A Peek Inside: Fishy Business, Composing and Decomposing Numbers - Math Coach's Corner

A Peek Inside: Fishy Business, Composing and Decomposing Numbers

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

I know I shouldn’t play favorites with my products, but I just LOVE Fishy Business! How could you not love these fish?

Aside from the adorable fish, however, the unit is about one of my favorite topics–composing and decomposing numbers.  I think it is also a good example of my philosophy for designing products.

  • First and foremost, my products are designed for a math workshop or guided math approach to instruction.  Although some units include printables, my products are really meant to be used in either (1) math workstations (centers), (2) small group instruction, or (3) whole group number sense routines.
  • All of my products are research based and very “mathy”.  I don’t specifically include references to the Standards for Mathematical Practice in my units, but that’s just how my mind thinks, so I always try to incorporate problem solving, critical thinking, multiple representations, CRA, and opportunities for students to justify their thinking into my products.
  • Although my products include engaging graphics, I don’t really do themes. I do have a few seasonal items, but for the most part, each of my units focuses on a skill or group of skills, and I usually include Common Core alignment.  The graphics are typically season-neutral (I think I just made that up…), so you can use them throughout the year.
  • I try to make my units as flexible as possible and give you plenty of ideas for using the materials.  My units all contain detailed teaching pages (which are usually included in the preview you can download) that show pictures of each of the activities with instructions for use.  I also include explanations of the math that’s behind the activities.
  • Finally, but certainly not unimportant, I design my products to be easy for you to prep.  With my products, your paper cutter is your best friend.  I lay out all of my cards so that you can cut them up with a few quick whacks of the paper cutter.

Now, on to Fishy Business…

As I already mentioned, this unit is about composing and decomposing the numbers from 5 to 10. Composing and decomposing are just fancy words for knowing that a whole is comprised of parts. For example, knowing that 5 can be ‘composed’ of, or ‘decomposed’ into, 0 and 5, 1 and 4, or 2 and 3.  Each of the activities is designed so you can focus on a target number, so the activities grow along with your kiddos. You might have the majority of your students working on combinations for 5, a couple others working on combinations for 6 or 7, with a few high-flyers working on combinations for 10–all using the same activities!

First up is one of my favorite activities, Shake and Spill.  Shake and Spill is an easy and flexible activity that can be used with any target number.  In the example shown below, the target number is 5.  To play, students need 5 of something to “shake and spill” onto the mat.  I chose jacks, because I had them lying around. Notice that I like to put the Shake and Spill mat inside the workstation box to contain the “spilling”. Students continue shaking and spilling the counters until they have found all the combinations for 5.  To change the target number, simply change the number of counters that are used.

One jack landed on the fishbowl and four are outside the fishbowl.  You can see how the combination is recorded on the accompanying printable.  Printables are included for the numbers 5 through 10.  A math journal could also be used to record combinations.

Who doesn’t like a good spinner game?  Spinner boards, with ten-frame representations, are included for the numbers 5 through 10.  Notice that student instructions are included on the board itself.  You can also use the recording sheets from Shake and Spill to record combinations.

A pencil and a paperclip are all you need to turn this board into a spinner.  For additional concrete support, include a ten-frame and counters in the workstation.

What would a unit on fish be without a Go Fish game?  Cards with ten-frame representations are included for the numbers 0-10, with a Wild Card.  The game can be played as Go Fish Make 5, or Go Fish Make 6, etc., all the way up to 10 by using only part of the cards.  For example, for Go Fish Make 5, you’ll only use the 0-5 cards and the Wild Card.  You’ll want to make several copies of the sheets, though, to make a full deck of cards.  To begin, players draw four cards.  If your kiddos can’t hold the cards in their hands, let them use a privacy folder and lay out their cards behind it.  All the remaining cards are face down in the “pool”.  The goal is to combine two cards to make the target number. When a player has a pair that make the target number, they lay them down.

This shows a hand for Go Fish Make 5.  The player is holding a 1, so he/she is looking for a 4 to make 5.  On their turn, they would ask, “Do you have a 4?”.  If the other player has a 4, they must surrender it.  If the other player does not have a 4, they say, “Go fish”.

The next cards included in the unit are the How Many More? cards.  Cards are included for the numbers 5 through 10, and the examples below show several ways you could use the cards for combinations for 5.  But remember, you could do these same activities for any target number or you could mix the cards up.

Pull out only the cards for the target number you are working with.  In this case, I pulled out the cards for 5.  Notice the cards have a pictorial representation of the number.  I’m always keeping that CRA sequence of instruction in mind!  You can use the cards with the printables to record combinations or they can record the combinations in their math journal.
To add a concrete component to the workstation, add blank ten-frames and counters.  In the example shown, the student drew the ‘3 fish’ card, so they put 3 counters on the ten-frame and added 2 more to make 5.  Click here to grab a sheet of blank ten frames.
The cards can also be used with the Back and Forth game board.  To play, the marker is placed on the START space.  Player 1 moves the marker toward the left and their ‘home’ space, while Player 2 moves the marker to the right toward their ‘home’ space.  Player 1 has drawn the 4 Fish card.  Using the ten-frame, they determine they need 1 more to make 5, so they move their marker one space to the left off the START space.
Player 2 draws the 1 Fish card.  Using the ten-frame, they determine they need 4 more to make 5, so they move the marker 4 spaces to the right.  See why it’s called Back and Forth?  The first player to make it to their home space wins.

Finally there is a set of equation cards.  These cards show both addition and subtraction equations for the numbers from 5 through 10.  Keep in mind that these cards are totally abstract (symbols only), so either they should be used with manipulatives or after students have had lots of concrete and representational practice.

These cards can also be used with the Back and Forth game board.  In the example shown above, I have included a ten-frame and counters to provide concrete support.  The player has drawn the card shown, 5 – 4 = ?.  To model the equation, they put five counters on the ten-frame to represent the starting number.  See the next picture for the next step.
To show the ‘minus 4’, the player turns 4 of the counters from the red to the yellow side.  They could also take 4 counters off the ten-frame.  On the Back and Forth board, the player would move 1 space toward their Home space.

Ready to grab yours?  Head over to my TpT store to pick it up!  Don’t forget to rate the product and leave feedback to earn TpT credits good for future purchases.


  1. Ronise Herbert

    Hello, my partner and I are noticing how closely related math is with reading. She is actually reading a book that uses metacignitI’ve strategies for math. She has been looking high and low for leveled math books. She wants to be able to have small math groups that can read at times. I also would pull from her leveled books and use them in my small guided reading groups. But we haven’t been successful finding a company that has leveled math books. Please advise! We are fourth grade teachers


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