Good morning! There is nothing like a sitting down with a morning cup of coffee and a good math book while the sunshine streaming through the windows. There is an appreciation for moments like these where professional growth can be absorbed instead of served up like fast food. We can take our time and think about the information. At least we can until the kids wake up. Then it's anybody's game!
So let's take a look at what we have for this week.
"Although children have an impression of division as more advanced than, say, addition, it is just as much a part of their day-to-day experiences as addition, subtraction and multiplication. Think of kindergartners passing out birthday treats or first graders sharing a bag of pretzels or a pizza." (Hazekamp, pg. 76)
So why is this such a difficult idea for kids to master? Hazekamp suggests it is because we are tied to the algorithms and not the concepts. In her division chapter, she suggests a sequence of 6 steps for teaching division.
1. Number Bonds
2. Place Value charts and disks
3. The distributive property
4. Partial quotient division
5. Traditional long division
6. Short division
I have spent the last month discussing number bonds but what intrigues me in this division chapter is using the distributive property. I actually spent some time online researching it further, looking for videos of teachers using it in their classes or even showing lesson plans for how they would introduce this concept in division. I have a few links below for your perusal but what I realized is that to use this strategy, kids have to have a VERY strong sense of numbers. They need to be completely comfortable with place value concepts and multiples of numbers, at least within basic fact families. Hazekamp mentioned that is is a strategy used with "friendly numbers". Kids would have to learn what a friendly number looks like and what an unfriendly number would look like.
Resources
https://m.youtube.com/watch?v=9PqQCCcP0u0
https://www.teachingchannel.org/videos/common-core-teaching-division
http://www.cpalms.org/Public/PreviewResource/Preview/72779
Reflection Questions
What strategy intrigued you?
Name your biggest challenge when teaching division and how you plan on addressing it this year.
What underlying knowledge and skills do you think are the most crucial to teaching division?
Thursday, July 16, 2015
Tuesday, July 7, 2015
Summer Book Study: Week 3 (approximately)
As we progress towards our last week of this book study, we take a look at multiplication. Even though some of you are primary teachers and perhaps not teaching multiplication to your students, it is good to look at how the strategies in your grade levels will continue on in later grades. The skills are not taught in isolation, but woven through the years to provide coherence for our students.
On page 52, we get see the stages for multiplication. Number bonds are named once again as a concrete method for teaching math. It continues on with thenplace value disks, adding place value charts. I want to point out that place value charts are used in division too. This is a great strategy for teaching division so I would definitely start using them with multiplication so they would be familiar to students before tackling a harder concept.
The stages continue with the distributive property, area models, and finishes with traditional multiplication. So there is our summary.
I was looking over the number bonds and could see the part-whole relationship. But as I read through the text, I felt that there should have been an example that demonstrated the connection to repeated addition. Since number bonds have been used thus far for addition and subtraction, Hazekamp's example of a multiplication number bond on page 53 might be a little confusing if there is not some more scaffolding. I could be wrong but I am also thinking of my population of ESOL, ESE and low-socioeconomic students. I think starting with 48 and showing 8 in six bubbles would have been a more appropriate way to start.
The guided conversation begins with manipulatives and moves into number bonds but here is what I would do before using digits:
This is from page 55 and I drew in what I would use if the students needed more support. I want to show the connection to repeated addition before simply writing out the fact families. Then we could discuss how to record such things more efficiently.
Reflection questions:
How would use introduce place value disks and charts for multiplication?
What did you think of the area models? What other resources can you find to help you teach using are models?
On page 52, we get see the stages for multiplication. Number bonds are named once again as a concrete method for teaching math. It continues on with thenplace value disks, adding place value charts. I want to point out that place value charts are used in division too. This is a great strategy for teaching division so I would definitely start using them with multiplication so they would be familiar to students before tackling a harder concept.
The stages continue with the distributive property, area models, and finishes with traditional multiplication. So there is our summary.
I was looking over the number bonds and could see the part-whole relationship. But as I read through the text, I felt that there should have been an example that demonstrated the connection to repeated addition. Since number bonds have been used thus far for addition and subtraction, Hazekamp's example of a multiplication number bond on page 53 might be a little confusing if there is not some more scaffolding. I could be wrong but I am also thinking of my population of ESOL, ESE and low-socioeconomic students. I think starting with 48 and showing 8 in six bubbles would have been a more appropriate way to start.
The guided conversation begins with manipulatives and moves into number bonds but here is what I would do before using digits:
This is from page 55 and I drew in what I would use if the students needed more support. I want to show the connection to repeated addition before simply writing out the fact families. Then we could discuss how to record such things more efficiently.
Reflection questions:
How would use introduce place value disks and charts for multiplication?
What did you think of the area models? What other resources can you find to help you teach using are models?
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