As our numeracy talks start to lean towards actual number talks, let’s look at conservation to 20!
Conservation to 20 numeracy talks are appropriate towards the end of the kindergarten year (the last two or three months). In 1st grade, we would start conservation to 20 around October, after starting with numeracy talks with conservation to 10 for the first few months of school. In 2nd grade, I like starting off the school year, just for the first month or two, with numeracy talks before moving into actual number talks in order to make sure that students have a really good foundation of being able to see the quantity of 20 in multiple modalities.
Just as we’ve talked about with conservation to five and conservation to ten, conservation to 20 numeracy talks help kids learn different ways that they can talk about how they know what they know in a seated number talk at the carpet area and then transition to the table, where students will use manipulatives and replicate the quantities they’ve identified.
Before we begin, as always, you first want to figure out where students are in their understanding of conservation to 20. ESGI has a really great screener that looks at conservation to 20 to see if students are able to identify quantities without counting one-to-one, looking at a double 10 frame, as well as a rekenrek.
There are three different ways that you can look at the quantity of 20: a double 10-frame with four stacks of five, a rekenrek (linear) with one row of five and five, and then below it, another row of five and five, and a Counting Buddy Sr., another linear representation which is not featured in the screener, but is something that we’ll use in the numeracy talks.
The ESGI screener is very simple and you can see in this tutorial video that very quickly, you can figure out which students in your classroom have a solid grasp of conservation to 20. Can they see 13 on a double 10-frame, and then see it in a different modality on a rekenrek and still identify it and transfer their skills?
Perhaps even more importantly than identifying the quantity is the reasoning behind the students’ answers. How do they know what they know? How did they know it was 13? If kids are still saying things like, “I know it’s 13 because there’s ten at the top and three at the bottom,” that’s okay, but we want to encourage more outside-the-box thinking at this stage. For example, “I know that it’s 13 because there are seven spaces empty on the double 10 frame, which means that the filled ones would be 13.”
You also want to look for kids to be able to tie in the part-part-total idea as you’re listening to their reasoning for understanding quantity. They have 13, but can they see that one part is 10 and the other part is 3? Can they see it in different configurations based on how they are decomposing it?
Doing a scatter arrangement at this level is a little bit over the top. It’s too much for the brain to be able to produce back how many they see when we’re dealing with conservation to 20, so we don’t present the scattered arrangements at this level.
After you conduct the ESGI Conservation to 20 screener, you’ll have a good idea of where your students are with this level. If a student, either at the beginning of 2nd grade or who has passed conservation to 10 in a scatter, fails this screener, you want to go back and ensure that their conservation to 10 is rock solid. Go back and do the ESGI Conservation to 10 screener to double-check. If the student does amazing with that screener, then their instructional level is right at conservation to 20. However, if you go back to check conservation to 10, you might find hidden areas of weakness within conservation to 10, so that is where you would concentrate your efforts.
Supporting the Development of Conservation to 20
When kids are ready for conservation to 20, what can we do? How can we help students develop skills in this area? Numeracy talks are one of the greatest things you can do, as they help students see quantities in different ways. Our Numeracy Talks Progression cards are designed to do just that! Progression Cards #1-12 will help you get started with numeracy talks in a systematic way.
Each set of Progression Cards comes with tutorial videos that walk you through how to do numeracy talks in your classroom, whether you’re face-to-face or virtual, and includes a classroom-ready PowerPoint presentation and a companion that goes along with it. We want to see if a student can really understand a quantity in a double 10-frame, in the linear Counting Buddies Sr. (which you can get in our store), as well as a rekenrek (which you can find in our store as well or make your own with these directions!). Get a freebie of Card #9, with all the activities and tutorial videos you’ll need to get started. Members have free access to Cards #9-12 with their M3 membership login, or you could purchase the Green Numeracy Talks Bundle in our store!
Card #12, the last in the progression, really mixes the modalities for students, as you can see in the video. Students will see the quantity in one way, say in a double 10-frame, but will then replicate it with another tool – the Counting Buddy Sr. for example.
Building Number Sense
Once students reach the end of the progression, we can extend it and help students start to gain number sense. Place value strips are a fan favorite at SIS4Teachers. They’re a great way to help kids associate what they’re seeing on the double-10 frame, the Counting Buddy Sr., and the rekenrek as “10 and some more.” Making a strong connection between how many 10s and how many 1s is really a precursor for what we’re going to be talking about next in our blog series, which is all about the importance of place value.
I recommend using the place value strips by starting with the numeracy piece. Say you flash the number 17 as a quantity in a double 10-frame and you want the students to build it with their place value strips. They’d use a 10 and a 7. Knowing how to look at a teen number and isolate the 10 will help students be more successful when the start expanded form, as well as partial sums and decomposing by place value in second grade.
Students could also build the quantity on non-proportional or proportional manipulatives. Proportional manipulatives would show the quantity in base 10 blocks so for 17, students would show me one 10 stick and 7 individual ones. T-Pops’ Place Value Mat and place value discs would be a non-proportional manipulative option where students could show their 10 and then 7 more.
Beyond Conservation to 20
Don’t stop when you get to 20! After this stage of conservation to 20, it’s really important to continue that growth of getting kids to understand numeracy as it starts to relate to number sense. I love going to dreambox.com/teachertools, and using their 1st grade tools, Numbers to Forty on the TenFrame to continue your numeracy talks (especially in first and second grade) so kids can start to understand the numeracy and connect the number sense.
So let’s say I flash up three 10-frames that are full, with two on the fourth 10-frame (32). Students could either build that with the place value strips, place value discs, or with place value, by using the base 10 blocks.
You could go all the way to conservation to 100 using an abacus. The abacus is a great tool for students to be able to understand our number system, because it’s all in 10s. Don’t have an abacus? Get one from our store, or use a virtual abacus from dreambox.com/teachertools or the virtual app from the Math Learning Center. Show an amount, maybe 63, and have kids build it in another way. You could even ask students to show you 10 more or 10 less than that number.
Last, but not least, don’t forget the Deck o’ Dots! Our Yellow Level cards are made up of 10-frames, but don’t limit yourself to one! Maybe you flip over four full 10-frames and then you flip another next to it. Maybe you flip three 10-frames and then add another number to it. Play around with the different Deck o’ Dots games and activities and see how this kind of activity helps solidify the connection from numeracy to number sense.
What’s next? Numeracy talks lead us to number sense, which is a pivotal piece to the understanding of place value. Join us next week to find out how it all works!