside to count moths, you can count the moths you see in these pictures and complete the same questions as above:

Some advice:

  • It’s a good idea to draw pictures and label them with numbers. Drawings can be a very helpful way to solve problems.
  • Write down all of your ideas and all of the math you do
  • It’s okay to work with a buddy!
  • Take a picture of your work. If you go outside, take a picture of that too! Talk to your teacher about how you can share your pictures.

 

Counting Outside

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Time to get some fresh air and do some counting (and exploring) outside! Here is what you are going to need:

  1. Sidewalk chalk or a pencil and paper.
  2. A device for taking pictures of your work.

Now that you have your supplies….

  1. Choose a number between 5 and 20. Make sure you can count to the number you choose. If you are in kindergarten, start with a number under 10. If you are in grade 1, start with a number under 20.
  2. Next, head outside with a parent to collect items to match your number. For example, if you choose the number 6, find six interesting items.
  3. Arrange the items in order from smallest to biggest on a surface that you can write on. If you have chalk, it can be a sidewalk. If you have paper, place your objects on your paper.
  4. Label your objects by recording the number you counted under each one.
  5. Take a picture of your work to share with your teacher!

Good luck everyone and happy counting!

Counting Inside

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Today we are going to practice your counting skills! If you can, do this activity with a buddy. It is really helpful to count together so that you can count carefully and accurately.

Here is what you should do:

  1. Find something small to count. It could be dried beans, macaroni, lego or anything else that you might have at your house.
  2. Select a small number of these items for you to estimate and count. You shouldn’t know how many ahead of time. Just reach in a pull out a small handful.
  3. Estimate! Do you think there are more or less than 10 items?
  4. Next, start counting! It can be a good idea to count with a buddy so that they can hear you. How many did you count? How do you know that you counted them all? A good strategy is to touch each item as you count or to move each item from one pile to another.
  5. Think: is there more or less than 10 items? Is this a surprise? If you would like a challenge, think about how many more than 10. Or how many less?
  6. Draw a picture of what you counted and label it with numbers. Take a picture of your work when you are done.

Parents:

If your child is in kindergarten, there is no need to rush beyond 10. The curriculum for kindergarten is centered around 10.

If your child is in grade 1, there is no need to rush beyond 20. The curriculum for grade 1 is centered around 20.

Fancy Counting

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Are your students just beginning to learn about what multiplication is and how it is useful?  These videos are a great place to start. These are all simple explorations of quantity with suggestions for hands-on tasks using basic materials that can be found around the house.  Connections to estimation, skip counting and repeated adding are explicitly made.  Why?  Because multiplication is just a fancy way to count.

Fancy Counting 1:  Grouping by 5’s (using bingo chips and pennies)

Fancy Counting 2: Grouping by 10’s (using dried beans and Cheerios)

Fancy Counting 3: Grouping by 2’s (using shoes and socks)

Fancy Counting 4: Complex groupings using food packets.

Fancy Counting 5: Complex groupings using Lego.

Fancy Counting 6: Practice writing equations (adding and multiplication) using dice or playing cards.

Numeracy Lab Counting Challenge! A counting routine with the following basic steps: select, sort, count and record!

Numeracy Lab Multiplicative Thinking Videos

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Curious about your student’s multiplicative thinking? Here are two videos you can use with your class to get a better understanding of:

  1. The tools of multiplicative thinking: Click here
  2. To what extent do your students think multiplicatively? Try these tasks! Click here
  3. Looking for those student printouts? Look no further! Multplicative Thinking student page

Fancy Counting 1:  A great place to start multiplicative thinking.  What is multiplication anyway, but a fancy way to count?  A simple exploration of quantity using counters with opportunities for estimation, skip counting, repeated adding and multiplying.

Fancy Counting 2: Follows the same format as Fancy Counting 1, but we’re grouping by 10’s this time.

Fancy Counting 3: Grouping by 2’s.

Fancy Counting 4: Complex groupings using food packets.

Fancy Counting 5: Complex groupings using lego.

