Last week, we talked about screening students to determine their level of kinesthetic development, looking for one-to-one correspondence.

The next level we screen for is conservation to a number, where we look to see if a child can use part of what they know about numbers to add on to other numbers. If you ask a child in 1st grade or kindergarten to add five + two, they often start counting at one. Even if you ask the child how many fingers they have on their hand, and they tell you five, they will still one-to-one count each finger before they add on the two to get the total of seven.

The concept of conservation is essential for kids to understand as they start to add and do things later on in math with larger numbers. We break down the larger concept of conservation into three levels: conservation to 5, conservation to 10, and conservation to 20.

Another important skill we look for when we screen students is subitizing, which means tell me how many without counting. Although many people think subitizing is mathematical milestone for students, it is really a strategy that helps kids start to master the concepts of conservation. Subitizing has become a buzzword in early childhood classrooms in math, and there are many types of activities that we do to help with subitizing. It’s important to understand the developmental sequence that goes with the use of subitizing as it relates to conservation to a number.

### Conservation to Five

To do this, we use our Understanding Number Quantity Screener. We start with the five frame, which we use to assess whether or not the child has conservation to five in an arranged line. Students that have conservation to five can determine what the number in the five frame is based on the structure they see. We can start by flashing a five frame, with colored circles (we use red circles in our screener). Ask the child how many they see and then we ask them how they knew.

In this video, this child is able to tell us reasons why he knows it’s five.

We really want to listen to kids’ reasoning within this arranged line of 5. Some kids reasons might be something like, “because it’s four” or “because I know!” or “because I’m super smart.” Some kids might say, “I know it’s four because it’s two and two.” A child might say, “because there’s an empty square. If that whole frame was filled, it would be five, but since they took away one, that’s why it’s four.”

Sometimes we overestimate the idea of five, thinking that it’s too simple and there’s not much we can do with it. However, in the early years, we really can dissect the idea of five a little bit more.

#### Change the Orientation

If a child is completely successful identifying quantities with the traditional horizontal five frame, although it seems silly, try turning the five frame vertically to see if they can still read it from top to bottom. Kids have different reactions when you turn the five frame vertical! Last year, in Midland, some kids thought it was funny when I turned the five frame vertically. One student told me “It’s still four, Mrs. Samulski, it didn’t change…” and he looked at me as if I was crazy. Another boy that had mastered horizontal five frames, just said, “Oh man, that’s a lot. I don’t know how many.”

#### Patterns/Scatters

We really want kids to understand this in different ways and be consistent in this concept, no matter how we change it. We can take away the structure of the five frame completely and arrange the dots in different patterns, like on a dice. Can students still identify the numbers 1-5 when the dots are not arranged in a straight line?

Arranging the dots in a scatter is another way to check for a solid understanding of conservation. You might have three going across the top with one in the middle. Or you might have a row of three along the side, and one on the other side. Do the kids go back and count all the dots? Or do they just recognize that it’s still four because they see groups of two or two, or three and one.

If they aren’t able to transfer that knowledge of number quantity from the five frame, we know that they may not actually have conservation, but may have actually just memorized that concept.

#### Building this Level

When we find kids in this area, we want to use different activities to build conservation. Our Deck o’ Dots are perfect for helping kids learn to subitize to five! The red deck is all five frames that are arranged and the green deck (where Dotson does not have any stars on his shoes) has scatters with 0-5. If a child does well with the five frame consistently, they can use one of the Deck o’ Dots games independently in a station. These games are also really appropriate as a guided area if the child does understand conservation within the arrangement of the five frame but is struggling when it’s in a more scattered formation.

If you’re doing numeracy talks in your classroom, you’ll want to be doing a lot of flashing with that five frame, not only horizontal, but vertical and also in a scatter. You can prompt the conversation with questions like “How many are empty?” “What’s one less?” “ What’s one more?”

Kids must be comfortable in the concept of conservation to five before you move on to conservation to ten. I often see scatters being flashed in kindergarten classrooms that are much higher numbers or higher level scatters. Sometimes I see teachers going too fast right from the five frame into the ten frame, when many of the students are actually still one-to-one counting each of the dots instead of having visual recognition.

**Conservation to Ten**

Conservation to ten follows a very similar pattern, but the jump from five to ten can be confusing for some students. If the students understand the five frame, can we add on one more? If we show them the five frame with five dots, and then show them another five frame with just one more to make it six, can they determine the quantity or are they lost?

