Investigations Blog

Are There Going to Be More Than 20? More Than 50?

Many of us were taught to “estimate” in elementary school. Maybe we were asked how many jellybeans there were in a jar. Or asked to round before finding the answer to a computation problem. But for many of us there was little connection between those activities and actually solving problems. I would argue that estimating — determining what an approximate and reasonable answer might be — should be a part of the process of solving problems. A visit I made to a 1st grade classroom at the end of...

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“Why are there so much 1s in these numbers?”

Last spring, I visited a Kindergarten classroom near the end of the year. Students were participating in a Math Workshop focused on the teen numbers, choosing among activities that asked them to identify and recognize teen numbers; to represent them in several different ways (e.g. on Ten Frames, with cubes, with numerals); and, ultimately, to come to see them as being composed of ten ones and some numbers of ones.  I wandered over to Stella, who was playing Race to the Top: Teen Numbers. In...

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When the Math Is What’s Exciting

I’ve been really lucky to spend time in a grade 1 classroom this spring, as they tackle the final number unit of the year. 1U7 is the culmination of students’ work with addition, subtraction, and place value. Building on the work of the earlier number units, it introduces some big, important ideas, many of which are new to the 3rd edition of grade 1. These are first graders who had the 3rd edition in Kindergarten and now have a self-proclaimed lover of math, who is teaching the 3rd edition for...

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“This is Only Getting Better!…And Harder!”

Who knew a deck of +10/-10 cards could be so exciting? A group of 25 first graders, that’s who. As their teacher, Karla, introduced them to Plus or Minus 10, she explained that they would need numeral cards (10-90), cubes (assembled in sticks of ten), and a new deck of cards. When she displayed the +10/-10 cards, the students, many of them on their knees, some literally bouncing up and down and clapping, were clearly excited. Oooo… Whoa… Plus ten… Minus ten. I hear two students exclaim This is...

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The Hard Work of Counting by Groups, Part 2

Last week, I wrote about some first graders’ work on problems about how many fingers were on 4 or 8 hands. This week, I want to share an interaction I had with one child, as the class’s work turned to thinking about groups of 10. Students were working on two types of problems about cubes, organized in towers of 10. ·      Given the number of towers of 10, how many cubes? ·      Given the total number of cubes, how many towers of 10? When I joined Nik, he had already solved problem 1, about a...

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