# 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...

read more## 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...

read more## “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...

read more## 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...

read more## The Hard Work of Counting by Groups

The other day I visited a class that was at the very beginning of How Many Tens? How Many Ones?, the final unit of the grade 1 sequence on Addition, Subtraction and the Number System. The class began with a conversation in which they modeled, recorded, and discussed the previous day’s work, about the number of hands on different numbers of people, organized as a table. The teacher then explained that today they were going to be thinking about fingers instead of hands. With minimal...

read more## What Happens When There Are More Than 10?

Imagine you are 6 years old. Or 7. You know you can use your fingers to model subtraction. For example, for a problem where there are 7 grapes and 2 get eaten, you can raise 7 fingers, put down 2, and count how many are left. But what do you do when the problem involves more than 10 things? Take a moment, before looking at the student work and video below. How would you use your fingers to solve a problem about having 12 scissors, and lending 5 to another class? A student I’ll call Miguel is a...

read more## How Do We Support Students in Reflecting on Mathematics?

As I worked with teachers in classrooms this fall, the topic of how to help students reflect on their learning and the learning of others kept coming up. I’m still thinking about how to recognize, encourage, and promote student reflection about math ideas. What traits do reflective students possess? How can a teacher nurture a learning culture where reflection is a natural part? When students engage in math experiences that include time to reflect on their reasoning and the thinking of others...

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