Investigations Blog
Counting is Serious Business
“One, two, three, four, five…” I was interested in how quickly Owen and Ravi figured out a way to count the set of 40 yellow hexagons in their Inventory Bag. The boys took turns saying a number as they placed the hexagons in a line which started to snake across the rug in the meeting area of their kindergarten classroom. “Twenty-eight, twenty-niiiinnnne…” Ravi pauses unsure about what number comes next. Owen whispers “30” and Ravi says “30” as he places the thirtieth block in the line....
read moreQ&A: Quizzes in Investigations 3
Question: The Quizzes in Investigations 3 are new to us. We are used to assessing the benchmarks with the Meeting/Partially Meeting/Not Meeting system outlined in the Assessment Teacher Notes. Can you help us get a better sense of how to use the Quizzes as they relate to the Unit’s benchmarks?Answer: Quizzes are included in grades 1-5 of Investigations 3, to give students experience with next-generation test formats, such as:multiple choicefill-in-the-blankquestions with more than one right...
read moreA Grade 3 Q&A: Assessing the Multiplication Facts
Question: Why do the assessments of the multiplication facts in Grade 3 include a time limit?Answer: In Investigations, the overwhelming majority of students’ work with the facts is focused on making meaning of the operation of multiplication, building connections between problems and images that represent them (e.g. problems about things that come groups, arrays), and using what they know to solve what they don’t (e.g. how can knowing that 3x4=12 help with 6x4?). This work happens in...
read moreAsked and Answered: Why Ask the Same Question When You’ve Already Gotten a Perfectly Good Answer?
I was watching one of those legal shows on TV the other night. The prosecutor was asking the defendant a version of the same question for the third time. The defendant’s lawyer, getting annoyed, objected: “Asked and answered!” I’ve heard this phrase a hundred times in the (made-up TV) legal context, but this was the first time it struck me how pervasive this idea was in my own mathematics education, and how powerful it still is: If a student has given a perfectly good answer to a math...
read moreWhat 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...
read moreWhat 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 moreThe Lesson? Students Never Cease to Surprise Me
On a recent visit to a school in a small city in the Midwest, Karen and I joined a class of 5th graders as they learned a game in Unit 3 called Roll Around the Clock. In the previous session, students used a clock to find and name fractions and equivalent fractions. For example, if the minute or hour hand moves from the 12 to 3, it has rotated 3/12 or 1/4 or 15/60 around the clock. Students would use these ideas in this lesson. In this game, players take turns choosing which of two dice to...
read moreHow 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...
read moreWatch, Notice, and Learn
Classroom video is a powerful tool for studying and reflecting on mathematics teaching and learning. Unlike in-the-moment interactions with students, watching video enables us to slow down and more closely examine student-to-student exchanges. This affords us a unique opportunity to learn about students’ mathematical thinking. Several months ago, I began watching and discussing video footage of elementary mathematics classrooms with a group of colleagues. We were using the footage to study...
read moreA Grade 3 Q&A: Why start with multiplication and division?
Question: Why does 3rd grade start with a multiplication/division unit and not addition/subtraction?Answer: We often hear from people who wonder why Grade 3 starts with a multiplication and division unit—just like it did in the 1st edition!—rather than an addition and subtraction unit. As we decided on the sequence of the units in any grade, we considered many different things. The most important was the development of mathematical content within and across grades.In Investigations 3,...
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