Multiplicative Thinking 1: Exploring arrays using grid paper.  Students thinking page: Array study

Multiplicative Thinking 2: Exploring arrays using square tiles.  Student thinking page: Array Study Part 2

Multiplicative Thinking 3: Building arrays using base 10.  Especially good for exploring two-by-two digit multiplication.

Multiplicative Thinking 4: Moving from concrete to symbolic representation of multiplication using the area model of multiplication.  I’ve also created practice pages for area model (to be used once the kids are comfortable with the connection): Area model of multiplication

Multiplicative Thinking 5: need to upload to You tube.  Coming soon!

Multiplicative Thinking 6: Multiplicative comparison!  Also good for proportional reasoning. I would follow this one up by having students build their own structures and compare them (differences in height, width, number of blocks used, etc.)

Multiplicative Thinking 7: Estimating and counting volume of rectangular prisms.  See if your students can figure out a way that multiplication might be helpful.

Counting Task Drafts

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These are links to draft counting task sheets that we are using to assess number sense from grades 2-5.  We are tinkering with these, but you are more than welcome to try them out. We are very happy with the shape of them so far, but nothing is ever perfect the first (or second or third) time around.  Please let us know what you think.

Grade 2: Spring 2018 organizer grade 2-1yxb50n

Grade 3: Spring 2018 organizer grade 3-1j1ma4x or if you are teaching a 3-4 split Spring 2018 organizer grade 3 for 3-4-2k3ejbk

Grade 4: Spring 2018 organizer grade 4-1m3p3qy

Grade 5: Spring 2018 organizer grade 5-26yv8ih

By the way, they are formatted to work on ll x 17 paper and require the use of counters.  We chose cheap and versatile buttons ($5.20 for a bag of approximately 1,400 buttons)!  They work for all levels of the task and are especially important for grades 4 and 5.  The grade 4 and 5 tasks also recommend the use of 10-sided dice.

Coming soon: curricular connections, examples of proficiency and recommended follow-up routines.

After counting, then what? Managing Counting Collections

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I’ve continued to tinker with this one!  I’ve been lucky to have been invited into a range of classes from kindergarten to grade four, all interested in building a counting collections routine.

Every class that I have been in has been very focused during the counting process.  It’s wonderful: partners with their heads together, murmuring quietly and placing items in cups, egg cartons or ten frames.  I call this the “counting bliss” phase.

Next comes the recording phase where the teacher is called for guidance.  This is where things start to get busier, especially when some groups are done and ready to show you their work and others need guidance.  And this is where you realize you should have thought about what they do once done!  Let’s keep ’em engaged and busy, am I right?

Here are some suggestions:

  1. Read the room.  This works really well at kindergarten and grade 1.  Teacher Taylor Lepore at Porter Elementary encourages her students to not only find their number around the room, but also to draw where they found it.  One of her K’s was having some difficulty drawing the book where she found the number 17, but could write a letter B for book.  This turned the activity into a joint math, writing and observing lesson.  Pretty impressive!
  2. Build using a number of blocks equal to the number counted. I have tested this idea out with good success in 3 kindergarten classrooms and am about to test it out in a grade 2/3 class.  This particular group of 2/3’s loves to build and really needs to practice their counting.  If they want more building materials, they need to count more collections and record their work!  We figure that we can motivate them to do more recording this way.  Plus in the end, we can get them to think about how many blocks all together.  We’ll see how it goes.
  3. Put their number on a class clothesline.  Soyoung Lee tried this with her grade 1 class.  The students had to first count their collections, record how they counted and then write their number on a blank paper tent.  The students needed to estimate where on the clothesline (between zero and 99) their paper tent should go.  It actually was a really good challenge for them and was certainly valuable for thinking about the magnitude of their number.
  4. Imagine sharing the collection.  This is a great step for grade 3 and 4.  Karin Allison encouraged her students to imagine sharing between 2 people after estimating and counting their collections.  The collection was there for them to actually share out if they wished, but many were ready to strategize without using the objects.  This abstraction can be leveraged to teach certain long division strategies.
  5. Count in a different way. If you counted by 5’s the first time, can you count in other ways?  It is a good question to explore, although I find that kids are keen to try a new collection and not simply recount the old collection in a different way.
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