Over the past weeks, I have done a lot of blogging about our work with decimal multiplication. All of this work has been focused around contexts that involve multiplication of a whole number by decimals both greater than and less than one. The students have very flexibly moved into using whole number strategies in order to multiply decimals during our number talks. Today I asked them to think about how whole numbers multiplication is similar or different from multiplication involving decimals. I was hoping to hear the relationship between the factors and the product and they did not disappoint. These are the findings from my two math classes…
I asked them to prove that a decimal greater than 1 times a whole number will have a product that is greater than both factors OR if a whole number, less than one, times a whole number will have a product that is less than one factor but greater than the other.
We shared out and ended the class predicting what they think would happen when we multiply two numbers that are less than one. This is where I saw an interesting difference in the way students thought about the problem. Some focused on the numbers and what it means in an “of” sense, while others connected to what happens with the multiplication process.
This makes for such an interesting conversation tomorrow! Excited to see the fractions come out and for students to revisit their predictions! This is the work tomorrow from last year’s experience: https://mathmindsblog.wordpress.com/2014/07/25/unanticipated-student-work-always-a-fun-reflection/
This is very interesting…
I would love to hear students talk about what it means to take a “decimal of a decimal?” Can they draw a picture that would make sense to them and their classmates?
I want to ask the student who made connections for “negatives” to say more about how they think that decimals less than one are like negative numbers. How similar are they? Do they always behave the same?
Some really cool fractional reasoning in their thinking already. I love it!
I would love to know more about how the student who wrote about repeated addition and the other student who likened this to adding two decimal numbers smaller than one explore their thinking tomorrow!
The thinking about number close to a whole perhaps behaving in a particular way fascinates me.
Don’t shut me out because I’m not there! I will drag myself there on Wednesday!
Oh trust me, I am taking all of these questions and looking for answers tomorrow!! Cant wait to see you on Wednesday!
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