Investigations Blog

“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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Getting Started: What’s Critical at the Beginning of the Year? Part 2

We recently asked a group of experienced Investigations teachers the following question: How do you think about creating a math community? What’s critical, particularly at the beginning of the year? In Part 1, we shared their thoughts about setting up the classroom, organizing the math materials, and establishing and maintaining norms. Here, we share their thoughts about Math Workshop and discussions – two structures they cited as critical to a successful and productive math learning...

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Getting Started: What’s Critical at the Beginning of the Year? Part 1

In our summer work with teachers, many of whom are new to Investigations and/or are rethinking the way they teach mathematics, we get lots of questions. Some come up after reading about a structure like Math Workshop, or seeing a list of materials needed for Unit 1. Others arise after “visiting” a classroom – via a Dialogue Box or video of a classroom. For example: How did students learn to discuss math ideas, and listen to each other, like that? Pairs were working independently, all over the...

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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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Developing Mathematical Language is Hard Work

Using language to effectively communicate one’s mathematical thinking is an important skill—one that is a focus of Math Practice 6: Attend to Precision. Many of us know firsthand that clearly articulating mathematical ideas is challenging work, and that when students use ambiguous, imprecise terms in their explanations, their language can actually get in the way of understanding. Developing precise language is key if we want to students to engage in rich, collaborative discussions in which...

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And Then, She Waited

Have you ever been teaching (or leading professional development) and asked a really good question only to be met with silence? We all have teacher moves in our back pocket for situations like this—maybe do a turn and talk, ask the student if they’d like to call on someone to help them, or ask a different question. I recently observed a third grade lesson when I saw a teacher face this exact situation. The lesson (Unit 5, Session 3.4) focused on strategies for solving division problems. The...

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“That Seems Way Too Big”

On a recent visit to a small district in the Midwest, I got the chance to visit a third grade class that was working on division (3U5, Session 3.4). When I joined Nicole, she was in the middle of working on the following problem: Gil loves toy cars. He saved enough money to buy 32 toy cars. How many 4-packs of toy cars did he get? (SAB p. 333) Below the problem, Nicole had written I asked her to tell me about her thinking. She said she wanted to start with something she knew, which I agreed...

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What Does It Mean To Be Smart?

“Wow, you’re so smart.” These words drew my attention to a pair of 5th grade girls in a class I was visiting, who I’ll call Cassie and Sophia. They were mid-way through a turn and talk, each sharing her strategy for solving 84 x 59. I casually moved closer, curious about what prompted the comment and trying hard to see each girl’s strategy, recorded in their math journals. Upon hearing Cassie’s comment, Sophia responded in an inviting tone, “No, no. Explain to me what you did.” She...

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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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