I've been grounding my math thinking and teaching of mathematics this week by reading Second Grade Math, A Month to Month Guide by Nancy Litton. This book is from the Math Solutions/Marilyn Burns group, which never steers me wrong. I've read and used the kindergarten and third grade books in this series and have found both filled with useful ideas to implement and make part of my current teaching assignment.
My class has been starting each morning with a good questions/rich math problem and one of the changes that lays ahead for us is to bring problem solving to the forefront of our daily work via the mini lesson and independent work time. Therefore, I wanted to change our beginning work for the day as students stagger in and begin thinking for the day.
When I read about Today's Number: A Daily Routine I knew this had potential for us to grow and think more about mathematics. This is an idea I've used randomly in the past and not as a daily routine. The target number for the day is either the number for how many days you've been in school or the calendar date. The students use a journal/notebook to make "A Book of Equations". The target number for the day guides equations the students will generate and record. Students will work independently. They will share ideas at the end of morning meeting and transition into math workshop by learning from the equations friends are sharing.
These are some key questions I read that I will be using with this new routine that will help us apply and be engaged with the eight mathematical practices.
Does this equation work?
Can you convince yourself that it does?
I see a problem with that equation. See if you can figure out what I mean.
Can you prove your equation is true?
What make you think that?
Did someone else think about it in a different way?
One new idea for me with a routine like this is to help expand a student's thinking by sometimes offering guidelines to reinforce concepts taught in class. Each month the reader will find suggestions to expand the students' thinking about equations. Some ideas shared from the September chapter are - "use only addition, use combinations of ten, use doubles, use only subtraction, and use both addition and subtraction."
I've tried this a few times this year within our good questions/rich problems and found my students needed encouragement to tell me several ideas about a number. I found many students would find equations by using an easy pattern, for example - minus one. I found my students didn't vary the operation used or use more than two parts to make the target number. I found this a bit disappointing. I want to see varying operations, a range of numbers, and a range of strategies. I think working with equations each day can help with this. I also think and know by conferring with students during this time, I can differentiate to help student's work with numbers that will extend their own thinking.
Here are some more thoughts grounding me with this new routine.
"...look for opportunities to help students see new ways to decompose numbers, notice number relationships, and use mathematical operations meaningfully."
Also, students will be recording lots of thinking within their equations and they are bound to record mistakes. "...remind yourself that such mistakes are OK and that you don't have have time to correct each child's book every day."
"...this routine is a playful way for the children to develop number understandings."
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