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?
I would use place value disks by using repeated addition. I truly can think of a better way to use them to teach the concept of multiplication. I think teaching patterns in addition to repeated addition on the chart would be beneficial. But to be honest, the place value chart has never been a tool I have used much of to teach in bigger grade levels.
ReplyDeleteArea models I never used prior to this previous year as I had never learned about them. Having found out about them and used them, I felt cheated going my whole life without them. They are amazing.
ReplyDeleteMe too Dawn! When we started using the word "arrays" more frequently a few years back, I felt the same way. I wondered where they had been when I was a kid.
DeleteMy favorite resource is YouTube. There are so many wonderful videos out there about area models.
ReplyDeleteI agree with you Carrie about the author not showing enough examples to link to repeated addition. I had a student who was working on multiplication in Success Maker this year and I showed him the repeated addition aspect more than anything because I knew he could relate to that better as he was only in first grade. Oh, and just fyi- not sure if I was the only one but I couldn't see your pic you used to show what you would do (from my phone or computer).
ReplyDeleteI love how no matter if it is addition, subtraction, or multiplication they all go through the same basic process- number bonds, place value disks, etc. If we can get everyone from K on up to go through the same process in that order I feel that our students will benefit greatly.
I think the place value disks are an awesome visual tool for the students to see (and concrete). You can see the repeated addition so clearly through them too! I wish I had learned things like this when I was in school, but all I can recall was the traditional method.
The area models were neat to experience too. I found myself practicing with the example as I also had never been taught that way. There are so many resources out there. I usually type in whatever I am looking for on pinterest, but there is also just a teacher board called proteacher.com (basically like pinterest but no pics or links sometimes). It is just teachers posting what they have a question about and other teachers respond.
You made a great point when you said you had a kid working on multiplication because some students will inevitably move faster than others. What a great way to prepared by knowing what upper grade levels will cover and the strategies they will use with students. I think that that coherence will help fight "summer slide".
ReplyDeleteI will be checking out proteacher! Thank you for sharing!
I totally agree with Carrie, the connection between repeated addition and multiplication must be made for students to really understand what is happening with the numbers. I would have students show concrete representations of both repeated addition and multiplication with the place value disks. By taking the time to be sure they solidly understand the relationship between both concepts, students will have tools to problem solve when rote memorization fails them (like going blank on a test). Also, I like the way the author uses kinesthetic activity to support learning. By holding a factor in each hand and combining them in the end to form a product over their heads. Students will have a physical representation to match the pictorial representation of the number bond. Another thing I think is worth mentioning...in the 2nd paragraph on page 53 Hazekamp stresses the importance of varying your vocabulary. HUGE! HUGE! HUGE! I have noticed that students who have a strong grasp of math concepts, but have weak math vocabulary will suffer greatly during standardized testing. When students get in the habit of explaining their work using specific math vocabulary (product, sum, difference, place value, factor), they are also able to talk their way through the process when working independently.
ReplyDeleteWhat did you think of the area models?
I LOVE area models! Again, this emphasizes the way numbers can be broken-up (decomposed) and then put back together in manageable pieces. Using arrays also helps reinforce the concept of expanded form and place value. By using area models the students form a much deeper understanding of multiplication. They become accustom to seeing numbers represented in a variety of ways, while still getting the same solution. This adds to their math tool box. The more ways the students can visualize what is happening mathematically, the less likely they will be confused when given a problem they’ve never seen before.
A resource I like to use as review is Mathantics.com
https://www.youtube.com/watch?v=xCdxURXMdFY