Check out the other posts in this series! Emergent Part 1, Perceptual Part 2, Initial Number Sequence Part 4, Intermediate Number Sequence Part 5, Facile Number Sequence Part 6.
Get the full overview in one place! Presented at the Making Math Moments Summit, you can get the full presentation here!
What is a Figurative Counter?
This type of counter can be kind of tricky to identify because they are very similar to the previous, perceptual counters.
Students who are in this stage of counting can count items if they are blocked from view but need to recreate the value of the collection using a re-presentation. If I showed this counter 7 items and then covered it, they would need to recreate 7 by way of fingers, taps, or in their heads to then use it for addition.
The counting they are doing may seem redundant to adults.
If they have two collections of counters that are covered, they can tell you how many in all but will have to count from one instead of counting on from one of the numbers. This is different from perceptual counters because perceptual counters will not be able to solve an additive task with a collection that is not visible.
What do I look out for?
There are some things you might see students do to let you know that this is where your students are:
Can count beyond 10 to 30 or more but may not be able to count to 100
Can count backward from 10 but perhaps not beyond or from any other number, 28, 35 etc.
Know finger patterns to 10
Can recognize errors and self-correct if asked
Understands cardinality, the last number said is the value
Can keep track of numbers not counted (screened) even if different arrangements
Writes or draws 1-10, then 20, 30
number after, with a running start
Can count concealed items, build either with fingers or mentally
How can I help students in this stage of counting?
Students at this stage have solidified the idea of one-to-one correspondence and can count, identify and write numbers to 20. At this point, you will want to give students opportunities to understand that their counting style may not be efficient and begin to develop counting on and not counting by ones counting strategies.
This includes
Working on the number sequence as it can be a tricky part of counting
Centers that encourage students to count on instead of counting from
Start to recognize common number relationships, number pairs, and making numbers to 10. Decomposing numbers to 10 and teen numbers. (15 is 10 and 5 etc.)
Number Talks with number stings to support counting on strategies, 1+2, 10+3, 9+4
Activities to Encourage Counting On Strategies
Roll + Pick
For this game, students will roll a die, and build it on a 10-frame. They will then pick a cart that says +1 or +2, they will then have to add 1 or two more and write their starting number, the number they picked, and the new number they created on the recording sheet.
Hide and Count
This is a partner game. Partner A rolls two dice, waits 3 seconds then hides only one die. Then partner B has to count how many dots there are altogether. Both partners check if the answer is correct and if partner B is correct, they can move their piece on the game board until one player finishes. You can also play the print-and-play version where students color in squares on the gameboard and the person with the most at the end wins! Get it here on TPT or the website store!
Or save with the Counting On Bundle!
Activities for Making 10, Decomposing Numbers & Number Talks
Note: While understanding decomposing numbers are needed this falls under "structuring numbers." below are some ideas to support that if need be.
Quick Images Number Talks
Quick Images in a number sense routine where you show students an image (like a dice face or 10 frames) quickly so they don’t have time to count and have to begin to subitize and go beyond counting by ones.
Using incomplete 10 frames is a visual way for students to start to make ten by filling the 10 frames mentally and counting the extras.
Shake and Spill
To play, students gently shake and spill their double-sided counters, they will need the same number for their whole sheet. They will write how many were red and yellow and continue until they finish their recording sheet. You can have them get a new sheet for each number, or copy them all into one booklet they can use over several days.
How Many More
This resource is perfect for supporting kindergarten and first grade students learning the number combinations of 3-10. To play, students spin a ten frame, write the number spun, and color in the same number of squares as the number spun with one color. Then with the other, color fill in the rest or write the number to begin to become familiar with number combinations within 10.
Snap It, Hide It!
1. Make a cube tower with the target number.
2. One partner holds the cube tower behind their back and breaks the tower in two.
3. Then the partner with the tower shows the other partner or partners one part of the tower, keeping the other hiding behind them.
4. Then the partner without the tower has to figure out how many are hiding.
5. Both partners record the two parts of the tower on their recording sheet
6. Repeat with the other partner having a turn with the tower.
Story Problems for Decomposing Numbers
You can easily pose a part-part whole problem with anything that has parts. For example, 2 soccer teams, Red Foxes and the Green Frogs played in the championship and 8 goals were scored. How many could have been scored by the Red Foxes and How Many by the Green Frogs? These types of problems are great to do with the Building Thinking Classrooms Framework because there are so many different answers! Giving students the opportunity to talk about their thinking with each other is an effective and culturally responsive way to help students make sense of numbers and how they relate to each other.