#### Change the Orientation

As we screen kids with our Number Quantity Screener in the ten frame, we know that we’re not just looking at being able to read the ten frame, but also looking at the concept of conservation to ten. Does that child see the seven in the ten frame and know why it is seven? Do they know why the three empty spaces in the ten frame means seven? Do kids have communicative understanding when looking at that ten frame where they can talk about what they see and why they know?

#### Change the Structure

If kids do well on the ten frame and are able to give good reasons for knowing, we then move into the Counting Buddy Junior. The Counting Buddy Jr. has five beads of one color and five of another that are moved in a macrame beaded style. It helps us see if kids have conservation when the quantity is more linear. If I were to look at a ten frame with six in it (five and the bottom and one at the top), are kids also see six when there’s five of one color and one of another color.

As we did with the five frame, we can change the orientation, but keep the dots arranged, to see if that child actually still has conservation to ten.

#### Patterns/Scatters

Once conservation to ten has been established, you can start to do things in a scattered arrangement in order to help kids understand the idea of part/part/whole. The image might have dots in dice or domino patterns, or groups in different colors. If students can see five in a dice pattern and then see a group of two on top, they can know the answer is seven. Scatter images take this concept a bit out of the ten frame or counting buddy structure, but this step can help us see if students are transferring that idea of conservation.

We want kids to be able to use this concept and get to the point developmentally where they feel comfortable with it before moving along to something more complex.

#### Building this Level

Of course, you can use our Deck o’ Dots here as well. The yellow deck uses the ten frame, and the green deck that has Dotson with stars on his shoes, show scatters with quantities from 6-10. Our Counting Buddy Book activity is another way to add some more practice with conservation. . It has over 50 activities that you can do with either the Counting Buddy Jr. or Counting Buddy Sr.

Again, in numeracy talks, or number talks, it’s also important to show this concept in a flashed way where kids can see it in different formats. Dreambox.com/teachertools can actually help you with this part – it flashes with ten frames, but it will also do the linear model as well (like the Counting Buddy Jr.) – where it has five of one color and five of another color in a line).

Asking questions like, “how many are empty?” “what’s one more?” “what’s one less?” At this point in the building of conservation, you might even ask “what’s two more?” or “what’s 2 less?” to see if kids are visualizing.

### Conservation to 20

This last stage is conservation to 20. Can students look at a double ten frame and be able to determine number quantity like they’ve been doing all along? We’re looking to see if kids can use what they know about a full ten frame with seven more in another ten frame to determine that the quantity is 17 because three are empty, so it’s three less than 20.

#### Change the Structure

Can they then transfer that knowledge to a rekenrek, which has a completely different, more linear orientation than anything we’ve seen so far? When you have two ten frames, you essentially have four stacks of five, top to bottom. When you have a rekenrek, the sets of five are broken up differently, going from left to right instead. Can a student look at a rekenrek and see 17? Some kids might see it as ten and seven, some kids might see five, five, five, and two.

The Counting Buddy Senior is the next level of conservation to 20. It is similar to the Counting Buddy Jr, but the senior version has ten of each color. The Counting Buddy gives kids a linear look at 20, ten and ten. If we’re looking at 13 again, we want kids to see that ten of the beads are over and then another seven are pushed over. Hopefully, they’ll see the seven left on the end of the string to know that that is 13 because it’s seven less than 20).

#### Build this Level

Our Deck o’ Dots Games are great for kids to use and experiment with at any level of building conservation. You can flip two cards at a time from the yellow deck to show the double ten frame, and there lots of other activities with double flipping or using concepts up to 20. In a scatter, to make it more challenging, see if kids can add those together.

In your number talks, make sure to flash the double ten frame and the rekenrek as well as the Counting Buddy, to get kids to use that structure and really have conversations about this.

Dreambox will let you flash up rekenrek images as well as the double ten frame. It’s really great to have kids replicate the things that the teacher assigns as a challenge . Be sure to ask them things like – “what is five less?” or “ how many are empty?” and questioning to find out why the know what they know.

We want to assess kids at the beginning of the school year and see where they coming with numeracy skills. As we talked about in other blogs, many kids are not counting and doing a lot of kinesthetic things or having experiences with this move. It’s very eye-opening for our kinder and even 1st grade teachers to look to see where kids are in the idea conservation.

Obviously, if you had a student that completely fails the five frame and is overwhelmed by that concept, our screener tells you to back up and start to look at that kinesthetic one to one correspondence

It’s kind of like the idea where if I can’t rhyme, then obviously I’ll be doing other things like changing the m in mop into a p and kids need to able to play with those concepts. **Think about the idea of number quantity and the ten frame and compare it to phonemic awareness and words – we want students to achieve literacy in both areas. Students must be able to play with these things, changing them in their heads in a way that makes sense.**