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John SanGiovanni’s book Daily Routines to Jumpstart Math Class
Welcome fellow Recovering Traditionalists to Episode 181: Exploring Patterns Through Number Routines
The coolest part of mathematics (to me anyways) is the predictability of it. There is a lot in mathematics that works in one situation and still works in every situation. Once kids are able to identify those, and apply them, it makes mathematics so much easier.
For example, let’s say I’m teaching multiplication to 3rd graders. I could just have them memorize their “times 5s” and they will probably get through school just fine. However, if we provide experiences for them so that they can see and use the structure of our number system and see how “times 5” is just half of “times 10,” the mathematical world can open up to them. Not only does 64×5 become a little easier (64 x 10 would be 640, so 64 x 5 would just be half of that) but things like figuring out my 5% discount on $64 becomes easier as well (10% discount would be $6.40, so 5% would be half of that). When children (and even us adults) can look for structure within mathematics, it allows for math concepts to be seen as connected understandings instead of isolated skills.
This is a part of Math Practice #7: Look for and make use of structure in which “Mathematically proficient students look closely to discern a pattern or structure.”
Last week I shared Steve Wyborney’s activity Leaping Numbers as a way to help students Look For & Make Use of Structure and this week I’m sharing another: Finding One and All. This is a routine that you can find in John SanGiovanni’s book Daily Routines To Jump Start Math Class. Rosalba Serrano, one of the PD facilitators here at Build Math Minds, and I recently created a set of slides of this routine for our Build Math Minds members and so I’ll use a couple of those to share with you how to do the Finding One and All routine.
The set up of the routine is basically that it looks like two Number Strings. You have a series of equations on the left and another series on the right, but unlike Number Strings you actually have all of these appear at once and all together.
The first equation has the answer given so in this first series we are looking at it has 5 + 5 = 10 then down the left side it has 5+6….and the right side as 5+5, 5+4…
The idea is to show all the equations at once and have students use the one that is given with the answer to help find the answers to all the equations. Many of the ones we created are like this one that have a pattern to how the equations were written to encourage the students to look for and then use that pattern. However, others are more about helping students explore the structure of mathematics.
This next slide is meant to highlight the structure of subtraction and how changing the subtrahend impacts the answer versus changing the minuend. So down the left side it starts with 225 – 80 = 145 and under that every equation still is subtracting 80, but the minuend is changing. So it has 224-80, 223-80,… on the right side we kept the minuend the same (225) but changed the subtrahend so we have 225-79, 225-78, 225-77…
We have slides for all the operations with whole numbers and we have addition & subtraction with decimals and fractions. This routine not only has students practicing the operations but they are engaging in Math Practice #7 Look For & Make Use of Structure while they do it. So if you are a member of Build Math Minds, log into the site and you will see the link to the Number Routines highlighted in the BMM PD videos area. For each routine we create, there is also a PD video that goes with it explaining the routine and how to do it in your classroom.
For anyone who is not a member here is the information we provided in the slides about how to do this in your classroom:
To create your own, write down an equation and then think about other equations that are related to it. If I went back to my example from the beginning and wanted to help students see how x5 relates to x10 I could create a set of equations like this for Finding One and All:
So, think about some pattern or structure of mathematics that you’d like your students to explore and create a Finding One & All routine. If you are a member of the Build Math Minds PD site, we have them already created for you.
Alright my fellow Recovering Traditionalists, until next week keep building math minds!
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